University of Southern California Rossier School of ...web-app.usc.edu/soc/syllabus/20131/27818.pdfUniversity of Southern California Rossier School of Education Course Syllabus EDUC

EDUC 566 Jan13 1

University of Southern California

Rossier School of Education

Course Syllabus

EDUC 566 - Teaching Mathematics and Science

January 2013

Complete the following information when you meet your instructor:

INSTRUCTOR:

Office Hours:

Phone Number:

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INTRODUCTION AND PURPOSE

From a cultural-historical perspective mathematics and science were not considered separate

disciplines and those who investigated the natural world were called natural philosophers. Perhaps the

acronym STEM - Science, Technology, Engineering and Mathematics – is an attempt to re-integrate

these disciplines into a more holistic approach to the teaching and learning about our natural world.

The philosophical underpinnings of this course are rooted in the cultural-historical viewpoint and

brought to life by challenging students to solve real-world problems through constructive activity and

modeling processes.

Model-based reasoning and inquiry are the heart and soul of what scientists, engineers, and

mathematicians do and therefore a natural means of integrating the STEM disciplines. For instance, we

challenge teacher candidates to create a model of a vehicle collision for a movie stunt company. Using

a ‘toy’ kit made by the K’nex Education Company student teams construct vehicles and drawings of

the vehicles, conduct performance investigations, create tables and graphs of their performance

characteristics, form diagrams of the collision, and present their complex model to their colleagues.

Such a process emulates the actual practices of the STEM community. We firmly believe that unless

our teacher candidates themselves experience this process first hand it is unlikely that they will engage

their own students in these critical dimensions of STEM practices.

COURSE OBJECTIVES

Candidates will develop:

an understanding of and flexible application of learning theories to the learning of elementary

mathematics and science.

general instructional strategies and those specific to mathematics and science.

learning experiences in which mathematics and science is related to and integrated with

students’ interests, community concerns, and societal issues.

balanced assessment practices.

a systematic approach based on learning theory to the analysis and design of curricula.

an attitude of inquiry toward one’s practice (lessons as experiments) through individual and

collaborative study, discussion, assessment, analysis, and classroom –based research and

practice.

self-efficacy, craftsmanship, collegiality, and flexibility in addressing problems of practice in

the classroom, school, and community.

EDUC 566 Jan13 2

SUMMATIVE COURSE ASSESSMENT

The Content Area Task – Science. In this assessment you will provide an overview of

important features of your classroom context that influence your instructional decisions. Your response

will provide evidence of: 1) your knowledge of students; and 2) your ability to identify and summarize

important factors related to students’ science learning and the school environment.

Use the learning cycle lesson plan format provided (see Appendix B and week 10 of the

syllabus for details). The plan should include the following information: student academic content

standards, ELD standards (if applicable), learning objectives, formal and informal assessments,

instructional strategies and learning tasks, and resources and materials.

Given the description of students that you provided, how do your choices of instructional

strategies, materials, technology, and the sequence of learning tasks reflect students’ backgrounds,

developmental levels, interests, and needs? Be specific about how your knowledge of these students

informed the lesson plans, such as the choice of text or materials used in lessons, how groups were

formed or structured, using student learning or experiences (in or out of school) as a resource, or

structuring new or deeper learning to take advantage of specific student strengths. (TPEs 4,6,7,8,9).

CTC STANDARDS

Standard Unit I or R Description Assessment

Standard 4

Relationships

Between Theory

and Practice

1, 2 Introduced Candidates examine

Feuerstein’s Theory of

Cognitive Modifiability and

its relationship to human

learning; instruction, and

student attitudes and

conduct.

Describe what you see as the

important concepts in this

article(s). Elaborate on why

you think so. How do you

view its connection to your

classroom practice?

Describe the relationship

between the article(s) and

what you have learned about

learning theories.

Candidates write a reflection paper in

week 1 and 2 (5 pages double spaced),

answering the following prompts:

Standard 5

Standard 6

Pedagogy and

Reflective Practice

3-10 Introduced Candidates evaluate

instructional alternatives,

articulate the pedagogical

reasons for instructional

decisions,

and reflect on their teaching

practices.

Candidates respond in writing and

verbally to prompts requiring them to

evaluate instructional strategies

presented from text, video, and

classroom observations.

Standard 7A

Standard 8A(a)

Pedagogical

Preparation for

Mathematics

3-10 Introduced As part of 566, candidates

learn specific teaching

strategies that are effective

in supporting them to teach

the state-adopted academic

content standards for

students in mathematics (K-

8).

Based on classroom observations, text,

and video resources candidates present

written and verbal analysis of a variety

effective instructional strategies

designed to:

develop students’

understanding of mathematical

computations, concepts, and

symbols; solve common

problems,

EDUC 566 Jan13 3

apply solutions to novel

problems,

help students understand

different mathematical topics

and make connections among

them,

solve real-world problems

using mathematical reasoning

and concrete, verbal, symbolic,

and graphic representations,

and

foster positive attitudes toward

mathematics, and encourage

student curiosity, flexibility,

and persistence in solving

mathematical problems.

Standard 8A(b)

Pedagogical

Preparation for

Science

3-10 Introduced As part of 566 candidates

learn specific teaching

strategies that are effective

in supporting them to teach

the state-adopted academic

content standards for

students in science (K-8).

They understand and

demonstrate through lesson

planning how to balance the

focus of instruction between

science information,

concepts, and investigations.

Their explanations,

demonstrations, and class

activities serve to illustrate

science concepts and

principles, scientific

investigation, and

experimentation. Candidates

emphasize the importance of

accuracy, precision, and

estimation.

Based on classroom observations, text,

and video resources candidates present

written and verbal analysis of a variety

effective instructional strategies

designed to balance the focus of

instruction between science information,

concepts, and investigations,

Candidates create an integrated math

and science lesson based on the

learning cycle. The lesson should

include mathematics standards in

addition to science standards. Use the

5e learning cycle model to design the

lessons. In your 5e lesson plan respond

to the specific bulleted items listed in

the description of the learning cycle. In

weeks 7 and 10 you will submit

modified drafts of components of the

final project thereby giving the

instructors an opportunity to critique

your progress.

Standard 13

Standard 14.2

Learning to Teach

through supervised

fieldwork

3-10 Introduced As part of 566, candidates,

demonstrate a fundamental

ability to teach in the major

domains of the Teaching

Performance Expectations.

Candidates create an integrated math

and science lesson based on the learning

cycle. The lesson should include

mathematics standards in addition to

science standards. Use the 5e learning

cycle model to design the lessons. In

your 5e lesson plan respond to the

specific bulleted items listed in the

description of the learning cycle. In

weeks 7 and 10 you will submit

modified drafts of components of the

final project thereby giving the

instructors an opportunity to critique

your progress.

Standard 14.5

Learning to Teach

through supervised

fieldwork

3-10 Introduced As part of 566 each

candidate observes,

discusses, reflects on and

participates lesson planning

Candidates create and analyze lesson

plans, analyze classroom observations

and videos of effective teaching as well

as videos of their teaching and videos of

EDUC 566 Jan13 4

and reflection and teaches

individual students and

groups of students before

being given daily

responsibility for whole-

class instruction.

Prior to or during the

program each candidate

observes and participates in

two or more K-12

classrooms, including

classrooms in hard-to-staff

and/or underperforming

schools.

their fellow classmates’ teaching events.

Candidates create and analyze lesson

plans, analyze classroom observations

and videos of effective teaching as well

as videos of their teaching and videos of

their fellow classmates’ teaching events.

Standard 14.6

Learning to Teach

through supervised

fieldwork

1 M As part of 566, each

candidate must have

satisfied the basic skills and

subject matter requirements.

All candidates must pass the multiple

subject CSET.

TEACHER PERFORMANCE EXPECTATIONS (TPEs)

TPE Unit I or

R

Description Assessment

TPE 1: Making

Subject Matter

Comprehensibl

e to Students

2-10 I Candidates demonstrate the ability

to teach the state adopted academic

content standards for students in

science and mathematics.

Candidates create an integrated math and science

lesson based on the learning cycle. The lesson

should include mathematics standards in addition

to science standards. Use the 5e learning cycle

model to design the lessons. In your 5e lesson plan

respond to the specific bulleted items listed in the

description of the learning cycle. In weeks 7 and 10

you will submit modified drafts of components of

the final project thereby giving the instructors an

opportunity to critique your progress.

TPE 3

Interpretation

and Use of

Assessments

9 I Candidates understand the

purposes and uses of different

types of diagnostic instruments,

including

entry level, progress-monitoring

and summative assessments.

Candidates access their state’s department of

education website and find a few released test

items used by their state to determine annual yearly

progress (AYP) as required by NCLB. Using

NCTM’s, Standard 3 Worthwhile Mathematical

Tasks for characteristics of good problem-based

assessment items, candidates analyze one of the

released problems using the seven criteria listed.

Then, if necessary, candidates try to improve the

item so that it becomes a problem-based

assessment that would be useful in the classroom.

TPE 4: Making

Content

Accessible

2-10 I Candidates incorporate specific

strategies, teaching/instructional

activities, procedures and

experiences that address state-

adopted academic content

standards for students in order to

provide a balanced and

comprehensive curriculum.











TPE 5: Student

Engagement

2-10 I Candidates clearly communicate

instructional objectives to students.

They ensure the active and




EDUC 566 Jan13 5

equitable participation of all

students.








TPE 6A:

Developmental

ly Appropriate

Teaching

Practices

Grades K-3

2-10 I Candidates create a structured day

with opportunities in mathematics

and science for movement. They

design math/science activities that

suit the attention span of young

learners. Their instructional

activities connect with the

children’s immediate world; draw

on key content from more than one

subject area; and include hands-on

experiences and manipulatives that

help students learn.

Candidates respond in writing and verbally to

prompts requiring them to evaluate instructional

strategies presented from text, video, and

classroom observations specific to K-3 students.

TPE 6B:

Developmental

ly Appropriate

Teaching

Practices

Grades 4-8

2-10 I Candidates design math/science

learning activities to extend

students’ concrete thinking and

foster abstract reasoning and

problem-solving skills. They help

students develop learning

strategies specific to math/science

to cope with increasingly

challenging academic curriculum.

They assist students, as needed, in

developing and practicing

strategies for managing time and

completing assignments.

Candidates develop students’

skills for working in groups to

maximize learning.

Candidates respond in writing and verbally to

prompts requiring them to evaluate instructional

strategies presented from text, video, and

classroom observations specific to 4-8 students.

TPE 7:

Teaching

English

Learners

2-10 I Candidates know and apply

pedagogical theories, principles

and practices for the development

of academic language,

comprehension, and knowledge in

the subjects of the core curriculum.

They use systematic instructional

strategies, including

contextualizing key concepts, to

make grade-appropriate or

advanced curriculum content

comprehensible to English

learners.











TPE 8:

Learning about

Students

2-10 I Candidates draw upon an

understanding of patterns of child

and adolescent development to

understand their students. Using

formal and informal methods, they

assess students’ prior mastery of

academic language abilities,

math/science content knowledge,

and skills, and maximize learning

opportunities for all students.

Through interpersonal interactions,

they learn about students’

math/science abilities,











EDUC 566 Jan13 6

ideas, interests and aspirations.

TPE 9:

Instructional

Planning

2-10 I Candidates plan instruction that is

comprehensive in relation to the

subject matter to be taught and in

accordance with state-adopted

academic content standards for

students.

They establish clear long-term and

short-term goals for student

learning, based on state and local

standards for student achievement

as well as on students’ current

levels of achievement. They use

explicit teaching methods such as

direct instruction and inquiry to

help students meet or exceed grade

level expectations. They plan how

to explain content clearly and

make abstract concepts concrete

and meaningful.











By addressing these Teacher Performance Expectations, this course assists you in preparing for the

Teacher Performance Assessment (TPA) at the conclusion of this program. Completion of the TPA is

required in order to be recommended for a credential from the University of Southern California.

COURSE REQUIREMENTS

1. Annenberg videos – In weeks 2, 4, 6, 8, and 10 you will view the assigned Annenberg video and

respond in writing to the prompts. Be prepared to discuss your written responses with your forum

group. These assignments are worth 5 points each, total of 25 points. Each of the five assignments

are found in Appendix E.

2. Reading Responses – Weeks 1, 2, and 8.

Read the assigned articles the week before they are to be discussed. Upload the responses

24 hours before Class Time to the appropriate on-line page before Class Time. A one-point

deduction will be incurred if the responses are late.

Write a reflection paper (2-3 pages double spaced) on the assigned article(s). Address the

following prompts:

a. Describe what you see as the important concepts in this article(s). Elaborate on why

you think so.

b. How do you view its connection to your classroom practice?

c. Describe the relationship between the article(s) and what you have studied regarding

learning theories.

d. Include citations.

3. Mathematics and Science Textbook Responses – Weeks 3 through 9

Read the chapter(s) and respond to the prompts for the chapter the week BEFORE they are

to be discussed. Upload the responses 24 hours before Class Time to the appropriate on-line

page before Class Time. A one-point deduction will be incurred if the responses are late.

EDUC 566 Jan13 7

Responses must be written using Word software so that the responses may be copied and

pasted to the Note Pods that will be used during Class Time. These responses to prompts

are to be completed prior to the week that the textbook assignment will be discussed in

class. Your responses will be used during Class Time in break out groups and whole class

discussions. Your instructor may require you to attach all or part of your paper to the Notes

Pod during group or whole-class instruction.

4. Class Time Requirements

Participation: We are encouraging you to use multimedia tools to create the most effective

learning environments for your classroom including this class. We expect you to be

connected through a computer/monitor, video camera, and audio connection. This makes

you eligible to earn maximum point value for the class time work. If you are connected by

audio only, you are not eligible for the maximum point value assigned during class time.

Each student will be required to copy and paste all or parts of homework assignments

during class time. Students are also required to examine text, image, audio, and video

information from the instructor and other students during class time. Instructors will award

points during class time for text, image, audio, and video contributions. Students who do

not meet these requirements will be deducted points during class time. Instructors will

notify students who are deducted points through the private chat option while on line. We

are aware that Internet and phone networks can be unpredictable and out of your control. In

our experience, these type of interruptions are not frequent, but when they do occur,

students will not be held accountable for such events.

