Leadership for the Mathematics Classroom 06.14c.ymcdn.com/sites/ · 2014-02-18 · Using questioning techniques to ... Listening to and reacting to others’ ... Leadership for the

Mathematics

Leadership for the Mathematics Classroom

06.14.13

Janet Dodd, District Instructional SpecialistElementary Mathematics, Pasadena ISD

Dr. Karen Hickman, Associate SuperintendentCurriculum & Instruction, Pasadena ISD

Mathematics


• Welcome!• Goals:

• Explore what mathematics instruction should “look like” and “sound like”

• Explore strategies for creating collaborative teams of mathematics teachers

Mathematics


• Let’s create a foldable

My Reflections & Next Steps:

NCTM Administrator’s Guide (2003, pg. 9)

What is the teacher doing? Choosing “good” problems – ones that

invite exploration of an important mathematical concept and allow students the change to solidify and extend their knowledge

Using questioning techniques to facilitate learning

Encouraging students to explore multiple solutions

Creating a variety of opportunities, such as group work and class discussions, for students to communicate mathematically

Modeling appropriate mathematical language and a disposition for solving challenging mathematics problems

NCTM Administrator’s Guide (2003, pg. 9)

What are students doing? Actively engaging in the learning

process Reasoning and making conjectures

about the problem Communicating their mathematical

thinking orally and in writing Listening to and reacting to others’

thinking and solutions to problems Using a variety of representations,

such as pictures, tables, graphs, and words, for their mathematical thinking

Using mathematical and technological tools such as physical materials, calculators, and computers, along with textbooks and other instructional materials



“Assessment and instruction are often conceived as curiously separate in both time and purpose. The key to high-quality formative assessment is to intertwine the two. What teachers and students need is assessment and instruction that are conceived as a unit, employed as a unit, and applied as a unit.”

Graue (1993, pg. 4) in Greenstein (2010, pg. 24)

Preparing: Know the TEKS and the Scope &

Sequence Attending (district) Focus PDs Planning: Nine-Week Planning Day

o Mapping out the nine-weeks o Mapping out the bundles

Weekly Team Planning o Implementing the Data Cycle o Determining instructional adjustments

Monitoring: Monitoring lesson plans Observations/Walk-throughs Examining student work Analyzing student data


Leadership for the Mathematics

Classroom 06.14.13

2013 TEPSA Summer Conference: Leadership for the Mathematics Classroom: Dr. Karen Hickman & Janet Dodd, Pasadena ISD Region 4 ESC materials used with permission from Region 4 ESC.

A&D Statements

Instruction

1. 5/7 is smaller than 9/16.

Agree Disagree It Depends Not Sure My thinking:

Curriculum

2. Numerators must be smaller than denominators.


Making It Happen

3. Fractions can be written as decimals.


Assessment

Adapted from Mathematics Formative Assessment (Keeley & Tobey, 2011)

Mathematics


• Supporting Curriculum and Instruction– What would you see? What would you hear?

• Modeling addition and subtraction story problems

© 2007, Region 4 Education Service Center All Rights Reserved. Reproduction authorized only for the students of the teacher that attended this professional development.

Types of Addition and Subtraction Problem Situations

Type of Problem Situation

Join

Result Unknown Sean had 6 crayons. Mayra gave him 8 more crayons. How many crayons does Sean have in all?

Change Unknown Sean has 6 crayons. His teacher gave him some more crayons. Now Sean has 14 crayons. How many crayons did Sean’s teacher give him?

Start Unknown Sean had some crayons. Mayra gave him 6 more crayons. Now Sean has 14 crayons. How many crayons did Sean have to begin with?

Separate

Result Unknown Sean had 14 crayons in his school supply box. He gave 8 crayons to Mayra. How many crayons does Sean have left?

Change Unknown Sean had 14 crayons. He gave some of his crayons to Mayra. Now he has 6 crayons left. How many crayons did Sean give to Mayra?

Start Unknown Sean had some crayons in his school supply box. He gave 6 crayons to Mayra. Now he has 8 crayons left. How many crayons did Sean have to begin with?

Part/Part/Whole

Whole Unknown Sean has 8 red crayons and 6 blue crayons. How many crayons does he have?

