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Third Annual Appalachian Ohio Mathematics and Science Teaching Research Symposium Schedule
September 15, 2012 Ohio University, Athens Morton Hall
9:30 Symposium Registration Foyer
10:00 Welcome 235 Ralph Martin, Noyce and WWTF Co-Director
10:15 Opening Remarks 235 Aimee Howley, Associate Dean of the Patton College
10:30 Introduction of Speaker 235 Gregory D. Foley, CAT Program Director
10:35 Keynote Address 235 Tom Reardon, Mathematics Teacher and Consultant
What I Have Learned While Teaching Math for 30+ Years
11:20 Break
11:30 Concurrent Sessions 219 Mark Lucas, Physics, Ohio University, 30 min
Science Outreach in Southeastern Ohio
222 Pam Beam, Teacher Education, Ohio University, 30 min
Classroom Strategies for the First Year Teacher
223 Lisa Gillespie1, Ohio Virtual Academy, 30 min
Being an Educator with Ohio Virtual Academy
227 Julio Camacho2, University of Rio Grande, 30 min
UDL and Scientific Creationism4
226 Sam Carpenter2, Ohio University, 15 min
Motivating the Modern Math Student
11:45 226 Justin Malone2, Shawnee State University, 15 min
Utilizing Classroom Seating Arrangement for Management
Purposes in the Secondary Science Classroom
12:00 Lunch and Conversations 226 CAT Scholar Meeting
in rooms 219–235 227 Noyce Scholar Meeting
12:50 Concurrent Sessions 219 Michael Smith3 and Kay Casto, Mathematics Education
and Mathematics, Ohio University and Vinton County
High School, 30 min
Statistical Literacy in the High School Mathematics and
Science Classroom
222 Donna Shepherd, Chemistry and Physics, Adams County
Ohio Valley High School, 30 min
Bringing STEM to K–12 Students: Locating and
Researching Sinkholes
223 Jeff Taylor3, Ohio University, 30 min
Algebra for All in Grade 8: What's Different about the
1 Noyce scholar 2 Choose Appalachian Teaching (CAT) scholar 3 OU PhD student 4 Julio Camacho did not present.
Third Annual Appalachian Ohio Mathematics and Science Teaching Research Symposium Schedule
September 15, 2012 Ohio University, Athens Morton Hall
Common Core?
12:50 Concurrent Sessions 227 Aaron Sickel, Teacher Education, Ohio University, 30 min
Struggles and Successes: What Beginning Mathematics and
Science Teachers Should Know About the First Three Years
226 Nick Conroy1, Ohio University, 15 min
The Wow Factor: Demonstrations in the Science Classroom
1:05 226 Calee Reeves1, Ohio University, 15 min
Science Teacher Methods Opinions
1:20 Break
1:25 Concurrent Sessions 219 Gregory D. Foley, Teacher Education, Ohio University,
