Does representation matter? Teacher-provided tables and drawings as cognitive tools for solving non-routine word problems in primary school

Abstract

According to the German educational standards, students should be familiar with problem-solving as a general mathematical competency by the end of grade 4. Non-routine word problems are suitable tasks for mathematical problem-solving in elementary mathematics classes. They are characterized by the fact that the problemsolver cannot simply use well-trained algorithmic calculating procedures (Rasch, 2001). As a result, many students struggle with word problems in mathematics, especially with non-routine word problems (Hohn, 2012). Representation plays a central role in the process of problem-solving. It involves representing a problem situation adequately, constructing a mental model and comparing it in a dynamic and iterative process with the information externalized in the representation (Schnotz et al, 2011). This study aims to shed light on teacher-provided representations as cognitive tools for students when working on non-routine word problems. In an experimental study, we examined a sample of 67 primary school students who worked on six non-routine word problems with provided representations. The tasks were accompanied by a table or a drawing. Furthermore, the tables and drawings differed with regard to the amount of information provided. Statistical data analysis generated, among other findings, two results: Overall solution rates were low (10 to 24%). Tables and drawings facilitated the solution process differently depending on the type of word problem. Consequences for subsequent future research are discussed.

Brain imaging provides insights about the interaction between instruction and diagram use for mathematical word problem solving

“…Therefore, inadequate problem-appropriate details included in instruction on diagram use may lead to such a utilization deficiency in using diagrams as a strategy (cf. Bjorklund et al, 1997;Reuter et al, 2015).…”

Matemati̇k Öğretmenleri̇ni̇n 5. Siniflarda Problem Çözme Yeterli̇kleri̇

“…Nitelikli bir matematik eğitimi, matematiksel kavramlar ve kavramlar arasındaki ilişkileri görebilen, gerekli stratejileri uygulayabilen, edindikleriyle mantıklı çıkarımlar yapabilen ve bunlar yardımıyla problem çözebilen öğrencilerin yetişmesini sağlamalıdır (Schoenfeld, 1989). Öğrenciler, problem çözme sürecinde, problemleri anlama ve matematiksel modelleme ile ifade etmede zorluk yaşamaktadır (Reuter, Schnotz & Rasch, 2015). Problemin Bilinmektedir ki, öğretmenlerin problem çözme yeteneği geliştirildiğinde öğrencilerde olumlu değişimler gözlemlenmektedir (Charles & Lester, 1984).…”

“…Mathematics teaching should ensure that students who can see mathematical concepts and the relationships between them, apply the necessary strategies, make logical inferences with what they have learned and solve problems with the help of these (Schoenfeld, 1989). During the problem-solving process, students have difficulties in understanding and expressing problems with mathematical modeling (Reuter, Schnotz & Rasch, 2015). Teachers play an important role in understanding and modeling the problem.…”

Evaluate Recovery of Prospective Elementary School Teachers Using Quizizz: Is It Effective?

“…Students tend to want to solve problems immediately without paying attention to the truth of the answers. This is certainly quite confusing for teachers who incidentally use Quizizz as an evaluation tool, if factor x such as "inaccurate" affects students in the process then it will be difficult for teachers to assess the extent to which students' understanding of a material (Reuter et al, 2015). Continuous technological innovations in education services sector are having a profound effect on educational systems at all levels encompassing various educational institutions.…”