In the seventeenth century, Guarino Guarini, mathematician and architect, affirmed that architecture, a discipline that primarily deals with measures, relies on geometry: therefore, the architect needs to know at least its basic principles. On behalf of Guarini's words, we designed a set of interdisciplinary teaching experiences, between…

Ability of solving mathematical non-routine problems among Malaysian students remains at a low level, therefore there is a need to introduce a new and effective teaching strategy for the teaching and learning of mathematical problem solving. This study aims to determine the effectiveness of Mayer's problem solving Model with Visual Representation…

Visualization is an effective method for students to internalize concepts and to establish correlations between concepts. Visualization method is especially more important in mathematics which is perceived as the combination of abstract concepts. In this study, whether 6th grade students can solve questions about "Fractions" by using…

The use of planar and volumetric geometric figures in the form of didactic games and exercises, the participants in the experiment showed a significant improvement in the results of the level of spatial representation compared with the control group. The methodology of the use of didactic games and exercises with geometric figures showed the…

The goal of this paper is to present a succinct consolidation of the why, what and how of the 'Model' method as there is a lack of such documentation for researchers, practitioners and policy makers thus far. The 'Model' method is a tool for representing and visualising relationships when solving whole number arithmetic (WNA) word problems. The…

The purpose of the study is to perform a less-dimensional thorough visualization process for the purpose of determining the images of the students on the concept of angle. The Ward clustering analysis combined with Self-Organizing Neural Network Map (SOM) has been used for the dimension process. The Conceptual Understanding Tool, which consisted…

This article presents results of a research study. Sixty-one first graders' responses to interview questions about negative integer values and order and directed magnitudes were examined to characterize the students' mental models. The models reveal that initially, students overrelied on various combinations of whole-number principles as…

Misconceptions in geometry are an essential problem in the understanding of geometric terms by primary and pre-primary aged children. Present research shows some misconceptions in geometry demonstrated in the understanding of circles, squares, triangles and oblongs for children in the last year of kindergarten and pupils in the last year of…

This paper introduces a revised model for the development of basic computation skills. The model draws on four key phases, which have proven to be important for the development of calculation strategies and stresses the use of gestures and the verbalisation of concrete and mental images. This seems to be of crucial importance for children with…

Service modelling has become an increasingly important area in today's telecommunications and information systems practice. We have adapted a Network Design course in order to teach service modelling to a mixed class of both the telecommunication engineering and information systems backgrounds. An integrated approach engaging mathematics teaching…

Teachers report that engaging students in solving contextual problems is an important part of supporting student understanding of algorithms for fraction division. Meaning for whole-number operations is a crucial part of making sense of contextual problems involving rational numbers. The authors present a developed instructional sequence to…

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,…

For some students, using the method of cross sections to find the volume of a solid is difficult to understand because of the abstraction involved. This paper demonstrates a fun way for students to visualize the method of cross sections. Although a fun activity, the paper implicitly conveys the importance of connecting theory and experiment.…

The aim of the 2018 International Association for Development of the Information Society (IADIS) Cognition and Exploratory Learning in the Digital Age (CELDA) conference was to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There have been advances in both cognitive…

Function Probe is a multi-representational software for Apple Macintosh computers. It was designed to allow students to approach problems in different ways and/or use different representations. This case study describes a 16-year-old student as he creates a path among a variety of representations of transformations of functions while using the…