5. IMAP CD Assignments – Weeks 2, 4, 6, 7, and 9.

Watch the prompt for each video labeled “To Consider Before Viewing the Video Clip”

and write out answers to the questions.

View the interactions and respond in writing to the prompts labeled “Reflection Questions

For Teachers.” Sometimes there is only one prompt labeled “for teachers”

Upload the responses 24 hours before Class Time to the appropriate on-line page before

Class Time. A one-point deduction will be incurred if the responses are late.

Responses must be written using Microsoft Word software so that the responses can be

copied and pasted to Note Pods that will be used during Class Time. These responses are to

be completed prior to the week that the CD assignment will be discussed in class. Your

responses will be used during Class Time in breakout groups and whole class discussions.

Your instructor may require you to attach all or part of your responses to the Notes Pod

during group or whole-class discussions. All videos will be found in Phillip, R., Cabral, C.,

& Schapelle, B. (2005). Searchable IMAP video collection; Children’s mathematical

thinking clips. San Diego, CA: Center for Research in Mathematics and Science Education,

San Diego State University.

IMAP CD-ROM: Integrating Mathematics and Pedagogy to Illustrate Children's Reasoning San

Diego State University Foundation Randy Philipp, San Diego State University

ISBN-10: 0131198548

ISBN-13: 9780131198548

Publisher: Allyn & Bacon

Copyright: 2005

Format: CD-ROM Only

EDUC 566 Jan13 8

6. Model-Based Inquiry Project, Weeks 2, 3, 4, 6, and 10.

For this project you will need to purchase the Forces, Energy, and Motion kit from K’Nex

Industries, Inc. Toll free number 1-888-ABC-KNEX. P.O. Box 700 Hatfield, PA 19440-

0700. The kit can be purchased online at www.knexeducation.com.

For each K’Nex lesson you will conduct the investigation and respond in writing to the

embedded questions and prompts.

During the Class Time discussions you will present and discuss your findings.

7. Lesson Design Project – Weeks 5, 7, and 10

Create a science lesson(s) based on the learning cycle. Use the 5E Learning Cycle Model

(see Appendix B; The K’Nex Forces, Energy, and Motion kit; and websites for descriptions

and examples of the learning cycle to design the lessons.

In weeks 5 and 7 you will submit first drafts of components of the final project thereby

giving the instructors an opportunity to critique your progress. For the final lessons due

Week 10 you will address the PACT Context for Learning and Science Content Task

components. In week 10 up to 10 points will be awarded based on the Planning Making

Content Accessible rubric.

Mathematics misconceptions resources

http://www.ericdigests.org/pre-9213/hispanic.htm

http://www.counton.org/resources/misconceptions/

http://www.svsu.edu/mathsci-center/uploads/math/gmmisconcept.htm

Science misconception lists

http://www.amasci.com/miscon/opphys.html

http://www.newyorkscienceteacher.com/sci/miscon/index.php

http://www.huntel.net/rsweetland/science/misconceptions/

http://scienceinquirer.wikispaces.com/misconception

http://www.emints.org/ethemes/resources/S00001766.shtml

http://www.svsu.edu/mathsci-center/uploads/science/gsmiscon.htm

http://www.digital-recordings.com/publ/pubscie.html

Learning Cycle websites

http://www.coe.ilstu.edu/scienceed/lorsbach/257lrcy.htm

http://www.learnnc.org/lp/pages/663

http://faculty.mwsu.edu/west/maryann.coe/coe/inquire/inquiry.htm

http://www.the-aps.org/education/lot/lotunits.htm

http://www.bioedonline.org/slides/slide01.cfm?q=learning+cycle+models

http://findarticles.com/p/articles/mi_hb6515/is_3_20/ai_n29459091

http://www.thefreelibrary.com/ASTE+invited+article:+why+the+learning+cycle%3F-

a0184150730

Examples of teacher created learning cycles – free for 10 days.

http://www.lessonplanet.com/search?keywords=learning+cycle&rating=3

All of the requirements for this course are described below. The MAT program adheres to the Carnegie

standard for course workload. The expected weekly “class time” or contact hours for a course of this

length and credit value is 3 hours 10 minutes. The expected weekly “out of class” workload for this

course is approximately 6 hours 20 minutes. The following provides a description of all of the Class

http://www.knexeducation.com/

http://www.ericdigests.org/pre-9213/hispanic.htm

http://www.counton.org/resources/misconceptions/

http://www.svsu.edu/mathsci-center/uploads/math/gmmisconcept.htm

http://www.amasci.com/miscon/opphys.html

http://www.newyorkscienceteacher.com/sci/miscon/index.php

http://www.huntel.net/rsweetland/science/misconceptions/

http://scienceinquirer.wikispaces.com/misconception

http://www.emints.org/ethemes/resources/S00001766.shtml

http://www.svsu.edu/mathsci-center/uploads/science/gsmiscon.htm

http://www.digital-recordings.com/publ/pubscie.html

http://www.coe.ilstu.edu/scienceed/lorsbach/257lrcy.htm

http://www.learnnc.org/lp/pages/663

http://faculty.mwsu.edu/west/maryann.coe/coe/inquire/inquiry.htm

http://www.the-aps.org/education/lot/lotunits.htm

http://www.bioedonline.org/slides/slide01.cfm?q=learning+cycle+models

http://findarticles.com/p/articles/mi_hb6515/is_3_20/ai_n29459091

http://www.thefreelibrary.com/ASTE+invited+article:+why+the+learning+cycle%3F-a0184150730

http://www.thefreelibrary.com/ASTE+invited+article:+why+the+learning+cycle%3F-a0184150730

http://www.lessonplanet.com/search?keywords=learning+cycle&rating=3

EDUC 566 Jan13 9

Time activities and Out-of-Class assignments that are required for this course.

Class Time Class Time and/or contact hours weekly: The class meets once a week for 2 hours. For on-line

students, in order to receive full credit for class time, you must be present via video and

teleconferencing. Class time and participation is worth 10% of the overall course grade.

GRADE DISTRIBUTION TABLE

A 100-95% B+ 89-86% C+ 79-76 % D+ 69-66% F 59-0%

A- 94-90% B 85-83% C 75-73% D 65-63%

B- 82-80% C- 72-70% D- 62-60%

DISTANCE LEARNING

This course is offered both on-line and on campus; the activities, expectations and requirements are

identical between the two versions. The on-line course is conducted through a combination of real time

and asynchronous modules, just as the on-campus version is conducted with some in-class and out-of-

class sessions. About 70% of the course will occur asynchronously. All candidates will be required to

complete assignments on-line, in the field and independently along with completing related reading

assignments. The time needed to complete all assignments fulfills course unit time requirements.

By this point in the program, candidates' level of technical competence should include basic

knowledge of the Internet. They should have an account on, at least, one site that allows people to

interact with one another (e.g. Facebook, MySpace, Skype, etc.). Basic tasks will include posting

attachments, opening and posting discussion forums and uploading assignments including video clips

(the mechanics of this will be taught). As in past courses, candidates will need to be able to video

record their interactions with candidates (which may be accomplished through the use of a portable

micro video camera) and upload edited versions (time limited) of their work. In addition, to complete

assignments and access course documents, candidates should have some familiarity with Microsoft

Word, Power Point, Excel, and basic Internet surfing.

Candidates will have ongoing access to the instructor and fellow classmates throughout the course.

Through the Course Wall, e-mails, course calendars, and Forums, the instructor will maintain ongoing

communication with candidates. These tools also provide candidates with a variety of ways to contact

the instructor, share their ideas, comments and questions through private and public means. In addition,

candidates will be made aware of real-time opportunities to engage in discussions with the instructor

and their fellow classmates. The Course Wall provides a place for the instructor to share new

information and new postings. Due dates will automatically appear both on a student’s homepage and

in their calendar.

E-mail and chat will be the primary forms of immediate communication with the instructor. E-mail

will be checked on a daily basis during the weekdays and will be responded to within 48 hours. The

course calendar provides candidates with assignment due dates and notification of scheduled office

hours for all faculty members teaching this course. Candidates may attend office hours with any

instructor; however, if a student has a specific question about assignments or coursework, it is

preferable to attend office hours with your instructor of record.

The Forum provides candidates a place to post questions, comments, or concerns regarding readings

and assignments at any time during the duration of the course. In addition to weekly Class Time

sessions, the Forum is the primary location for candidates to communicate their learning with one

another. It will be open at all times for postings and reactions.

EDUC 566 Jan13 10

All required materials will be prepared and posted prior to the start of the course, but an instructor may

add additional optional material at any point. All links and attachments will be checked weekly for

updates.

In the Event of Technical Breakdowns

Candidates may submit assignments to the instructor via e-mail by the posted due date. Remember to

back up your work frequently, post papers on the LMS (Learning Management System) or in

Blackboard once completed, load files onto a power drive, and keep a hard copy of papers/projects.

Standards of Appropriate Online Behavior:

The protocols defined by the USC Student Conduct Code must be upheld in all online classes.

Candidates are not allowed to post inappropriate material, SPAM to the class, use offensive language

or online flaming. For more information, please visit:

< http://www.usc.edu/student-affairs/SJACS/ >

ACADEMIC ACCOMMODATIONS

The University of Southern California is committed to full compliance with the Rehabilitation Act

(Section 504) and the Americans with Disabilities Act (ADA). As part of the implementation of this

law, the university will continue to provide reasonable accommodation for academically qualified

candidates with disabilities so that they can participate fully in the university’s educational programs

and activities. Although USC is not required by law to change the “fundamental nature or essential

curricular components of its programs in order to accommodate the needs of disabled candidates,” the

university will provide reasonable academic accommodation. It is the specific responsibility of the

university administration and all faculty serving in a teaching capacity to ensure the university’s

compliance with this policy.

Any student requesting academic accommodations based on a disability is required to register with

Disability Services and Programs (DSP) each semester. A letter of verification for approved

accommodations can be obtained from DSP. Please be sure the letter is delivered to me as early in the

semester as possible. DSP is located in STU 301 and is open 8:30 a.m. - 5:00 p.m., Monday through

Friday. The phone number for DSP is (213) 740-7766.

ACADEMIC INTEGRITY

The University’s Student Conduct Code articulates violations that are most common and readily

identifiable. Conduct violating university community standards that is not specifically mentioned

still may be subject to disciplinary action. General principles of academic honesty include and

incorporate the concept of respect for the intellectual property of others, the expectation that

individual work will be submitted unless otherwise allowed by an instructor, and the obligations

both to protect one’s own academic work from misuse by others as well as to avoid using another’s

work as one’s own. All candidates are expected to understand and abide by these principles.

Sanctions for violations of the university Student Conduct Code are assessed appropriately for the

cited violation. Sanctions will be considered in light of candidates’ entire conduct records at the

university and will be designed to hold candidates accountable for their actions and the resulting or

potential consequences of such actions, to promote the educational well-being of candidates and to

protect the educational environment of the university and the safety of its community.

http://www.usc.edu/student-affairs/SJACS/

EDUC 566 Jan13 11

All academic integrity violations will result in an academic consequence. Failure to comply with

the terms of any imposed sanctions may be considered an additional violation.

Scampus, the USC student guidebook contains the Student Conduct Code and information on

Academic Integrity. It is the student’s responsibility to be familiar with and abide by these

guidelines, which are found at:

http://web-app.usc.edu/scampus/

A summary of behaviors violating University standards can be also found at:

http://web-app.usc.edu/scampus/1100-behavior-violating-university-standards-and-appropriate-

sanctions/

INCOMPLETES

IN – incomplete (work not completed because of documented illness or some other emergency

occurring after the eighth week of the semester; arrangements for the IN and its removal should be

initiated by the student and agreed to by the instructor prior to the final exam); IX – lapsed incomplete.

Conditions for Removing a Grade of Incomplete - If an IN is assigned as the student’s grade, the

instructor will fill out the Incomplete (IN) Completion form which will specify to the student and to

the department the work remaining to be done, the procedures for its completion, the grade in the

course to date and the weight to be assigned to the work remaining to be done when computing the

final grade. A student may remove the IN by completing only the portion of required work not finished

as a result of documented illness or emergency occurring after the eighth week of the semester.

Previously graded work may not be repeated for credit. It is not possible to remove an IN by re-

registering for the course, even within the designated time.

Time Limit for Removal of an Incomplete - One calendar year is allowed to remove an IN.

Individual academic units may have more stringent policies regarding these time limits. If the IN is not

removed within the designated time, the course is considered “lapsed,” the grade is changed to an “IX”

and it will be calculated into the grade point average as 0 points. Courses offered on a Credit/No Credit

basis or taken on a Pass/No Pass basis for which a mark of Incomplete is assigned will be lapsed with a

mark of NC or NP and will not be calculated into the grade point average.

http://web-app.usc.edu/scampus/

EDUC 566 Jan13 12

COURSE AND ASSIGNMENT OVERVIEW

EDUC 566 Jan13 13

Week

and

Unit

No.

HW Assignments Due

Date

Points

1 Read the Feuerstein article pgs 50-75. 8 points awarded before class

time.

Write a reflection paper (2 pages double spaced), answering the

following prompts:

1. Based on the most important concepts in this article describe how

you will use them as part of your instructional practices (at least one

page).

2. Describe the relationship between the article(s) and what you have

learned about learning theories.

3. Create a graphic organizer that depicts the important ideas in the

article.

Describe your experiences as a learner of mathematics and science - 2

points to be awarded during Class Time.

Include recollections from elementary, middle, high school, and

college experiences. Equally important, describe informal learning

experiences that are related to science and mathematics.

24 hours

before

class

time

10

points

total

2 Read the Feuerstein article pgs 75-100. 8 points awarded before class

time.

Write a reflection paper (2 pages double spaced), answering the

following prompts:

1. Based on the most important concepts in this article describe how

you will use them as part of your instructional practices (at least one

page).

2. Describe the relationship between the article and what you have

learned about learning theories.

3. Create a graphic organizer that depicts the important ideas in the

article.

IMAP video 1. 2 points awarded during class time.

Video Clip 1. View the interactions on video clip 1. Read the prompt

labeled “To Consider Before Viewing the Video Clip” and write out

answers to Reflection Questions 1, 1a, 1b, 1c, 2,3,4,5a, and 5c For

Teachers.

