What is math?

What does it mean to do

math?

What Do Mathematicians Do? Expanding Students’ Visions through

the Standards for Mathematical Practice

Nicole RigelmanPortland State University

Teachers of Teachers of Mathematics Annual MeetingFriday, September 9, 2011

Session OverviewWe will:

Consider key questions: What is math? What does it mean to do math? and how they relate to the standards for mathematical practice.

Explore how the tasks we pose and the moves we make during implementation of those tasks develop students’ visions of what mathematicians do.

Mathematics Tasks Framework

Student Learning

Henningsen & Stein, 1997; Stein & Smith, 1998; Stein, Smith, Henningsen, &Silver, 2000, 2009

Standards for Mathematical Practice

The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students.

These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.

- CCSS, 2010

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.

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.

Penny Jar Situation Start with 4 pennies in the jar.

Add 5 pennies each day.

Create a table and graph for the first seven days.

Predict how fourth graders might reason about the total number of pennies for the 14th day without determining the number of pennies for all the days in between.

0 1 2 3 4 5 6 70

5

10

15

20

25

30

35

40

45

Number of Days

Nu

mb

er

of

Pen

nie

s

Number of Days

Number of Pennies

01234567

n

49

141924293439

Video case: A non-proportional linear

relationship

4th graders

Penny Jar Situation Start with 4 pennies Add 5 pennies each round

Consider the following as you take notes; What mathematical thinking do the

students offer?

Video case: A non-proportional linear

relationship

What specific moves did this teacher make to support the development of the mathematical practices in her students?

Mathematics Tasks Framework

Student Learning

Henningsen & Stein, 1997; Stein & Smith, 1998; Stein, Smith, Henningsen, &Silver, 2000, 2009

What is math?

What does it mean to do

math?

Reflecting on Our Practice

Do all students have the opportunity to engage in mathematical tasks that promote students’ attainment of the mathematical practices on a regular basis?

How are we, as teacher educators, equipping teachers (preservice and inservice) for implementing the standards for mathematical practice?