30 min
Advanced Quantitative Reasoning: Ohio Core Mathematics
for High School Seniors
222 Donald Storer, Chemistry, Southern State Community
College, 30 min
How a Chemical Education Research Project Led to a
“Flipped" Classroom
223 Nina Sudnick, Elementary School Mathematics and
Science, Athens City Schools, 30 min
"I LOVE Math! This is my BEST year ever!!" 4th grader,
West Elementary 3
226 Al Coté and Mark Lucas, SEOCEMS and Physics, Ohio
University, 30 min
Bring STEM to the Classroom: Integrating Science and
Math through Real World Investigations
227 Art Trese, Environmental Biology, Ohio University, 30 min
Garden Spaces as Educational Tools
2:00 Panel Discussion 235 Voices from the Field, 30 min
Starr Adkins2, Mathematics, Collins Career Center
Micah Freeman2, Mathematics, Grove City Christian High
School
Zachary Graves1, Mathematics, Wellston High School
Dan Oliver2, Mathematics, Ripley-Union-Lewis-Huntington
High School
Mallory Spengler1–2, Science, Jackson High School
2:30 Closing Remarks 235 Gregory D. Foley, CAT Program Director
Jeff Connor, Noyce and WWTF Co-Director
1 Choose Appalachian Teaching (CAT) scholar 2 Noyce scholar 3 Nina Sudnick was unable to attend and present.
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Advanced Quantitative Reasoning Ohio Core Mathematics for
High School Seniors
Gregory D. Foley Morton Professor of Mathematics Education
Ohio University
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Advanced Quantitative Reasoning (AQR) is a course in mathematics, statistics, and modeling for students who have completed Algebra I, Geometry, and Algebra II—or Integrated Mathematics I–III.���
In Ohio, students graduating in 2014 and beyond will be required to complete 4 years of high school mathematics. AQR is a 4th-year course designed for the average student.���
The AQR project is developing and testing student materials and teacher resources (75% done) for such a course. AQR has pilot-tested textbook materials for the past three school years and now is field-testing them at 10 high schools in 2012–2013.
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Our society thrives on numbers, yet many high school graduates are ill-equipped to make informed judgments using quantitative information. ���
Many graduates are not ready for the mathematical and statistical demands of college, with 35.1% of U.S. college mathematics enrollments in remedial courses: 1.4 million out of 3.9 million in fall 2010.
(R. Blair, 7 April 2012)
Perhaps the worst thing that can happen to a student at the end of his or her secondary mathematics preparation is to enter college not having studied mathematics after a lapse of a year or more.
(Seeley, 2004, p. 24)
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NCTM Math Takes Time position statement (2006): • Every student should study mathematics every year through high school,
progressing to a more advanced level each year.
• All students need to be engaged in learning challenging mathematics.
• At every grade level, students must have time to become engaged in mathematics that promotes reasoning and fosters communication.
• Evidence supports the enrollment of high school students in a mathematics course every year, continuing beyond the equivalent of a second year of algebra and a year of geometry.
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The aims of the AQR springboard course are"• to reinforce, build on, and solidify the student’s working
knowledge of middle grades mathematics through Algebra I, Geometry, and Algebra II
• to develop the student’s quantitative literacy for effective citizenship, for everyday decision making, for workplace readiness, and for postsecondary education
• to develop the student’s ability to investigate and solve substantial problems and to communicate with precision
• to prepare the student for postsecondary course work in STEM and non-STEM fields—and
• for students who complete the course in the 11th grade—to prepare them to study AP Statistics, AP Computer Sciences, or Precalculus in their senior year of high school.
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Common Core conceptual categories for high school mathematics"
• Number & Quantity • Algebra • Functions • Modeling • Geometry • Statistics & Probability
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Common Core standards for mathematical practice!
1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of
others. [mathematical communication] 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
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Advanced Quantitative Reasoning course outline!
Core. Quick questions, explorations, investigations, examples, exercises, and increasingly involved projects and presentations.
• Numerical reasoning • Statistical reasoning • Modeling using discrete and continuous functions • Geometric modeling and spatial reasoning
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Some AQR numerical reasoning topics"
• Problem solving strategies • Fractions, decimals, percent • Proportional reasoning • Quarterback ratings • Reading indices • ID numbers and check digits • Richter scale analysis • Transition matrices • Applications of Pascal’s triangle • Probability
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Probability task"Drug testing. Suppose a recent national study
indicates that about 3% of high school athletes use steroids and related performance-enhancing drugs. Suppose further that the accuracy of the standard test used is roughly 97%. That means that 3% of the time, the test returns an incorrect result (either a false positive or a false negative).
What is the probability that a randomly selected student athlete who tests “positive” is actually a user of performance-enhancing drugs?
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How to design an investigation"Is a DoubleStuf Oreo cookie really double stuffed?
What concepts and relationships are involved?"
Ancient Alligators. Alligators, crocodiles, and their relatives and ancestors are known as crocodilians. On Earth for 250 million years, they have survived mass extinctions that killed other animals. The modern American alligator thrives in the coastlands of the Southern states from Texas to the Carolinas. A typical adult male is about 12 ft long and weighs 800 lb.
