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 hands-on 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.
Highlights
Previous researchers have focused on various aspects of mathematical problem posing within elementary school environments
Looking at students who improved their problem-posing skills on the posttest allowed researchers to determine that students who were more engaged in hands-on learning with multiple representations in real-world contexts posed more valid problems
Building early problem-posing skills at the elementary level may help students build a stronger understanding of mathematical content when they are engaged in authentic learning experiences that are meaningful to their lives (Cai & Hwang, 2020; Xu et al, 2019)
Summary
Previous researchers have focused on various aspects of mathematical problem posing within elementary school environments. Kafai et al (1998), and Lowrie (2005) both examined elementary students as they posed problems in a game-based environment. Previous researchers have focused on various aspects of mathematical problem posing within elementary school environments. Kafai et al (1998), and Lowrie (2005) both examined elementary students as they posed problems in a game-based environment. Yamamoto et al (2012) studied an interactive learning environment populated with first graders, who demonstrated their ability to pose problems within a virtual environment. Studies have been conducted on older students; for example, one researcher found that Singaporean upper elementary students were able to pose more complex problems as they advanced from fourth to sixth grade (Cai, 2003). Pose problems using expression cards and their Halloween erasers (see full intervention lesson below) Pictures Plastic. Pose a problem based on one of three pictures: dinos, farm animals, or a farm animals & dinos pet shop Pictograph Coloring graph Pass out “Writing Good Questions” and candy corn – students pose questions after placing candy corn in groups 3* Expression cards
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