Transcript Relearning to Teach Arithmetic

Relearning to Teach
Arithmetic
Addition, Subtraction,
Multiplication and Division
SD Counts-Mini Foundations
Summer 2007
Introduction
In today’s session you will see a significant shift in the
way students experience mathematics, this shift will be
-“toward” mathematical reasoning; away from merely
memorizing procedures
-toward conjecturing, inventing, and problem-solving;
away from an emphasis on mechanistic answer-finding
SD Counts-Mini Foundations
Summer 2007
The way “they” learn math is
different than the way “we” learned
math.
• Most of us sitting here today learned math
my memorizing particular algorithms for
each operation. We don’t have images,
experiences, or knowledge about how
students can develop their understanding of
whole-number computation because we
never had to build it ourselves.
SD Counts-Mini Foundations
Summer 2007
The question of fluency
has come up several time in conversation with current
SD Counts principals and teachers.
Fluency will happen if….
• students have knowledge of the base10 number
system
• a repertoire of number relationships
• an understanding of the characteristics of each
operation and how the operations are related
SD Counts-Mini Foundations
Summer 2007
Do I need to know about every number
operation if I will not teach it?
• By learning about computation across
the grades, teachers will better
understand how concepts build and
connect and about the range of student
understanding within their classroom.
Teachers will also gain a better
understanding of whole-number
computation.
SD Counts-Mini Foundations
Summer 2007
Let us begin the journey
Addition
Mental Math
Solve and be ready to share your thinking of
48 + 25
SD Counts-Mini Foundations
Summer 2007
Video-Segment
Stacie, Harrison, Zoe, Elthea, James and
Chris
example of a “Math Talk”
• Watch closely as these students solve the same
problem as we just did
48 + 25
SD Counts-Mini Foundations
Summer 2007
The 2nd stop on our Journey
Subtraction
Mental-math activity
Solve and be ready to share your thinking
35-16
SD Counts-Mini Foundations
Summer 2007
Video Segment
Lisa, James and
Naillil (NY-JILL)
• Watch closely as these three students solve
the following subtraction problem
40 - 26 =
SD Counts-Mini Foundations
Summer 2007
The Teacher’s Role
Teaching and Learning About Addition
and Subtraction
SD Counts-Mini Foundations
Summer 2007
The 3rd stop
Multiplication
Mental-math activity
Solve and be ready to share your thinking of
27 x 4
SD Counts-Mini Foundations
Summer 2007
Video Segment-Multiplication
Darren, Tatia, Daniel, Rona, Jonathan,
Rosa, Erica, and Terrance
27 x 4 and 128 x 38
SD Counts-Mini Foundations
Summer 2007
The Last Stop
Division
Mental-math activity
Solve and be ready to share your thinking of
140/8
SD Counts-Mini Foundations
Summer 2007
Video Segment-Division
Elaine, Yuriy, Amelinda, and Thomas
159/13
SD Counts-Mini Foundations
Summer 2007
The Teacher’s Role
Teaching and Learning About
Multiplication/Division.
• Watch for the following:
- behavior/comments of the teacher
- how and when does the teacher intervene
- what kinds of questions do they ask?
SD Counts-Mini Foundations
Summer 2007