Annenberg Video – Problem Solving. View the Problem Solving

video and respond in writing to one question from each group. Be

prepared to discuss your written responses with your forum group. 5

points.

Conduct the K’nex Vehicle Gravity Design Competition found in

Appendix C.

You should complete the activities through the second vehicle design.

The completed competition will be due in week three.

24 hours

before

class

time

15

points

total

EDUC 566 Jan13 14

3 Read Van de Walle Ch. 9 Developing Meanings for Operations 145-

166 (21 pp.). Create 6 comparison problems a follows: Difference

unknown, larger unknown, smaller unknown, product unknown, set

size unknown, and multiplier unknown. 2 points awarded before class

time.

Read Lawson Ch 1. Respond to question 1 p 21. 4 points awarded

before class time.

Conduct the K’nex Vehicle Gravity Design Competition found in

Appendix C. 4 points to be awarded during Class Time.

You should complete all of the activities.

24 hours

before

class

time

10

points

total

4 Van de Walle Ch 10 – 20 pgs. 2 points awarded before class time. HW

Activity 10.18: Patterns in the Nines facts. P. 179. Describe the

patterns you found and identify the cognitive functions used in pattern

identification.

Lawson Ch. 3. How Students Think. – 20 pgs. Answer question 2, pg

59. 3 points awarded before class time. Read Lawson Chapter Lawson

Ch. 3. How Students Think. – 20 pgs.

Answer question 2, pg 59.

Administer Puzzle 2 pg. 44 to three students: How High Will

the Water Rise? Give the Puzzle to one student at a time so that

he or she can explain his or her answers and reasoning. Record

students’ responses and classify the answers and explanations

into developmental levels.

3 points awarded before class time.

IMAP Video 3 - 2 points to be awarded during Class Time.

Read the prompt labeled “To Consider Before Viewing the Video

Clip” and write out answers to the questions.

View the interactions on video clip 3 and respond in writing to

prompts 4b and 5 in the section “Reflection Questions For Teachers.”

Annenberg video

Workshop 1. Astronomy: Eliciting Student Ideas

(http://www.learner.org/resources/series29.html) –. Be prepared to

discuss your written responses with your forum group. 5 points.

Model-Based Inquiry – Invent an egg protection device. 3 points

awarded during class time.

24 hours

before

class

time

15

points

total

5 Lawson Ch 6. Inquiry Instruction, 13 pgs.

Lawson Ch. 7. Planning for Inquiry. 16 pages.

Learning cycle lesson plan – first draft. Create a science lesson based

on the learning cycle. Use the 5e learning cycle model to design the

lesson. In your 5e lesson plan respond to the specific bulleted items

24 hours

before

class

time

10

points

total

http://www.learner.org/resources/series29.html

EDUC 566 Jan13 15

listed in the description of the learning cycle. 8 points awarded before

class time.

Van de Walle Ch 12 - 27 pgs. Ch 12 Developing Strategies for Whole-

Number Computation 213-239 (26 pp). 2 points. Activity “Pause and

Reflect” p. 234. Identify the cognitive functions you used to solve the

problems.

6 Van de Walle Ch 14 – 32 pgs. Ch 14 Algebraic Thinking:

Generalizations, Patterns, and Functions pp. 254-286.

HW Activity 14.3, p 258: What Do You Know about the Shapes? 2

points awarded before class time. Create another problem and identify

the cognitive functions you used to solve the problem you created.

Ch 14 Activity 14.9 Conjecture Creation. Challenge your students to

make up conjectures on their own after you have modeled the process.

Describe in writing the model(s) you created and how the students

responded. 4 points before class time.

IMAP Video 13. Read the prompt labeled “To Consider Before

Viewing the Video Clip” and write out answers to the questions.

View the interactions on video clip 13 and respond in writing to the

prompts labeled “Reflection Questions For Teachers.” 2 points


Annenberg Video – Workshop 2. Biology: Why Are Some Ideas So

Difficult?

Focuses on the need for conceptual understanding and examines the

scope of student ideas by exploring the central idea of photosynthesis;

that the substance of plants comes mostly from the air.5 points.

Collides Investigation. Use knowledge from your K’nex experiences

to create a model of a two vehicle collision. 2 points awarded during

class time.

24 hours

before

class

time

15

points

total

7 Learning Cycle Lesson Plan revised draft. 4 points awarded before

class time.

Van de Walle Ch 18 – 21 pgs. Respond in writing to Pause and Reflect

prompts on pages 351 and 364. 4 points awarded during class time.

IMAP video 15. 2 points awarded during class time. Read the prompt

labeled “To Consider Before Viewing the Video Clip” and write out

answers to the questions.

View the interactions on Video Clip 15 and respond in writing to the

prompts labeled “Reflection Questions For Teachers.”

24 hours

before

class

time

10

points

total

EDUC 566 Jan13 16

8 Read Schmittau, J. 2003. Cultural historical theory and mathematics

education (pp. 225-245). 6 points awarded before class time. Write a

reflection paper, about three pages double spaced, answering the

following prompts:

1. Describe what you see as the important concepts in this article(s).

Elaborate on why you think so.

2. How do you view its connection to your classroom practice? This

section should be about two-thirds of the paper.

Peters & Stout Science in Elementary Education Ch 4 - 35 pgs. 2

points awarded during class time. Create a concept map for the big

idea in your learning cycle lesson (pg 81,82)

Annenberg Video – Workshop 5. Vision: Can We Believe Our

Own Eyes? (90 min.)

Explores the origins of student ideas to find out whether experience

equals learning. Shows how experience can work for or against

learning because students can disbelieve concepts that they have

“learned.”Be prepared to discuss your written responses with your

Forum group. 5 points.

24 hours

before

class

time

13

points

total

9

Access your state’s department of education website and find a few

released test items used by your state to determine annual yearly

progress (AYP) as required by NCLB. For the released items, first

decided if they are good problem-based assessments that help you find

out about students understanding of the concepts involved. In Van de

Walle see Appendix B, Standard 3 Worthwhile Mathematical Tasks

for characteristics of good problem-based assessment items and

analyze one of the released problems using the seven criteria listed.

Then, if necessary, try to improve the item so that it becomes a

problem-based assessment that would be useful in the classroom. 6

points awarded before class time.

Read Van de Walle Chapter 16. Ch 16 Developing Strategies for

Fraction Computation 309-327 (19 pp). HW Activity 16.1 First

Estimates p. 311. 2 points awarded during class time. Randomly

estimate and write 10 addition or subtraction fraction problems each

on 10 index cards on 1 side. Quickly look at each card for no more

than 5 seconds and write on the back if it is more or less than 1.

Upon completion, explain why you made your decisions.

IMAP video 17. 2 points awarded during class time. Watch video clip

17 – Sharing of story-problem solutions. Read the prompt labeled “To

Consider Before Viewing the Video Clip” and write out answers to the

questions. View the interactions on video clip 17 and respond in

24 hours

before

class

time

10

points

total

http://www.learner.org/workshops/privuniv/pup05.html


EDUC 566 Jan13 17

writing to the prompts labeled “Reflection Questions For Teachers.”

10 PACT event – Content Area Task in Science 10 points

Annenberg video – Following Children’s Ideas in Mathematics. View

the Following Children’s Ideas in Mathematics video and respond in

writing to the prompt: describe what you learned about the long-term

development of students’ mathematical thinking.

Be prepared to discuss your written responses with your forum group.

5 points.

Tug-Of-War – 2 points awarded during class time. Your task is to

design a vehicle that will win a tug-o-war against any other vehicle.

24 hours

before

class

time

17

points

total

EDUC 566 Jan13 18

UNIT 1 – Week 1

The Theory of Mediated Learning Experience

LEARNING OBJECTIVES

Introduce participants to Reuven Feuerstein’s theory of Structural Cognitive Modifiability

through Mediated Learning Experience (MLE). MLE is the engine that drives cognitive

modifiability and develops an individual’s cognitive functions.

Analyze mathematics and science standards using Bloom’s Taxonomy.

READER - TEXT BOOK ASSIGNMENTS

Feuerstein, R., Falik, L., & Rand, Y. (2006). Chapter 3 The Theory of Mediated Learning Experience

pgs 55-95. Jerusalem, ICELP Publications.

1. Reading Response - 8 points. Upload 24 hours before Class Time. A one-point deduction will be

incurred if the responses are late.

Read the Feuerstein article.

Based on the most important concepts in this article describe how you will use them as part of

your instructional practices (at least one page).

Describe the relationship between the article(s) and what you have learned about learning

theories.

Create a graphic organizer that depicts the important ideas in the article.

2. Describe your experiences as a learner of mathematics and science - 2 points to be awarded

during Class Time. Upload 24 hours before Class Time. A one-point deduction will be incurred if

the responses are late.

Include recollections from elementary, middle, high school, and college experiences. Equally

important, describe informal learning experiences that are related to science and mathematics.

3. Class Time – 2 points to be awarded during Class Time.

UNIT 2 – Week 2

Applying the Theory of Mediated Learning Experience

LEARNING OBJECTIVES

Apply Mediated Learning Experience’s universal criteria, situational parameters, and cognitive

functions to the teaching and learning of mathematics and science.

Introduce elements of model-based inquiry and reasoning.

Analyze mathematics and science standards using Bloom’s Taxonomy and cognitive functions.

Analyze student thinking about addition.

Understand model-based reasoning and inquiry by invent a model of energy.

READER - TEXT BOOK ASSIGNMENTS

Read the Feuerstein article pgs 75-100. 8 points awarded before class time.

EDUC 566 Jan13 19

1. Reading Response. Upload 24 hours before Class Time. A one-point deduction will be incurred if

the responses are late.

Read the Feuerstein article pgs 75-100. 8 points awarded before class time.

Based on the most important concepts in this article describe how you will use them as part of

your instructional practices (at least one page).

Describe the relationship between the article(s) and what you have learned about learning

theories.

Create a graphic organizer that depicts the important ideas in the article.

2. IMAP CD Assignment. Upload 24 hours before Class Time. A one-point deduction will be

incurred if the responses are late. 2 points to be awarded during Class Time.

Watch video clip: Children solve a missing addend problem.

Video clip 1. View the interactions on video clip 1. Read the prompt labeled “To Consider

Before Viewing the Video Clip” and write out answers to Reflection Questions 1, 1a, 1b, 1c, 2,

3, 4, 5a and 5c For Teachers.

Upload the responses to the appropriate online page before Class Time. A one-point deduction

will be incurred if the responses are late. Responses must be written using Microsoft Word

software so that the responses can be copied and pasted to Note Pods that will be used during

Class Time. These responses are to be completed prior to the week that the CD assignment will

be discussed in class. Your responses will be used during Class Time in break out groups and

whole class discussions. Your instructor may require you to attach all or part of your responses

to the Notes Pod during group or whole-class discussions.

3. Conduct the K’nex Vehicle Gravity Design Competition found in Appendix C. Upload 24

hours before Class Time A one-point deduction will be incurred if the responses are late. 2 points

to be awarded during Class Time.

You should complete the activities through the second vehicle design. The completed

competition will be due in week three.

4. Class Time 3. 2 points to be awarded for IMAP assignment along with discussion.

5. Annenberg Video – Problem Solving. View the Problem Solving video and respond in writing to

one question from each group. Be prepared to discuss your written responses with your forum

group. 5 points.

UNIT 3 - – Week 3

Nature of Science

LEARNING OBJECTIVES

Understand the development of number ideas and meaning for number operations.

Understand the nature of science.

Identify and apply MLE-based strategies for engaging students in the learning of mathematics

and science concepts.

Identify, understand, and apply components of model-based reasoning and inquiry.

EDUC 566 Jan13 20

READER - TEXT BOOK ASSIGNMENTS –

1. Textbook Assignment - 6 points. Upload 24 hours before Class Time. A one-point deduction will

be incurred if the responses are late.

Read Van de Walle Chapter 9 and respond to the prompts below for the chapters BEFORE

week 3. Responses must be written using Microsoft Word software so that the responses can

be copied and pasted to Note Pods that will be used during Class Time. Your responses will be

used during Class Time in break out groups and whole class discussions. Your instructor may

require you to attach all or part of your paper to the Notes Pod during group or whole-class

instruction.

Chapter 9 - Developing Meanings for Operations 145-166 (21 pp.). Create 6 comparison

problems a follows: Difference unknown, larger unknown, smaller unknown, product

unknown, set size unknown, and multiplier unknown. 2 points awarded before class time.

Read Lawson Chapter 1: Educational Goals and the Nature of Scientific. Respond to question 1

p 21. 4 points awarded before class time.

2. Conduct the K’nex Vehicle Gravity Design Competition found in Appendix C. 4 points to be

awarded during Class Time. Upload 24 hours before Class Time.

You should complete all of the activities and responded to all of the questions and prompts. Be

prepared to show your vehicle on the video camera and discuss this investigation.

3. Class Time - 4 points awarded during Class Time for K’Nex Vehicle Gravity Design

Competition.

Conduct the K’nex Vehicle Gravity Design Competition found in Appendix C. 4 points to be

awarded during Class Time. You should complete all of the activities.

Unit 4 – Week 4

Patterns of Thinking By Scientists And By Adolescents

LEARNNG OBJECTIVES

Analyze classroom interactions based on MLE universal criteria and situational parameters.

Understand how to help children master the basic facts and develop place value concepts.

Understand patterns of thinking by scientists and by adolescents.

Model the design-redesign engineering concept and apply it to a real world problem.

READER – TEXTBOOK ASSIGNMENTS

1. Textbook Assignments – 5 points for the two assignments. Upload 24 hours before Class Time. A

one-point deduction will be incurred if the responses are late. Responses must be written using

Word software so that the responses can be copied and pasted to Note Pods that will be used during

Class Time. Your responses will be used during Class Time in break out groups and whole class

discussions. Your instructor may require you to attach all or part of your paper to the Notes Pod

during group or whole-class instruction.

Read Van de Walle Chapter 10 Helping Children Master the Basic Facts 167-186 (20 pp.). HW

Activity 10.18: Patterns in the Nines facts. P. 179. Describe the patterns you found and identify

the cognitive functions used in pattern identification. 2 points.

