Collaboratively Engaging with GCFs and LCMs

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Ellen Robinson
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Xiaowen Cui
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Hiroko K. Warshauer
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Christina Koehne
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Collaborative engagement provides an opportunity for students to construct and solidify their own knowledge and understanding of important mathematical ideas. According to Van de Walle, Karp, and Bay-Williams, “learning is enhanced when the learner is engaged with others working on the same idea” (2015, p. 52). In allowing students to work with their peers to practice problems and construct important mathematical connections, the students build on their combined prior knowledge to formulate newfound ideas and conjectures. We recognize that grouping students so that each group will function in a productive manner can often be difficult. Therefore, we have devised this activity that allows students to work together and communicate with ten different students individually. In a usual group setting, the students would get to work with one or two other students, but the format of this activity allows for more forms of mathematics communication and collaboration.

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Footnotes

Edited by Marilyn Howard, marilyn-howard@utulsa.edu, University of Tulsa, Oklahoma; Christine Kincaid Dewey, dewey@wcskids.net, Macomb Mathematics Science Technology Center, Warren, Michigan; and Hiroko K. Warshauer, hw02@txstate.edu, Texas State University, San Marcos.

Contributor Notes

Ellen Robinson, ebr21@txstate.edu, is a lecturer of mathematics at Texas State University in San Marcos. Her research interests are in the areas of graph theory and combinatorial matrix theory

Xiaowen Cui, x_c5@txstate.edu, is a PhD student of mathematics education at Texas State University. She is interested in the instructional coherence in the classroom on the topic of introduction of fractions.

Hiroko K. Warshauer, hw02@txstate.edu, is an assistant professor of mathematics at Texas State University. She is interested in teacher preparation and in-service professional development, with a focus on teaching practices that support productive struggle and noticing of student thinking.

Christona Koehne, crz7@txstate.edu, is currently pursuing a PhD in mathematics education at Texas State University and working as a teaching assistant for the department of mathematics during the academic year and as a researcher for Texas Mathworks during the summers.

(Corresponding author is Robinson ebr21@txstate.edu)
(Corresponding author is Cui x_c5@txstate.edu)
(Corresponding author is Warshauer hw02@txstate.edu)
(Corresponding author is Koehne crz7@txstate.edu)
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