In this research study, an instructional intervention protocol is described. This intervention was designed to help teachers to engage English Learner students (ELs) in mathematical problem-solving lessons and reasoning through discourse. The "Discursive Mathematics Protocol" (DMP) integrates Polya's classic problem-solving framework and…

This study used a holistic multi-case research design to investigate fourth-grade students' skills for solving non-routine mathematics problems. The participants were three 4th grade students (primary school) with low, moderate and high achievement in mathematics respectively, who were educated in the same class at a state school of middle…

In classroom learning, students need mathematical cognitive flexibility to be able to solve mathematical problems with the various ideas they express. To solve the problems, they must be able to grasp the problem, see it from various points of view, and should not be rigid thinking with one solving method. In fact, the students still lack the…

The theme that structure determines function is one of the most significant cornerstones in understanding natural sciences. On the other hand, recently revised science curriculum in Turkey has emphasized science and engineering practices to help students be able to converge science with the other disciplines by applying theory into practice and…

The aim of this study is to investigate both the planning and implementation process of a modelling task by a middle school mathematics teacher. The participant of the study, which was conducted as a single case study, is a middle school mathematics teacher who have knowledge and experience in modelling. The data collecting tools of this study…

Research in computer-based learning environments has long recognized the vital role of adaptivity in promoting effective, individualized learning among students. Adaptive scaffolding capabilities are particularly important in open-ended learning environments, which provide students with opportunities for solving authentic and complex problems, and…

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…

In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis…

This article reports on elementary students' understanding of time in the context of common classroom manipulatives and notational systems. Students in Grades 2 (n = 72) and 4 (n = 72) participated in problem-solving interviews involving different clocks. Quantitative results revealed that students' performances were significantly different as a…

This article highlights the main ideas that underlie the differences in potential pragmatic knowledge constructs students experience when solving problems, between the zone of proximal development (ZPD) and the zone of potential construction (ZPC). This qualitative research is based on a phenomenological approach to finding the meaning of things…

This study aims to investigate a mathematical-metacognitive discourse model with IMPROVE metacognitive self-question prompts (What, How/When, and Why) in order to promote a deeper level of discourse in mathematics classes. The study involved 32 math teachers and 824 fifth-grade students (from 32 public schools) from one district in Israel.…

A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a "Modelling" conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity,…

Highly capable mathematics students are not usually considered strugglers. This paper reports on a case study of a Year 6 student, Debbie, her response to a lesson, and her learning involving a challenging mathematical task. Debbie, usually a highly capable student, struggled to complete a challenging mathematical task by herself, but as the…

The purpose of this case study was to improve the reading accuracy and reading comprehension of a 10-year-old fourth-grade female student with reading difficulties. For that purpose, the problem- solving model was implemented in four stages. These stages included problem identification, problem analysis, intervention, and evaluation. During the…

The underperformance of South African learners in literacy and numeracy is a cause of concern, especially at the transition from Grade 3 to Grade 4. At Grade 4 in South Africa, the majority of learners begin learning in English, which to them is an additional language posing transition challenges of a linguistic nature. The sustained poor…