A Review of the Effects of Visual-Spatial Representations and Heuristics on Word Problem Solving in Middle School Mathematics

Abstract

Mathematics word-problems continue to be an insurmountable challenge for many middle school students. Educators have used pictorial and schematic illustrations within the classroom to help students visualize these problems. However, the data shows that pictorial representations can be more harmful than helpful in that they only display objects or persons while neglecting the spatial relationships between those components (Hegarty & Kozhevnikov, p. 686). Research supports schematic diagrams that highlight spatial relationships and focus on related information within the problem (Hegarty & Kozhevnikov, 1999; van Garderen & Montague, 2003). In addition to these strategies, educators have used heuristics (systematic scripted procedures to solve word problems) as a way to provide structure and routine to a variety of word problems. This review of the literature found varying results for the use of some heuristics being implemented in present-day classrooms. On the other hand, both visual-spatial diagrams and heuristics have demonstrated value in middle school special education classrooms. These findings support the further use and research of visual-spatial representations and problemsolving heuristics in order to solve mathematics word problems.

Developing a Teaching Unit Based on (STSE) and Its Effects on the Development of Decision-Making Skills and Ethical Thinking among Female College Students in Israel

“…This result is consistent with research by Mansor et al (2021), which highlights the transformative potential of cutting-edge educational initiatives in developing ethical consciousness. The inclusion of ethical difficulties and concerns in the STSE approach, as emphasized by Intan (2021) and Kribbs and Rogowsky (2016), cultivates students' ethical sensitivity and motivates them to reflect on moral and societal issues. The ability of the STSE approach to foster open discussion, respect for differing viewpoints, and the development of a feeling of social responsibility is what makes it effective at increasing ethical thinking (Williams, 2017;Zhang, Zhang, & Wang, 2023).…”

“…The method develops a well-rounded decision-making process based on ethical considerations by immersing students in settings that call for ethical reflection. According to Kribbs and Rogowsky's (2016) views, the approach's emphasis on holistic reasoning and diverse problem analysis strengthens students' analytical skills and gives them the cognitive tools necessary to make morally correct decisions.…”

“…This finding is consistent with Mansor et al's research from 2021, which emphasizes the transformative potential of cuttingedge educational initiatives in fostering ethical consciousness. According to Intan (2021) and Kribbs and Rogowsky (2016), the STSE approach's incorporation of real-world ethical conundrums forces students to engage profoundly with moral and societal issues, developing ethical sensitivity and a propensity for moral debate.…”

Kesan Teknik Mnemonik dan Pembelajaran Koperatif terhadap Pencapaian Pelajar Sekolah Luar Bandar dalam Pendaraban Indeks

“…Menurut Smaldino, Lowther dan Mims (2018), bahan manipulatif merupakan objek yang boleh dilihat dan ini sesuai untuk situasi pembelajaran berasaskan kaedah visualisasi yang semakin popular masa kini. Penggunaan visualisasi membolehkan pelajar menggunakan keupayaan kognitif untuk menggambarkan proses dalam soalan dengan berbantukan imej visual dalam bentuk yang lebih konkrit contohnya model, gambar rajah atau jadual (Garderen, 2006;Kribbs & Rogowsky, 2016). Namun demikian, pelajar mungkin masih belum dapat menguasai sepenuhnya pengetahuan matematik yang dipersembahkan secara visual kepada mereka disebabkan oleh batasan dari segi beban kognitif (Drushlyak et al, 2021).…”

Abilities and Difficulties of Eight Grade Students in Solving Geometry Transformation Problems

“…The subject matter of transformation is useful for developing spatial abilities, analytical thinking skills, and improving mathematical proof. This ability encourages students to further explore mathematical concepts to solve mathematical problems precisely and accurately (Kribbs & Rogowsky, 2016).…”