Suppose that a scientific team excavates an ancient crocodilian with the same proportions (same shape) but twice as long (24 ft) as an adult male American alligator. How much would you expect this ancient beast to have weighed?
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What is the relationship between the area and the side length of an equilateral triangle?
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Modeling activity: Zipfʼs law"
“In a given country . . . , the largest city is always about twice as big as the second largest, and three times as big as the third largest, and so on” (Strogatz, 2009).
How accurate is this model for city population in the United States?
2010 U.S. Census Bureau Data (in millions of persons)"
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1 New York 8.175 2 Los Angeles 3.793 3 Chicago 2.696 4 Houston 2.099 5 Philadelphia 1.526 6 Phoenix 1.446 7 San Antonio 1.327 8 San Diego 1.307 9 Dallas 1.198 10 San Jose 0.946
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Modeling activity: Zipfʼs law"
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Modeling activity: Zipfʼs law"
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Modeling longitude and latitude with fruit"
(a) Identify two antipodal points as the north and south poles. Mark and label the two points as N and S.
(b) Draw an arc from the north pole to the south pole. Label it as 0° longitude. This is the prime meridian.
(c) Locate and mark the midpoint of the prime meridian. Mark the midpoints for 4 or 5 other meridians (lines of longitude). Draw in the great circle that represents the equator.
(d) With the aid of a globe, an atlas, or the Internet—locate, mark, and label points for London, England; Quito, Ecuador; and your home city or county on the orange.
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Geometric modeling: Spherical geometry"If you are traveling along a great-circle shortest
path from Athens, Texas to Athens, Greece will you pass closer to Athens, Georgia, USA or Athens, Ohio?
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Advanced Teacher Capacity: An associated professional development program"
• Two-week summer institutes (60 contact hours). !• Two daylong follow-up workshops plus online support
• TPACK: technology, pedagogy, & content knowledge
• Technology: TI-nspire (additional tools for Modspar)
• Pedagogy: Tasks, tools, and talk
• QUANT: Statistics and probability
• Modspar: Modeling and spatial reasoning
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QUANT: Quantifying uncertainty and analyzing numerical trends"• Words of statistics; measurement and data collection "• Formulating statistical questions and designing of
statistical studies
• Data analysis and descriptive statistics
• Combinatorics, random processes, and probability, including conditional probability
• Using data, probability, and distributions to justify conclusions and to make decisions
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Modspar: Modeling and spatial reasoning"• What is modeling? !• Discrete dynamical systems: Finite differences,
difference equations, web plots
• Recursively and explicitly defined functions
• General proportional model and reexpressing data
• Modeling with polar and parametric equations
• Three-dimensional geometry and modeling
• Spherical geometry and modeling
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Acknowledgement and appreciation"• Thomas R. Butts, Stephen W. Phelps, Daniel A. Showalter,
Joseph T. Champine, Carmen Wilson, Allen Bradley, Tarasa Sheffield, Mary Harmison, Andy Lovejoy, Sara Vance, Wei Lin, George A. Johanson, Jeffery Connor, Laura J. Moss, Jeremy F. Strayer, Michael Todd Edwards, Sigrid Wagner, Pascal D. Forgione, Jr., Cathy L. Seeley, Michelle Reed, Jerry L. Moreno, Ralph Martin, S. Nihan Er, Michael A. Smith, Heba Bakr Khoshaim, Maha Alsaeed, David A. Young, Ruth M. Casey, Rebekah Boyd, Douglas Roberts, Michael Houston, John Ashurst, Michael Lafreniere.
• Advanced Teacher Capacity QUANT and Modspar scholars • A host of other colleagues, graduate students, and support staff • Our wives and families
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Acknowledgement and appreciation"AQR and ATC have been supported by grants from • the Improving Teacher Quality Program of the Ohio
Board of Regents, • the Mathematics Professional Development Program
of the Ohio Department of Education, • the U.S. Department of Education, • the South East Ohio Center for Excellence in
Mathematics and Science, and • Texas Instruments, Inc.
