The present study aims to examine mathematical creativity in students' work in geometry. Research conducted was based on two aspects: (a) examining the influence of geometrical figure apprehension on the production of multiple solutions and (b) how the necessity to construct auxiliary lines in the given shape promotes the production of multiple…

This study takes a closer look at Form Four students' initial mathematical modelling process when solving mathematical problems using GeoGebra. The modelling process was observed from cognitive perspective to learn the difficulties students faced during the process and the result would give ideas for intervention. Qualitative approach by using…

Collaborative gestures in the mathematics classroom occur when multiple learners coordinate their bodies in concert to accomplish mathematical goals. Collaborative gestures show how cognition becomes distributed across a system of dynamic agents, allowing for members of groups of students to act and gesture as one. We explore ways high school…

Background: Spatial skills have been linked to better performance in mathematics. Aim The purpose of this study was to examine the relationship between teacher spatial skills and their instruction, including teacher content and pedagogical knowledge, use of pictorial representations, and use of gestures during geometry instruction. Sample:…

We develop a theory of grounded and embodied mathematical cognition (GEMC) that draws on action-cognition transduction for advancing understanding of how the body can support mathematical reasoning. GEMC proposes that participants' actions serve as inputs capable of driving the cognition-action system toward associated cognitive states. This…

This study highlights the importance of cognition-affect interaction pathways in the construction of mathematical knowledge. Scientific output demands further research on the conceptual structure underlying such interaction aimed at coping with the high complexity of its interpretation. The paper discusses the effectiveness of using a dynamic…

We conducted an intervention-based study in secondary classrooms to explore whether the use of geometric transformations can help improve students' ability in constructing auxiliary lines to solve geometric proof problems, especially high-level cognitive problems. A pre- and post-test quasi-experimental design was employed. The participants were…

The aim of the study is to conceptualize the technology-aided mathematical modelling process in the frame of cognitive modelling perspective. The grounded theory approach was adopted in the study. The research was conducted with seven groups consisting of nineteen prospective mathematics teachers. The data were collected from the video records of…

What is it that makes learners "think"? What geometrical problem, simply posed, can switch on the thinking processes of students? The author describes one such starting point that worked in a real classroom with Year 9 students. A group of learners for whom "mathematics comes easy" experience being stuck, they learn to handle this unfamiliar…

This study explores the effects of the "presence of external representations of a mathematical object" (ERs) on problem solving performance associated with short double-choice problems. The problems were borrowed from secondary school algebra and geometry, and the ERs were either formulas, graphs of functions, or drawings of geometric…

We examined geometric calculation with number tasks used within a unit of geometry instruction in a Taiwanese classroom, identifying the source of each task used in classroom instruction and analyzing the cognitive complexity of each task with respect to 2 distinct features: diagram complexity and problem-solving complexity. We found that…

Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After…

The present study investigated (a) whether the perceived cognitive load was different when geometry problems with various levels of configuration comprehension were solved and (b) whether eye movements in comprehending geometry problems showed sources of cognitive loads. In the first investigation, three characteristics of geometry configurations…

This study analyzed treatment of geometric transformations in presently available middle grades (6, 7, 8) student mathematics textbooks. Fourteen textbooks from four widely used textbook series were evaluated: two mainline publisher series, Pearson (Prentice Hall) and Glencoe (Math Connects); one National Science Foundation (NSF) funded curriculum…

Technology use and a focus on 21st century skills, coupled with recent adoption of Common Core State Standards for Mathematics, marks a new challenge for mathematics teachers. Communication, discourse, and tools for enhancing discourse (NCTM, 1991, 2000) play an integral role in successful implementation of technology and mathematics standards.…