1. Meeting Students Where They Are…
Math Alliance
February 23, 2010

2. Learning Intention Success Criteria
We Are Learning To…
Deepen understanding about constructivism and how to use it effectively with mathematics instruction.
We know we will be successful if…
By the end of the session you will be able to connect features of constructivism to classroom activities.

3. Solving A Problem
Working on your own. How would you solve the following problem in two different ways?
159 ÷ 13 = ?

4. Debriefing the Math Place an identifying mark in the top right corner.
Gather the papers in the center of the table.

5. Constructivism
Learning theory based on the idea that children construct their own knowledge.
They must be active participants in the development of their own understandings.
Connections are developed through effort that is active and reflective.

6. Elements of Constructivism
Use the Clinking Glasses Problem to connect ideas from Chapter 1 to the ideas address in the book about how children learn.
Split your table up into 3 groups.
Discuss your assigned area of the chapter. Make connections to the Clinking Glasses problem.
Each group share their insights about their topic. Create one poster. Use examples from Clinking Glasses to make connections.

7. Reading Assignments Understanding vs. Knowledge pg. 2-3
Classroom Influences on Learning
Pg. 4-6
Conceptual vs. Procedural Knowledge
Pg. 6-8

8. Conceptual vs. Procedural Knowledge
Conceptual - knowledge that consists of rich relationships or webs.
Procedural - knowledge of procedures and rules used to carry our a mathematical task. Knowing step-by-step procedures.
The most skillful use of procedures will not develop conceptual knowledge.

9. Understanding is a measure of the quality and quantity of connections that a new idea has with existing ideas. The greater the number of connections to a network of ideas, the better the understanding.
(Van de Walle, p. 3)

10. Classroom Environment
Community of Learners
Multiple Models
Pictures
Manipulatives
Symbols
Oral Language
Real-world situations

11. Relational vs Instrumental Thinking
Relational - Connected or webbed ideas.
Instrumental - isolated and essentially without meaning.

12. Reviewing the Work 159 ÷ 13 Each person selects one paper to review:
In what way did this person show an understanding of mathematics?
What mathematical representations are displayed on the paper?
Use a sticky note to provide feedback.
Repeat the process one more time.

13. Looking For Evidence of Understanding
Analyze samples of student work.
What evidence is captured on this work that demonstrates understanding of division.
There are 159 oranges to be packed into bags. Each bag holds 13 oranges. How many bags can be filled?

14. Why Focus on Relational Thinking?
Intrinsically rewarding
Enhances memory
Less to remember
Helps with new concepts
Improves problem solving
Self-generative
Improves attitudes and beliefs

15. Homework For February Try these 3 division problems.
Do not use a traditional algorithm.
Write up how you approached solving all three problems.
110 ÷ ÷ ÷ 27