Read Lawson Chapter Lawson Ch. 3. How Students Think. – 20 pgs.

o Answer question 2, pg 59.

o Administer Puzzle 2 pg. 44, How High Will the Water Rise?, to three students. Give the

Puzzle to one student at a time so that he or she can explain his or her answers and

EDUC 566 Jan13 21

reasoning. Record students’ responses and classify the answers and explanations into

developmental levels.

o 3 points awarded before class time.

2. IMAP CD Assignment – 2 points to be awarded during Class Time

Watch video clip 3 – Gretchen and subtraction. Read the prompt labeled “To Consider Before

Viewing the Video Clip” and write out answers to the questions.

View the interactions on video clip 3 and respond in writing to prompts 4b and 5 in the section

“Reflection Questions For Teachers.”

Upload the responses 24 hours before Class Time to the appropriate on-line page before Class

Time. A one-point deduction will be incurred if the responses are late.

Responses must be written using Word software so that the responses can be copied and pasted

to Note Pods that will be used during Class Time. These responses are to be completed prior to

the week that the CD assignment and will be discussed in class. Your responses will be used

during Class Time in break out groups and whole class discussions. Your instructor may

require you to attach all or part of your responses to the Notes Pod during group or whole-class

discussions.

3. Invent an egg protection device. Details in Appendix C. 3 points awarded during class time.

4. Class Time – 5 points to be awarded during Class Time for the IMAP video responses and K’nex

Egg-citing design competition.

5. Annenberg Video - Workshop 1. Astronomy: Eliciting Student Ideas.

(http://www.learner.org/resources/series29.html ). Click on the icon titled VoD for the

assigned workshop.

Introduces constructivism by examining student beliefs on what causes the seasons and their

explanations for the phases of the moon.

See appendix E for the required responses to the video. Be prepared to discuss your written

responses with your forum group. 5 points.

Unit 5 – Week 5

The Learning Cycle

LEARNING OBJECTIVES

Analyze classroom interactions based on MLE.

Identify the elements of the learning cycle.

Understand how to help students develop strategies for whole-number computation.


1. Textbook Assignments. Lawson Ch 6. Inquiry Instruction, 13 pgs. Lawson Ch. 7. Planning for

Inquiry. 16 pages.

4. Learning cycle lesson plan – first draft. Create an integrated math and science lesson based on

the learning cycle. The lesson should include mathematics standards in addition to science

standards. Use the 5e learning cycle model to design the lesson. Use the 5e learning cycle

model (see Appendix B; The K’Nex Forces, Energy, and Motion kit; and websites for

descriptions and examples of the learning cycle) to design the lessons. In your 5e lesson plan


EDUC 566 Jan13 22

respond to the specific bulleted items listed in the description of the learning cycle. In weeks 7

and 10 you will submit modified drafts of components of the final project thereby giving the

instructors an opportunity to critique your progress. 8 points awarded before class time. Upload

24 hours before Class Time. A one-point deduction will be incurred if the responses are late.


to Note Pods that will be used during Class Time. Your responses will be used during Class

Time in break out groups and whole class discussions. Your instructor may require you to

attach all or part of your paper to the Notes Pod during group or whole-class instruction.

Ch 12 Developing Strategies for Whole-Number Computation 213-239 (26 pp). 2 points


Activity “Pause and Reflect” p. 234. Identify the cognitive function you used.

Class Time. 2 points to be awarded during Class Time for Van de Walle text assignment.

Unit 6 – Week 6

Algebraic Thinking

LEARNING OBJECTIVES

Analyze classroom interactions based on MLE.

Examine in detail how algebraic thinking can be developed starting in elementary school

through mathematics and science.

Identify the components of algebraic thinking and how they can be applied to the learning of

mathematics and science.



1. Textbook Assignments – 6 points. Upload 24 hours before Class Time. A one-point deduction

will be incurred if the responses are late.

Read Van de Walle chapter 14 and respond to the prompts below for the chapters BEFORE

week 6.


Time. A one-point deduction will be incurred if the responses are late. Responses must be

written using Word software so that the responses can be copied and pasted to Note Pods that

will be used during Class Time. Your responses will be used during Class Time in break out

groups and whole class discussions. Your instructor may require you to attach all or part of

your paper to the Notes Pod during group or whole-class instruction.

Ch 14 Algebraic Thinking: Generalizations, Patterns, and Functions pp. 254-286

HW Activity 14.3, p 258: What Do You Know about the Shapes? 2 points.

Create another problem and identify the cognitive functions you used to solve the problem you

created.

Ch 14 Activity 14.9 Conjecture Creation. Challenge your students to make up conjectures on

their own after you have modeled the process. Describe in writing the model(s) you created and

how the students responded. 4 points.

2. IMAP CD Assignment – 2 points to be awarded during Class Time.

Watch video clip 13 – Procedural vs. Conceptual Teaching.

EDUC 566 Jan13 23

Read the prompt labeled “To Consider Before Viewing the Video Clip” and write out answers

to the questions.

View the interactions on video clip 13 and respond in writing to the prompts labeled






the week that the CD assignment will be discussed in class. Your responses will be used during

Class Time in break out groups and whole class discussions. Your instructor may require you to

attach all or part of your responses to the Notes Pod during group or whole-class discussions.

3. Collides – 2 points to be awarded during Class Time. Upload 24 hours before Class Time. A one-

point deduction will be incurred if the responses are late.

Use knowledge from your K’nex experiences to create a model of a two vehicle collision.

See appendix C for details. Include algebraic expressions in your model.

4. Class Time – 4 points to be awarded for the IMAP video responses and Collides model.

5. Annenberg Video – Workshop 2. Biology: Why Are Some Ideas So Difficult? (90 min.) Focuses on the need for conceptual understanding and examines the scope of student ideas by exploring the central idea of photosynthesis, that the substance of plants comes mostly from the air.

See appendix E for the required responses to the video. Be prepared to discuss your written


Unit 7 – Week 7

Analyzing Student Thinking

LEARNNG OBJECTIVES

Understand student thinking by analyzing students’ written responses to cognitively demanding

tasks.

Understand and apply proportional reasoning.



1. Learning Cycle Lesson Plan. 4 points. Upload before class time.

Based on comments and suggestions from the first draft submitted in week 5, modify and

improve your lesson.

2. Textbook Assignments – 4 points awarded during class time. Upload the responses 24 hours

before Class Time to the appropriate on-line page before Class Time. A one-point deduction will

be incurred if the responses are late


week 7. 2 points awarded during class time.




EDUC 566 Jan13 24



Ch. 18 Proportional Reasoning pgs 348-369. Respond in writing to Pause and Reflect prompts

on pages 351 and 364.

3. IMAP CD Assignment. 2 points to be awarded during Class Time.

Watch video clip 15 – Felisha Adding Fractions.


to the questions.

View the interactions on Video Clip 15 and respond in writing to the prompts labeled









4. Class Time – 6 points - 4 points to be awarded for Van de Walle, and 2 points for the IMAP video

responses.

Unit 8 – Week 8

Mathematics and Science Reform

LEARNING OBJECTIVES


Explore the mathematics and science reform process in the United States. The contribution that

the cultural-historical process described by Vygotsky to the reform process is examined in the

article written by Jean Schmittau. Application of the cultural-historic process will require

significant changes in the ways teachers view the teaching of mathematics and science and

changes in their own understanding of fundamental concepts such as multiplication.

Identify and describe the different views on the reform process in mathematics and science in

the United States.

Identify components of the PACT process.


1. Reading Response – Read Schmittau, J. 2003. Cultural historical theory and mathematics

education.(pp. 225-245). In A. Kozulin, B. Gindis, S. Miller, & V. Ageyev (Eds.). Vygostky’s

educational theory in cultural context. Cambridge. UK: Cambridge University Press. 6 points.

Upload 24 hours before Class Time. A one-point deduction will be incurred if the responses are

late.

Write a reflection paper, three pages double spaced, answering the following prompts:

Describe what you see as the important concepts in this article(s). Elaborate on why you think

so.

EDUC 566 Jan13 25

How do you view its connection to your classroom practice? This section should be about two-

thirds of the paper.

2. Textbook Assignment – Read Chapter 4 Peters & Stout Science in Elementary Education and

respond to the following prompt BEFORE week 8. Chapter 4 Peters & Stout Science in Elementary

Education. Create a concept map for the big idea in your learning cycle lesson (pg 81,82). 2 points

to be awarded during Class Time.







3. Class Time – 2 points to be awarded the Peters & Stout assignment.

4. Annenberg Video – For week 8 go to the Annenberg Private Universe Project in Science website

by entering this URL in your browser: http://www.learner.org/resources/series29.html

Click on the icon titled VoD for Workshop 5. Vision: Can We Believe Our Own Eyes?

Explores the origins of student ideas to find out whether experience equals learning. Shows how

experience can work for or against learning because students can disbelieve concepts that they have

“learned.”

See appendix E for the required responses. Be prepared to discuss your written responses with

your forum group. 5 points.

Unit 9 – Week 9

Assessing Student Progress

LEARNING OBJECTIVE

Analyzing effective means of assessing student progress.


1. Textbook Assignment. 6 points awarded before class time.

Access your state’s department of education website and find a few released test items used by

your state to determine annual yearly progress (AYP) as required by NCLB. For the released

items, first decide if they are good problem-based assessments that help you find out about

students understanding of the concepts involved. In Van de Walle see Appendix B, Standard 3

Worthwhile Mathematical Tasks for characteristics of good problem-based assessment items

and analyze one of the released problems using the seven criteria listed. Then, if necessary, try

to improve the item so that it becomes a problem-based assessment that would be useful in the

classroom.


Week 9. 2 points awarded during class time. Developing Strategies for Fraction Computation

309-327 (19 pp).

HW Activity 16.1 First Estimates p. 311. 2 points awarded during class time.


EDUC 566 Jan13 26

Randomly estimate and write 10 addition or subtraction fraction problems each on 10 index

cards on 1 side. Quickly look at each card for no more than 5 seconds and write on the back

if it is more or less than 1. Upon completion, explain why you made your decisions.

Upload the responses 24 hours before Class Time to the appropriate on-line page before


Responses must be written using Word software so that the responses can be copied and

pasted to Note Pods that will be used during Class Time.

Your responses will be used during Class Time in break out groups and whole class

discussions.

Your instructor may require you to attach all or part of your paper to the Notes Pod during

group or whole-class instruction.

2. IMAP CD Assignment – 2 points to be awarded during Class Time.

Watch video clip 17 – Sharing of story-problem solutions.


to the questions.

View the interactions on video clip 17 and respond in writing to the prompts labeled









3. Class Time – 4 points to be awarded for IMAP CD responses, Van de Walle text assignment.

UNIT 10 – Week 10

Context for Learning and Science Content Task

LEARNING OBJECTIVES

Create a learning event that includes the PACT requirements described below. 10 pts.

1. Annenberg video – Following Children’s Ideas in Mathematics. View the Following Children’s

Ideas in Mathematics video and respond in writing to the prompt: describe what you learned about

the long-term development of students’ mathematical thinking. Be prepared to discuss your written


2. Conduct the Tug-of-War Competition described below. 2 points to be awarded during Class

Time. Upload the responses 24 hours before Class Time to the appropriate on-line page before


Your task is to design a vehicle that will win a tug-o-war against any other vehicle. Each

participant will build a vehicle that they think will beat the competition. Each pair of competitors

will take a picture of their vehicle and send it to their competitor. The competitor will then build

this vehicle from the picture. Verbal or written instructions should be included with the pictures so

each competitor can build the vehicle as intended. Each participant will then conduct the tug-o-war

EDUC 566 Jan13 27

with their own vehicle and the vehicle they built based on their competitors picture and other

information

3. PACT: Context for Learning and Science Content Area Task. 10 points. Upload 24 hours

before Class Time. A one-point deduction will be incurred if the responses are late.

EDUC 566 Jan13 28

Context for Learning

Purpose

The Context for Learning evidence provides a brief overview of important features of your classroom

context that influence your instructional decisions. Your response will provide evidence of: 1) your

knowledge of students; and 2) your ability to identify and summarize important factors related to

students’ science learning and the school environment. You’ll be referring to your description of

students and the teaching context in your responses to the Content Area Task in Elementary

Science.

Overview

If you teach science to more than one class of students, focus on only one class.

Identify learning objectives for both the curriculum content and the development of academic

language related to that content.

Provide descriptive information about the instructional context and instructional resources.

Describe important features of the class that will affect your instructional decisions.

What Do I Need to Do?

Complete the Context for Learning Form. The form is located after the prompts for the

Context Commentary.

Respond to each of the prompts in the Context Commentary.

Context Commentary

Write a commentary of 3-5 single-spaced pages (including prompts) that addresses the following

prompts. You can address each prompt separately, through a holistic essay, or a combination of both,

as long as all prompts are addressed.

1. Briefly describe the following about the context in which the learning segment would be

taught:

a. Type of school/program, (e.g., elementary/middle school, themed magnet, or charter

school)

b. Kind of class (e.g., third grade self-contained, sixth grade core math/science) and

organization of subject in school (e.g., departmentalized, interdisciplinary teams)

c. Degree of ability grouping or tracking, if any

2. Describe your class with respect to the features listed below. Focus on key factors that

influence your planning and teaching of this learning segment. Be sure to describe what your

students can do as well as what they are still learning to do.

a. Academic development

Consider students’ prior knowledge, key skills, developmental levels, and other special

educational needs. (TPE 8)

b. Language development

Consider aspects of language proficiency in relation to the oral and written English required

to participate in classroom learning and assessment tasks. Describe the range in vocabulary

EDUC 566 Jan13 29

and levels of complexity of language use within your entire class. When describing the

proficiency of your English learners, describe what your English learners can and cannot

yet do in relation to the language demands of tasks in the learning segment. (TPEs 7, 8)

c. Social development

Consider factors such as the students’ ability and experience in expressing themselves in

constructive ways, negotiating and solving problems, and getting along with others. (TPE 8)

d. Family and community contexts

Consider key factors such as cultural context, knowledge acquired outside of school, socio-

economic background, access to technology, and home/community resources.

