Encouraging Conversations In Math Class.

One of the most important things in math involves conversation between students.  Unfortunately, many students arrive in high school without having the basic skills needed to share ideas or explanations of how or why they completed a certain problem.  In fact, the principal discussed that one thing they have to look for evaluations is a certain level of talk carried out during class.  

When she read out every thing the third party evaluation said students should be doing, I was surprised. We didn't get to that level of discussion in my college math classes.

In today's world it is important to encourage frequent mathematical conversations in class because it helps them deepen their own understanding while clarifying their own thoughts.  In addition, it helps turn students into a community of learners. 

Before beginning the discussion, it is important for the teacher to define exactly what they want to accomplish at the end.  With the goal in mind, the teacher has somethings to think about.  Before the discussion begins, the teacher should choose a problem which guides students towards the goal, and think about possible student responses so as to be prepared for misconceptions that might need to be addressed.

During the discussion, the teacher should monitor student responses, listening for misconceptions, and areas of concern.  Think about which students have a solution that meets the teachers original goal so the students can share with the rest of the class.  Furthermore, take time to decide what order the solutions will be presented in.  One might consider arranging the solutions from the most widely used method to one that is unique.  Finally connect solutions so students are able to discuss similarities and difference.

Finally, after the discussion, teachers need to go back through the solutions to look for misconceptions or areas requiring clarification.  As students to review their solutions to see if they seem reasonable or select a solution and have students find a method to determine if the answer is reasonable.  In addition, students should be able to justify the method they used to arrive at a solution.  Finally, take time to have students examine errors to discover where they went wrong and what they need to correct the problem. They should be given time to rework the problem until it is correct.

There are seven techniques teachers can use with students to help them learn. These can easily be used in the classroom.

1.  Revoicing or repeating - The teacher can do this or have another student do it.  The person repeats what the student said and asks if this is what the student said.  This technique can help clarify a student's thoughts or emphasize the thought.  When this technique is used frequently in class, it can help students recognize the important elements of a conversation and select these to remember.

2. Repeating - this is different than revoicing in that a student repeats or paraphrases the important ideas stated by another student.  This one helps students identify important ideas and slows down the conversation so students have time to process the information.

3. Reasoning - in this activity, the teacher asks one student to compare their reasoning with that of another student.  Students have to analyze the other student's reasoning before they can begin to compare the other student's logic with theirs.  Students end up diving deep into things, while making sense of the other person's thinking patterns.

4. Adding on - this is where once a student has finished sharing their thoughts, the teacher asks others to add on to what was said.  This encourages students to participate and is best used when only a few students are involved in the discussion.

5. Wait time - This is hard for many instructors because we don't like silence and even waiting 10 seconds is so hard as it feels like we are waiting forever.  Many students need just a bit extra time to assemble their thoughts.  When we don't give enough wait time, we discourage some students from sharing.  

6.  Turn and talk - is more of a think-pair-share. This technique allows students to talk in pairs, where they are able to express ideas in a more secure situation.  It also gives the teacher a chance to listen in to discover misconceptions, ideas that need clarification, or students who need just a bit more to be there.  This is a great assessment tool.

7. Revise - this is where students revise their thinking as a result of all this talk.  Students are able to explain how their thinking changed from where they were in understanding to where they are now.  In addition, they can explain why their thinking changed.

These are techniques to help encourage conversation in class.  Unfortunately, you cannot just implement all seven in one day.  It is important to introduce one technique to the students and have them practice it over a period of time until they have it down.  When practiced enough, students will do these automatically and their ability to discuss the material will increase accordingly.

On Monday, I'll share some conversation starters and response starters to help students who might have trouble getting started.  Let me know what you think, I'd love to hear. Have a great day.