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Advanced Quantitative Reasoning Ohio Core Mathematics for
High School Seniors
Greg Foley [email protected]
Science
Teacher
Methods
Opinions Calee Reeves
Ohio University CAT Scholar
Background for Survey
Science teachers grades 7-12
Appalachian Ohio counties
813 emails
13
14
13 16
24
8
Grade
Seventh
Eighth
Ninth
Tenth
Eleventh
Twelfth
5
18
16
8 5
17
5
0 14
Class Taught
A & P
Biology
Chemistry
Earth
Life
Physical
Physics
Space
Other
0
3
2
29
38
14 2
Class Size
0-5
6-10
11-15
16-20
21-25
26-30
30+
Methods and Modes Surveyed Direct Instruction v. Lecture
Labs v. Demonstrations
Bookwork, Seatwork, Homework
Availability of Blackboard, Whiteboard, SmartBoard
Participants were asked to rate how frequently a
method is used and then offer an amount of
agreement or disagreement with various
statements about the method.
Frequency of Use
Direct Instruction:
daily
Lecture: 2
times/week
Labs: 1 time/week
Demonstrations: 1
time/week
Bookwork:
rarely/never
Seatwork: 2
times/week
Homework: 2
times/week
Delivery Modes
Available
Blackboard: 25
Whiteboard: 61
SmartBoard: 45
Use
Blackboard: 19
Whiteboard: 59
SmartBoard: 45
Direct Instruction
Helps students learn
Is not a difficult teaching method
Is beneficial
Lecture
Benefits students
Easy teaching method
Students do not prefer lecture over other
methods
Labs
Helpful to student learning
Not easy to plan
Students benefit from hands-on
Best performed in pairs
Students enjoy
Demonstrations
Cost effective
Easy to set up and perform
Preferable during lessons
Effective teaching method
Students prefer labs over demonstrations
Bookwork
Good use of time
Students don’t resist bookwork
Effective
Seatwork
Effective
Helpful for reinforcement
Not meant to be busy work
Students don’t resist seatwork
Homework
Meant to be graded
Useful reinforcement tool
Not better than bookwork or seatwork
Standout Quotes “I present students with the questions I will ask in
advance and then spend class time listening to
their responses a[nd] correcting errors and honing
their answers to be sure they have understanding.”
“No one method fills a whole class period.”
“A good mix of several methods/styles in any given
class period will reach all types of learners. I believe
each method has an impact and is effective when
not overused.”
Standout Quotes Continued
“Students benefit only if they understand
what they are supposed to be learning in
lab.”
“ I think that demonstrations are
beneficial as a precursor to a hands-on
lab experience.”
Ideal Modes of Delivery
SmartBoard* with Smart Slates
Promethean Board
Laptops or iPads for each student
Document camera and Smart Pad
Edmodo (online community for teachers,
students, schools, and districts to
communicate)
Elmo
Modes Most Enjoyed by
Students
SmartBoard*
Promethean Board
Laptops or iPads
“All of them! Students love technology!”
Modes Most Beneficial for
Students
SmartBoard*
Promethean Board
“I think all modes have some benefit to
the students, depending on how they are
used.”
“All of them.”
Simplest Modes to
Learn/Manipulate
White board
Blackboard
Smart Board
Overhead
“THEY ARE ALL EASY!”
Struggles and Successes: What Beginning Mathematics and Science Teachers Should Know About the First Three Years
Aaron J. Sickel
Department of Teacher Education
Ohio University
Question
• Why do you / did you want to become a teacher?
• #1 Reason: Desire to work with young people and help them succeed
• Other Reasons
• Drawn to subject / grade level (enjoys math, high schoolers)
• Drawn to teaching-learning process (“light bulb” moment)
• Drawn to teaching lifestyle (e.g. conducive for family)
• (www.teachersnetwork.com; www.scholastic.com)
Question
• What are the goals of teacher preparation programs?
• Introduce preservice teachers to the teaching profession
• Prepare preservice teachers in both content and pedagogy
• Learn to teach in reform-based ways
Teach in Reform-Based Ways?
• What does “reform” mean in teacher education?
