Collaborative Learning Groups Construct Viable Arguments and Critique the Reasoning of Others

PurposesEffective teaching; Professional development activity
DescriptionThis Analytic demonstrates enactments of Common Core Mathematical Practice 3: To construct viable arguments and critique the reasoning of others.
There has been much research and documentation which supports the benefits of collaborative group work in the classroom versus the traditional teacher led and fed instruction that we have seen in the past. This teaching philosophy has an even stronger impact with the implementation of the new Common Core Mathematical Practices, particularly Mathematical Practice 3

The Common Core Mathematical Practice 3 Standard states that students should be able to "construct viable arguments and critique the reasoning of others"

Enabling students to work in collaborative groups, or pairs, affords them the opportunity to apply the principles outlined in the third mathematical practice of the common core standards. Group work promotes conversation and sharing of ideas that would not normally take place in whole group discussion or teacher-led instruction. The traditional classroom environment where students sit in rows, looking at the back of their peers, and focusing on a lecturing instructor, does not facilitate the type of learning which the common core mandates.

Marilyn Burns, founder of Math Solutions Professional Development, supports these ideologies in her article Uncovering the Math Curriculum when she writes “Embracing the Common Core mathematical practices requires that we help students uncover knowledge by conducting firsthand investigations, working with physical materials when appropriate, and having opportunities to interact with others." (Burns, 2014, 66)

The events in this analytic are taken from several video clips which were part of a longitudinal study conducted by Dr. Carolyn Maher through the Robert B Davis Institute for Learning. The students in these events range in age from elementary school to high school, and date as far back as 1993. The events demonstrate how students working in groups are able to more readily apply the principals outlined in MP3, even at an early age. In the article, Conditions for promoting reasoning in problem solving: Insights from a longitudinal study, Drs Francisco and Maher state “The longitudinal study experience highlighted the importance of another form of collaborative work among students, whereby the group members rely on each other to generate, challenge, refine and, accordingly, drop or pursue new ideas.” (Francisco & Maher, 2005, 369)

In these events, we view students working in groups or pairs demonstrating the following
ideals as outlined by MP3:

• Mathematically proficient students justify their conclusions, communicate them to others, and respond to the arguments of others.
• Mathematically proficient students are able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is.
• Students at all grades can ask useful questions to clarify or improve arguments.
• Students at all grades can listen or read the arguments of others and decide whether they make sense
• Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions.

Dr. Maher quantifies these points nicely in Chapter 1 of her book, Combinatorics and reasoning with her statement “In summary, students learn mathematics by engaging in the process of building their own personal representations, communicating them as ideas, and then providing support for those ideas by reorganizing and restructuring representations.” (Maher, 2010, 4)

Group dynamics is the ultimate forum to facilitate this type of learning.

Work Cited

Burns, M. (2014). Uncovering The Math Curriculum. Educational Leadership, 72(2), 64-68

Francisco, J., & Maher, C. (2005). Conditions for promoting reasoning in problem solving: Insights from a longitudinal study. The Journal of Mathematical Behavior, 24, 3-4,361-372. (Print)

Maher, C. (2010). The Longitudinal Study. In Combinatorics and reasoning: Representing, justifying and building isomophisms (p. 3-8). New York: Springer.
Created on2014-11-14T17:19:55-0400
Published on2015-06-18T14:02:55-0400
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