Ratios and proportions are new topics in the primary curriculum. Previous research shows that Year Five pupils have difficulty in learning ratio and proportion. This study aims to identify the conceptions of ratio and proportion of seven year five pupils. It is based on radical constructivism using qualitative case study. Data was collected…

The aim of this study is to examine the concept images of mathematics educators and pre-service elementary mathematics teachers regarding the relationships between the concepts of slope, rate of change and derivative. Four mathematics educators working in different state universities and responsible for Analysis courses, three pre-service…

The aim of this research was to explore the mathematical connections that pre-university students make when they sketch the graph of a derivative function and an antiderivative function. Also, we tried to explain the origin of the mathematical connections identified. We assume mathematical connections as a cognitive process through which a person…

In the same chapter of his book "Opera Geometrica," Torricelli published two discoveries: 1) initial velocity of a jet from a container increases with the square root of the depth of the hole; 2) he drew the pattern of jets from three openings at the wall of a container filled with water to constant level "H" and determined the…

In this research, a new test for understanding simple fractions has been developed for students at the beginning of lower secondary education. In many countries, mathematics education in Grade 5 builds on elementary students' developing concepts of fractions. Understanding fractions causes many difficulties for students, and research on mental…

The visual method in this paper solves linear inequalities in one variable by considering them initially as two competing linear expressions, each of which is then expressed as a linear equation. When the solution of these two linear equations exist, it is viewed as a highlighted area or a line. These linear equations convey the intended visual…

In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the "philosophy of mathematical practice." In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice…

Teachers whose mathematical meanings support understanding across different contexts are likely to convey them in productive ways for coherent student learning. This exploratory study sought to elicit 67 secondary mathematics pre-service teachers' (PSTs) meanings for quadratics with growing pattern creation and multiple translation tasks. A…

This article shares two activities geared toward students in middle school that engage students in analyzing measures of center, specifically the arithmetic mean, and using transnumerative thinking with the ultimate goal of improving students' statistical literacy. Both activities support the Common Core standard, 6.SP.B.5 "Summarize and…

A pretest-training-posttest design assessed whether training to improve spatial skills also improved mathematics performance in elementary-aged children. First grade students (mean age = 7 years, n = 134) and sixth grade students (mean age = 12 years, n = 124) completed training in 1 of 2 spatial skills--spatial visualization or form…

Young children are capable of engaging with ratio, measurement and operator meanings of fractions earlier than many national curriculum standards indicate, yet current trends in children's understanding of fractions in Australia, remain weak. Research suggests that spatial reasoning can positively influence mathematical knowledge; however, the…

This work refers to a research project named 'Math walks', whose aim is to investigate a few students' common conceptions and difficulties related to symmetries as well as to guide the student in the transition from visualization to conceptualization. As far as this issue is concerned, we designed a learning activity (LA) according to Dina van…

A key aspect of young children's development of algebraic reasoning is the process of visualising and identifying structures to both abstract and generalise. There has been a growing body of research focused on how students form generalisations, this article adds to the existing body of research by examining how young culturally diverse students…

Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with…

A pretest-training-posttest design assessed whether training to improve spatial skills also improved mathematics performance in elementary-aged children. First grade students (mean age = 7 years, n = 134) and sixth grade students (mean age = 12 years, n = 124) completed training in 1 of 2 spatial skills-spatial visualization or form…