3. Describe any district, school, or cooperating teacher requirements or expectations that might

impact your planning or delivery of instruction, such as required curricula, pacing, use of

specific instructional strategies, or standardized tests.

EDUC 566 Jan13 30

Context for Learning Form

Provide the requested context information for the class selected for this task. This form is designed to be completed electronically. The blank space does not represent the space needed. Use as much

space as you need.

About the subject area/course

1. How much time is devoted each day to specific instruction in science in the class which is the focus

of this task? ______________________________________________

About the students in the class

2. How many students are in the class you are documenting? _____

3. How many students in the class are: English learners ____

Redesignated English Learners _____ Proficient English speakers ____?

4. Please complete the following table about your

English Learners’ latest CELDT scores (if available):

# of Students at Each CELDT Level in Different Modalities

Score Level Listening Speaking Reading Writing Overall

Beginning

Early

Intermediate

Intermediate

Early Advanced

Advanced

EDUC 566 Jan13 31

5. How many students have Individualized Education Plans (IEPs) or 504 plans? _____

6. How many students participate in a Gifted and Talented Education (GATE) program? _____

About the school curriculum and resources

7. Describe any specialized features of the classroom setting, e.g., bilingual, Structured English

Immersion, team taught with a special education teacher.

8. If there is a particular textbook or instructional program used for science instruction, what is it? (If

a textbook, please provide the name, publisher, and date of publication.)

9. What other major resources are typically used for science instruction in this class?

Content Area Task-Science

Be sure to address the learning of curriculum content and related academic language.

To identify standards, please list the standard number, followed by the text of the standard. If only a

portion of a standard is being addressed, then only list the relevant part(s).

Use the preferred lesson plan format in your program or the optional lesson plan format provided. The

plan should include at least the following information: student academic content standards, ELD

standards (if applicable), learning objectives, formal and informal assessments, instructional strategies

and learning tasks, and resources and materials

1. Given the description of students that you provided in Task 1.Context for Learning, how do your

choices of instructional strategies, materials, technology, and the sequence of learning tasks reflect

students’ backgrounds, developmental levels, interests, and needs? Be specific about how your

knowledge of these students informed the lesson plans, such as the choice of text or materials used

in lessons, how groups were formed or structured, using student learning or experiences (in or out

of school) as a resource, or structuring new or deeper learning to take advantage of specific student

strengths. (TPEs 4,6,7,8,9)

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PLANNING MAKING CONTENT ACCESSIBLE

ES2: How do the plans make the curriculum accessible to the students in the

class? (TPEs 1,4,5,6,7,8,9)

Level 1 Level 2 Level 3 Level 4

Plans refer to students’

experiential

backgrounds1, interests,

or prior learning2 that

have little or no

relationship to the

learning segment’s

standards/objectives. OR

There are significant

content inaccuracies in

plans that will lead to

student

misunderstandings.

Plans draw on students’

experiential

backgrounds, interests,

or prior learning to help

students reach the


standards/objectives.

Plans for the

implementation of

learning tasks include

support3 to help

students who often

struggle with the

content.

Plans draw on students’

prior learning as well as

experiential backgrounds

or interests to help

students reach the


standards/objectives.

Plans for learning tasks

include scaffolding or

other structured forms

of support4 to provide

access to grade-level standards/objectives.

All components of

Level 3 plus:

Plans include well-

integrated instructional

strategies that are

tailored to address

a variety of

specific student

learning needs.

1 Cultural, linguistic, social, economic

2 In or out of school

3 Such as strategic groupings of students; circulating to monitor student understanding during independent or group work;

checking on particular students. 4 Such as multiple ways of representing content; concrete models; modeling strategies of scientific inquiry; providing

graphic organizers, rubrics, or sample work.

EDUC 566 Jan13 33

Appendix A

MLE classroom observation notes template

Universal

Criteria Strategies Evidence

Intentionality-

Reciprocity

Cognitively demanding tasks implemented, lesson

types vary (project-based, games, procedural, etc.)

Rules and procedures negotiated with students

Interventions – reinforcement, recognition, balanced

with negative consequences.

Relationships with high need students developed,

e.g. Passive, aggressive, attention problems.

Non-verbal behavioral cues established

Meaning Importance of subject matter conveyed including the

processes of learning.

Energy and enthusiasm for teaching and learning are

clearly demonstrated.

Transcendence Lessons connected to previous and future learning.

Process questions balanced with fact based

questions.

Teacher models the process of generalizing and asks

students to generalize from specific instances to the

underlying rule

Prompts students’ need to seek and find complex

relationships by providing analogies, models, and

representations.

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Cycle of Inquiry for Mathematical and Scientific Problem Solving Using Cognitive Functions

Engaging: Approaching and Connecting to Problems

Cognitive Function Teacher definition Evidence

Defining (Understanding)

the problem

Recognizing that something has to be done

and figuring what to do by forming

relationships between the various sources

of information in the problem; devising a

plan; and implementing the plan.

Activating prior knowledge Searching through past experiences in order

to make associations between aspects of the

problem and similar aspects of past

experiences with similar problems.

Analyzing Breaking a problem into its parts and

figuring how the parts are connected or

related to one another; determining which

parts are relevant and which are irrelevant;

and identifying missing parts or

information.

Visualizing Generation of a symbolic, figural, or

pictorial representation of a verbal

stimulus.

Paraphrasing through

rereading

Rewriting, rewording, or restating in your

own words the problem you have just read,

seen, or heard.

Systematic exploration and

planning

Exploring the problem in an organized and

orderly manner, representing the problem

in multiple ways, and constructing a logical

plan to solve the problem.

Comparing Looking for similarities and differences

between two or more objects, events, or

situations in the problem.

EDUC 566 Jan13 35

Exploring: Discovering relationships and patterns; employing tools; explaining possible solution paths, concepts and strategies while

problem solving; manipulating problem elements and representations.


Analogical reasoning Thinking about, representing, and exploring

the problem and ways to solve it based on

analogs, models, and examples from prior

experience.

Modeling Designing a representation of a system with

interactive parts and with representations of

those interactions. Designing models can be

performed with the use of conceptual,

physical, mathematical, and computation

models, or combinations of these.

Forming relationships Making connections between

representations, objects, events, or

situations in the problem.

Forming functional

relationships

Making connections between two or more

things that are changing their values in the

problem in such a way that the changes are

related or are working together in an

interdependent way.

Hypothetical thinking

(Using inductive and

deductive thinking)

If …. Then… thinking. Making a

conjecture (or educated guess) about the

solution to the problem, and searching for

the logical evidence to support the claim or

deny it.

Providing logical evidence -

falsifying

Giving and explaining details, clues, and

proof that connect together and make sense

for supporting a tentative solution to the

problem.

Conserving Constancy Identifying and describing what stays the

same in terms of an attribute, concept or

relationship within the problem while some

other things are changing.

EDUC 566 Jan13 36

Explaining, Elaborating, and Validating: Determining whether a solution is complete and moving beyond a particular problem by

generalizing to other situations


Evaluating Determining the reasonableness of the

solution in the context of the original

problem.

Inductive thinking Taking aspects from various details that

seem to form a pattern, categorizing them

into general relationships of attributes

and/or behaviors, and organizing the results

to form a general rule, principle, formula,

recipe, or guide that can be applied to solve

similar problems.

Deductive thinking Applying the newly found solution, general

rule, principle, or formula to a novel

problem, situation, or a set of details.

EDUC 566 Jan13 37

Appendix B

The Learning Cycle Model of Instruction

The learning cycle is a research-supported, constructivist instructional model based on how humans learn. From a constructivist

perspective, learning can be perceived as a conceptual transformation: “The learning theory that emerges from Piaget’s work can be

summarized by saying that cognitive change and learning a specific direction take place when a scheme, instead of producing the expected

result, leads to a perturbation, and perturbation, in turn, to an accommodation that maintains or reestablishes equilibrium.” (von

Glasserfeld, 1995, p.68). The learning cycle is useful in science and mathematics for organizing curricula at the unit and daily lesson plan

level.

The Five Phases of the Learning Cycle

1. Engagement

In the first phase the teachers develops a ‘hook’ or context to capture the student’s attention. A hook or context provides motivation

that develops anticipation and induces curiosity and suspense. Selected tasks should be cognitively demanding (see criteria for cognitively

demanding tasks). Examples include:

Hands-on

Scenario – real world or teacher created

Demonstrations – discrepant or ill-structured events

Simulations and games

Observe: plants growing; animal behavior; phenomena depicted on video

Use a set of materials to solve a given problem

Minimize or maximize something

Identify an unknown

Field trips

The activities of this phase make connections to past and future activities. The connections depend on the learning task and may be

conceptual or procedural. Successful engagement results in students being puzzled and actively motivated in the learning activity.

Planning for the engagement and exploration phase

What are your mathematical/scientific goals/standards for the lesson (i.e., what is it that you want students to know and understand

about mathematics/science as a result of this lesson)?

EDUC 566 Jan13 38

In what ways does the task build on student’s previous knowledge? What definitions, concepts, or ideas do students need to know

in order to begin to work on the task?

What are all the ways the task can be solved?

Which of these methods do you think your students will use?

What misconceptions might students have?

What errors might students make?

What are your expectations for students as they work on and complete this task?

What resources or tools will students have to use in their work?

How will the students work—independently, in small groups, or in pairs—to explore this task? How long will they work

individually or in small groups/pairs? Will students be partnered in a specific way? If so in what way?

How will students record and report their work?

How will you introduce students to the activity so as not to reduce the demands of the task?

What will you hear that lets you know students understand the task?

2. Exploration

Exploration activities are designed so that during class students have common, concrete experiences that begin building concepts,

processes, and skills. In Piagetian terms, engagement brings about disequilibrium while exploration initiates the process of equilibration.

The aim of exploration activities is to establish experiences that a teacher can use later to formally introduce a concept, process, or skill.

As a result of their mental and physical involvement in the exploration activity, students establish relationships, observe and identify

patterns, identify variables, and pose questions. The teacher guides the students as they explore, suggesting strategies to use and monitors

levels of frustration.

Teacher actions during exploration include the function of stimulating students’ mathematical and scientific constructions via the

introduction of new mathematical/scientific ideas into a classroom conversation (Lobato, et al. 2005). These actions may include:

1. Describing a new concept.

2. Summarizing student work in a manner that inserts new information into the conversation.

3. Providing information that students need in order to test their ideas or generate a counterexample.

4. Asking students what they think of a new strategy or idea (perhaps from a “hypothetical” student).

5. Presenting a counterexample that the teacher has not seen any students introduce and thinks no one will.

6. Engaging in Socratic questioning in an effort to introduce a new concept.

7. Presenting a new representation.

EDUC 566 Jan13 39

As students are working independently or in small groups:

What questions will you ask to focus their thinking?

What will you see or hear that lets you know how students are thinking about the mathematical/scientific ideas?

What questions will you ask to assess students understanding of key mathematical/scientific ideas, problem solving strategies, or the

representations?

What questions will you ask to advance student’ understanding of the mathematical/scientific ideas?

What questions will you ask to encourage student to share their thinking with others or to assess their understanding of their peer’s

ideas?

How will you ensure that students remain engaged in the task?

What will you do if a student does not know how to begin to solve the task?

What will you do if a student finishes the task almost immediately and becomes bored and disruptive?

What will you do if students focus on non-mathematical aspects of the activity (e.g. spend most of their time making a beautiful poster

of their work)?

3. Explanation

The process of explanation provides the students and teacher with a common use of terms relative to the learning task. The teacher

directs student attention to specific aspects of the engagement and exploration activities. Students are asked to give their explanation of

what occurred (or attempt to answer the guiding question). The teacher introduces a mathematical or scientific explanation in a direct and

formal manner. Explanations are ways of listing, labeling, and ordering the exploratory experiences. The teacher should base the initial part

of this phase on students’ explanations and clearly connect the explanations to experience in the engagement and exploration phases. The

explanation phase can be teacher-, textbook- or technology-directed. Teachers commonly use oral explanations, but there are other

strategies, such as reading, video, film, and educational courseware. This phase continues the process of cognitive construction and

provides scientific and mathematical words for explanations. In the end, students should be able to explain exploratory experiences using

common mathematical /scientific terms.

How will you orchestrate the class discussion so that you accomplish your mathematical/scientific goals? Specifically:

Which solution paths do you want to have shared during the class discussion? In what order will the solutions be presented? Why?

In what ways will the order in which solutions are presented help develop students understanding of the mathematical/scientific ideas

that are the focus of your lesson?

What specific questions will you ask so that students will:

make sense of the mathematical/scientific ideas that you want them to learn?

expand on, debate, and question the solutions being shared?

make connections between the different strategies that are presented?

look for patterns?

EDUC 566 Jan13 40

begin to form generalizations?

What will you see or hear that lets you know that students in the class understand the mathematical/scientific ideas that you intended for

them to learn?

4. Elaboration

Once students begin developing an explanation of their learning tasks, it is important to involve students in further experiences that

extend or clarify the concepts, processes, or skills. In some cases students may still have misconceptions or they may only understand a

concept or procedure in terms of the exploratory experience. Elaboration activities provide further time and experience that contribute to

learning.

5. Evaluation

Students need feedback on their progress and this can occur informally or formally. Informal assessment (formative) occurs from

the beginning of the teaching sequence whereas formal assessment is best done after the elaboration phase.

As you write the specifics for each phase in the “What the teacher/student does,” estimate the time it will require and place the estimate

under the name of each phase.

Learning Cycle – generalized lesson format

Phase Purpose What the teacher does What the student does

Engage

(time)

To elicit students’

interest in the

concept(s).

1. Creates interest.

2. Generates curiosity.

3. Raises questions.

4. Identifies what the

students know about the

topic.

5. Gives a general

introduction about what the

student will be studying.

1. Asks questions, such as: Why

did this happen? What do I

already know about this? What

can I find out about this? How do

I approach this task?

2. Shows interest in the topic.

Explore

(time)

1. Provides experiences

needed for

understanding.

2. Stimulates inquiry.

3. Provides students

1. Encourages students to

work together without

direct instruction from the

teacher.

2. Observes and listens to

1. Thinks freely, but within the

limits of the activity

2. Uses previously acquired

strategies (or develops new ones),

skills, and concepts to find

EDUC 566 Jan13 41

with the opportunity to

make their own

discoveries and to figure

things out for

themselves.

