A new classification for semantic structures of one-step word problems is proposed in this paper. The classification is based on illustrations of word problem situations in Common Core State Standards (CCSSM, 2010) and related historical studies (e.g. Weaver, 1973, 1979, 1982), as well as conceptual elaborations of embodied and grounded nature in…

Students with learning disabilities/difficulties in mathematics often apply ineffective procedures to solve word problems. Given that current mathematics curriculum standards emphasize conceptual understanding in problem solving as well as higher-order thinking and reasoning, the purpose of this study was to evaluate the impact of a model-based…

This study aimed to evaluate the effectiveness of a remedial teaching intervention in improving learners' understanding of trigonometric equations. Using a mixed methods exploratory case study design, a purposive sample of 24 Grade 11 learners from a rural school in the Eastern Cape province participated in the intervention. The research involved…

Duncan Symons and Derek Holton discuss the different types of mathematical reasoning and what each of these might look like in the classroom. By suggesting language that can be used to describe the different methods of reasoning, they hope to provide teachers with the tools they need to better recognise and assess student reasoning.

The beginning of the school year is a time of intense work for students and teachers, especially if it means learning mathematics in new ways (Ruef 2016). Students need guidance and support if they are shifting beliefs about what it means to do mathematics. This article shows how Torres and her students co-created new ways to be good at…

The hammer-and-nail phenomenon highlights human tendency to approach a problem using a tool with which one is familiar instead of analyzing the problem. Pedagogical suggestions are offered to help students minimize their mathematical impulsivity, cultivate an analytic disposition, and develop conceptual understanding.

Any effort to integrate problem-posing instruction in school mathematics must attend to teachers' beliefs about the advantages of teaching through problem posing and especially their beliefs about the challenges of teaching in this way. This study investigated teachers who were learning how to teach mathematics through problem posing. The primary…

In educational research, the cognitive activity of problem posing is recognized as an important component of mathematics teaching and learning. Compared to the prevailing educational paradigm of problem solving, problem posing features less commonly in classroom instruction. During the past 20 years, numerous studies examining the use of problem…

The research literature on middle grades mathematics teachers' mathematical literacy indicates that mathematical problem solving and problem posing are essential skills for mathematics instruction, and that teachers must be skilled in mathematical problem solving and mathematical problem posing. However, it is not well known how these two skills…

Often, mathematics teachers do not incorporate whole-class discourse of students' various ideas and solution methods into their teaching practice. Particularly complex is the in-the-moment decision-making that is necessary to build on students' thinking and develop their collective construction of mathematics. This study explores the…

Non-digital games are a tool that can help children to build and improve problem solving skills in early mathematics learning. Teachers need to design a learning activity using non-digital games taken account problem solving skills in the learning activities. However, the application of problemsolving skills in early mathematics learning…

Research has shown assistance can provide many benefits to novices lacking the mental models needed for problem solving in a new domain. However, varying approaches to assistance, such as subgoals and next-step hints, have been implemented with mixed results. Next-Step hints are common in data-driven tutors due to their straightforward generation…

Existing computational thinking (CT) research focuses on programming in K-12 education; however, there are challenges in introducing it into the formal disciplines. Therefore, we propose the introduction of non-programming plugged learning in mathematics to develop students' CT. The research and teaching teams collaborated to develop an…

Problem solving has been the focus of the Common Core State Standards for Mathematical Practice. Helping students acquire critical-thinking and problem-solving skills has become the primary goal of mathematics education across all grade levels. However, research has found that many students struggle with word problems because of poor text…

Students often look to the standard algorithm, which requires rewriting the task, regrouping tens to create enough ones to subtract, and other opportunities to make errors. However, when the authors apply structural thinking, the resultant strategy is an efficient and elegant shortcut and even brings a positive connotation to the word…