Algebra problem solving is one of the most difficult areas in the mathematics curriculum for secondary students with learning disabilities (LD) due to the higher-order reasoning demands and strategic thinking required. The purpose of this review is to examine how effective algebra problem-solving interventions conceptualize the cognitive processes…

We describe how a group of secondary mathematics teachers posed and solved a real-world problem. The problem was posed by teachers on a sandbar off the coast of an island in the Bahamas, where panoramic views of water meeting sky spurred the teachers to wonder how far away they could see. We analyze how the teachers translated the natural…

Capturing the breadth and variety of children's understanding is critical if studies of children's mathematical thinking are to inform policy and practice in early childhood education. This article presents an investigation of young children's counting. Detailed coding and analyses of assessment interviews with 476 preschoolers revealed…

Patterns pervade our everyday life and are natural and familiar to children. Exciting new research in the field of Early Algebra describes the development of young children's algebraic thinking through the meaningful study of patterns. This paper contributes to this research by reporting on a case study of two primary schools in South Africa and…

A relative extrema optimization problem is one in which the domain of the objective function (i.e. the function whose maximum or minimum value is to be found) is an open interval. An absolute extrema optimization problem is one in which the domain of the objective function is a closed interval. Analysis of task-based interviews conducted with 12…

In this piece, I recount some events in which I was called upon to speak in te reo Ma ori on behalf of others in a variety of formal situations. I call this being 'on the paepae' but the paepae should be understood more properly as the paepae tapu. I will leave the further explanation of this for others who should rightly speak about such things.…

High school students often ask questions about the nature of infinity. When contemplating what the "largest number" is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of mathematical sets, or "set…

Focused reflection is teacher directed professional learning that uses ongoing formative assessment aligned with research-based instructional practices and standards. It allows teachers to operate as researchers and hold themselves accountable for what they are teaching and what students are learning. This article provides a table that outlines…

Teaching quantitative methods at the undergraduate level is a difficult yet rewarding endeavor due to the challenges instructors face in presenting the material. One way to bolster student learning is through the use of statistical software packages. Google Sheets is a cloud-based spreadsheet program capable of many basic statistical procedures,…

Students' ability to reason for themselves is a crucial step in developing conceptual understandings of mathematics, especially if those students are preservice teachers. Even if classroom environments are structured to promote students' reasoning and sense-making, students may rely on prior procedural knowledge to justify their mathematical…

The aim of this study is to determine the effect of the emotion "happy" as induced by colors on the addition performance of grade 1 pupils. The experiment involved the pupils in the experimental group (n=80) were taught addition, using modules developed by the researcher which utilized seductive augmentation of learning materials through…

Both the Common Core State Standards (CCSSI 2010) and the NCTM Process and Content Standards distinguish between Standards for Mathematical Practice (SMP) and standards for mathematical content. We believe this distinction is important and note that students often acquire knowledge of mathematical content without necessarily developing the related…

Ever try to captivate students with real-world applications only to discover that they live in a very different world? Assigning an Extreme Word Problem activity to students alleviates this dilemma by placing the authorship of a problem squarely into the hands of learners. Rather than trying to be hip and finding word problems that resonate with…

The present study aims to investigate the effectiveness of Research Based Learning (RBL) in improving students' learning achievement in solving two dimensional arithmetic sequence problems. The study applied triangulation method including qualitative and quantitative methods. The research subjects were 4th-semester students of higher education.…

The purpose of this analysis was to assess whether effects of first-grade mathematics intervention apply across the range of at-risk learners' initial skill levels. Students were randomly assigned to control (n = 213) and two variants of intervention (n = 385) designed to improve arithmetic. Of each 30-minute intervention session (48 over 16…