What Does TIMSS Say about Instructional Practices?

Goals

• To explore differences in the structure of lessons, goals, and beliefs about mathematics teaching in Germany, Japan, and the U.S.

• To examine the “scripts” that shape characteristics of a typical lesson in each country

• To identify issues for further reflection and dialogue in your own setting

Agenda

• Video Viewing: U.S. and Japan

• Key Findings

• Issues for Further Reflection

Overview of Videotape Study

• First of its kind

• Nationally representative sample of Population 2 mathematics classrooms in Germany, Japan, and the U.S.

• Purposes

  • To describe how each country teaches mathematics

  • To allow us to see teaching with a fresh perspective

  • To encourage reflection

Video Study Analyzed

• Teachers’ goals for lessons

• Treatment of concepts and applications

• The presence of alternative solution methods

• How mathematical principles, properties, and definitions were used

• Whether proofs were included

• Whether concepts were connected

• The kinds of tasks assigned

Prediction & Observation

Jigsaw Topics of the Report

• Lesson Structure

• Objectives of Lessons

• Beliefs about Mathematics Teaching

• Teaching Scripts

Key Findings—Simple Jigsaw: Teams of Four

• Divide the four topics among team members.

• Read and study the section you are assigned.

• Teach your teammates about your section.

Comparing Instruction in Three Countries

Variations in Instructional Practice

• Lesson Structure

• Tests, Quizzes, External Exams

• Homework

• Calculators and Computers

Lesson Structure—Percentages of Math Tasks that Students Decide How to Solve Rather than Using a Teacher-Prescribed Method

From: The TIMSS Videotape Classroom Study

Percentages of 8th-Grade Mathematics Lessons with Instances of Mathematical (Deductive) Thinking

From: The TIMSS Videotape Classroom Study

Lesson Structure—Type of Mathematics Seatwork

What do you think?

• Practice Routine Procedures

• Apply Concept

• Invent New Solutions/Think

• Compare Japan, Germany, U.S.

Lesson Structure— Type of Mathematics Seatwork

From: The TIMSS Videotape Classroom Study

Tests, Quizzes, External Exams

• U.S. math and science teachers test more than any other country.

• In many countries, external exams require extended student responses.

Lessons in Which Class Worked on and Shared Homework

From: The TIMSS Videotape Classroom Study

Calculators and Computers

From: Pursuing Excellence: A Study of U.S. Twelfth-Grade Mathematics and Science Achievement in International Context

Lesson Structure—Summary and Analysis

U.S. lessons…

• Demand less mathematical reasoning

• Emphasize routine procedures over inventing something new

• Use more class time for homework than in Japan or Germany

• Use tests more than other countries

Stop and Discuss

• How do these findings compare with your observations?

• What additional issues or questions do they raise for you?

Influences on Instructional Practices

• Deciding What to Teach

• Objectives of Lessons

• Beliefs about Mathematics Teaching

• “Scripts” that Shape Teaching

Deciding What to Teach

From: Global Perspectives for Local Action

Objectives of Lessons

• Germany—developing advanced procedures

• Japan—solving structured problems

• U.S.—learning terms and practicing procedures

From: The TIMSS Videotape Classroom Study

Beliefs Inferred about Mathematics Teaching

From: The TIMSS Videotape Classroom Study

From: The TIMSS Videotape Classroom Study

Scripts Are…

Mental Images of How One Should Teach Based on Beliefs about:

• Goals for instruction

• The nature of mathematics and science

• Ways these subjects are taught that shape the characteristics of a typical lesson

From: The TIMSS Videotape Classroom Study

U.S. Script for Eighth-Grade Mathematics (Inferred)

• Teacher reviews previous material, homework.

• Teacher demonstrates how to solve problem for the day.

• Students practice.

• Teacher corrects problems, assigns homework.

From: The TIMSS Videotape Classroom Study

Japanese Script for Eighth-Grade Mathematics (Inferred)

• Teacher reviews previous material.

• Teacher presents problem for the day.

• Students work on problem.

• Whole class discusses solution method.

• Teacher highlights and summarizes major points.

From: The TIMSS Videotape Classroom Study

Are U.S. Mathematics Teachers Implementing Reform Recommendations?

• 95% of the teachers in the video study indicated that they were “aware” or “somewhat aware” of current ideas about mathematics teaching and learning.

• 75% indicated that the lessons in the study were “a lot” or “a fair amount” in accordance with current ideas about mathematics teaching and learning.

• 20% indicated that they had implemented the focus on mathematical (deductive) thinking.

From: Pursuing Excellence: A Study of Eighth-Grade Mathematics and Science Achievement in International Context

Stop and Discuss

• What are our scripts for teaching mathematics? Other subjects?

• What do the scripts and other results of the video study indicate about the implementation of reform recommendations in the U.S.?

• What additional issues/questions do these findings raise?

Reflection and Dialogue

• In groups of four, cluster, categorize, and name the issues on Post-Its.

• Move to the table with a theme that is interesting to you. Assign a reporter and recorder. Discuss the theme.

• Briefly report out.

• Reflect on an insight gained or an action intended.

Wrap Up

• What insight do you have or action will you take as a result of this workshop?

• How might the NCTM standards for teaching and the National Science Education Standards for teaching help you?