When Two Heads Are Better Than One

  • When Two Heads Are Better Than One

    By Jamie Walker, posted April 24, 2017 —

    Hearing students whine about math being hard is akin to hearing nails on a chalkboard. Because it drove me crazy, I decided to head it off.

    At the beginning of the school year, we have a little conversation about how math is hard. I start by acknowledging my students’ feelings. “Math is hard. I get it. I found math to be challenging in school.” I can see the confusion on their faces as they realize that their teacher just said that math was challenging for her. However, I follow it up with an explanation. “It was that challenge that made it so great. You know that feeling when you finally get something that was hard, that wonderful aha! moment? I love that feeling, and that is why I fell in love with math. I love a good challenge, but I also know that I can’t always do it alone. In here when things get hard, we work together to find answers, and we help each other learn.” In a society that values the individual, this can be a difficult concept to get across to students. It is my job to help my students learn to value collaboration.

    Collaboration is extremely beneficial. Through collaboration, students are introduced to another valuable resource: their friends. Together, students can learn from one another and deepen their understanding. Collaborative learning values a good argument. It allows students to test their theories, validate their conclusions, and critique the reasoning of others. However, collaboration is a skill that must be learned. In this post, I will discuss some strategies for encouraging productive collaboration.

    How is your classroom set up? If you wish to promote discussions and collaborative learning, your classroom set up should lend itself to this. Think about what type of collaboration you would like to promote. If you prefer whole-class discussions, perhaps it would be best to shape the classroom into a giant U. This gives all students an equal seat at the table. If you use such partnering strategies as “think, pair, share,” pushing desks into groups of two will facilitate partner discussions.

    Mixed-ability pairing is also a useful strategy. Research shows that both high-achieving and low-achieving students benefit from peer tutoring, but only if the abilities are not too far apart. If the gap between students is too large, it can result in frustration for one or both. It can also result in one student just giving the other the answer. This situation requires closely monitoring students; step in to help guide discussions when necessary. Remind them not to simply answer for the other student, but to help the other student find the answer. Model this behavior, and have them try it.

    Collaboration can truly challenge your students. If the activity is just a little beyond their skill set, the students will need the assistance of their group to complete the task. This sets the stage for valuable discussions. Inevitably, one group will be uncomfortable with this format and seek out guidance from me. Rather than doing a mini-lecture, I ask guided questions to help students formulate a theory. Once they have a theory, let the group critique the theory or further justify it.

    When working with groups, it helps to give the students well-defined roles within the grouping to promote accountability and equality. I usually place one student in charge who is responsible for making sure that everyone is working at the same pace and that no one is falling behind. It is also useful to have one person make sure that everyone has been given a chance to speak. This will facilitate more balanced discussions and fair arguments.

    In my posts, I have discussed the value of a good argument in a math class. To have a proper discussion, there must be collaboration. Although a little competition can be a good thing, I prefer a classroom in which students are working together to overcome a challenge. Anything worth achieving in life will be challenging. I want my students to not only build resources so that they become resilient when faced with a challenge but also actively seek out challenges in school and in life.


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    Jamie Walker, walker.jamielynn@gmail.com, is a mathematics teacher at Providence Catholic High School in New Lenox, Illinois, where she teaches algebra 1 and geometry in a 1:1 environment. She shares literacy strategies on her webpage http://mathematicsplusreading.weebly.com/ and tweets from @walkerjamielynn. Walker has a passion for increasing literacy in mathematics and works to collaborate and share on the Twittersphere. 

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