Part Unknown Sean has 14 crayons in his school supply box. 6 crayons are red and the rest are blue. How many blue crayons does Sean have?

Compare

Difference Unknown Sean has 14 crayons in his school supply box. Mayra has 6 crayons in her school supply box. How many more crayons does Sean have than Mayra?

Larger Unknown Mayra has 8 crayons. Sean has 6 more crayons than Mayra. How many crayons does Sean have?

Smaller Unknown Sean has 14 crayons in his school supply box. He has 6 more crayons than Mayra. How many crayons does Mayra have?

Mathematics



• Engaging Mathematics: Grade 4 “Strategy Match”

Student Name: ________________________________ Date: ________________

Engaging Mathematics © Region 4 Education Service Center Grade 4 200 All rights reserved.

Strategy Match Activity Page • Cut apart the cards on the Strategy Match Activity Master. • Match each multiplication fact with a strategy that could be used to find the fact’s

product. • Glue or tape the cards in My Workspace. My Workspace

Communicating about Mathematics Choose a set of matched cards. What is another strategy that could be used to determine the product?

Student Name: ________________________________ Date: ________________

© Region 4 Education Service Center Engaging Mathematics All rights reserved. 201 Grade 4

Strategy Match Activity Master

7 3× 8 6× 9 4×

6 3× 7 5× 10 2×

4 4× 3 9×

6,12,18

9+9+9

Mathematics



• Math Talks

Mathematics



• What does NCTM (National Council of Teachers of Mathematics) say?

– Reflections & Next Steps

Mathematics


• Supporting Assessment– What would you see? What would you hear?

• A&D Statements

Mathematics


• Supporting Assessment– What would you see? What would you hear?

• Comments-Only Marking

Mathematics

“Assessment and instruction are often conceived as curiously separate in both time and purpose. The key to high-quality formative assessment is to intertwine the two. What teachers and students need is assessment and instruction that are conceived as a unit, employed as a unit, and applied as a unit.”

Graue (1993, pg. 4) in Greenstein (2010, pg. 24)


Mathematics


• Supporting Assessment– Reflections & Next Steps

Mathematics


• Administrative Support – How do you create an effective structure for

collaborative planning?• Preparing

Mathematics


Pasadena ISD 3rd Grade Mathematics Standard Clarification: 3.4B (Readiness Standard)

© Pasadena ISD All rights reserved. Reproduction authorized only for the teachers of Pasadena ISD. 1

Mathematics TEKS

3.4 Number, Operation, and Quantitative Reasoning (Reporting Category 1) The student recognizes and solves problems in multiplication and division situations. 3.4B Solve and record multiplication problems (up to two digits times one digit).

(Readiness Standard)

Process Standards

The Process Standards should be incorporated into instruction on a daily basis. The student applies Grade 3 mathematics to solve problems connected to everyday

experiences and activities in and outside of school. (TEKS 3.14A, 3.14B, 3.14C, 3.14D) The student communicates about Grade 3 mathematics using informal language.

(TEKS 3.15A, 3.15B) The student uses logical reasoning. (TEKS 3.16A, 3.16B)

ELPS & Language Objective

Possible ELPS: Speaking (c)3(D) Share information in cooperative learning interactions; Possible Language Objective: TSW share information about how she/he solved multiplication problems in an “inside

outside circle”.

Prior Knowledge

2.4A Model, create, and describe multiplication situations in which equivalent sets of concrete objects are joined.

Possible Core

Vocabulary array, factor, product, partial product, area model, equal groups matriz, factor, producto, productos parciales, modelo del área, grupos iguales

Instructional Clarifications Select and use multiplication to determine the solution to a problem.

o Utilize a problem-solving model/guide such as the "UPS Check/Reflect" tool or “RAPS”. o Utilize a variety of contexts that might include tables, pictures, and/or other graphic

organizers. o Problems could be single or multistep, could incorporate multiple operations, could have

extra information, could incorporate the word “not”, and could have “not here” listed as an answer choice (if multiple choice format).

o Problems could embed concepts from within the same Reporting Category or from other Reporting Categories.

o Estimate solutions before computing a solution. o Represent multiple solution strategies (including flexible strategies) with words and

number sentences. o Explain a solution process and justify the reasonableness of the solution.