• Education is a constantly evolving field – we are constantly learning about how to facilitate meaningful learning for students
• Mathematics and Science Education Reforms
• Elicit students’ mathematical thinking; ideas about the natural world
• Manage and facilitate discourse in the classroom
• Support students’ abilities in doing the things that mathematicians and scientists do – problem-solving; engaging in scientific inquiry
(Bennett, 2010; Kelly, 2007; National Research Council, 1996; Sleep & Boerst, 2012)
Problem
• Good News
• Preservice teachers are excited to join the profession
• The teacher education community has developed research-based teaching strategies to teach mathematics and science in reform-based ways
• Problem?
• Beginning teachers are not likely to teach in reform-based ways
• Beginning teachers are likely to leave the profession within the first 3-5 years
Beginning Teachers’ Practices
• 1999 – Simmons et al. interviewed and observed 69 beginning teachers
• What percentage of beginning teachers consistently engaged in student-centered practices?
• 5-10%
Beginning Teacher Practices
(Luft et al., 2011)
Beginning Teacher Practices
(Ingersoll et al., 2012)
Why, Why, Why?
• Why do these difficulties persist?
Teachers Must Learn To:
• Interact with the next generation
Teachers Must Learn To:
• Develop classroom management strategies
Teachers Must Learn To:
• Teach students who lack motivation
Teachers Must Learn To:
• Give up some control of the learning process to students
Teachers Must Learn To:
• Work in professional learning teams
• Prepare students for state assessments
• Learn the scope and sequence of the curriculum
• Learn to assess students in equitable ways
• Learn to teach in culturally relevant ways
• Learn to incorporate technology in the classroom
• Develop practical knowledge and skills for teaching in reform-based ways
Why Teachers Leave…
• Lack of support mechanisms (Ingersoll et al., 2012)
• Administrative support
• Support in discipline (mathematics; science)
• Inability to reconcile images of ideal teaching with the realities of the classroom (Friedrichsen et al., 2007) • Classroom management
• Perceived students’ abilities
Stay or Leave?
Ideal Images of Teaching
Realities of Classroom
Teacher Preparation
1st Three Years
Stay in Profession
Leave Profession
Coping strategies – find support
No coping strategies – little support
Sources of Support
• Friedrichsen et al. (2007)
Internal (Local Teacher Preparation Program)
External (Outside Local Program)
People Assigned Mentor District PD Teacher Down the Hall University staff / faculty Feedback from students
Other Math/Science Teachers Family, Friends
Programs Local Induction Program Professional organizations Conferences Graduate programs
What is the Point?
• Important to find mentors! – Effect of Online Paired Mentoring
Pedagogical Content Knowledge
Content • Cells • Genetics • Evolution • Ecology
Pedagogy • Students’
difficulties • Teaching
Strategies
PCK • Students
misunderstand Punnett Squares – Teach rules of probability
Managing Tensions
• Classroom Management
• Being understanding vs. being consistent
• Curriculum
• Giving students ownership vs. covering the curriculum
• Student Frustration
• Letting students struggle vs. providing support
• Assessing
• Providing opportunities for formative vs. summative assessment
• Personal Life
• Committing yourself to teaching vs. spending time with family / friends
Conclusions
• Struggles
• Classroom management
• Adjusting to school culture
• Perceived student abilities
• Practical knowledge and resources
• Support
• Mentors – especially discipline-specific mentors
• Induction programs
• Finding strategies to balance tensions
• Seeking out opportunities to become a part of the larger math and science education community
S
Statistical Literacy in the
High School Mathematics
and Science Classroom Michael Smith, Ohio University
Kay Casto, Vinton County High School
Goals for the project
S Our goals are both to integrate mathematics and science
learning into one lesson
S To make mathematics more relevant to their own lives
S To cause the students to question findings and investigate
statistical conclusions, instead of accepting verbatim
S To allow the students to make informed decisions based on
data
Motivation for the lesson
S “Statistics are like diamonds. Like diamonds, statistics are
not found naturally without context; they are socially
constructed by people who make decisions about how they
will be cut” -Lawrence M. Lesser
The BooKS2 project
S Students collected data from the
Ohio River on key water quality
measurements
S The students then submitted their
findings to ORSANCO for
inclusion on the multi-state water
quality testing
S Next we learned how water
quality indices are calculated
Statistics are Everywhere
S Slugging percentage (baseball)
S Quarterback rating (football)
S GPA (school)
S Index of Social Progress (sociology)
Global Warming as Example
S This is from Forbes Magazine, in
which the author uses the
argument that global warming
has stopped to talk about people
“cherry-picking” data to fit their
agenda. The author used the
NOAA climate data to argue that
there is definite global warming
if you look at long term analysis.
