Mathematical sense-making through learner choice

Students’ Inconsistency when Solving a Geometry Problem in Three-Dimensional Context

“…The concept is integrated with different ways and stages (Fauskanger & Bjuland, 2018). Students produce these conceptual tools for constructing, writing, and explaining mathematically significant systems (Biccard, 2018;Dossey, 2017;Lesh & Harel, 2003). Guarino et al (2004) state that people who solve problems have the same goals but each does something to achieve that goal, but because they do not work together it is appropriate that there are different thinking patterns in the conceptualization process.…”

“…Guarino et al (2004) state that people who solve problems have the same goals but each does something to achieve that goal, but because they do not work together it is appropriate that there are different thinking patterns in the conceptualization process. Furthermore, each person has different expertise and understanding when solving the same problem (Alghadari et al, 2019;Biccard, 2018), due to the work environment, the cases they experience, and the knowledge they build (Hwang et al, 2012), formal and informal knowledge, heuristics, control and belief systems (Dossey, 2017). Each student with his thinking ability creates a diverse design because it suits the needs of the completion process (Biccard, 2018).…”

“…Because of the problem of consistency, there is a certain part of relevance between students' concept knowledge, abilities, and learning processes that should be considered for their cognitive activities in class geometry (Fiki Alghadari et al, 2020;Isnawan et al, 2022;Noor & Alghadari, 2021a), including representation of 3D shapes, spatial structuring, conceptualization of mathematical properties, and measurement (Pittalis & Christou, 2010). Therefore, some researchers have recommended the need for an analysis of how students conceptualize problem solving to explain the phenomena of cognitive restructuring and conceptual reorganization when they engage in complex domains that describe problem solving behavior and affect their performance (Biccard, 2018;Suwa, Gero, & Purcell, 1998;Yee, 2017).…”

“…Solving a problem is the same mean to schematizing concepts and component of information from the initial and goal states. Information on initial and goal states is conceptualized so that binding and connecting bonds are characterized by the emergence of conceptual tools as an appropriate solution (Biccard, 2018;Lesh & Harel, 2003). The solution is the goal of conceptual design in solving problems (Alghadari et al, 2020;Dossey, 2017).…”

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“…In other words, sensemaking relates to how people interact with information and make sense of a problem situation, how they proceed to understand narratives or processes. Sensemaking has been discussed with regard to various areas of education (e.g., Biccard 2018, Fitzgerald and Palincsar 2019, Lim et al 2019, Odden and Russ 2019. To the author's knowledge, with the exception of a few recent publications by Macquet (2016), Macquet and Kragba (2015), and Rönnqvist et al (2019), sensemaking as such has not been largely discussed in relation with the learning or practice of sports and other non-utilitarian physical activities (see author's note 2).…”