The number of e-learning platforms and blended learning environments is continuously increasing and has sparked a lot of research around improvements of educational processes. Here, the ability to accurately predict student performance plays a vital role. Previous studies commonly focused on the construction of predictors tailored to a formal…

This study presents part of a research project that aims to develop prospective mathematics teachers' Technological Pedagogical Content Knowledge (TPCK). The project considers various TPCK components. This report focuses on a particular component, namely the "knowledge of using multiple representations (MRs) with technology". A course…

It is common for both algebra and calculus instructors to use power functions of various degrees as well as exponential functions to examine and compare rates of growth. This can be done on a chalkboard, with a graphing calculator, or with a spreadsheet. Instructors often are careful to connect the symbolic and graphical (and occasionally the…

This case study describes an "out of field" teacher's use of the Internet to teach a range of mathematical topics in a modified Year 8 mathematics class. It highlights the importance of three factors for implementing a discernible web-based teaching strategy: appropriate choice of web objects, effective "virtual" pedagogy, and technical support…

More and more things that humans used to do can be automated on computer. In each case, complex tasks have been automated -- not to the extent that they can be done as well as humans, but better. I will draw and develop parallels to education -- showing how and why advances in the Structural Learning Theory (SLT) and the AuthorIT development and…

Adult developmental mathematics students often work under great pressure to complete the mathematics sequences designed to help them achieve success (Bryk & Treisman, 2010). Results of a teaching experiment demonstrate how the ability to reason can be impeded by flaws in students' mental representations of mathematics. The earnestness of the…

In this paper, we consider theories about processes of visual perception and perception-based knowledge representation (VPR) in order to explain difficulties encountered in figural processing in junior high school geometry tasks. In order to analyze such difficulties, we take advantage of the following perspectives of VPR: (1) Perceptual…

Current technologies incorporating sophisticated mathematical analysis software (calculation, graphing, dynamic geometry, tables, and more) provide easy access to multiple representations of mathematical problems. Realising the affordances of such technology for students' learning requires carefully designed lessons. This paper reports on design…

Manipulatives have been used in many mathematics classrooms across many age groups with the aim of helping students to understand abstract concepts through concrete, kinesthetic, and visual experiences. In this paper, after we provide a background for the use of physical and virtual manipulatives in teaching and learning of mathematics, we will…

Assigning difficulty level indicators to the knowledge units helps the learners plan their learning activities more efficiently. This paper focuses on how to use the topology of a knowledge map to compute and rank the difficulty levels of knowledge units. Firstly, the authors present the hierarchical structure and properties of the knowledge map.…

This article reflects on the author's experience in teaching courses in mathematics content and methods in teacher preparation programs. It shows how technology-enhanced inquiry into a seemingly mundane task on situated addition found in a popular textbook for prospective elementary teachers, can reveal hidden properties of integers associated…

This article describes a mathematics session in which students explored a challenging combinatorics task, a topic shown to be difficult for students when taught traditionally. The students developed a progression of personal representations, increasingly symbolic and abstract, which they used to find a solution and justification. (Contains 8…

This paper reports on a case-study design experiment in the domain of fraction as number-measure. We designed and implemented a set of exploratory tasks concerning comparison and ordering of fractions as well as operations with fractions. Two groups of 12-year-old students worked collaboratively using paper and pencil as well as a specially…

Summarizes theoretical and empirical aspects of research that is investigating how best to support conceptual learning and the critical role that representations have in complex scientific and mathematical domains. Explains Law Encoding Diagrams (LEDs) and considers how computers may further enhance the potential benefit of LEDs for conceptual…

Analyzes students' representations of fractions as they work on fraction comparison tasks and justify their solutions in a collective classroom activity. Emphasizes the importance of setting a problematic situation and encouraging students to make various representations for their learning. Suggests some implications for teacher activities and…