Global Warming rebuttal
S On Fox News, they post an article saying that global
warming isn’t as strong a trend as previously reported
because the weather monitoring stations aren’t positioned so
that they avoid people.
S These two articles are looking at the same data and drawing
completely different conclusions. What’s a student
supposed to believe?
Our lesson
S Our lesson takes the raw data that students collected from
the river, and gives them the task of using both the
weighting factors given by ORSANCO as well as creating
weighting factors of their own to tell the exact opposite
story. They then were to find out who created the
ORSANCO factors, and whether or not the students felt
these people were credible.
Integrating math and science
S Our students collected the water quality markers on their
own.
S They measured the Ph, Phosphate Levels, Dissolved
Oxygen, Fecal coliform bacteria, Nitrate Levels, and
Turbidity of the water
S The students took this data and calculated the water quality
index
Weighted grades as an
introduction
S Before we introduced the water quality index, we wanted
the students to understand the idea of weighting
S To make the idea more relevant, the students first were given
their own list of grades
S They were then introduced to the idea of weights, and asked
to create a weighting system that would be the most useful
for their grades, as well as the worst possible weighting
system
Water quality index
Student participation
S The students both collected their own data and calculated
the water quality index
S They created the new indices as a class, as well as creating
their own
S There was rich discussion between students as well as whole
class discussion on the idea of credibility
Student comments
S It was interesting to see how we rely on others to interpret
our data
S It was great to see hands on applications of math
Did we meet our goals?
S Students saw the interplay between mathematics and
science, and actively participated in the discussion
S The relevance of the mathematics was noted in students
comments
S Discussion about credibility showed that the students were
now questioning instead of accepting
S The students did choose the ORSANCO model after more
information
Conclusions
S This project was useful for mathematics classes by allowing
the students to develop some actual relevance in their
mathematics class, as well as develop higher levels of
statistical literacy
S In a science classroom, this would also be useful for having
the students to create their own conjectures based on data
they have collected, as well as creating more informed
science consumers of information.
Citations
S http://www.foxnews.com/scitech/2012/07/30/weather-
station-temp-claims-are-overheated-report-claims/
S http://www.forbes.com/sites/petergleick/2012/02/05/glob
al-warming-has-stopped-how-to-fool-people-using-cherry-
picked-climate-data/2/
S Lesser, Lawrence M. “Sizing up class size: A deeper
classroom investigation of central tendency”, Mathematics
teacher Vol 103 No 5, December 2009
Thank You
S Mike Smith, Ohio University
S Kay Casto, Vinton County High School
S http://www.seocems.org/books2/lessons/lesson5.html
BY: Nick Conroy
“I remember how exciting it was when the teacher had “stuff” on the front desk: unfamiliar objects and other things out of place in the traditional classroom”
-Richard Black
Demonstrations don’t have to be in your face activities or even teacher centered.
Have things set out so they can spark discussion.
Toys are great because it is what students are most familiar with.
Research
Great for getting instructions.
Google is your Best friend:
See Resources Section for good Online Resources.
Great for putting a purpose to the Demonstration
Keep it Simple, Stupid!
Keep it simple sir
Keep it Stupidly Simple
Keep it Straightforward and Simple
The KISS principle states that most things work best if they are kept simple rather than made complex, therefore simplicity should be a key goal in designing a demonstration and unnecessary complexity should be avoided.
When there is more going on there is more room for error
Be Prepared and Practice
Have Fun!!
