Understanding Student Thinking in Algebra Relational Thinking

Revisit Accountability Piece  “Fostering Relational Thinking While Negotiating The Meaning of the Equal Sign”

Problem-solving Activity  Rachel’s age

Outcomes for this session  Develop an understanding of the concept of relational thinking  Consider how to encourage student to develop and engage in relational thinking.

What is Relational Thinking?  Looking at expressions and equations in their entirety rather than as procedures to be carried out step-by-step

BIG IDEA’s Relational Thinking

Purpose for Relational Thinking See handout

Take out handout titled “Introduction to Relational Thinking”  Solve individually  Share with your partner  Share with your table  Share on strategy  10 minutes

Video Clip 2.2  Good example of “Relational Thinking” 8:34 minutes in length

Video Clip 2.1 Emma Problems  Watch as a child learns to use relational thinking to reason about number sentences.  Write down strategies that Emma used on the handout provided  Listen to questions the teacher asks  Think about how you as a teacher could encourage children to look for relationships?  18 minutes in length

Challenge Problem on Page 41  With your table try to think of at least two ways that students might solve this problem using relational thinking  Record your problem and the solution strategies you used  30 minutes

Video Clip 2.4 and 2.5 Solve this problem before we watch the students = = ___  A teacher poses this problem to five fourth graders. Three different strategies are shared. Children are very clear in explaining their strategies.  Record thinking on handout provided  What type of problem does the teacher use?  20 minutes in length

Writing Our Own Number Sentences to Encourage Students to Use Relational Thinking  Grade Levels (K-1, 2-3, 4-5)  Use Emma’s problems as examples  Use relationships that are more complex for older students while retaining the relationship structure and not “tricky” computation.  Post on chart paper  20 minutes

Homework  Understanding the Properties of Arithmetic-A Prerequisite for Success in Algebra  Use number sentences in your classroom and continue to visit and revisit  Bring back examples and be ready to share how the students did