Mathematical reasoning, a fundamental aspect of human cognition, poses significant challenges for artificial intelligence (AI) systems. Despite recent advancements in natural language processing (NLP) and large language models (LLMs), AI's ability to replicate human-like reasoning, generalization, and efficiency remains an ongoing research…

Conceptual model-based problem solving (COMPS) was tested for its efficacy in teaching a student diagnosed with autism spectrum disorder to solve word problems involving multiplication and division. A single-case, multiple-baseline across behaviors design was conducted. The ability to solve each of three types of multiplication problems examined…

A growing body of literature supports the effectiveness of Modified Schema-Based Instruction (MSBI) to improve mathematical problem-solving for students with autism spectrum disorder (ASD) and intellectual disability (ID). MSBI is an intervention package that teaches students to identify the problem structure and use a problem-solving heuristic to…

In this study, the author examined student attempts to translate a verbal problem into an algebraic statement relating two variables, after they had solved an arithmetic question from the same problem. A total of 645 students from New England (U.S.A.) answered the problem on a mathematics assessment administered at the beginning of the school…

Mathematics is an important but also under-explored area of education for students with disabilities, including middle school students with intellectual and other developmental disabilities. In this study, researchers taught middle school students with intellectual and developmental disabilities (IDD) to solve word problems grounded in life skills…

We conducted a comprehensive synthesis of computer-assisted instruction (CAI) research that aimed to facilitate the learning of mathematical word problem solving involving elementary and secondary school students with learning disabilities or difficulties in mathematics. We examined a total of 13 studies under the four instructional categories:…

The Common Core State Standards for Mathematics highlight the importance of not only content standards for mathematics but also mathematical practices such as communication, representation, and reasoning, skills that are often difficult for students with autism spectrum disorder (ASD). Through a single-case multiple-probe-across-participants…

The purpose of this study was to evaluate the effect of a multicomponent mathematics intervention (modified schema-based instruction, video anchors, and goal setting with self-graphing) on mathematical problem-solving skills of secondary students with intellectual and developmental disabilities. Three participants were taught to solve percent of…

In this article, Scott Smith presents an innocent problem (Problem 12 of the May 2001 Calendar from "Mathematics Teacher" ("MT" May 2001, vol. 94, no. 5, p. 384) that was transformed by several timely "what if?" questions into a rewarding investigation of some interesting mathematics. These investigations led to two…

There is a need to teach the pivotal skill of mathematical problem solving to students with severe disabilities, moving beyond basic skills like computation to higher level thinking skills. Problem solving is emphasized as a Standard for Mathematical Practice in the Common Core State Standards across grade levels. This article describes a…

This article presents "The Two Children Problem," published by Martin Gardner, who wrote a famous and widely-read math puzzle column in the magazine "Scientific American," and a problem presented by puzzler Gary Foshee. This paper explains the paradox of Problems 2 and 3 and many other variations of the theme. Then the authors…

The No Child Left Behind Act (NCLB, 2006) set a precedent that established even higher expectations for all students, including those with disabilities. More recently, the National Governors Association Center for Best Practices and the Council of Chief State School Officers developed a common set of state standards for proficiency in English…

Mathematics can be a difficult topic both to teach and to learn. Word problems specifically can be difficult for students with disabilities because they have to conceptualize what the problem is asking for, and they must perform the correct operation accurately. Current trends in mathematics instruction stem from the National Council of Teachers…

The authors' purpose was to determine the effects of computer-based practice and conceptual interventions on computational fluency and word-problem solving of fourth- and fifth-grade students with mathematics difficulties. A randomized pretest-posttest control group design found that students assigned to the computer-based practice intervention…

The purpose of this study was to describe elementary preservice teachers' difficulties with understanding algebraic generalizations that were set in an authentic context. Fifty-eight preservice teachers enrolled in an elementary mathematics methods course participated in the study. These students explored and practiced with authentic, hands-on…