Water Rocket ◦ Air Pressure moves High to low
◦ Newton’s 3rd Law
Note: Title of projects are
Hyperlinks to Instructions
Ping Pong Cannon ◦ Air Pressure moves High to Low
◦ Air Resistance
Rueben's Tube : Another version Here ◦ Sound Wave Anatomy
Note: the Larger
Diameter of the
Pipe the easier
It is to see the
Waves.
http://littleshop.physics.colostate.edu/index.html
Physics Demonstrations: A sourcebook for teachers of physics ◦ By: Julien Clinton Sprott
http://www.artistsupplysource.com/home.php?cat=9010&path=alt
My family ◦ Mom, Dad and My 3 Brothers
Sara Beyoglides
Cody Price
Dr. Lucas
Dr. Foley
FedEx
Algebra for All? The Common Core & Doctor Hacker
Jeff Taylor
Mathematics Education
Ohio University
www.wivalley.net
To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.
Another dropout statistic should cause equal chagrin. Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math.
-Andrew Hacker (2012) “Is Algebra Necessary?”
Algebra in U.S. Schools
1742: at Yale, “Specious Arithmetic”
1840s: Required for college admission
1894: Committee of Ten “Algebra for All” (10% of 14-18 year olds in HS)
1910: 57% of HS students in Algebra, now “a major source of failure”
1950: Less than 25% of HS students take Algebra
2.5 Rationales for “Algebra for All”
Global competitiveness
Learning to Reason
Social Equity
Global competitiveness?
The “STEM elite”—BA+ in Math/Sci/Engineering —make up 5% of the U.S. workforce
The greatest projected growth in STEM is for those with HS diploma or Associate degree
Health care professionals and Management/finance careers have higher projected lifetime earnings
“virtualism”: a vision of the future in which we somehow take leave of material reality and glide about in a pure information economy.
-Matt Crawford, Shop Class as Soul Craft
Learning to Reason
The “Mental Muscle” theory of learning went out with faculty psychology around 1900.
Learning transfer is not straightforward or common.
Social Equity
Algebra as “Gatekeeper” of our economic system.
- Robert P. Moses, Radical Equations
“I believe that the absence of math literacy in urban and rural communities throughout this country is an issue as urgent as the lack of registered Black voters in Mississippi was in 1961.”
The great tragedy is we create this school structure, at least in the old days of tracking, where kids were either vocational education kids or college prep kids. The result is that vocational types view mathematics, say, with suspicion, and think that studying mathematics is, well, bullshit. And the college prep kids develop a terribly narrow sense of intelligence.
-Mike Rose, interview on The Mind at Work
Transcript studies indicate that 83 percent of students who take geometry in ninth grade, most of whom completed algebra in eighth grade, complete calculus or another advanced math course during high school. Research also suggests that students who take algebra earlier rather than later subsequently have higher math skills.
These findings, however, are clouded by selection effects.
-Loveless, T. (2008) The Misplaced Math Student
0
10
20
30
40
50
60
70
260 265 270 275 280 285 290 295 300
Alg
eb
ra %
NAEP
NAEP
Linear (NAEP)
-Loveless, T. (2008) The Misplaced Math Student
-Loveless, T. (2008) The Misplaced Math Student
-National Center for Educational Statistics
(2010). Eighth-Grade Algebra: Findings
From the Eighth- Grade Round of the
Early Childhood Longitudinal Study,
Kindergarten Class of 1998–99 (ECLS-K).
-National Center for
Educational Statistics (2010).
Eighth-Grade Algebra:
Findings From the Eighth-
Grade Round of the Early
Childhood Longitudinal Study,
Kindergarten Class of 1998–99
(ECLS-K).
-National Center for Educational Statistics (2010). Eighth-Grade Algebra:
Findings From the Eighth- Grade Round of the Early Childhood
Longitudinal Study, Kindergarten Class of 1998–99 (ECLS-K).
