Right vs. wrong answers

In Classroom Discussions, the authors write about the importance of mathematical reasoning. It's important for students to have the ability to decide for themselves whether their answers are right or wrong. Instead of telling students whether the answer is or isn't correct, invite others to agree or disagree. Offer multiple answers (generated from your students' work, or even from teacher-created samples) and allow students to explain why they believe one of the answers is the correct one.

Problem-Solving Strategies

The authors of Classroom Discussions talk about how George Polya outlined a four-step problem solving method. It's interesting to me because our school was part of an Action Research project a few years ago that focused on problem-solving. Teachers within our school created a method called "RIDE" (Read It, Imagine and Plan, Do It, Explain). At the time, I didn't realize that it was based off of Polya's method.

The four-step problem-solving method:

1. understand the problem;
2. make a plan for solving the problem;
3. carry out the plan; and
4. look back and reflect on the answer in terms of the initial question.

What to talk about?

Chapter 4 in Classroom Discussions is all about what students should be talking about during Math Congress. Here are some interesting points:

- with young students, partner talk should be framed with a very specific question

- students can talk about how they found their answer, and then compare their strategies with others (e.g., What did you both do that was the same? You both used counting to find the answer? What was different? One of you used manipulatives and the other drew a picture?)

- summarizing what students have been talking about

- instead of having 1 person explain their whole answer, they can talk it through while the teacher records what they say (the student tells the teacher what/where to record their ideas)

- invite students to explain others' answers to encourage student engagement. Check back with the original student. Did they explain your ideas correctly? Do you have anything to add or to explain?

- not everyone understands by hearing the right answers. Choose students with incorrect answers (even after the correct answer has been shared) because students often learn more (and deepen their understanding) when they consider incorrect options and then reject them

 - discuss everything! What does a + mean? Where do we write numbers when recording a multiplication question? Why?

- many students do not understand the meaning of symbols. For example, many students do not see the equal sign (=) as a statement of equivalence or balance. They see it as a signal to "write the answer" (p. 136).