Nurturing Problem Posing in Young Children: Using Multiple Representation within Students’ Real-World Interest

Abstract

Problem-posing activities have been shown to motivate students' learning while promoting a multifaceted and interesting educational environment. Moreover, these activities enable students to be engaged in personal interpretations of their own mathematical thinking. The purpose of this study was to determine if using a handson learning intervention with multiple representations could improve students' problem-posing skills. The researchers examined the answers of the participants (n = 14) with the greatest increase in scores from pre to posttest after participating in 20 problem-posing intervention activities to determine how the intervention allowed students to pose valid, real-world semi-structured problems. The researchers qualitatively analyzed the posed problems for logical real-world contexts and the alignment of the setup of each problem to determine if the students' posed problems were logical and solvable. Results from this study confirm that students were able to build stronger understanding of mathematical content when they were engaged in authentic problem-posing activities that were meaningful to them. Thus, teachers need to include purposeful and focused problem-posing activities into their classroom lessons.

Comparison of Problem-Posing Skills of Gifted and Non-Gifted Primary School Students

“…In these studies, it is seen that students who are not gifted have difficulties in posing problems; there are deficiencies in the expressions of the problems they pose, they do not use the language well in the problems they pose; and therefore the problems are not understood to solve them, and the understood ones do not match the procedure used in the solution (Arıkan & Ünal 2013;Can & Yıldız, 2021;Çarkçı, 2016Çarkçı, Kartal, 2017. Contrary to these results, there are also results showing that non-gifted students are successful in posing problems; the problems they pose are logical and solvable, but the problems that the students pose are similar to the problems they pose in the classroom with their teachers (Dölek & Çalışkan, 2018;Kwon & Capraro, 2021;Özçakır-Sümen, 2021). When the situations of gifted students and non-gifted students posing arithmetic problems are compared, it is seen that the problems posed by mathematically gifted students are, require different steps, contain different computational processes to solve, and contain higher numbers with different semantic relationships.…”

“…There seems to be a limited number of studies examining the problem posing skills of gifted secondary school students (Erdoğan & Gül, 2020;Manuel & Freiman, 2017) in the literature. It is seen that there are many studies examining the problem posing skills of non-gifted primary and secondary school students (Alzahrani, 2021;Bevan & Capraro, 2021;Bulut & Serin, 2020;Can & Yıldız, 2021;Dae-Hyun & Jinhee, 2010;Dölek & Caliskan, 2018;Kwon & Capraro, 2021;Özçakır-Sümen, 2021;Peng, Cao & Yu, 2021;Tertemiz, 2017;Yurtbakan & Aydoğdu-İskenderoğlu, 2020). The fact that there is only one study comparing the problem-posing skills of gifted and nongifted secondary school students (Espinoza, Lupiáñez & Segovia, 2016) and that the study did not compare the problem-posing skills of gifted and non-talented primary school students makes the study necessary.…”

Mathematical Representations Based on Field-Dependent and Field-Independent Cognitive Styles

“…Representational ability is one of the student abilities used to help students understand ideas in mathematics (Kwon & Capraro, 2021). Students need mathematical representation abilities to understand mathematics and to construct abstract knowledge into concrete knowledge through logical thinking (Goldin, 2014).…”

The Analysis of Problem Posing Skills about Integers of Prospective Primary School Mathematics Teachers Who Have Experienced in Problem Posing

“…For this reason, teachers should design the mathematics course for students to participate in mathematics lessons actively. Problem posing is on the agenda as one of the activities that foster active learning (Kwon & Capraro, 2021). There are studies emphasizing the importance of posing problems in our country (Akay & Boz, 2010;Arıkan & Ünal, 2014;Dede & Yaman, 2005;Ev-Çimen & Yıldız, 2018;Kaba & Şengül, 2016;Kılıç, 2013).…”