Learners in general struggle when working with word problems. South African learners in particular have an added barrier owing to the many official languages that have been legislated. The South African Department of Basic Education, through its curriculum statements, envisages that problem solving will play a fundamental part in mathematics…

The study aims to define the processes of pre-service mathematics teachers in reaching spatial visualisation generalisations within the context of drawing surface nets of solids. Two theories, Polya's problem-solving steps and novice-to-expert problem-solving schemas, were used as reference frameworks to describe the participants' spatial…

In the context of a multiplicative problem, our study investigated young children's ability to visualise and draw equal groups. This paper reports the results obtained from 18 Australian children in their first year of school (age 5-6 years). The task "12 Little Ducks," taught by their classroom teacher, provoked children to visualise…

Since middle school is a critical time for literacy learning in general and comprehension in particular, educators are left to ponder how best to teach these students. In addition, what role might student perception of reading strategies through visual depictions have in order to help teachers decide how best to guide their students with…

The cognition processes of students with autism spectrum disorder (ASD) in solving mathematical problems is still rarely studied in depth, although the prevalence of the students is increasing. The purpose of this research was to describe the cognition processes of students with ASD in solving mathematical problems. The subjects in this research…

The study was designed to assess the effectiveness of an alternative teaching approach strategy called the Hybrid Strategy. It was intended specifically in minimising the common errors made by students, which were Comprehension and Transformation errors, and aimed at helping students to perceive word problems as a story line to be completed using…

In this research, we gave to technical university students (N=50) and high school students (N=75) a verbally described situation of a partially defined physics problem. The task for the both groups of the students was to generate drawings of how they imagined the situation that the problem referred to. A fully abstract drawing was generated by 48%…

This account of practice describes how a manufacturing company in the North of England transformed their approach to problem-solving and action through the use of a Critical Reflection Action Learning (CRAL) methodology. The company, who had been in business for over 25 years, experienced problems due to a diminishing customer base and substantial…

This paper explores young children's drawings (6 years old) in early number and addition activities in Malaysia. Observation, informal interviews and analysis of drawings revealed two types of drawing, and gave insight into the transitional process required for children to utilise drawings in problem solving. We argue the importance of valuing and…

Non-routine word problem solving is an essential feature of the mathematical development of elementary school students worldwide. Many students experience difficulties in solving these problems due to erroneous problem comprehension. These difficulties could be alleviated by instructing students how to use visual representations that clarify the…

This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This…

Enabling learning through meaningful classroom experiences has always been a challenge for teachers. Bringing about a balance of the "conceptual" and the "hands-on", along with contextual embeddedness in problem-solving situations, broadly characterises the experience of development and trials of three Design and Technology…

Research (Fish, 2004) suggests that everybody should be taught how to freehand sketch and utilise it as a tool for supporting the visualising instinct. A fundamental shift in philosophy of the technology education system in Ireland towards design driven subjects brought with it a need to develop practising teacher's technological capabilities.…

The purpose of this study was to determine whether or not the use of solid modeling software increases participants' success in solving a specified technical problem and how visualization affects their ability to solve a technical problem. Specifically, the study sought to determine if (a) students' visualization skills affect their problem…

As the result of a qualitative investigation into spatial ability, a teaching technique called mentored sketching was found to be effective for teaching visualization skills to freshman engineering students. This contribution describes the technique, how it evolved, and comments made by students as to its effectiveness. While mentored sketching…