Evaluating the suitability of mathematical thinking problems for senior high‐school students by including mathematical sense making and global planning

Abstract

To cite this article: Joke H. van Velzen (2016) Evaluating the suitability of mathematical thinking problems for senior high-school students by including mathematical sense making and global planning, The Curriculum Journal, 27:3, 313-329, DOI: 10.1080/09585176.2016 ABSTRACTThe mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an evaluation method by including mathematical sense making and global planning. Eighteen 11th-grade high-school students, divided into three groups of three pairs, solved six mathematical thinking problems that included the finding of a numeric solution and the writing of mathematical texts and arguments. Content analysis of the students' solution procedures provided for three kinds of hierarchically ordered mathematical sense-making categories. The results showed the expected statistically significant difference between the kinds of problems, though only mathematical sense making enabled the exclusion of the routine problem. The implications for practice are discussed.

Ortaöğretim Öğrencilerinin Anahtar Yetkinlikler Becerilerinin İncelenmesi

“…Studies measuring students' mathematical thinking skills found that secondary school students were good at mathematical thinking (Akçakın & Kaya, 2020;Arslan & Yıldız, 2010;Göl, 2017;Kocaman, 2017). Similarly, studies conducted abroad reported that secondary school students had high mathematical thinking skills (Cortez, Cuevaz, & Castillo, 2019;Gine, 2010;Lutfiyya, 1998;Mashaqbah, 2017;Mustafa, Sari, & Baharullah, 2019;van Velzen, 2016). Lastly, various studies have measured secondary school students' scientific thinking skills.…”

What Neuropsychology Says about Mathematical Word Problem Solving: Contribution of Executive Function in Educational Setting

“…Three of components EF are equal each other (Miyake, et al, 2000) and play an important role to multi-step strategy of mathematical word problem solving. In the other side, planning, monitoring and procedural are components in using strategy to solve mathematical word problem (van Velzen, 2016). In other words, how to solve mathematical word problem depend on working memory, inhibitory control and shifting flexibility.…”

Mathematical sense-making through learner choice

“…Mathematics teachers would like to see learners engage in mathematical sense-making. The term 'sense-making' is often interwoven with ideas of deepening understanding and application of mathematical concepts (Van Velzen, 2016). This article uses a conceptual approach to explore learner choice as a property of sense-making.…”

“…of Teachers of Mathematics (NCTM) defined sensemaking more generally as 'developing understanding of a situation, context, or concept by connecting it with existing knowledge' (NCTM, 2016, p. 1). Sense-making is more about flexible application of mathematical knowledge(Van Velzen, 2016) than it is about performing procedures.http://www.pythagoras.org.zaOpen Access…”