Model method drawing acts as a double-edged sword for solving inconsistent word problems

Abstract

Drawing bar diagrams has been shown to improve performance on mathematical word problems wherein the relational keyword is consistent with the required arithmetic operation. This study extends this by testing the effectiveness of bar diagram drawing for word problems with an inconsistent keyword-arithmetic operation mapping. Seventy-five fifth graders solved consistent and inconsistent word problems while encouraged to draw bar diagrams. For each word problem, we assessed problem type (consistent/inconsistent), performance (correct/incorrect), and bar diagrams (accurate/inaccurate/no drawing). Overall, bar diagram drawing was associated with increased performance on both consistent and inconsistent word problems, but the strongest benefits of drawing were found for inconsistent word problems. For inconsistent word problems, bar diagram accuracy was more clearly related to performance (accurate bar diagrams related to correct answers, but inaccurate ones to incorrect answers) than for consistent word problems. We conclude that bar diagram drawing provides an effective graphical support for solving inconsistent word problems.

Unveiling problem-solving strategies of pre-service mathematics teachers: A visual and discursive exploration

“…In addition to the example of PMT6 being able to identify that there was a problem with her calculations after sketching her solution, other participants were able to verify that their solutions were correct using iconic visual mediators. These results align with those of other studies (de Koning et al, 2022;Pantziara et al, 2009) that have established that the significance of diagrams in solution verification for mathematical problems has long been acknowledged by the mathematics education community.…”

Implementation of the Connected Mathematics Project Learning Model on Students' Mathematical Problem Solving Abilities

“…Students' in learning utilize connections from concepts that students' already understand. To be able to solve the questions contained in the student worksheets, students' need to be able to connect relevant mathematical concepts with solutions to problems (de Koning et al, 2022). This stimulates students' to make varied answers.…”

Vzgoja in izobraževanjemed preteklostjo in prihodnostjo / Upbringing and Education between the Past and the Future

“…Solving arithmetic word problems with the model method involves essentially three phases (Koning et al 2022). The first phase is focused on the problem text: the solver reads the given word problem with the intention to identify the known as well as the unknown variables, quantities, and relations.…”

“…Indeed, in consistent word problems the required mathematical operation can be derived straightforwardly from the keyword. There is no need to internally or externally represent the described problem situation to reach the solution (Koning et al 2022).…”