reflecting on the practice of teaching pcmi secondary school teachers program july 2007

42
Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Upload: prosper-sutton

Post on 27-Dec-2015

220 views

Category:

Documents


1 download

TRANSCRIPT

Page 1: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Reflecting on the Practice of Teaching

PCMI

Secondary School Teachers Program

July 2007

Page 2: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

deLange, et al, 1993

Page 3: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

The Teaching Principle

Effective teaching requires understanding what students know and need to learn and challenging

and supporting them to learn it well. (NCTM, 2000)

Page 4: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

As teacher learned to

•Choose tasks carefully

•Listen to students(’) work

•Students are often smarter than I am

•Manage student responses carefully

•Take risks

•Let students do the work

Page 5: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Learning from Experience

Working with Japanese Colleagues

Working with Preservice Students

Conducting Demonstration Lessons

Developing Curriculum

Designing Professional Development

Using new technology

Page 6: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Learning from Experience

Working with Japanese Colleagues

Page 7: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Typical flow of a class

United States• Demonstrate a

procedure• Assign similar

problems to students as exercises

• Homework assignment

Japan• Present a problem to the

students without first demonstrating how to solve the problem

• Individual or group problem solving

• Compare and discuss multiple solution methods

• Summary, exercises and homework assignment

Takahashi, 2005

Page 8: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Introduction: HatsumonThought provoking question

Key question – shu hatsumonIndividual or small group work

Walking among the desks – kikan-shidoAnticipated student solutions

Student solutions - NoriageMassaging students’ ideas

Summing up- Matome Bass et al, 2002

The Lesson

Page 9: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Which shape will hold the same amount of spaghetti and be the most

economical?

Area of base

Surface area

Volume Ratio of surface area to volume

Cylinder

Rectangular prism

Shape 3

MDoE, 2003

Page 10: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Learned the importance of

• Being explicit about the math students are to learn

• Anticipating student solutions• Lesson plan• Starting investigations with a “launch”

that invites students into the math• ……

Page 11: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Teaching means having “eyes” to see the mathematics

Can teacher identify the mathematical essential points of materials?

Does teacher deprive students’ of the opportunity to think mathematically?

Ikeda & Kuwahara, 2002

Page 12: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

And “eyes” to see the students

Can teacher understand what students understand?

・ Can students understand teacher’s asking questions?

・ Does teacher ignore students’ ideas by his/her selfish reason?

・ Can teacher accept and evaluate students’ ideas appropriately?

・ Can students discuss cooperatively?Ikeda & Kuwahara, 2002

Page 13: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Learning from Experience

Conducting Demonstration Lessons

Page 14: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Pencils cost 15 centsErasers cost 25 Cents

How many pencils and erasers can you buy for $1.10?

For $1.50?

Kindt, et al, 1997

Page 15: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

15 40

0 25

Number of erasers

0 1 2 3 4

0

1

2

3

Number of pencils

Page 16: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

155

115 140 165

100 125 150 175 200

60 85 110 135 160 185 210

45 70 95 120 145 170 195

30 55 80 105 130 155 180

15 40 65 90 115 140 165 190

0 25 50 75 100 125 150 175

Number of erasers

0 1 2 3 4

0

1

2

3

Number of pencils

Page 17: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

15 40

0 25

Number of erasers

0 1 2 3 4

0

1

2

3

Number of pencils

Page 18: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Number of erasers

0 1 2 3 4

0

1

2

3

Number of pencils

Page 19: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Scaffolding matters

Preactivities leading to main goal

1x25

2/25

3x25

4x25

5x25

1x15

2x15

2x15

4x15

5x15

Page 20: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

What and how the work is recorded matters

2x 15 + 25x3 15

25

x2x3

3075

2x15 + 3x25

Page 21: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

What and how the work is recorded matters

2x15 + 3x25 = 30+ 75 = 105

3x15 + 2x25 = 45 + 50 = 95

4x15 + 2x25 = 60 + 50 = 110

15

25

x2x3

3075

Goal: Ax+By = C

Page 22: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Learned to deliberately think about:

• How will students work?• What tools will be useful and how should

they be made available?• How will the work be recorded? • How will they share their work?• How will I know what the students

understand and do not understand?