4. Reveals students’

ideas and thoughts.

5. Sets the stage for

more structured

activities.

students as they interact.

3. Asks probing questions

to redirect students’

investigations when

necessary.

4. Initiates introduction of

mathematical/scientific

concepts when necessary:

Description of a new

concept which can include

an idea, the meaning

associated with a

mathematical symbol, why

something works, an

image, a relationship, or

connections among ideas

or representation;

summarizing student work

in a manner that inserts

new information into the

conversation; provide

information that students

need in order to test their

ideas or generate a

counterexample; ask

students what they think of

a new strategy or idea,

perhaps from a

hypothetical student;

present a counterexample

that the teacher has not

seen any students introduce

and thinks no one will;

engage in Socratic

questioning in an effort to

solutions

3. Forms new predictions and

hypotheses

4. Tests predictions, conjectures,

and hypotheses

5. Tries alternatives and

discusses them with others

6. Records observations and

ideas

7. Suspends judgment

EDUC 566 Jan13 42

introduce a new concept;

present a new

representation.

5. Elicits responses to

initiation of concepts.

6. Proves time for students

to puzzle through

problems.

7. Acts as a

consultant/coach for

students.

Explain

(time)

1. Introduce new

concepts, ideas, skills,

relationships, solutions,

and explanations.

2. Verify or validate

students’ ideas,

discoveries, solutions.

3. Challenge students’

alternative concepts.


explain concepts and

definitions in their own

words

2. Asks for justification

(evidence) and clarification

from students

3. Uses students’ previous

experiences as the basis for

explaining concepts

4. Formally provides

definitions, explanations,

and new labels

1. Explains possible solutions or

answers to others.

2. Listens critically to another

students’ explanations offered by

the teacher.

3. Refers to previous activities.

4. Uses recorded observations in

scientific/mathematical

explanations.

Elaborate

(time)

1. Correct students’

misunderstandings.

2. Broaden and deepen

students’

understandings.

3. Provide the

opportunity for students

to practice the new ideas

1. Expects students to use

formal definitions and

explanations.


apply the concepts and

skills in new situations and

tasks.

3. Reminds students of

1. Applies new labels,

definitions, explanations, and

skills to new, but similar,

situations.

2. Uses previous information to

ask questions, propose answers,

make decisions, create and solve

similar problems, design

EDUC 566 Jan13 43

and skills so they

develop the feeling of

being competent.

4. Promote

generalization and

transfer of learning.

alternative explanations

and probes them.

4. Refers students to data

and evidence and asks:

What do you already

know? Why do you

think…?

experiments.

3. Draws reasonable conclusions

from evidence

4. Records observations and

explanations.

5. Checks for understanding

among peers.

Evaluate

(time)

1. Assess students’

level of conceptual,

procedural and problem

solving understanding.

1. Observes students as

they apply new concepts

and skills

2. Assesses students’

knowledge and/or skills

3. Looks for evidence that

students have changed

their thinking or behaviors

4. Allows students to

assess their own learning

and group-process skills

5. Asks open-ended

questions, such as: Why do

you think…? What

evidence do you have?

What do you know about?

How would you explain?

1. Answers open-ended questions

by using observations, evidence,

and previously accepted

explanations.

2. Demonstrates an

understanding or knowledge of

the concept or skill.

3. Evaluates his or her own

progress and knowledge.

4. Asks related questions that

would encourage future

investigations.

Use the following format for your Learning Cycle lesson in weeks 5, 7, and 10. Respond to all of the bulleted prompts in the column

“What the Teacher does”. Fill in what you expect the student will do cognitively (use the cognitive functions found in appendix D) in the

column “What the student does.”

EDUC 566 Jan13 44

5E Time

Frame

What the

teacher does

What the

student does Prompts

En

ga

ge


In what ways does the task build on student’s previous knowledge? What definitions, concepts, or ideas do students need to know in order to begin

to work on the task?

What are your mathematical/scientific goals/standards for the lesson (i.e., what is it that you want students to know and understand about

mathematics/science as a result of this lesson)?

What are all the ways the task can be solved?

Which of these methods do you think your students will use?

What misconceptions might students have?

What errors might students make?

What are your expectations for students as they work on and complete this task?

What resources or tools will students have to use in their work?

How will the students work—independently, in small groups, or in pairs—to explore this task? How long will they work individually or in small

groups/pairs? Will students be partnered in a specific way? If so in what way?

How will students record and report their work?

How will you introduce students to the activity so as not to reduce the demands of the task?

What will you hear that lets you know students understand the task?

Ex

plo

re


What questions will you ask to focus their thinking?

What will you see or hear that lets you know how students are thinking about the mathematical/scientific ideas?

What questions will you ask to assess students understanding of key mathematical/scientific ideas, problem solving strategies, or the representations?

What questions will you ask to advance student’ understanding of the mathematical/scientific ideas?

What questions will you ask to encourage student to share their thinking with others or to assess their understanding of their peer’s ideas?

How will you ensure that students remain engaged in the task?

What will you do if a student does not know how to begin to solve the task?

What will you do if a student finishes the task almost immediately and becomes bored and disruptive?

What will you do if students focus on non-mathematical aspects of the activity (e.g. spend most of their time making a beautiful poster of their work)?

Ex

pla

in

How will you orchestrate the class discussion so that you accomplish your mathematical/scientific goals? Specifically:

Which solution paths do you want to have shared during the class discussion? In what order will the solutions be presented? Why?

In what ways will the order in which solutions are presented help develop students understanding of the mathematical/scientific ideas that are the focus

of your lesson?

What specific questions will you ask so that students will:

make sense of the mathematical/scientific ideas that you want them to learn? expand on, debate, and question the solutions being shared?

make connections between the different strategies that are presented?

look for patterns? begin to form generalizations?

What will you see or hear that lets you know that students understand the mathematical/scientific ideas that you intended for them to learn?

Ela

bo

rate [No prompts]

Ev

alu

ate [No prompts]

EDUC 566 Jan13 45

Learning Cycle Lesson Scoring Rubric

1 or

1-2

2 or

3-4

3 or

5-6

or

7-8

Learning cycle

lesson All phases of the

LC are not

clearly elaborated

based on

descriptions

provided in the

template.

A significant

prompts in each

phase of the

learning cycle are

clearly addressed.

Only a few

cognitive

functions for

each phase of the

LC are identified.

Most are not

clearly applied to

students’ learning

of the

math/science

concepts.

All phases of the

LC are clearly

elaborated based

on descriptions

provided in the

template.

A significant

number of

prompts in each

phase of the

learning cycle are

not clearly

addressed.

Only a few

cognitive

functions for

each phase of the

LC are identified.

Most are not

clearly applied to


of the

math/science

concepts.

All phases of the

LC are clearly

elaborated based

on descriptions

provided in the

template.

Most, but not all,

prompts in each

phase of the

learning cycle are

clearly addressed.

Cognitive

functions for

each phase of the

LC are identified

but not clearly

applied to


of the

math/science

concepts.

All phases of the

LC are clearly

elaborated based

on descriptions

provided in the

template.

All prompts in

each phase of the

learning cycle are

clearly addressed

based on

descriptions

provided in the

template.

Cognitive

functions for

each phase of the

LC are identified

and applied to


of the

math/science

concepts.

EDUC 566 Jan13 46

Appendix C

K’nex Vehicle Gravity Design Competition

The Scenario

The National Automobile Association is looking for engineering teams to design, construct, and test

gravity powered vehicles that can travel in a straight line for six meters from the end of an 18 inch high

ramp.

Contest procedures and rules

1. Open up your kit and investigate all of the components.

2. Create a ramp for your vehicle that is 12 inches high at one end. The ramp can be as long as

you want but the vehicle release point must be no more than 12 inches above the floor.

3. Design and test your first vehicle. Your first vehicle may not travel the full six meters from the

end of the ramp.

4. Draw a sketch of this first vehicle, no matter how far it traveled.

5. The sketches must use lines and geometric shapes that represent the actual structural pieces that

the vehicle was built from. The sketches should also include the actual number and names for

the pieces.

6. The design sketches must show a top and a side view projection.

7. The sketches must be smaller scaled down versions of the vehicle that will be built.

8. The vehicle must travel 6 meters in a straight line from the end of an 18 inch high launching

ramp.

9. After you design, test, and sketch the first vehicle, you will redesign the vehicle a second and

third time. For the second and third redesign include a new top and side sketch of the modified

vehicle along with the number of each of the different pieces that were used.

Engage

Vehicle Design 1 – make a top view and side view sketch of your first vehicle no matter how far it

traveled down your 12 inch high ramp. The sketches must use lines, circles, and other geometric

shapes that represent the actual structural pieces that the vehicle will be built from.

Top View

EDUC 566 Jan13 47

Side View

EDUC 566 Jan13 48

Explore

Vehicle 1

1. Based on your sketch, make a table listing the names and the number of each of the K’Nex

pieces that you used to build your first vehicle.

After you build your first vehicle, you will release it from the top of the 12 inch high ramp.

Why is it important that you always release your vehicle from the top of the ramp?

What do you think the variables are so far in this investigation?

What are the values of the variables?

2. Let your vehicle roll down from the top of the ramp without pushing it.

3. Estimate how much of the six meters it traveled. Express this estimate as a percent. For

instance, if it traveled about half of the six meters then it went 50% of the way. Or, if it went

about one-fourth of the way then it went 25% of the way. Express this distance as a decimal

and a fraction. Record these values in Table 1.

4. Measure the distance in meters it travels from the bottom of the ramp until it stops. Record this

value in Table 1.

5. Make three trials with your vehicle and record your data in the chart below.

Why should you conduct three trials with your vehicle and not just one trial?

EDUC 566 Jan13 49

When the vehicle stops, describe how you are going to measure the distance the vehicle

traveled. Think about the front and back of the vehicle when you write out your procedure.

Describe how you are going to determine whether or not the vehicle has traveled in a straight

line before you measure the distance. How straight does the line have to be before you measure

the distance?

TABLE 1 Original

Vehicle Design

Trial 1 Trial 2 Trial 3 Average

Estimated

distance

traveled as a

percent

Estimated

distance

traveled as a

decimal

Estimated

distance

traveled as a

fraction

Actual distance

traveled in

meters

How close was

your estimate

as a percent

compared to the

actual value?

Express this

comparison as a

percent.

Are there any new variables in this investigation?

If so, what are they?

What do you think the relationship is between the variables you have identified so far?

Distance Vehicle Travels in Meters

EDUC 566 Jan13 50

Vehicle 2

Vehicle Design 2 – make a top view and side view sketch of your second vehicle.

Top View

Side view

EDUC 566 Jan13 51

Vehicle 2


pieces that you will use to build your second vehicle.


2. Let your vehicle roll down from the top of the ramp without pushing it. Measure the distance it

travels from the bottom of the ramp.

3. Estimate how much of the six meters it traveled. Express this estimate as a percent. For

instance, if it traveled about half of the six meters then it went 50% of the way. Or, if it went

about one-fourth of the way then it went 25% of the way. Express this distance as a decimal

and a fraction. Record these values in Table 2.

4. Measure the distance in meters it travels from the bottom of the ramp until it stops. Record this

value in Table 2.

Make three trials with your vehicle and record your data in the chart below.

EDUC 566 Jan13 52

TABLE 2

Vehicle 2


Estimated

distance

traveled as a

percent

Estimated

distance

traveled as a

decimal

Estimated

distance

traveled as a

fraction

Actual distance

traveled in

meters

How close was

your estimate

as a percent and

the actual

value?

1. Did vehicle 2 outperform vehicle 1? Why or why not?

2. Are there any new variables in this investigation? If so, what are they?

3. What do you think the relationship is between the variables you have identified so far?


entimeters

EDUC 566 Jan13 53

Vehicle 3 Vehicle Design 3 – make a top view and side view sketch of your third vehicle.

Top View

Side view


pieces that you will use to build your third vehicle.

EDUC 566 Jan13 54


2. Let your vehicle roll down from the top of the ramp without pushing it. Measure the distance it

travels from the bottom of the ramp.

3. Make three trials with your vehicle and record your data in the chart below.

TABLE 3

Vehicle 3


Estimated

distance

traveled as a

percent

Estimated

distance

traveled as a

decimal

Estimated

distance

traveled as a

fraction

Actual distance

traveled in

meters

How close was

your estimate

as a percent and

the actual

value?

1. Did vehicle 3 outperform vehicle 1 and 2? Why or why not?


EDUC 566 Jan13 55

2. Are there any new variables in this investigation? If so, what are they?

3. What do you think the relationship is between the variables you have identified so far?

Summary of data

Design Type Trial 1 Trial 2 Trial 3 Average

Original vehicle

Second vehicle

Third vehicle

Explain

Look at the data table and describe any patterns that you notice.

What do you think caused the pattern that you noticed?

Make a sketch of the gravity design system that your team has been investigating. Identify critical parts

of this system. This is a model of the gravity design challenge that you have been working on. Be

prepared to explain your model and your investigation to the rest of the class.

Egg-citing Design

The Scenario

Automobile laws in California require all passengers to wear a seat belt. Many cars now have safety

features called air cushions. What is the purpose of these safety devices?

EDUC 566 Jan13 56

The Challenge

As a member of the automotive engineering team you have been assigned the responsibility of

improving the overall safety of the company’s cars. You and your team believe that the current

restraint system of the vehicles needs to be revised, especially since the testing procedures have been

upgraded and more sensitive raw eggs will be used instead of the standard electronic dummy.

The Constraints

1. Each engineer must submit a detailed diagram of their car.

2. Each engineer must submit a procedure for testing their safety system.

3. During the investigation phase engineers will use imitation eggs.

4. Raw eggs, in plastic bags, will be used for the final test.

The Rules

1. All ramps will be 120 centimeters long and must be maintained at a ramp height of 18 inches.

The lower end of the ramp will be butted against a wall.

2. Detailed sketches must accompany each final report. The terms potential and kinetic energy

must be used in the explanation of how the safety system functions. Kinetic and potential

energy are described in the teachers guide found in the kit.

3. During final testing all eggs must be housed inside a plastic bag.

4. Evaluating and rating of the safety system after the final test run is as follows:

Excellent – The shell is not cracked and the yolk is unbroken.

