Abstract
The goal of this chapter is to present and theorize our more successful and less successful attempts to enhance long-term collaborative problem solving in high school, by means of online problem-solving forums. We focus on two classroom communities and their interactions, during two school years, with an additional community, a research group that initiated the use of the forums. In one of the classroom communities, online problem solving has eventually become a routine practice and a valuable addition to classroom problem solving. In another classroom community, the forum did not become active despite considerable effort made, but enduring attempts to activate it led to enhancement of student-student interactions in the classroom. All three communities (i.e., two classroom communities and the research group) gradually developed. Taking the Diffusion of Innovations perspective, we characterize stages of the development and identify its main agents. Taking the Communities of Practice perspective, we characterize each community and illustrate boundary interactions between them as a driving force for their development.
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- 1.
- 2.
This sub-section is a slightly modified version of a section in Koichu and Keller (2017).
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Our initial plan was to use Facebook and Moodle as technological platforms of the project. In practice, we quickly switched to Google+ and then added WhatsApp following the student choice.
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Let us mention here that another problem-solving-related idea worked very well in AP and ES classes. In brief, these teachers successfully engaged their students in long-term extracurricular mathematics research in the context of numerical sequences. This enterprise, which lasts for five consecutive years in their school, is presented elsewhere (Palatnik, 2016; Palatnik & Koichu, 2015, 2017).
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Acknowledgements
This study was partially supported by the Israel Science Foundation (Grant No. 1593/13; PI Koichu). We are grateful to all the participants, and especially to the research group of the first year of the project: Yaniv Biton, Igor Kontorovich, Royi Lachmy, Ofer Marmur and Alik Palatnik.
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Appendix: Examples of Problems Used in the Project
Appendix: Examples of Problems Used in the Project
Trapezoid Problem (from Fraivert, 2016): Let ABCD be a trapezoid (see the drawing). M and N are the midpoints of AB and CD respectively, O is an intersection of the diagonals AC and BD, and OP is perpendicular to BC. Prove that OP is an angle bisector of the angle MPN.
Two Circles Problem (translated from Sharygin & Gordin, 2001, No. 3463): Two circles with centers M and N are given. Tangent lines are drawn from the center of each circle to another circle. The points of intersection of the tangent lines with the circles define two chords: EF and GH (see the drawing). Prove that EF = GH.
Nested Parallelograms Problem (translated from Sharygin & Gordin, 2001, No. 565,566): Given is a quadrilateral inscribed in a parallelogram. Prove that the inscribed quadrilateral is a parallelogram if and only if the intersection point of its diagonals coincides with the intersection point of the diagonals of the external parallelogram.
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Koichu, B., Keller, N. (2019). Creating and Sustaining Online Problem Solving Forums: Two Perspectives. In: Liljedahl, P., Santos-Trigo, M. (eds) Mathematical Problem Solving. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-030-10472-6_12
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