*Algebraic ThinkingEquality

*Outcomes: *Participants will establish that

students have some very common misconceptions about the meaning and use of the equal sign

*Participants will explore strategies to help students develop an understanding of the meaning and use of the equal sign.

*Participants will develop an understanding of the importance of the concept of equality in algebraic reasoning.

*Reading:

*Read forward and chapter 1

*Use notecards to record important statements

*Go-Around One Protocol*Person #1 reports one idea that she/he recorded

*While Person #1 reports, other group members listen, but do not question Person#1, comment, or give clues.

*When Person #1 finishes, Person #2 reports while the group listens.

*Repeat until all group members have reported all of their ideas.

*The group discusses ideas that were reported.

*8+4= + 5

*What answers did your students give?

*Why did they give these answers?

*Was this what you expected students to be able to do?

*For your students who got 7, how did they get it?

*8+4= + 5Grade 7 12 17 12&17 Other

1

2 3 2 1

3 9 1 2

4 1 3

5

6

7 1 1

8 1 1

*8+4= + 5*Are the students we observed struggling with the concept of equality?

*Why are students struggling with this elementary idea?

*Do students appear to get better with more experience?

*How does the calculator lead to the misconception of the meaning of equality?

*Read Chapter 2, page 9

*Reading – Children’s Understanding of Equality

*Highlight your big ideas for later discussion

*Go-Around One Protocol*Person #1 reports one idea that she/he recorded

*While Person #1 reports, other group members listen, but do not question Person#1, comment, or give clues.

*When Person #1 finishes, Person #2 reports while the group listens.

*Repeat until all group members have reported all of their ideas.

*The group discusses ideas that were reported.

*Article Big Ideas

*How did the student in this study do compared to our students?

*What are some common misconceptions that students have about the equal sign?

*How should students be thinking about the equal sign?

*What are some ways Karen Falkner used to help her students develop a better understanding of the equal sign?

*Understanding EqualityVideos 1.1-1.3*Equality Handout for notes

*Prepare for table discussions

*T/F Sentences

*Read pages 15-16

*Work with grade level groups

*Write a series of T/F sentences that you will use with your students

*Record on chart paper

*Share how you hope that the student thinking would progress with this series.

*Why is each sentence important?

*What does equality mean?

*Understanding EqualityVideo 1.5*Talk about teacher decisions

*Why were certain number sentences particularly good?

*What number sentences might you have added to help out?

*How does the sequence build understanding?

*Revise your T/F sentences

*Homework*Do the T/F sentences you developed with your students

*Be prepared to share student observations

*Read chapter 2