New Wisconsin Promise Conference: Closing the Achievement GapJanuary 16, 2008

Beth Schefelker, Math Teaching Specialist Milwaukee Public SchoolsSchefeba@milwaukee.k12.wi.us

Lee Ann Pruske, Teacher in ResidenceUniversity of Wisconsin MilwaukeeLapruske@uwm.edu

Paige Richards, Teacher-in-ResidenceUniversity of Wisconsin MilwaukeeRicharda@uwm.edu

A Recipe for Blending The Five Essential Ingredients Kneaded For Effective Mathematics Instruction

Something to think about…

What does it mean to be successful in mathematics?

Session Goals

Participants will…• Understand the strands of mathematics proficiency as

defined by the National Research Council in Adding It Up and as components of the MMP Comprehensive Mathematics Framework (CMF).

• Engage in a math activity in order to develop an understanding of how the components weave together to support instruction and build mathematical understanding for students.

National Research Council’sStrands of Proficiency

Adding It Up, 2001

Adaptive Reasoning Strategic Competence Conceptual

Understanding Productive Disposition Procedural Fluency

National Research Council’sStrands of Proficiency

Adding It Up, 2001

• Conceptual Understanding - comprehension of mathematical concepts, operations, and relations •Procedural Fluency - skill in carrying out procedures flexibly, accurately, efficiently, and appropriately •Strategic Fluency - ability to formulate, represent, and solve mathematical problems

• Adaptive Reasoning - capacity for logical thought, reflection, explanation, and justification

• Productive Disposition - habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy

MMP Comprehensive Mathematics Framework

Exploring the Framework Through a Mathematics Activity

First… Figure out the area of the 2-D shapes

provided. Prove your answer using snap cubes. How would you describe your work to help

someone understand exactly what you did to cover the area?

Activity Part 2

Next, Look at the 3x4 shape… If we confine the boundary, is it possible to

add more area to our shape?

Using the same language (rows & columns) that we developed earlier, how would you now describe your new shape?

Activity Part 3

Think about the 4x3 shape…

How would you design a net to fit

this shape?

What would a net look like for this shape?

Activity Part 5

Look at the 4x3 base.

What would a net look like for this 4x3x2 block? (It does not need a lid.)

Making Connections...

How could you use the same number of cubes to create a shape with a base of 2x3?

Associative Property

(2 x 3) x 4 = 2 x (3 x 4)

What Are The Big Ideas Behind The Lesson?

•Volume is filling.

• Surface area is to volume as Perimeter is to area.

• There are connections between geometry and algebra

MMP Comprehensive Mathematics Framework

Making Connections to the Five Essential Components

Use the cards inside the envelopes to help you think deeper about the about the components of the

Comprehensive Mathematics Framework (CMF)...

1. Pull a card from the envelope and read it to your table group.

2. Decide which heading from the CMF best fits the definition.

MMP Comprehensive Mathematics Framework

#1 Comprehending mathematical concepts, operations, and relations-knowing what mathematical symbols, diagrams and procedures mean.

#2 Carrying out mathematical procedures, such as adding, subtracting, multiplying, and dividing numbers flexibly, accurately, efficiently and appropriately.

MMP Comprehensive Mathematics Framework

#3-Being able to formulate problems mathematically and to devise strategies for solving then using concepts and procedures appropriately.

#4- Using logic to explain and justify a solution to a problem or to extend from something known to something not yet known.

Last One…

#5-Seeing mathematics as sensible, useful, and doable-if you work at it and being able to do the work.

A closing thought…What would be the valueof staff members at yourschool learning about thefive essentialingredients kneaded foreffective mathematicsinstruction?

Defined by the National Research Counciland illustrated in the MMP

Comprehensive Mathematics Framework.

MMP Resources

You can find MMP resources at…

www.mmp.uwm.edu