REL Southeast developed this facilitator's guide on the topic of mathematical problem solving for use in professional learning community (PLC) settings. The facilitator's guide is a set of professional development materials designed to supplement the What Works Clearinghouse practice guide, Improving Mathematical Problem Solving in Grades 4…

If an organic chemistry student explains that she represents a mechanistic step because ''it's a productive part of the mechanism,'' what meaning could the professor teaching the class attribute to this statement, what is actually communicated, and what does it mean for the student? The professor might think that the explanation is based on…

The purpose of this study is to determine the impact of heuristic strategy on students' mathematical abilities in high order thinking. This descriptive research uses a correlation design. The population of this study were all second-grade public and private high school students representing schools from eight districts in North Sumatra province,…

Proportional relationships and geometric similarity are two of the critical topics in school mathematics. Students and even teachers often struggle with recognizing the proportional relationships in geometric similarity problems. The purpose of this study was to investigate preservice middle-grades mathematics teachers' (PSTs) strategies when…

Vygotsky measured his 'zone of proximal development' in years. To do this, he needed a scheme of age periods, and a set of tasks that could diagnose the next age period without defining it. In this paper, we compare the age periods in his late lectures with Halliday's categories of logico-semantic expansion as used by three adolescent…

Implementing an integrated sequence of concrete-representational-abstract depictions of mathematics concepts (CRA-I) can improve the mathematics achievement of students with disabilities, and explicit instructional strategies involving problem-solving heuristics and student verbalizations can help facilitate students' conceptual understanding of…

Teachers and students commonly use various concrete representations during mathematical instruction. These representations can be utilized to help students understand mathematical concepts and processes, increase flexibility of thinking, facilitate problem solving, and reduce anxiety while doing mathematics. Unfortunately, the manner in which some…

This study examined how a child constructed a scheme (abbreviated QRE) for producing mathematical equivalence via operations on composite units between two multiplicative situations consisting of singletons and composite units. Within the context of a teaching experiment, the work of one child, Joe, was analyzed over the course of 14 teaching…

Based on the findings of a larger study on middle school students' problem solving behaviors, we identified three sub-components for understanding the iteration of unit area in this paper: the mechanism of iteration, an identical unit, and the specificity of the identical unit. A three-stage progression on the acquisition of these components is…

Proficiency in mathematics involves the seamless synchronization of conceptual understanding, procedural knowledge, computational fluency, and problem solving (NMAP, 2008). Clearly, fluency with mathematics facts is one element embedded within mathematical proficiency and important for students with disabilities to develop. As more and more…

This article explains how high-stakes standardised tests are distorting primary school mathematics and failing to promote pupils' cognitive development. It argues for observation and journaling for both formative and summative assessment in order to recover an emphasis on reflective mathematical understanding and problem-solving.

This article reports analysis of students' written reflections as to what helps them learn in an active learning environment. Eight hundred and twenty seven responses from 403 students in four different studio courses over two years were analyzed. An emergent coding scheme identified 55% of the responses as associated with cognitive processes…

Self-efficacy represents an individual's belief that he or she can perform a particular task in a given domain. It is a strong predictor for performance and persistence in STEM education. Research shows that there is a large and persistent gender gap in student self-efficacy in STEM academic disciplines. In some cases, active teaching strategies…

This study tested the hypothesis that exploratory learning, with and without analogous problems, would improve students' ability to make connections between conceptually-related topics. In this randomized experiment, undergraduates in introductory physics (N = 171) studied a new topic under three different instructional conditions. Order and type…

Scaffolding is defined as help that can assist students to solve problems or understand concepts that were not able to complete independently. In modern times, the concept of technology-based Scaffolding in learning has developed. In this study an educational game called "Telolet" was designed with the aim of providing Scaffolding to…