Five Dimensions of Quality Math Instruction

1. Five Dimensions of Quality Math Instruction

2. Welcome! During today’s session, you will… • …develop an understanding of the Five Dimensions and Core Features of classrooms that promote understanding, • …experience the dimensions and features in your mathematics learning in this session, • …reflect on how to implement the dimensions and features in your teaching. SD Counts-Mini Foundations Summer 2007

3. Here are our group norms… • Honor each others’ thinking. • Be willing to share your thoughts. • Limit side conversations. • Turn off cell phones. • Take care of your own needs. • Anything else? SD Counts-Mini Foundations Summer 2007

4. Introductions • Please take a couple of minutes to think about how you can introduce yourself using a representative object. SD Counts-Mini Foundations Summer 2007

5. Pretend that you are going to write a book and the list below is the beginning of your Table of Contents. What will you have to say about each of these topics? • The Nature of Classroom Tasks • The Role of the Teacher • The Social Culture of the Classroom • Mathematical Tools as Learning Supports • Equity and Accessibility SD Counts-Mini Foundations Summer 2007

6. Most of the information provided in this session comes from the book Making Sense by James Hiebert et al. All of this means that students must learn mathematics with understanding. Understanding is crucial because things learned with understanding can be used flexibly, adapted to new situations, and used to learn new things. Things learned with understanding are the most useful things to know in a changing and unpredictable world. There may be debate about what mathematical content is most important to teach. But there is growing consensus that whatever students learn, they shoud learn with understanding. SD Counts-Mini Foundations Summer 2007

7. A Framework for Thinking About Classrooms The four sections of the framework are: • Learning with Understanding • Definition of Understanding • Understanding Through Reflecting and Communicating • Is There a Trade-off Between Understanding and Skill? SD Counts-Mini Foundations Summer 2007

8. Did you notice that there were two major cognitive processes emphasized? Communication Reflection SD Counts-Mini Foundations Summer 2007

9. Dimensions and Core Features • Nature of Classroom Tasks • Make mathematics problematic • Connect with where students are • Leave behind something of mathematical value SD Counts-Mini Foundations Summer 2007

10. Dimensions and Core Features • Role of the Teacher • Select tasks with goals in mind • Share essential information • Establish classroom culture SD Counts-Mini Foundations Summer 2007

11. Dimensions and Core Features • Social Culture of the Classroom • Ideas and methods are valued • Students choose and share their methods • Mistakes are learning sites for everyone • Correctness resides in mathematical argument SD Counts-Mini Foundations Summer 2007

12. Dimensions and Core Features • Mathematical Tools as Learning Supports • Meaning for tools must be constructed by each user • Used with purpose—to solve problems • Used for recording, communicating, and thinking SD Counts-Mini Foundations Summer 2007

13. Dimensions and Core Features • Equity and Accessibility • Tasks are accessible to all students • Every student is heard • Every student contributes SD Counts-Mini Foundations Summer 2007

14. Dimensions and Core Features of Classrooms • Please read pages 7-12 of your handout. • Take notes on your graphic organizer as you wish. • Share notes and/or ideas at your tables when you are asked to do so. SD Counts-Mini Foundations Summer 2007

15. Towers Problem • How many different towers--four cubes tall--can you build using two different colors of cubes? • You will have approximately seven minutes to work and then you will share with a partner. • You can use whatever tools you wish. SD Counts-Mini Foundations Summer 2007

16. Towers Video • The researcher in the video will interview fourth graders Michelle, Milan, Jeff who’s been absent for awhile), and Stephanie. • Filming takes place 16 months after their initial experience with this problem. • Notice the communication style and confidence! SD Counts-Mini Foundations Summer 2007

17. Apple Tarts Problem Please use whatever method you like to solve the following problem: “Mom makes small apple tarts, using three quarters of an apple for each small tart. She has 20 apples. How many small apple tarts can she make?” Can you solve it using another method? SD Counts-Mini Foundations Summer 2007

18. Making Sense… • These authors collaborated to write this book… • James Hiebert • Thomas P. Carpenter • Elizabeth Fennema • Karen C. Fuson • Diana Wearne • Hanlie Murray • Alwyn Olivier • Piet Human SD Counts-Mini Foundations Summer 2007

19. Making Sense • “The authors are all members of a working group of the National Center for Research in Mathematical Sciences Education at the University of Wisconsin in Madison. The purpose of the group is to consider the teaching and learning of whole number arithmetic in elementary school. At the time of this publication, they had spent five years focusing on essential classroom features for facilitating mathematical understanding.” SD Counts-Mini Foundations Summer 2007

20. They all agree on the following principles… • Understanding can be characterized by the kinds of relationships or connections that have been constructed between ideas, facts, procedures, etc. • Two cognitive process are key in students’ efforts to understand mathematics: reflection and communication. • Five dimensions play a prominent role in defining classrooms in terms of the kinds of learning that they support. • There are core features within these dimensions that provide students with the opportunity to reflect on and communicate about mathematics. SD Counts-Mini Foundations Summer 2007

21. To Learn More… • Making Sense • by James Hiebert, et al • published by Heinemann • ISBN 0-435-07132-7 SD Counts-Mini Foundations Summer 2007