Teaching Strategies
Math Discussions
Engaging student in math discussions has a multitude of benefits.
Re-voicing: by teachers- sometimes students are unclear in their descriptions and explanations, if they’re unclear, other students remain unclear. If only students who can explain themselves clearly participate, it does not build participation or understanding. I need to clarify in a way to continue to engage and include my students. One way that I have found useful in math classroom is to restate what has been said and then ask my students to respond and or verify if that is what they stated: “So you’re saying”. This helps me to determine whether the student does or does not understand, and provides an opportunity for me to guide the discussion. - It also allows me to clarify when a student adds to the discussion but is not clear or not understood by the other students. This makes ideas of one student available to others, give students time to hear what is being discussed more than once, helps students to develop a critique or viable argument, and allows students to change their thinking. By asking students, "Can you explain what he/she said in your own words?"-- I give students another opportunity to hear discussion, more time to process, improves engagement and the likelihood that students are listening. Over time, students come to realize that others are listening closely to what they say, and begin to make more effort to contribute in positive way.
Math Circles
I had a big ah-ha moment as I wrote another geometry unit a few years ago. I frequently use literature circles in my English/Language Arts classes. Literature circles are an excellent strategy that infuses student centered inquiry with collaborative learning. Using this strategy encourages students to take responsibility for their learning based on the plan and choices they make. Students choose their own reading materials, lead the discussion, and engage with the texts and each other in a positive, authentic way. Why can’t we create the same experience in math class?
I have now developed Math Problem Solving Circles where small groups of students engage with a problem and have designated roles that will help students to make sense of the problem, facilitate discourse, and decide which tools or strategies to use to help solve the problem. I create student groups of 3 to 4 students, then present the problem, and assign roles. I have developed four roles to best suit my classroom needs, they are; Reporter, Questioner, Strategizer, and Reflector. Each role has a purpose, yet the purpose is not to isolate the problem into pieces, the purpose is to provide all students the opportunity to access a problem, comprehend what the problems is asking, discuss a variety of possible strategies, and make connections to other mathematical concepts. The following descriptions provide a starting point and have suggestions for students’ engagement. Students will be using a KWCSR chart while participating in a Math Problem Solving Circle. What a KWCSR is, is explained in detail below.
REPORTER: The reporter’s role is to read the problem to the group and to fill in the “What do we KNOW” portion of the chart. The reporter will also lead the group’s presentation to the rest of the class.
QUESTIONER: The questioner’s role is to lead a discussion about what the problem is asking, what needs to be solved. The questioner should fill in the “What do we WANT to know” portion of the chart. The questioner should be asking throughout the process, does this solution make sense? Are we solving the question the problem is asking? Have we used the correct units? Do we need more information? Have we ever solved a problem like this before?
STRATEGIZER: the strategizer’s role is to lead the discussion about which strategies would be most efficient to solve the problem. The strategizer should fill in the “What STRATEGIES will we use?” portion of the chart. They will help to ensure that group members are using a variety of strategies.
REFLECTOR: the reflector’s role is to lead the discussion about following the plan the group is setting up and to think about its efficacy. Some questions the reflector can ask the group are; Will this plan help find a solution to the problem? Is there another way we could solve this problem? If there are multiple ways to solve the problem, is one way better than the other? The reflector should fill in the “What is the ANSWER?” section of the chart. After the problem is solved, the reflector will help lead the discussion about what each group member learned and how this new information can be used again by asking questions like, What have we learned? How can we use this information again? I believe this type of approach to problem solving will enable more students to become successful as they tap into their collective knowledge. I believe a barrier to problem solving for many students is the lack of experience and the issue for students of not knowing where to start
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