From Student to Teacher: The Role of Argumentation and Collaboration in Matt’s Progression and Understanding of an Inductive Argument

The goal of this analytic is to show the remarkable power of student collaboration and teacher questioning by following the progression of one student throughout an open ended problem situation presented by researchers. The structure of the environment allows for multiple student interactions. These interactions allow the student, Matt, to move from a passive listener to a confident, active participant who is able to articulate his understanding to others. This progression would not have been possible if not for the parameters set and freedoms allowed for by the researchers. The role of the teacher, or researcher, cannot be overlooked as we consider Matt’s transformation through the following events. The researchers structure the entire work session to be focused around small group activity and discussion. This includes partner work and small group work, which typically includes four students. Davidson identified several teacher tasks that are essential to successful collaborative learning which include giving thought to the size and of groups before assigning them, choosing appropriate mathematical problems to be worked on, interacting with groups and scaffolding when necessary, providing guidance and encouragement, ensuring participation and appropriate roles for all group members, assessment and questioning techniques to ensure comprehension, promoting shared leadership, and fostering consensus on group norms (Davidson, 1990). All of these tasks appear to be attended to by the researchers, but this analytic will focus on the organization of groups and the questioning techniques employed. In order to promote individual cognitive growth, students need to be placed in an environment in which ample time and opportunity for exploration and discussion is provided. The teacher must be vigilant in promoting the tenet of student justification of their solutions (Maher & Martino, 1999). By allowing students to work one at one to begin the activity, all students are forced to speak and be engaged with their partner. The transition to larger groups allows students the opportunity to convince others that their reasoning is sound while also taking in the ideas of others’. These opportunities are essential in Matt’s progression. Maher and Martino state “that the teacher’s role of questioning students becomes critical after students working alone or together have taken their ideas as far as they can……. They are ready for the challenge to justify and/or generalize their solutions” (Maher & Martino, 1999). It is a worthwhile exercise to pay close attention to the questioning techniques employed during the session. The progression exhibited in this analytic highlights ideas that are essential to the achievement of the Common Core Mathematical Practice 3 Standard, which states that students should be able to “construct viable arguments and critique the reasoning of others” (CCSS.Math.Practice.MP3). It also provides visual evidence supporting the findings of Francisco, who after a qualitative analysis of the mathematical activity of a group of high school students participating in the same longitudinal study concluded that “all this supports the claim that collaborative activity can help promote students’ mathematical understanding by creating opportunities for students to reexamine the validity of their reasoning and build new, more sophisticated forms of reasoning from suggested hints” (Francisco, 2013). WORKS CITED Davidson, Neil (1990). “Cooperative Learning in Mathematics: A Handbook for Teachers”. Addison-Wesley Publishing Company. Francisco, J. (2013) Learning in collaborative settings: students building on each other’s ideas to promote their mathematical understanding. Educational Studies Mathematics, Volume 82, pgs. 417-438. Maher, C. & Martino, A. (1999). Teacher Questioning to Promote Justification and Generalization in Mathematics: What Research Practice has Taught Us. Journal of Mathematical Behavior, Volume 18, pgs. 53-78