Page 23: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Learning from Experience

Working with Preservice Students

Page 24: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Expect the Unexpected

Change

0

50

100

150

200

250

300

350

1 3 5 7 9 11 13 15

Change

Person

Linear (Change)

Page 25: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Learned that

• Boards are disappearing• Modeling is not enough; need to be

explicit• Preservice students are not really aware

that others have different ways of thinking

• Difficult to honor mistakes

Page 26: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Learning from Experience

Developing Curriculum

Page 27: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

In the figure below, what fraction of the rectangle ABCD is shaded?

A B

D C

a) 1/6

b) 1/5

c) 1/4

d) 1/3

e) 1/2

NCES, 1996

Page 28: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Dekker & Querele, 2002

Page 29: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007
Page 30: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Comparing Quantities. Kindt et al, 2006

Page 31: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Learned to

• Pose tasks that go beyond routines• Ask what would happen if…? What

should you do if you want…..• Frame a situation and let students

comment• Collaborative work is better than

individual - in doing math and in thinking about lessons

Page 32: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Teaching is a profession with a body of knowledge that can be learned and applied to improve

the practice of enabling students to learn.

Page 33: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Research in mathematics education

Quantitative Studies -experimental -quasi-experimental

Experimental-observation

Theories of learning - frameworks for thinking about teaching and learning

Qualitative Studies--Case studies--Ethnographic studies

Page 34: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Research findings

Synthesis of the literature

Nature of conclusions-suggestions-insights-causal

Meta-analysis

Peer reviewed journals

Page 35: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Other sources of information

Visions - projections of what might/should be possible

Information from colleagues

Doctoral theses

Professional organizations

Lecture notes

Exhortions

Beliefs

Page 36: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Teaching involves

• Choosing and setting up tasks Adaptation/modification

• ImplementationResponse to student questionsDiscussionManage solution strategies

• Probing for understandingEvidence of learning

Page 37: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Our Work

• Formative Assessment

• Cognitive Demand/Scaffolding

• Discussion/Questioning

• Transfer/Learning for Understanding

Page 38: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Research Report

• Describe what the topic means and why it is important

• Give three or four key findings and their relevance for teaching

Page 39: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Reflect on your own teaching

• What are some questions you have?

• What are one or two things about your teaching you would like to improve?

• What would you like to learn about teaching?

Page 40: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

Teaching is harder than it looks - making students come to life in the world of mathematics.

But we can learn not only from our own experience and that of our colleagues but from the research that helps explain and provides insights into teaching and learning math

Page 41: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

References •Bass, H., Usiskin, Z, & Burrill, G. (Eds.) (2002). Classroom Practice as a Medium for Professional Development. Washington, DC: National Academy Press.•Dekker,T. & Querelle, N. (2002). Great assessment problems (and how to solve them). CATCH project www.fi.uu.nl/catch•deLange, J., Romberg, T., Burrill, G., von Reeuwijk, M. (1993). Learning and testing mathematics in context: Data visualization. Los Angles CA:, Sunburst. •Ikeda, T. & Kuwahara, Y. (2003). Presentation at Park City Mathematics Institute International Panel.•Kindt, M., Abels, M., Meyer, M., Pligge, M. (1998). Comparing Quantities. From Mathematics in Context. Directed by Romberg, T. & deLange, J. Austin, TX: Holt, Rinehart, Winston•Michigan Department of Education. (2003). MMLA Lesson Study Project. Burrill, G., Ferry, D., & Verhey R. (Eds). Lansing, MI•National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

Page 42: Reflecting on the Practice of Teaching PCMI Secondary School Teachers Program July 2007

•Takahashi, Akahito. (2005). Presentation at Annual Meeting of Association of Mathematics Teacher Educators. •Teachers for a New Era (2003). Michigan State University grant from Carnegie Foundation. •Third International Mathematics and Science Study (TIMSS). (1995). Released Item. National Center for Education Statistics. U.S. Department of Education. (1999).