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Relearning to Teach Arithmetic. Addition, Subtraction, Multiplication and Division. 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

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relearning to teach arithmetic

Relearning to Teach Arithmetic

Addition, Subtraction, Multiplication and Division

SD Counts-Mini Foundations Summer 2007

introduction
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
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

slide4
The question of fluencyhas 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
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
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
Video-SegmentStacie, Harrison, Zoe, Elthea, James and Chrisexample 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 2 nd stop on our journey subtraction
The 2nd stop on our JourneySubtraction

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
Video SegmentLisa, 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
The Teacher’s RoleTeaching and Learning About Addition and Subtraction

SD Counts-Mini Foundations Summer 2007

the 3 rd stop multiplication
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
Video Segment-MultiplicationDarren, 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
The Last StopDivision

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
Video Segment-DivisionElaine, Yuriy, Amelinda, and Thomas

159/13

SD Counts-Mini Foundations Summer 2007

the teacher s role teaching and learning about multiplication division
The Teacher’s RoleTeaching 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