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…

Undergraduate students usually study Laurent series in a standard course of Complex Analysis. One of the major applications of Laurent series is the classification of isolated singular points of complex functions. Although students are able to find series representations of functions, they may struggle to understand the meaning of the behaviour of…

Reasoning is handled as a basic process skill in mathematics teaching. When the literature was examined, it was seen that many types of reasoning related to mathematics education were mentioned. In the present study, it was focused on visual reasoning, which is one of the types of reasoning and also used in different research areas. The purpose of…

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…

Within the South African school curriculum, the section on graphical functional relationships consists of signs which include symbols, notation and imagery. In a previous article we explored the role visualisation played in the way learners understood mathematical concepts. That paper reported on the learners' fixation with the physical features…

This article argues for a shift in how researchers discuss and examine students' uses of representations during their calculus problem solving. An extension of Zazkis, Dubinsky, and Dautermann's (1996) Visualization/Analysis-framework to include physical modes of reasoning is proposed. An example that details how transitions between visual,…

The role of mental representations in mathematics and computer science (for teaching or research) is often downplayed or even completely ignored. Using an ongoing work on the subject, we argue for a more systematic study and use of mental representations, to get an intuition of mathematical concepts, and also to understand and build proofs. We…

The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…

A student might find a certain representational format (e.g., diagram, text) more attractive than other formats for learning. Computer technology offers opportunities to adjust the formats used in learning environments to the preferences of individual learners. The question addressed in the current study was: does the match between a student's…

Many epistemic activities, such as spatial reasoning, sense-making, problem solving, and learning, are information-based. In the context of epistemic activities involving mathematical information, learners often use interactive 3D mathematical visualizations (MVs). However, performing such activities is not always easy. Although it is generally…

Not all children are made the same. Learning disabilities like dyslexia, dysgraphia or dyscalculia are either not understood or ignored in schools. As a result, the schoolchildren suffer for no fault of theirs and they lag behind in their course of learning. They may find it difficult to achieve the basic skills of learning such as reading,…

The paper looks into visualisation in learning mathematics from three perspectives: It starts from a discussion what it takes to make a sign, an inscription on the blackboard, on paper or on a computer screen to an image. Here we will look into the question of "similarity" and point to the possibility of having different perspectives on the same…

Presents activities to visually explore the algebraic concepts of variable, constant, the distributive property, and combining like terms. Presents four transparencies that use visual models to understand exercises in students perform the same mental calculations on a number of their choice and obtain the same result. (MDH)

One of the best ways to give students the background knowledge they need to understand math concepts is to teach them the vocabulary and comprehension skills that are essential to understanding math. So here's a book that explains how to do that and provides teachers with lots of classroom-proven ways to prepare students to be successful math…