2. What Do Mathematicians Do?
Expanding Students’ Visions through the
Standards for Mathematical Practice
Nicole Rigelman
Portland State University
Teachers of Teachers of Mathematics Annual Meeting
Friday, September 9, 2011
3. Session Overview
We 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.
4. TASKS
as they appear in
curricular/instructional
materials
TASKS
as set up by the
teacher
TASKS
as implemented by the
students
Student Learning
Mathematics Tasks
Framework
Student
Learning
Henningsen& Stein, 1997; Stein & Smith, 1998; Stein, Smith, Henningsen, &Silver, 2000, 2009
5. 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
6. 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.
7.
8. 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.
10. 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?
11. 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?
12. TASKS
as they appear in
curricular/instructional
materials
TASKS
as set up by the
teacher
TASKS
as implemented by the
students
Student Learning
Mathematics Tasks
Framework
Student
Learning
Henningsen& Stein, 1997; Stein & Smith, 1998; Stein, Smith, Henningsen, &Silver, 2000, 2009
14. 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?
Notes de l'éditeur
According to Stein and Smith (1998, p. 269), “the day-in and day-out cumulative effect of classroom-based tasks leads to the development of students’ implicit ideas about the nature of mathematics – about whether mathematics is something about which they can personally make sense and about how long and how hard they should have to work to do so.” Further, as tasks pass through the phases shown in the Mathematics Tasks Framework, the nature of the tasks may change and, hence, influence what mathematics students learn.
