Understanding Student Thinking in Algebra

Opener At your tables, read one item from your reading that was an important statement. Continue until all important statements are exhausted. Record your table’s top three or most significant statements on a piece of chart paper and display on wall.

Outcomes Participants will: Establish that students have some very common misconceptions about the meaning and use of the equal sign. Explore strategies to help students develop an understanding of the meaning and use of the equal sign. Develop an understanding of the importance of the concept of equality in algebraic reasoning.

Literature in Mathematics Equal Shmequal Web activity: calculation.html#nbKS2 calculation.html#nbKS2

8 + 4 = M:\Homework Spreadsheet.xlsx Discussion: 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? Are the students we observed struggling with the concept of equality? Why are students struggling with this elementary idea? How does the calculator lead to the misconception of the meaning of equality?

How did the students 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? “Children’s Understanding of Equality”

True/False Number Sentences Read pages in textbook On chart paper: In grade levels (K-1, 2-3, and 4-6), generate a sequence of number sentences that might be used to help students develop the meaning of the equal sign. You are NOT to use the examples from the book. Include the open number sentence that you would hope that the students could do at the end of that series of true and false sentences.

Homework for tomorrow: Read chapter 2 and do challenge 2 on page 24 Read chapter 3 pages and do challenge 4 on page 41. On a note card answer the following questions: What big idea are you walking away with today? If this applies to you, what misunderstandings are you having at this point? Closure for Monday

Homework Discussion Discuss in small groups what you concluded for challenge question number 2 on page 24. Four levels of children’s conceptions of the equal sign: 1.Getting children to be specific about what they think the equal sign means. 2.Children first accept as true a number sentence that is not of the form a + b = c. 3.Children recognize that the equal sign represents a relation between two equal numbers. 4.Children are able to compare the mathematical expressions without actually carrying out the calculations.

True/False Presentations Why is each sentence important? Share how you hope that the student thinking would progress with this series.

Connecting Equality to Formal Algebra 2x + 3 = 9  What properties and relations do you need to understand to comprehend this problem?  How would you begin to solve this?  How do you know this works?

Summarizing Equality What do students need to know and understand about equality? Why is it important to understand equality?

Outcomes for Relational Thinking Participants will: Develop an understanding of the concept of relational thinking. Consider how to encourage students to develop and engage in relational thinking. Develop an understanding of the basic properties of number operations and the order of operations. Work with a student to develop the concepts of equality and relational thinking.

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

Challenge Problem #1 page 41 In small groups, decide how students might solve these problems using relational thinking. Think of at least 2 ways that students might think about that problem. Record your thinking.

Writing Number Sentences to Encourage Relational Thinking In grade level groups, write some problems to encourage relational thinking. Are we asking students to use properties in any of these examples?