Learning to Do the Mathematical Work of Teaching . Deborah Loewenberg Ball Hyman Bass, Tim Boerst, Yaa Cole, Judith Jacobs, Yeon Kim, Jennifer Lewis, Laurie Sleep, Kara Suzuka, Mark Thames, and Deborah Zopf University of Michigan. New England Comprehensive Center
Deborah Loewenberg Ball
Hyman Bass, Tim Boerst, Yaa Cole, Judith Jacobs,
Yeon Kim, Jennifer Lewis, Laurie Sleep,
Kara Suzuka, Mark Thames, and Deborah Zopf
University of Michigan
New England Comprehensive Center
Mathematics Leadership Network Webinar • November 25, 2008
How can we improve students’ learning?
. . .
Teachers’ mathematical knowledge is a key factor shaping what they are able do.
What mathematical knowledge do teachers need?
From teacher knowledge to knowledge for teaching:
Subject Matter Knowledge
Pedagogical Content Knowledge
Content and Students (KCS)
Specialized Content Knowledge (SCK)
Knowledge of curriculum
the mathematical horizon
Knowledge of Content and
What might be difficult for students about this task?
What are the different answers students might give for this problem?
How do students’ experiences with fractions lead them to think that the blue triangle is 1/6 of the whole?
Knowledge of teaching and content (KCT)
What questions would you pose about this figure?
How could you help students understand that the green rectangle and the blue triangle are each 1/8 of the whole?
In a whole-class discussion, what answers to this task would you want presented, and in what order?
What drawing would you present to students next, and why?
What is the difference between a good mathematics task
and one that is good for developing
mathematical knowledge for teaching?
What are tasks that afford opportunities to learn to do the mathematical work of teaching?
Write as many different stories as you can that correspond to this division expression and that represent different interpretations of the meaning of division or what it means in specific situations.
For each problem:
MKT task #1:Analyzing solutions
What fraction of the rectangle is shaded?
What reasoning could produce each of these answers?
Examine three different textbooks to see how fractions are defined.
How are “equal parts” defined? How is the notion of the “whole” addressed?
How is the difference between counting and areas dealt with?
set up by
learningThe Mathematical Task Framework (MTF)
Stein, Grover & Henningsen (1996), Smith & Stein (1998); Stein, Smith, Henningsen & Silver (2000)
set up by
learningThe Mathematical Task Framework adapted to teacher education