Fair – The shell cracked but the yolk is unbroken.

Unacceptable – The shell cracked and the yolk is broken.

All engineers must prepare a final report that details the safety features implemented, how the testing

was conducted, and the results of this testing. Reports must also include additional safety

recommendations that might be considered.

“Collides” You are the stunt coordinator for the new movie “Collides”. In the movie one of the scenes requires

three types of cars to participate in a chase and a subsequent collision. The cars should have different

sources of energy and travel at different speeds. The producer has given you the following conditions

for the collision:

EDUC 566 Jan13 57

1. The cars must be built from the K’nex kit - Force, Energy and Motion.

2. Two cars are involved in a chase, going the same direction on the same street.

3. Another car is traveling on a different street from the two cars in the chase.

4. The lead car in the chase will make it through the intersection without a collision.

5. The following car in the chase and the car traveling on the other street will collide.

6. The collision takes place at the intersection of the two streets.

7. The minimum distance of the lead chase car and the collision car from the intersection is 120

meters.

Your task is to provide the producer with a model of the collision.

Components of the models that will evaluated for the winning production company.

1. A scale model to depict your collision.

2. Diagrams, graphs, tables, equations, and written explanations to describe the cars’ movements.

3. A video of the actual collision scene along with a formal presentation of the model.

Standards: Algebra I: 5.0, 6.0, 9.0, 15.0

Vehicle Tug-O-War

Your task is to design a vehicle that will win a tug-o-war against any other vehicle. We will use a

playoff elimination system to determine the winner. Each participant will build a vehicle that they

think will beat the competition. Each pair of competitors will take a picture of their vehicle and send it

to their competitor. The competitor will then build this vehicle from the picture. Verbal or written

instructions should be included with the pictures so each competitor can build the vehicle as intended.

Each participant will then conduct the tug-o-war with their own vehicle and the vehicle they built

based on their competitors picture and other information

EDUC 566 Jan13 58

Appendix D

Cognitive Functions – The Prerequisites of Learning*

Input phase – collecting the information

Description of

cognitive

strength

Definition Examples of prompts and questions to ask to

develop the cognitive functions

Description of cognitive weakness and

examples

1. Clear and

focused

perception

Focused perception; use all

senses to perceive all data

correctly and clearly. Keep

your focus on one spot.

What do you see?

What is here?

Have you perceived everything?

Where do you have to look?

Blurred and sweeping perception. Not

knowing where to start looking, look at

everything as a whole.

Look very quickly here and there.

2. Searching

systematically

Collect the data step by step in

a systematic way so that

nothing is lost and nothing is

done twice.

We are going to look step by step. One by one. In what

order? Let’s start here, on the left at the top, then from

left to right, then the second row, etc.

Look up a word in a dictionary, a place on a map,

check that all words are correctly spelled.

Counting one by one.

Unplanned, impulsive, and unsystematic

behavior.

Criss-cross perception, here-there-

everywhere without rhyme or reason.

Counting the same things twice.

3. Labeling Enrich vocabulary to describe

objects, events and

experiences precisely.

Describe the objects according to their characteristics

and definition.

What are the characteristics? In what way do they

differ? In shape, distance, color, number, size,

direction?

How can we call a four-sided closed figure with equal

sides, but no equal angles?

Lack of, or impaired receptive verbal tools

that affect discrimination (e.g. objects,

events, relationships, etc. do not have

appropriate labels).

Because of lack of correct names to describe

objects, events and relations, with their main

features, they are not adequately observed;

the child does not see a difference e.g.

between a rectangle and a square, it’s the

same for him.

4. Spatial

reasoning

Use concepts to indicate place,

direction, position and

orientation in relation to each

other or to a frame. Be able to

use spatial concepts.

How are things related to each other? Parallel, at a right

angle, central, in the middle of…?

Where is this? (e.g. top-left; bottom-middle; next to…;

left of…; in front of; etc.

In what direction are they running: towards…; coming

from left to right, east to west, north to south?

Lack of, or impaired, spatial orientation, the

lack of stable systems of reference impairs

the establishment of topological and

Euclidean organization of space.

Problems with left/right discrimination.

Problems with map reading.

Problems with drawing simple objects,

especially their 3-D relationships.

Problems with describing where you are and

EDUC 566 Jan13 59

where you want to go.

5. Temporal

reasoning

Use the correct concepts to

describe time and sequence.

Look for data which give you

indication of the sequence of

things and the ordering in

time.

How do you know what comes first and thereafter?

Lack of, or impaired, temporal concepts.

Problems with planning – starting on time.

6. Conserving

constancy

Be attentive that some

characteristics of an object or

a relationship change while

others remain the same.

What changes and what stays the same?

Which characteristics change?

If a square is rotated, does it remain a square?

If gasoline costs $2.00 per gallon how much will you

pay for 5 gallons?

Lack of, or impaired, conservation of

constancies (size, shape, quantity,

orientation) across variation in the factors.

Using additive thinking when

multiplicative thinking is required.

7. Being precise Being attentive to details

when it is important to do so. Have you noticed the details?

Are these two objects really the same height?

Lack of, or deficient need for, precision and

accuracy in data gathering.

Not noticing the place of the comma in a

number.

Not being precise in measuring lengths,

weights, etc.

8. Using more

than one source

of information at

once.

Take into account more

characteristics at the same

time (height, length, width,

number, shape, etc. Feel the

need to collect information

from different sources.

Have you been complete in gathering the data?

Where can you find information on what to do?

How many ways are we being presented with

information on what to do?

Lack of capacity for considering two or

more sources of information at once, this is

reflected in dealing with data in a piecemeal

fashion rather than as a unit of organized

facts.

Dealing with data in a piecemeal fashion

rather than as an organized unit, e.g. with a

school task – text, drawings, numbers

indicating order, tables, maps, index,

dictionary.

9. Activating

Prior Knowledge

Remembering and retrieving

relevant information from

memory.

Where have you seen or heard of this before?

Does this look or sound familiar? Why?

Lack of or deficient need for retrieving

relevant knowledge from long-term memory

in order to make connections among

characteristics of something currently being

considered or a problem to be solved.

10. Analyzing Identifying a structure,

process, concept, object, etc.

as a whole or unit and the

parts or elements the make up

the whole.

What are the parts of this thing?

How are the parts related to one another and to the

whole?

What are the steps of this process or procedure? Are

they in order? Why is this order important?

Impaired or deficient propensity for

breaking material, structures, or processes

into its parts and determining how the parts

relate to one another and to an overall

structure or purpose.

EDUC 566 Jan13 60

Elaboration phase - processing the gathered information

Description of

cognitive

strength




examples

1. Defining the

problem

Recognizing the problem and

being able to define it. What’s the problem here?

What do we have to do?

Is there a problem?

What is it?

Does it fit? Is everything all right? Is it correct?

Inadequacy in the perception of the

existence and definition of an actual

problem.

There is little or no awareness that

something doesn’t fit, or it is not right.

Difficulty in getting started because there is

a lack in knowing what to do.

2. Selecting

relevant

information

In a multitude of information,

select the information which

you need to solve the problem

and neglect/eliminated the

rest.

What information do you need to solve the problem?

What do you not need to solve this problem?

What is a key word in this task?

What is the important information and what is not

important information for solving this problem?

Inability to select relevant vs. non-relevant

cues in defining a problem.

Difficulty in finding key words in a reading

passage, and in forming a summary.

Difficulty in selecting the information

which is needed to solve a word problem.

3. Comparing Developing the need to

compare things, to look a

similarities and differences

with other things and events.

In what way are they same? Different?

Expand the repertoire of criteria to compare.

How should we compare these things, by size, color,

shape, quantity, etc.?

What does ‘greater than/less than’ mean?

What does ‘n times as much’ mean?

Let’s look at the first as, what are the words to the left,

now let’s look at the second as, what are the words on

the right of this as?

Prepositional relations compared – eight divided by

four compared to eight into four.

Lack of spontaneous comparative behavior

or limitation of its application by a restricted

need system.

Compare on the basis of only one arbitrary

criterion.

Compare on the basis of non-relevant

criteria.

Lack of spontaneous comparison with prior

knowledge.

Difficulty in identifying the lack of

correspondence between mathematical

symbols and the words they represent (e.g.

if the expression eight divided by 2 is

translated word-for-word in the order in

which it is written, the resulting

mathematical expression 82 would be

incorrect .

EDUC 566 Jan13 61

4. Broadening

your mental field

Have an overview, take into

account as many factors as

possible. Effective memory

capacity. Analogous to

computer with a large hard

disk and a fast retrieval speed.

We are confronted here with a mass of data. Can’t we

put them into order? Can’t we recognize groups? What

things could belong together? On what basis?

How can we memorize better?

Writing down key words.

Making a schema, a table, a matrix.

Keeping an agenda.

Have a system of visual retrieval (post-it-notes),

writing in the margins.

Narrowness of the mental field.

Forget things easily.

Deal with things as pieces one by one,

rather than in units or chunks.

Not able to process two things at the same

time.

When you learn something new, you forget

the previous learning(s).

5. Forming

relationships,

making

connections

Put things in relation to each

other.

Cause – effect relations.

Means – ends relations.

Have you seen something similar before?

How are these connected?

Is A the cause of B, or does B cause A? Why?

Episodic grasp of reality.

Dealing with events and objects as if there is

no connection between them, in an episodic

way.

6. Need to pursue

logical evidence

Have a need to justify the

answer and be able say why

choose a certain solution.

Spontaneously search for date

to justify a statement.

How do you know this? How do you know whether

your answer is correct?

Why is it correct? Why not?

Explain your answer.

Lack of, or impaired, need for pursuing

logical evidence.

Giving an answer but not knowing why the

answer is right or wrong.

The student accepts statements without

critically examining them.

Beliefs are either unexamined and

unjustified or justified by their

correspondence with the beliefs of an

authority figure, such as a teacher or parent.

7. Internalizing

and representing

information

Composing a mental image of

the information. Visualizing

and mentally representing

information in different ways.

Make a mental picture of the information.

Visualizing the information in more than one way.

Lack of, or impaired interiorization.

8. Hypothetical

deductive –

predictive

thinking

If … then thinking. Represent

mentally what could possibly

happen, if… Inference: draw a

conclusion; one thing follows

from another.

What do you think could happen?

What do you predict will happen?

What could the possible solutions be?

What can you infer from this statement?

What can you conclude from this?

Lack of, or impaired, inferential-

hypothetical thinking.

Limited capacity to come up with

possibilities.

9. Developing

strategies to test

hypotheses

Check a hypothesis mentally:

what could be the effect of an

event. Find means to check

and confirm a hypothesis.

If a possibility is thought of,

look for data which confirms

or refutes it.

Shall we look for a strategy to check it?

Let’s compare with the model, analyze the model’s

characteristics, make a drawing, schema, write down

the steps, look for more data; use additional reliable

sources of information like encyclopedias, use a

calculator after making the operations mentally; use the

reverse operation.

Lack of, or impaired, strategies for

hypothesis testing.

Have a need to check solutions in a concrete

rather than a mental way.

Have no need to check at all.

Difficulty in representing possible effects.

EDUC 566 Jan13 62

10. Selecting a

frame of

reference,

structure, or

framework for

problem solving

Choose a framework in which

a solution can be found. Where shall we look for a solution?

What operation should we do here: is this a

multiplication problem or an addition problem? Is this a

problem of classification?

Do we need a science text or dictionary? Shall we got

to the library or ask an expert?

Lack of, or impaired ability to define the

framework necessary for problem solving

behavior.

Have no idea where to start looking.

Have no idea which operation to choose.

11. Planning

systematically

Represent the steps toward a

solution one by one. What are the steps we have to take in order to arrive at

our goal?

What are you going to do first? And then? And then?

Lack of, or impaired, planning behavior.

Start working in an unsystematic way.

12. Categorizing Develop vocabulary for

superordinate words and

concepts to indicate cognitive

categories and describe mental

operations.

Let’s compare – find the similarities and differences.

This belongs to a larger group, let’s find the class or

category that it belongs to. What is the name of this

category?

Let’s order these things. What comes next?

Let’s think this through, what thinking action(s) do we

need to use to solve this problem?

Non-elaboration of certain cognitive

categories because the verbal concepts are

not a part of the individual's verbal

inventory (on a receptive level) or they arc

not mobilized at the expressive level.

Lack of words to describe categories.

13. Accounting

for all

information

Encourage counting. Make an

inventory. How much do you have?

Are you sure we did not miss anything?

Lack of, or impaired summative behavior.

Paraphrasing

Through

Rereading

After reading (or hearing)

something, restating the main

idea in your own words.

Tell me in your own words what I just said.

Tell me in your own words what you just read.

Tell me exactly what the problem is.

Lack of or impaired need for writing or

saying something in your own words that

you have just read or seen (or heard).

Transforming a

Representation

Changing the modality of a

representation from one type

to another.

Make a diagram of what you just read.

Make a picture with stick figures to represent this

problem or story.

Use numbers and symbols to represent the

relationships and things in this word problem.

Make a table, a graph.

Lack of or impaired need for changing the

modality of presentation from one form to

another.

Inductive

Thinking

Forming relationships among

data or information so that a

general rule or formula can be

created.

What is common to all of these?

Do you see a pattern?

How could you classify these things?

Write out the rule or formula that clearly states the

relationship(s) that you discovered.

Lack of or impaired propensity for forming

abstract relationships among items or data

that seem to form a pattern, categorizing

them into general relationships, and

organizing the results to form a general

rule, principle, formula, recipe, or guide.

Analogical

Reasoning

Transferring relationships

discovered in one task to a

new task where the prior

discoveries will be helpful in

What have we just learned that may be helpful in

solving this problem?

Do we have any examples or models that will help us

Lack of or impaired need for transferring

relational information from existing

concepts to a new problem that needs to be

EDUC 566 Jan13 63

solving the new task. solve this problem? solved. Deficiency of abstracting a solution

strategy from a previous problem and

relating that information to a new problem

that one is trying to solve.

Synthesizing

Connecting things to form a

new structure. How can we modify these things and then put them

together to make something new?

