6 Ways To Encourage Mathematical Conversation.

 We are always trying to find ways to encourage students to talk to each other rather than having students rely on us to get help.  By the time most of my students begin high school, they are so used to getting help directly from the teacher that they don't think about talking to each other.

There are six things a teacher can do to help encourage mathematical conversation among students.  One of the first things a teacher can do is to teach students to ask at least three other students for help before asking them.

This asking at least three other students has to be clarified because I've had students ask three students "Do you know how to do this?".... No and they will tell me they asked three other students.  We have to take time to teach them the specific questions to ask each other such as "Have you started # ____" or "How did you start the problem?" or "Why did you do it this way?".  The questions have to be ones that request information on solving the problem.  If the three people asked have not started the question, suggest students check with a few more to see if anyone has done the problem before asking the teacher for help.

Another thing is to ask students to work independently before they begin working in pairs or groups because most need a few minutes to process the problem and gather their thoughts.  This gives them time to determine what they know or don't know so they have a better idea of what to do during the mathematical discussion.  Once students gather into groups to discuss things, they should spend a bit of time comparing and contrasting approaches and solutions of everyone in the group.

It is also important for the teacher to pose questions to students which guide the discussion.  The questions might be open ended or designed to focus on certain processes, or justify their thinking, or explain their choice of processes or are designed to deepen their thinking.  Questions that have only one answer do not promote much dialogue but ones that ask students to justify, explain, compare and contrast do more towards deepening their thinking and understanding.

Furthermore, it is important to get students to understand that it is alright to make mistakes because we learn from mistakes.  Students need to understand that they will make mistakes as they explore new material or they are making conjectures.  In addition, making errors lead to better learning especially if students are asked to make corrections while taking time to explain where they made the mistake and why.  Analyzing mistakes is helping students learn to spot errors and it helps clarify their misunderstandings.

Then implement a variety of collaborative strategies such as think pair share or numbered heads so help boost student confidence because they can work in small groups to come up with an answer to share with the whole class.  If you haven't heard of numbered heads it is where each person in the group is given a number.  The people in the group know that anyone of them could be called on to share the answer so everyone needs to talk and be prepared to answer.

Finally, use strategies that allow all students to participate in class such as thumbs up/thumbs down, classroom response system or even corners as a quick way for teachers to assess student understanding quickly.  It takes a moment to check.

If you introduce these strategies to increase mathematical discussion, students will soon be talking about math with little to no guidance.  Let me know what you think, I'd love to hear.  Have a great day.