mathematical knowledge for teaching

1. Selecting, Designing & Using
Mathematical Tasks in the K-5 Classroom

2. Critical Question…
o What mathematics matters for
What
teaching?
Distinguishes o Is it different from mathematics
Mathematical knowledge as known and used by
mathematicians, engineers, biologists,
Knowledge
candy sellers? If so, how can we
From The
characterize what makes it different?
Specialized o What of that mathematics is “content,”
Knowledge
and what is more properly called by
other names such as “practices,”
Needed For
“sensibilities,” or “orientations”?
Teaching
Mathematics? o What is the difference between “pure”
content knowledge and knowledge used
in pedagogical situations?

3. Mathematical Knowledge for
Teaching
Common mathematical knowledge
 Number halfway between 1.1 and 1.2
Specialized knowledge for teaching mathematics
 Representing mathematical ideas and operations
 Providing explanations for mathematical ideas and
procedures
 Appraising unusual student methods, claims, or
solutions

4. Examining Mathematical
Knowledge
Solve:
25 x 35 = ?

5. Appraising Unusual Student Solutions
Student A
35
x 25
125
+750 _
875
Student B
35
x 25
175
+700 _
875
Student C
35
x 25
25
150
100
+600
875
Which of these students is using a method that could
be used to multiply any two whole numbers?

6. Reflect and Discuss
o What did you do to solve the original
problem of 25 x 35?
o What did you do to solve the task
concerning the varied student solutions?
o What was different in the way you thought
mathematically about each task, and what
you needed to know?

7. Subject Matter
Knowledge
Common
Content
Knowledg
e (CCK)
Knowledge
at the
mathematica
l horizon
Pedagogical Content Knowledge
Specialize
d Content
Knowledg
e (SCK)
Knowledge
of Content
and Students
(KCS)
Knowledge of
Content and
Teaching (KCT)
Knowledg
e of
Curriculu
m
Diagram created by Deborah Ball & colleagues, University of Michigan