This study examined how word-problem characteristics influenced students' learning and retention of word-problem knowledge during and after an intervention. The participants were 221 fourth-grade students (average age at pretest = 8.8 years) who experienced word-problem difficulties (WPD) and had received a word-problem intervention in third…

Evidence in South Africa of poor performance on word problems points to particular challenges among learners relating to difficulties with, on the one hand, making sense of mathematical word problems and, on the other, moving beyond inefficient counting based calculation methods. While many studies in mathematics education in South Africa have…

In this article the authors describe how standard textbook questions can be turned into open questions to promote problem solving and reasoning. Six example solutions are given to one problem showing how an open problem can cater to the diversity of students in your class.

In XVII century, presumably between 1637 and 1638, with a note in the margin of Diophantus' "Arithmetica", Pierre de Fermat stated that Diophantine equations of the Pythagorean form, x[superscript n] + y[superscript n] = z[superscript n], have no integer solutions for n > 2, and (x, y, z) > 0. Of this statement, however, Fermat…

The purpose of this study was to explore the paths by which word-problem intervention, with versus without embedded prealgebraic reasoning instruction, improved word-problem performance. Students with mathematics difficulty (MD; n = 304) were randomly assigned to a business-as-usual condition or 1 of 2 variants of word-problem intervention. The…

Research on mathematical problem solving has a long tradition: retracing its fascinating story sheds light on its intricacies and, therefore, on its needs. When we analyze this impressive literature, a critical issue emerges clearly, namely, the presence of words and expressions having many and sometimes opposite meanings. Significant examples are…

This study compared the problem-solving abilities of ChatGPT and 58 pre-service teachers (PSTs) in solving a mathematical word problem using various strategies. PSTs were asked to solve a problem individually. Data was collected from PSTs' submitted assignments, and their problem-solving strategies were analyzed. ChatGPT was also given the same…

Several studies have shown that children do not only erroneously use additive reasoning in proportional word problems, but also erroneously use proportional reasoning in additive word problems. Traditionally, these errors were contributed to a lack of calculation and discrimination skills. Recent research evidence puts forward an additional…

Despite the increasing amount of research into mathematical problem posing, research shows that much is still unknown about students' cognitive processes when engaged in problem posing. In this study, 16 undergraduate students' problem-posing products and processes are examined in order to shed light on the forms of mathematical reasoning that the…

The invention of problems is a fundamental competence that enhances the didactic-mathematical knowledge of mathematics teachers and therefore should be an objective in teacher training plans. In this paper, we revise different proposals for categorizing problem-creation activities and propose a theoretical model for problem posing that, based on…

Examples play a variety of roles in proving and disproving. Buchbinder and Zaslavsky (2019) have produced an a priori mathematical framework for assessing students' understanding of the role of examples when proving and disproving universal and existential statements. In this paper, I highlight three important aspects that suggest an extension of…

Combinatorial proofs of binomial identities involve establishing an identity by arguing that each side enumerates a certain set of outcomes. In this paper, we share results from interviews with experienced provers (mathematicians and upper-division undergraduate mathematics students) and examine one particular aspect of combinatorial proof, namely…

The transition from arithmetic to algebra in middle school can be critical for students having persistent difficulties in mathematics. The leading perception in our project is that holistic relational thinking is an effective problem-solving tool in both arithmetic and algebra. We worked in collaboration with two teachers of special classes to…

The purpose of this qualitative research is to analyze the reflective thinking process of prospective elementary teacher in numeracy problems in terms of their mathematical disposition. The subjects in this study were 26 prospective elementary school teachers who had attended elementary mathematics lectures. The focus in this research is the…

The integration of artificial intelligence (AI) into mathematical problem-solving has shown significant potential to enhance student learning and performance. However, while AI tools offer numerous benefits, they are prone to occasional conceptual and arithmetic errors that can mislead users and obscure understanding. This research examines such…