Algebra enrollment is related to fifth grade mathematics ability Only 3/5 of the top 40% in Mathematics ability in fifth grade, are in Algebra in grade eight 19% of eighth grade algebra students were in the lowest 40% in fifth grade mathematics achievement Algebra enrollment is associated with slightly higher eighth grade mathematics scores Average mathematics score for students in high algebra enrollment schools was lower than scores for students in low enrollment schools, but there was no difference in scores for students who had been in the top 20% in fifth grade.
The TIMSS Data
-Schmidt, W. H. (2009). Exploring the Relationship of Content Coverage
and Achievement: Unpacking the Meaning of Tracking in Eighth
Grade Mathematics.
-Schmidt, W. H. (2009). Exploring the Relationship of Content Coverage
and Achievement: Unpacking the Meaning of Tracking in Eighth
Grade Mathematics.
-Schmidt, W. H. (2009). Exploring the Relationship of Content Coverage
and Achievement: Unpacking the Meaning of Tracking in Eighth
Grade Mathematics.
-Schmidt, W. H. (2009). Exploring the Relationship of Content Coverage
and Achievement: Unpacking the Meaning of Tracking in Eighth
Grade Mathematics.
-Schmidt, W. H. (2009). Exploring the Relationship of Content Coverage
and Achievement: Unpacking the Meaning of Tracking in Eighth
Grade Mathematics.
s.d.=100
-Schmidt, W. H. (2009). Exploring the Relationship of Content Coverage
and Achievement: Unpacking the Meaning of Tracking in Eighth
Grade Mathematics.
More-qualified and prepared teachers were in fact more likely to enroll in content-focused workshops.
teachers [in the neediest schools] do not more often take mathematics professional development, do not select into the most mathematically intensive of these opportunities, and do not overpopulate the one opportunity found to be associated with 2006 scores: math methods coursework.
-Hill, H (2011) “The Nature and Effects of Middle
School Mathematics Teacher Learning
Experiences”
Professional Development programs remain brief, disconnected and incoherent
Individual and school level incentives for professional development remain perverse.
Mathematization
“Mathematics as a human activity”
Re-invention
vs “Didactic Inversion”
Quine insisted that elementary arithmetic, elementary logic, and elementary set theory get started by what he called “the regimentation of ordinary discourse, mathematization in situ.” To which we now add elementary algebra. Scientists, Quine said, put a straitjacket on language.
- Robert P. Moses, Radical Equations
Algebraic
Formula
Table Graph
Concrete or pictorial
representation
Verbal description
Multiple Representations
The goal is not the apex…
…but moving fluidly between all five vertices!
Carlos took a trip on I-70, at a constant 60 miles per hour. a. How far had he gone in 3.5 hours?
b. How long did it take him to go 440 miles?
Carlos took a trip on I-70 at a constant rate of speed. After some time, he noticed he had been speeding, so he reduced to a lower constant speed. When he arrived at his destination, he noticed that he had driven 510 miles in 8 hours. a. Sketch a time-distance graph showing one way this
might have occurred.
b. Suppose Carlos slowed down to the speed limit, 50 miles per hour. Give one possible speed he could have started at, and show how many miles he would have travelled at each speed.
The Professional Development Dilemma
15 to 20 sessions over a school year 20 teachers per course 150,000 HS math teachers + 28,000 Elem math teachers + 1,100,000 elem classroom teacher = 1,278,000 teachers Dividing by 20 gives 639,000 workshops Dividing by 1,200 colleges granting education BA/BE/BS gives a mean of 53 workshops per college Assume 1 fulltime professor can do 5 workshops a year…
Then every teachers college would need to commit 11 full time professors for a full year to meet the need!
With 1 full-time professor, a year each, it would take 11 years….
Summary
1. Here comes everybody!
2. Focus on students’ mathematizing skills
3. Focus on Algebraicizing tasks
4. Teaching growth comes from talking about teaching tasks, both the making and the enacting of them
In Tanzania, where I lived for a time in the 1970s, the Swahili word fundi refers to a concept of passing on knowledge through direct contact with people who are fundis—skilled craftsmen and instructors
- Robert P. Moses, Radical Equations
