1. New Wisconsin Promise Conference: Closing the Achievement Gap
A Recipe for Blending The Five Essential Ingredients Kneaded For Effective Mathematics Instruction
New Wisconsin Promise Conference: Closing the Achievement Gap
January 16, 2008
Beth Schefelker, Math Teaching Specialist
Milwaukee Public Schools
Lee Ann Pruske, Teacher in Residence
University of Wisconsin Milwaukee
Paige Richards, Teacher-in-Residence
University of Wisconsin Milwaukee

2. Something to think about…
What does it mean to be successful in mathematics?

3. 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.

4. National Research Council’s Strands of Proficiency Adding It Up, 2001
Adaptive Reasoning
Strategic Competence
Conceptual Understanding
Productive Disposition
Procedural Fluency

5. National Research Council’s Strands 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

6. MMP Comprehensive Mathematics Framework

7. 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?

8. 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?

9. 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?

10. Activity Part 5 Look at the 4x3 base.
What would a net look like for this 4x3x2 block? (It does not need a lid.)

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

12. Associative Property
(2 x 3) x 4 = 2 x (3 x 4)

13. 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

14. MMP Comprehensive Mathematics Framework

15. 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.
Decide which heading from the CMF
best fits the definition.

16. 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.

17. 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.

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

19. A closing thought… What would be the value of staff members at your
school learning about the
five essential
ingredients kneaded for
effective mathematics
instruction?
Defined by the National Research Council
and illustrated in the MMP
Comprehensive Mathematics Framework.

20. MMP Resources
You can find MMP resources at…