Building Math Power: Content-Based Professional Development

Integrating Mathematics and

Pedagogy to Maximize Teacher

Effectiveness

Kimberly Rimbey, NBCT, M.Ed.

Peggy Akin, author

Why are we here?• True stories…• 5th Grade Class…

4 + 8 = 1 + 11

• 1st Grade Teacher…

• 6th Grade Teacher…

So why are we here?• Concurrent content & pedagogy development

• Tools for teachers as learners:– Provide/develop classroom activities– Use pedagogy-rich mathematics curriculum– Model best practices and good pedagogy for the

adults as learners • Writing mathematical ideas• Discourse• Cooperative learning

Outcomes for Session• What mathematics content do elementary

teachers need? (discuss)• What pedagogy and best practices skills do

elementary teachers need? (discuss)

If we know both of these…• How can professional development be

designed to develop both content and pedagogy? (look at one model)

Relevant Research

According to D. Ball (2005), teachers need

• Common content knowledge (WHAT & HOW)• Specialized content knowledge (WHY)• Knowledge of content and students (PEDAGOGY)• Knowledge of teaching and curriculum (PEDAGOGY

& BEST PRACTICES)

Relevant Research

According to D. Ball (2003), what mathematical problems arise in teaching?

• Analyzing errors• Giving and evaluating explanations• Appraising unexpected claims, solutions, methods

Unexpected Method

1 2

2 x 2 = 4

Relevant ResearchAccording to D. Ball (2003), what mathematical

problems arise in teaching?

• Analyzing errors• Giving and evaluating explanations• Appraising unexpected claims, solutions, methods• Choosing and using representations• Investigating correspondences among representations and

solutions

Solutions & Representations

2 x 5 = 10

11 x 11111 = 1111111111

Relevant ResearchAccording to D. Ball (2003), what mathematical

problems arise in teaching?

• Analyzing errors• Giving and evaluating explanations• Appraising unexpected claims, solutions, methods• Choosing and using representations• Investigating correspondences among representations and

solutions• Choosing and using definitions• Interpreting and responding to students’ ideas

Relevant Research

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

D. Ball, 2003

Common vs. Specific KnowledgeSubtraction with Regrouping…

Common Knowledge - HOW to subtract (usually understood as an algorithm using “borrowing”)

Specific Knowledge - the concept behind the subtraction - understanding the WHY’s as well as alternative algorithms

Active Participation Time…What are some common misperceptions among

elementary teachers (think about both common & specific knowledge)?– Number Sense– Operations– Patterns, Algebra, & Functions– Geometry & Measurement– Process Standards (CPR’s)

• Think of 1 and write down• Round Robin - share at table

Getting to the heart of content

• Go beyond fun activities

• Go beyond elementary content

• Look at middle/high school curriculums

• Teach the general content with an easy-to-see path to the specific content

• I planned to write my own curriculum…

I wanted something that…• Tempers bad feelings about high school/college mathematics experiences• Builds on prior knowledge

• Deals with sound mathematics• Focuses on the big ideas of mathematics• Is activity based• Has best practices built in• Develops critical and creative thinking• Develops understanding through guided discovery• Teaches to the whole [child]

Then I found

Planning for the Course

Generate Lists• Content (strands, concepts, PO’s)• Best Practices/Pedagogy Strategies• Content Lessons• Grade-Level Lessons• Classroom Materials

7 Patterns, Algebra, & Functions II• Overview• Review unwrapped standards• Criti cal content• Big Ideas & Essential Questions• Connections with other strands & real lif e• Best Practice: Real-Li fe Connections

Fun Foam Shapes

8 Data Analysis• Overview• Review unwrapped standards• Criti cal content• Big Ideas & Essential Questions• Connections with other strands & real lif e• Best Practice: Questioning Strategies

Make-and-Take – posters

9 Number Sense I – Number Sense• Overview• Review unwrapped standards• Criti cal content• Big Ideas & Essential Questions• Connections with other strands & real lif e• Best Practice: Manipulatives &

Management

Make & Take – center signsDigi blocksPlace value diceFun FoamFraction Works packs

10 Number Sense II – Operations• Overview• Review unwrapped standards• Criti cal content• Big Ideas & Essential Questions• Connections with other strands & real lif e• Best Practice: Problem Solving Processes;

rewriting problems to involve deeperthinking

Double DiceBIG dice10-sided dice

Best Practices (Marzano)What teaching techniques must be implemented?

• Work & study habits• Big ideas & essential questions• Identifying similarities and differences• Reinforcing effort & providing recognition• Homework & Practice• Nonlinguistic representations• Setting objectives & providing feedback• Cues, questions & advanced organizers

Good Pedagogy StrategiesWhat should teachers be able to do?

• Develop vocabulary• Analyze errors• Use cooperative roles & structures• Implement good questioning strategies• Encourage writing across the curriculum• Represent ideas (manipulatives, pictures, symbols)• Relate to real life

Putting the Pieces Together

Content

Pedagogy Best Practices

Effective Mathematics

Teacher

Case Study…Functions • 24 second and third grade teachers• Beforehand -

– 1 could define a function– 1 could relate a function to graphic representations– 0 could identify a real-life situation that could be represented

by a functional relationship

• Afterward - – 24 “light bulbs” went off when introduced to the “function

machine” and how it related to equations– 23 gasps when the function table was graphed on a

coordinate grid

Tools• Pedagogy-Rich Mathematics Curriculum

– Building Math Power by Peg Akin

• Provide/develop classroom activities– Video– On-Level Lessons– Teaching Student-Centered Mathematics by John

Van De Walle

Tools (cont.)Model Pedagogy & Best Practices for teachers as

learners (during delivery of content & activities)

• Used cooperative structures– Round Robin sharing during “pre-test”– Assigned roles & structure for reading– Groups were looser when doing content work - asked

quicker participants to hold comments• Representing ideas• Incorporating structured discourse• Developing vocabulary• Using technology (video clip)

Active Participation Time…

• Take a look at the 4th paper in the BMP handout (second 17)

• Take a look at the 3rd paper from the back (25)

Video & Lesson

• Teachers need to SEE this in action– Live is best (as with “Lesson Study” format)– Video is sufficient

Functions Video

• Sample lessons modeled and extended with teachers

Active Participation Time…

• View first 3 min. of “The Function Machine” lesson (first page after outline)

• Try out the “Object Functions” lesson

• Biggest “aha” of the day… “Graphing Functions” lesson from the t-tables (geometry PO)

Student Work

“Graphing Functions”

Insects Wings

1 2

2 4

3 6

4 8

5 10

Evidence of SuccessIn order to determine your effectiveness

• Teacher pre-post tests (content)• Surveys before and after (pedagogy, best practices,

& attitudes)• Anecdotal records (reflective as learners & as

teachers)• Student assessments

***Difficulty - determining exactly what impacted student learning unless using a control group

Outcomes for Session• What mathematics content do elementary teachers

need? (discuss)• What pedagogy and best practices skills do

elementary teachers need? (discuss)

If we know both of these…• How can professional development be designed to

develop both content and pedagogy? (look at one model)

In Closing…

• Tools– Use pedagogy-rich content materials– Provide or allow time to develop classroom

activities– Model best practices– Let them SEE it in action

• One more story…kindergarten teacher…

ContactsKimberly Rimbey, Creative Learning Specialistsmathspec@cox.netwww.geocities.com/kimrimbey/index.html623-261-2199

Peg Akin, Building Math Powerpegakin@mindspring.comwww.buildingmathpower.com623-8455-6923