The present study aimed to analyse the context-based problem solutions of pre-service mathematics teachers, their mathematical sentences formation skills and misconceptions. Thus, the participating pre-service mathematics teachers were asked to solve context-based problems, form mathematical sentences formation, predict misconceptions that they…

The purpose of this study was to investigate eight preservice middle and high school mathematics teachers' solution strategies when solving single and multiple proportion problems. Real-world missing-value word problems were used in an interview setting to collect information about preservice teachers' (PSTs) reasoning about proportional…

Many people consider problem solving as a complex process in which variables such as "x," "y" are used. Problems may not be solved by only using "variable." Problem solving can be rationalized and made easier using practical strategies. When especially the development of children at younger ages is considered, it is…

We address the question: How can a student's conceptual transition, from attending only to singleton units (1s) given in multiplicative situations to distinguishing composite units made of such 1s, be explained? We analyze a case study of one fourth grader (Adam, a pseudonym) during the course of a video recorded cognitive interview. Adam's case…

The purpose of the present study was to gather data regarding the implementation of Prodigy in elementary schools in a mid-sized school district in the southern United States. Prodigy is a free, adaptive mathematics game provided by Prodigy Education. The program integrates curriculum-aligned mathematics content (Grades 1-8) in a game-based…

This paper uses multimodal discourse analysis to show that discursive form, in addition to words, gestures and sound dimensions of speech, is an important linguistic resource for expressing mathematical meaning. During a collaborative task, a student spoke an insight about an algebraic property five times over a few minutes, in slightly different…

Visualisation plays a critical role in the teaching and learning of mathematics word problems. It is an essential tool for enabling learners to create meaningful mental pictures necessary for solving mathematical problems. Appropriate visualisation requires good reading skills, English proficiency and an understanding of mathematical vocabulary,…

This case study investigates how preservice primary school teachers describe their experiences with digital story-based problem solving applications and their plans for the future integration of this technology into their teaching. Totally 113 preservice primary school teachers participated in the study. Data collection tools included a…

The case study focuses on the interactional mechanisms through which online collaborative teams co-construct a shared understanding of an analytical geometry problem by using dynamic geometry representations. The collaborative study consisted of an assignment on which the learners worked together in groups to solve a ship navigation problem as…

Metacognition encompasses knowledge and regulation that, through reflection, sustain problem solving behaviour. How metacognitive awareness is constructed from reflection on metacognitive knowledge and regulation and how these reflections enable metacognitive skills for Mathematics problem solving remain unclear. Three secondary schools…

In this study, ways in which 9-year old students from one Singapore school solved 1-step and 2-step word problems based on the three semantic structures were examined. The students' work and diagrams provided insights into the range of errors in word problem solving for 1- step and 2-step word problems. In particular, the errors provided some…

Although well-designed scaffolding may assist students to accomplish learning tasks, its insufficient capability to dynamically assess students' abilities and to adaptively support them may result in the problem of overscaffolding. Our previous project has also shown that students using scaffolds to solve mathematical word problems for a long time…

Reform efforts in mathematics education arose, in part, in response to constructivist works on conceptual learning. However, little research has examined how students with learning disabilities (LD) respond to constructivist-oriented instruction in mathematics, particularly in moment-to-moment interactions. To understand the nature of…

This qualitative research study used a multiple, holistic case study approach (Yin, 2009) to explore the perceptions of reluctant problem solvers related to mathematical tasks without words and word problems. Participants were given a choice of working a mathematical task without words or a word problem during four problem-solving sessions. Data…

Being told procedures and concepts before problem solving can inadvertently undermine the learning of deep structures in physics. If students do not learn the underlying structure of physical phenomena, they will exhibit poor transfer. Two studies on teaching physics to adolescents compared the effects of "telling" students before and after…