Lack of or impaired propensity to connect

elements together to form a coherent or

functional whole so that a new pattern or

structure emerges that is not just a

reordering of the elements.

Output phase – expressing the solution correctly

Description of

cognitive

strength




examples

1. Expressing

yourself clearly

Put yourself in the other

person’s shoes in order to

communicate your answer

clearly.

I can understand what you mean, but please, could you

say your answer so that others can understand it as

well?

I can see you know, but nobody else sees it.

Encourage a student whose habit is to speak in one

word sentences, to speak in full sentences.

Egocentric communicational modalities.

A student who does not bother to write

down or tell his answer, because he is

satisfied he knows it.

Difficulty in explaining a familiar way to go

somewhere.

2. Projecting

virtual

relationships

Make hidden relations

explicit. Make relationships visually obvious with graphic

organizers, markers, schemata, arrows, etc.

Infer future events from present trends in a sequence of

events (making graphs, statistics, analyzing historical

processes, weather forecasting).

Difficulties in projecting virtual

relationships.

Some students may be aware and know the

relationships but are unable to make them

visible because they do not have techniques

to do this.

3. Preventing

blocking

When a solution does not

appear to be found

immediately, or is not correct,

stay calm and start looking

again in a different way.

You didn’t find it immediately? Never mind. Let’s

analyze what happened. What were you doing, looking

for, what strategy did you use? Is there another

strategy? Let’s look again at the model, the data. Where

else could we start?

Don panic when you haven’t found it! There’s no harm.

We’re going to look again.

Convey a message to the class that it’s all right to make

mistakes as long as we learn form them.

Blocking.

That student panics and doesn’t know

anything anymore.

The student stops searching.

The student has fear of failure or is angry

and doesn’t proceed.

EDUC 566 Jan13 64

4. Avoiding trial-

and-error

Stop guessing until a right

solution is found incidentally. “You’re only guessing now. Start thinking! What are

the data? Look at them. What do you think you have to

do?”

Define the problem, plan a solution, gather the data.

Trial-and-error responses.

Students who give answers without

thinking.

5. Using correct

wording

To express an answer

correctly, one needs precise

vocabulary.

Give the child the proper wording to formulate an

answer correctly.

Organize class discussion to talk about solutions.

Encourage journal writing.

Lack of, or impaired, verbal tools for

communicating adequately elaborated

responses.

The child knows the answer but does not

have enough or adequate vocabulary to

formulate it.

6. Being precise Have a need to communicate

an answer with enough detail

in order to avoid confusion.

Ask for more precision in formulating, in drawing, etc.

Create a need to be more precise when giving an

answer.

Lack of, or impaired, need for precision and

accuracy in communicating one's response.

Students who give vague answers.

7. Transporting

visually

Transport the data and

solution from the starting

place to the place where the

answer must be expressed or

drawn without changing the

characteristics.

Compare with the model constantly, go back and forth;

make sure you haven’t changed it.

Deficiency of visual transport.

The student who changes the4 date from the

top to the bottom of the page.

Difficulty in copying numbers, words, and

drawings from a book or the blackboard to

the page.

8. Restraining

impulsivity

Think before acting. Are you sure of your answer/ Have you checked

everything?

I want to hear you answer only when you are really

sure.

Impulsive, acting-out behavior.

The child who starts answering before

thinking or before the question has been

fully asked.

EDUC 566 Jan13 65

Appendix E

Problem Solving – Due Week 2

The half-hour program includes 13 classroom excerpts from the content standards lessons which

illustrate students investigating and learning mathematics through problem solving. Teachers share

their approaches and observations.

http://www.learner.org/resources/series32.html?pop=yes&pid=1088#

17. Problem Solving

Excerpts from 10 classrooms where students are learning mathematics through problem solving.

Teachers use multilayered tasks to engage students in making conjectures, constructing meaning, and

developing strategies.

Respond in writing to one question from each group. Be prepared to discuss your written responses

with your Forum group.

Observing Student Problem Solving

How can teachers create enthusiasm and interest in all students for problem solving?

What are the criteria teachers can use to select problems for introducing new material?

Problems should offer a rewarding challenge for students, being neither so obvious that they put no

demands on them nor so difficult that they are clearly beyond their ability. How do you make a

determination about the appropriate level of difficulty in your own class?

Different students solve problems at different speeds and with different approaches in this

classroom, or in any classroom. Given this factor, what is the role of the teacher in fostering

effective problem solving? Be specific.

It is often straightforward to assess whether a student found the correct final answer. How do you

assess whether the strategies and ability to apply them were sound? If a student has found a correct

answer despite a faulty strategy, how do you respond?

Exploring Problem Solving

Examine the work you did to solve the problem, any notes you made. If you were now asked to

hand this work in to your instructor, what might it reveal to that instructor about your problem-

solving practices?

How does your personal problem-solving approach influence your teaching and assessment

practices?

As a student, do you remember using problem situations to help you make sense of new concepts

and procedures? What was the effect? Did this work help you make new connections?

How can questioning be used to help students learn from errors or wrong turns in problem solving?

What questions do you ask yourself when you are struggling while solving problems? Are these the

same questions you would ask your students? Why or why not?

http://www.learner.org/resources/series32.html?pop=yes&pid=1088

EDUC 566 Jan13 66

Defining Problem Solving

We've provided a range of points that help in formulating a working definition of the problem-

solving standard. If a colleague or parent were to ask you to define problem solving in the context

of your own classroom, how would you do so?

Although research has shown that problem solving can be taught, and that kids of varying skill

levels can still improve with respect to their ability at the beginning of the year, many teachers

believe deep down –– and privately –– that some kids are just good problem solvers and some

aren't. Do you believe this? Why or why not? How does this belief relate to your own problem-

solving practice?

Do you believe the practices developed in solving in high school mathematics problems can be

extended to contexts outside the mathematics classroom? Why or why not?

How does technology influence how you work with and define problems in the classroom? Has it

expanded your repertoire? Has it presented challenges?

Identify some problem-solving strategies that you wish to introduce to your class. What are

important considerations as you incorporate them in your classroom?

Applying Problem Solving

What can you do in your classroom to help students learn by exploring new concepts and skills in a

problem-solving situation rather than by direct teaching? Do you see drawbacks to this approach?

How could you address them?

What are some of the advantages of having students work in groups? When might you want

students to work individually on problem-solving experiences? Give an example.

How long do you let students struggle with a problem before helping them find a solution? What

are some questions that help without giving away a solution method?

If different individuals and groups are using different strategies on the same problem at the same

time, what tools can the teacher use to assess individual understanding?

Evaluating Problem Solving

Small changes can have big differences. What one change in your classroom could you make to

improve your students' problem-solving skills? Could you make that change the next time you walk

into your classroom, say tomorrow? Why or why not?

Imagine a video team was to arrive tomorrow to film your class as a study of problem solving in

action. What would it show? What would you be proud of? What might you want to change?

Where would you like to be as a teacher with respect to problem solving in a year? How might you

get there? How will you know you've arrived?

Eliciting Student Ideas – Due Week 4

Week 4 Annenberg Video Assignment

For Week 4 go to the Annenberg Private Universe Project in Science website by entering this URL in

your browser:



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Click on the icon titled VoD for Workshop 1. Astronomy: Eliciting Student Ideas.

Workhshop 1. Astronomy: Eliciting Student Ideas. Introduces constructivism by examining student

beliefs on what causes the seasons and their explanations for the phases of the moon.

What is the theme of this workshop? The theme of Workshop One is "Eliciting Student Ideas."

Pre-Workshop Activity

Prior to this workshop, workshop participants should spend 5-10 minutes interviewing a student and an adult about what

causes the changes in the seasons. Record their responses. Did you discover some good ways to uncover students' ideas?

Explain.

Whom do we see in the videotape? We see several Harvard students and faculty who are enormously

confused about what causes the seasons. We also see Heather, an articulate, intelligent high school

student who has a great many ideas about astronomy. Interviews with Heather both before and after

her classroom lessons about astronomy reveal that she has learned much but is still confused about

some key aspects of the subject.

What happens in the videotape? While some of Heather's ideas after instruction are solid, others

seem wildly "off base" from a scientist's point of view. Some of her ideas stubbornly resist change,

either in the classroom or during on-camera challenges.

What problem does this workshop address? Many of us think that the cause of the seasons has

something to do with our distance from the sun, even though this "wrong idea" was never taught to us.

Why is it we seem to learn some things that teachers don't teach us?

What teaching strategy does this workshop offer? Many techniques for eliciting student ideas have

been tested in the classroom. Interviews with students, poster presentations, prediction questions,

group discussions, and journal keeping are some of the most common approaches. This workshop will

address interviewing techniques and journal keeping.

Using the Forum, post answers to the following questions. Reply to at least one other of your classmate’s responses.

1. Is understanding the causes of the seasons or lunar phases important in the lives of students?

2. Why is an understanding of basic scientific principles important for all citizens?

3. What are some surprising ways in which a good science understanding can enhance the abilities

of non-scientists to perform their work and live their lives? (For example: Could chemical

understanding affect the work of professional cooks and homemakers; could understanding

weather and fluid dynamics help make better airline pilots and sailors; and could understanding

how plants make food affect anyone who gardens?)

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4. What are some examples of important social or political issues that require a scientific

understanding by voters and policy makers? (For example: Would knowledge of science be

important for understanding toxic waste, screening for genetic diseases, global warming, or

energy conservation issues?)



your browser:


Click on the icon titled VoD for Workshop 2. Biology: Why Are Some Ideas So Difficult?

Focuses on the need for conceptual understanding and examines the scope of student ideas by exploring the central idea of photosynthesis, that the substance of plants comes mostly from the air. What is the theme of this workshop? The theme of Workshop Two is "discovering the scope of student ideas".

Whom do we see in the video? Jon, a seventh-grade student, is interviewed before and after a traditional lesson on photosynthesis. Bob Holden, Jon's teacher, watches the video of Jon's interviews, discovering that Jon's problems in biology concern his confusion about the physics and chemistry of matter and energy. Jon also has no concept of energy and the relationship of energy to chemical changes. He seems to be missing the concept that chemical changes may either require an input of energy or may release energy.

What happens in the video? Interviews with Jon suggest that teaching can be more effective when the full scope of a student's ideas are considered.

What problem does this workshop address? Photosynthesis is among the most widely taught of all concepts in biology. Why, then, do many people have difficulty grasping the central idea of photosynthesis-that most of the substance of plants comes from the air?

What teaching strategy does this workshop offer? Among many possibilities to help students reflect on their own thinking, we offer such techniques as concept mapping and journal keeping.



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1. Devise a simple explanation, demonstration, or activity for understanding how plants convert carbon dioxide from the air and water from the ground into food through photosynthesis.

2. Invent a way that allows even the skeptical students to convince themselves that the air does, indeed, have mass/weight. Whenever possible, allow students to test the idea.

3. Often the ideas established prior to and outside the teaching of a subject block learning. How can this problem be addressed in the classroom? For instance, the student in the video has trouble

understanding photosynthesis because of his belief that air has no weight. An understanding that air

is made of invisible particles with weight is usually a topic for chemistry or a physics lesson, and a

lack of this understanding prevents the student from learning an idea in biology.



your browser:


Click on the icon titled VoD for Workshop 5. Vision: Can We Believe Our Own Eyes?

Explores the origins of student ideas to find out whether experience equals learning. Shows how

experience can work for or against learning because students can disbelieve concepts that they have

“learned.”

What is the theme of this workshop? The theme of Workshop Five is "the origins of student ideas."

Whom do we see in the video? Richard and Karen, eighth graders, and Conor, a fifth grader, are three

students who constructed many of their ideas from personal experience, television nature specials, and

classroom activities. Conor blends the various resources and constructs rich and imaginative

explanations of light and vision; Richard vacillates between scientific and non-scientific ideas, even

after instruction; and Karen never waivers from her personal construction about vision.

What happens in the video? Students of various ages discuss their ideas of how we "see." Their

ideas, many of which seem to come from sources outside of school, often differ from those accepted

by scientists. Where do students' ideas come from and can (or should) they be changed?

What problem does this workshop address? Although mirrors are among the most common of

scientific devices, they remain enigmatic. The average adult in the United States may use a mirror

30,000 times in a lifetime. Why is it that, even with all of this experience, so many adults still cannot

answer simple questions about the properties of mirrors?

"Can We Believe Our Own Eyes?" addresses students' "conceptual change," a process by which

students replace old ideas when new ones become more acceptable. This workshop explores how

students construct ideas from the many sources available to them. Television, radio, books, parents,

teachers, and peers all play a role in promoting the ways in which students see and understand natural


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phenomena. In contrast, seeing often contradicts their understanding and, as a result, seeing is not

always believing. What can we learn about children's concepts of light and vision that can shed some

light on this problem?

What teaching strategy does this workshop offer? The role of students' experience can be very

powerful in shaping their ideas and beliefs. Does this experience always lead to a better understanding?

Teachers learn to confront students' understanding by offering alternative experiences that contradict

old ideas.


1. Do you think it is possible for a teacher to control the way a student interprets ideas? Please

explain your response.

2. When teachers see their students espousing non-scientific ideas picked up from television,

books, and other sources, often the immediate reaction is to suggest ways to eradicate the

sources of "misconceptions" and replace the alternative ideas with the science ideas. The more

experience we have with something, the more difficult it can be to understand. Experience can

reinforce or create misconceptions. Experience does not equal understanding. Should or can

we as educators "misconception-proof" the student's world? Explain. 3. Light allows us to see and yet light itself seems invisible. What activities might we

devise to help students in grades K-3 develop concrete images of the abstract concept of

light?

Following Children’s Ideas in Mathematics - Due Week 10

An unprecedented long-term study conducted by Rutgers University followed the development of

mathematical thinking in a randomly selected group of students for 12 years - from 1st grade through

high school - with surprising results. In an overview of the study, we look at some of the conditions

that made their math achievement possible.

Private Universe Project in Mathematics. Following Children’s Ideas in Mathematics.


Using the Forum, describe what you learned about the long-term development of students’

mathematical thinking. Respond to the post of at least one other student.


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Documents

University of Southern California Rossier School of ...web-app.usc.edu/soc/syllabus/20131/27818.pdfUniversity of Southern California Rossier School of Education Course Syllabus EDUC