TEKS Clarifications

Multiplication

Solve and record multiplication problems. Example: There are 8 spiders in a jar. If each spider has 8 legs, how many spider legs are there all together? Possible Solution Strategies: Draw a picture, use concrete models, use repeated addition, or use multiplication.

Answer: The product is 64. 8+8+8+8+8+8+8+8=64 or 8 8 = 64.



Example: James loads boxes on trucks for a shipping company. On Tuesday, James loaded 5 trucks with 52 boxes in each truck. How many boxes did James load on trucks on Tuesday? Possible Solution Strategy: Use base ten blocks in an area model.

Using partial products:

52 5 10 52 = 10 + 250 550 = 250 260

Answer: The product is 260. 52 5 = 260.

Solve multiplication problems. Example: Jacquelyn’s choir had 95 members. Each member sang 3 solos for individual competitions during last month’s regional performance. How many solos did Jacquelyn’s choir sing all together? Understanding the Problem:

Ask the students, “What are you trying to find out?” Ask the students to restate the problem.

Possible Answer: “We need to find out how many total solos were sung by the 95 choir members.” Making a Plan:

Ask the students, “Are you joining equal sets or separating sets of objects into equal groups?” Ask the students, “What is the important information in the problem?”

Possible Answer: “We are joining equal sets, so we will multiply. The important information in the question is the number of choir members and the number of solos.” Carrying out the Plan:

Ask the students, “How did you solve the problem?” Possible Answer: “We multiplied 95 by 3.” Evaluating for Reasonableness:

Ask the students, “How do you know your answer is reasonable?” Possible Answer: “We knew that each choir member sang 3 solos, and there were 95 choir members. We estimated 95 as 100. So, 100 ×3 = 300 and 300 is close to 285. We multiplied 95 by 3 to get our answer.” Answer: 285 solos Additional components of Standard Clarification documents: resources for instruction, assessment, technology connections, intervention, and enrichment.



Mathematics TEKS

Process Standards

ELPS & Language Objective

Prior Knowledge

Possible Core

Vocabulary

Instructional Clarifications

TEKS Clarifications

Possible Resources for Instruction

Possible Resources for Assessment

Possible Resources for Computer-Based Instruction/Assessment

Intervention Enrichment

4th Grade Writing

Sample provided by Pasadena ISD. Adapted from lead4ward standard clarification tools.

4.15A Readiness (4.15) Writing/Writing Process. Students use elements of the writing process (planning, drafting, revising, editing, and publishing) to compose text. Students are expected to (A) plan a first draft selecting a genre appropriate for conveying the intended meaning to an audience and generating ideas through a range of strategies (e.g., brainstorming, graphic organizers, logs, journals)

Content Builder Rigor ImplicationsWhat do students need to know? Content

Connections

To what degree will this learning impact learning two years down the road?

Create Evaluate Analyze Apply

Understand Remember

Verb

Level of Bloom’s Taxonomy

Instructional Implications:

Academic Vocabulary

Distractor Factor

Mathematics


• Administrative Support – How do you create an effective structure for

collaborative planning?• Planning

Mathematics


• Administrative Support – How do you ensure the effectiveness of

collaborative planning?• Monitoring

– Reflections & Next Steps

Mathematics


• Closure: – Find a Partner: What is one of your “take-aways” from

today’s discussions?– Sum It Up: Rephrase what your partner said in a shorter

version.• You may start with one of the following sentence starters:

– I hear you saying …– So, if I understand you correctly …– I like how you said …

Sum it Up Card

Rephrase what your partner said in a shorter version. You may start with one of the following sentence starters:

I hear you saying … So, if I understand you correctly … I like how you said …

Sum it Up Card



Sum it Up Card



Sum it Up Card



Adapted from Total Participation Techniques (Himmele & Himmele, 2011)

Mathematics


• Goals:• Explore what mathematics instruction should

“look like” and “sound like”• Explore strategies for creating collaborative

teams of mathematics teachers

Documents

Leadership for the Mathematics Classroom 06.14c.ymcdn.com/sites/ · 2014-02-18 · Using questioning techniques to ... Listening to and reacting to others’ ... Leadership for the