1. Adapted from: Dawn Smith RUSD Instructional Services

2. “Talk Amongst Yourselves” What purpose should a math wall serve? How should students use it? How should teachers use it? Who should maintain it? Create a list of objectives for your math wall.

3. “We understand something if we see how it is related or connected to other things we know.” -James Hiebert, 1999 The Teaching Gap: Best ideas from the worlds’ teachers for improving education in the classroom. New York: Free Press. “The degree of understanding is determined by the number and strength of the connections.” - Hiebert and Carpenter, et al 1992 Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.

4. A Big Idea (unifying concept) is a statement of an idea that is central to the learning of mathematics, one that links numerous mathematics understandings into a coherent whole. Each one is written as a statement. There may be more than one per topic. What are Big Ideas?

5. Turn to the complete list of “Big Ideas” are found on p. 46 of the Overview and Implementation Guide. These same 20 ideas run through K-6.

6. Understanding Big Ideas of mathematics means students and teachers no longer see mathematics as a set of disconnected concepts, skills, and facts.

7. Big Ideas : Provide a Central Focus Are motivating Promote understanding Promote memory Promote development of autonomous learners Reduce the amount that must be remembered Enhance transfer and academic vocabulary

8. Math becomes a coherent set of ideas.

9. When teaching: Make connections explicit: transfer previously learned big ideas to new concepts and problem solving situations. Consistently connect and reinforce throughout the year.

10. Learn how Big Ideas connect across grades, unifying content from previous to subsequent grades.

11. How does it look in practice? Math Big Ideas can be continually used to teach a variety of math skills/processes: they form the center of your “Concept Map.” This is the starting point for students when learning new math concepts/skills. Examples include "objects and groups", place-value, area, proportion, (part-whole relationships) estimations, etc.) Math Big Ideas should be explicitly described and modeled by the teacher. Academic vocabulary must be taught. Include words from the Big Ideas in sentence frames.

12. Use the Essential Question to set the objective. Teacher checks for understanding throughout the lesson.

13. Essential Question is posed prior to Interactive Learning: “How can you write a fraction as a decimal?”

14.  The Essential Question sets the objective for student learning.  All students should understand that they will be expected to ANSWER that question by the end of the lesson, using correct VOCABULARY while providing an EXAMPLE.

15. Essential Question is repeated in Part 3 and in student text. Reference it again. Are there any students prepared to answer?

17.  Answering the question is Part 2 of the objective- demonstrating understanding.  Explain to a partner  Write to Explain  Journal notes  Ticket out the door…  Format answer to accommodate time and need.

18. Students can record their own version of the concept map

19. Students should employ Q.A.R. and correct vocabulary when framing their answer. Use examples from Interactive Learning to post on the Math Wall.

20. What are your ideas for organizing a concept wall (Interactive Math Wall) in your classroom? Discuss ideas for having students record their answers to the essential question. Partners? Demonstrate with manipulatives? Work in teams?

21. ALL students should ORALLY be able to answer the question at the end of each lesson.

23. There are many ways to preserve the content of your concept map after the topic. One way is with an Inspiration® organizer that is posted. Students could also use one as a template.

24. 1 st Grade 5 th Grade The Mathematical Processes Big Idea is the same for every topic at every grade. Post it permanently!

25. Some examples (not an exhaustive list!)

36. Prior to adding student content; it might be preferable to post EQ’s each day as you ask them. (Blank space is ok!)

37. Student Examples (It helps if they are larger )

38. Early in the topic

39. By the end of the topic Properties or key ideas remain all year

42. PHOTO OF YOUR MATH WALL HERE. For more information or to schedule a training at your site, Contact Dawn Smith 951.788.7315 Ex. 45281 dlsmith@rusd.k12.ca.us