Encouraging Mathematical Discussions

Encouraging mathematical discussions among students can be very difficult for many reasons.   First there is mathematical vocabulary.  Many words mean one thing in general conversation while it means a totally different thing in math.  One such word might be product.  In the general population, it means something made to sell at a business while in math it means the result of a multiplication problem.

Many of the mathematical equations using symbols such as a * b can be read as "a times b", "the product of a and b" or "multiply a and b" so there is more than one way to read it.  In addition, when translating from the symbols to verbal or vis-versa there are rules to it's context and students have to aware of it.

Sometimes one of the hardest things is to get students to talk to each other rather than only asking the teacher for help.  One way to work around this is to have students ask for help from three different students before they ask the teacher for help.  One has to take time to help students learn to ask for help because I've heard them ask like this "Did you do 12 yet? No? OK" and repeat the question rather than asking "Could you look at this problem and suggest a way I could start it?"  One other way to handle this is to assign "expert" students that other students can ask before they ask you.

Next, have students work independently before having them work in small groups because they need time to assemble their thoughts and figure out what they know or don't know.  Once they've had time to do this, they can work with other to compare and contrast their approaches and answers.  During the process, they are conducting a mathematical discussion.

Teachers can use questions to help promote mathematical discussions in class.  I know I often get stuck looking for new ways to ask questions but I found this list that helps.  It is a list of 100 questions designed to help encourage discussion among students.  Some of the questions are designed to help their perseverance, while others help students connect mathematics to their application or conjure, invent, or solve problems.  Check it out if you need help with your questioning.

Help students understand that they learn when they make mistakes.  Too many students want to get the "right" answer the first time, not understanding that every time they make a mistake and correct it, they are developing a deeper understanding.  If students do not like the grade on their work, they are allowed to go back and make corrections but they are also required to explain why they made the mistake.  This process helps them learn the material so much better.

Teach students to work collaboratively using think-pair-share or numbered heads.  Numbered heads is great for groups of three or four because each person in every is assigned a number between one and three or one and four.  The teacher calls out a number and the student with that number is expected to provide a response so it is necessary for everyone in the group to understand.  This encourages students to talk so everyone in the group has the same level of understanding so they are all prepared to answer the question when called upon.

Run some quick assessments so the teacher knows the level of understanding.  Quick assessments can include thumbs up/ thumbs down, choose a corner, use a random name generator to get a name to call on, or red/yellow/blue cups to have students show how well they think they understand the material.

It is important to encourage mathematical discussions because students need to be able to express themselves.  I've noticed that students who have low scores in reading and writing often struggle in math because they lack the vocabulary to understand what is being asked.  This is one reason to encourage vocabulary development.

Let me know what you think, I'd love to hear.  Have a great day.