This research aims to increase our understanding about the effects of active learning, applying problem-based learning (PBL) methodologies to increase student motivation in various graphic engineering classes. The measurement instruments included a cross-sectional survey (n = 269) carried out during the years 2015 to 2019 through triangulation of…

Geometrography, "alias the art of geometric constructions" was proposed by Emile Lemoine between the late 1800s and the early 1900s. It consisted originally of a system to measure the complexity of ruler-and-compass geometric constructions, capable of: designate every geometric construction by a pair of values that manifests its…

The regular pentagon had a symbolic meaning in the Pythagorean and Platonic philosophies and a subsequent important role in Western thought, appearing also in arts and architecture. A property of regular pentagons, which was probably discovered by the Pythagoreans, is that the ratio between the diagonal and the side of these pentagons is equal to…

Building from the evidence-based learning progression in geometric reasoning from the RMFII project, this paper presents data from students' solutions to three problems in geometry and measurement situations to identify key components needed to nurture reasoning. To show emerging analytical reasoning students must coordinate multiple pieces of…

Manipulation of physical models such as tangrams and tiles is a popular approach to teaching early mathematics concepts. This pedagogical approach is extended by new computational media, where mathematical entities such as equations and vectors can be virtually manipulated. The cognitive and neural mechanisms supporting such manipulation-based…

We asked: "What are the similarities and differences in mathematical processing associated with solving learning-based and insight-based problems?" To answer this question, the ERP research procedure was employed with 69 male adolescent subjects who solved specially designed insight-based and learning-based tests. Solutions of…

Geometry students have few opportunities to apply geometric concepts and solve geometry problems in authentic contexts. We developed a Ubiquitous Geometry (UG) system to teach geometry to elementary students by using it to measure common objects in authentic contexts. The instant study investigates the effects of UG on student geometry estimation…

Students' difficulties in mathematics and science may stem from interference of irrelevant salient variables. We focus on the comparison of perimeters task, in which area is the irrelevant salient variable. A previous fMRI brain-imaging study related to the comparison of perimeters task suggested that increasing the level of salience of the…

This study investigated the effect of van Hiele Phase-based Instruction (VHPI) on Ghanaian Pre-service Teachers' (PTs') geometric thinking in terms of the van Hiele Levels. A pre-test post-test quasi-experimental design was employed. There were 75 PTs each in the experimental group and the control group. Van Hiele Geometry Test (VHGT) was…

This study examined the effectiveness of 3 curriculum interventions focused on strengthening children's ability to solve area measurement problems and explored the instructional perspectives of the instructor who implemented the interventions. The interventions involved various degrees of emphasis on area measurement and knowledge of 2-dimensional…

In this paper we report the results obtained when implementing Activities related to the visualization of geometric representations in paper-and-pencil and technological environments with students1 grade 11. This is a qualitative research supported by both the representation theory and the visualization of mathematical objects using technological…

Problem solving in the field of quantitative composition of solutions (QCS), expressed as mass share and molar concentration, is essential for chemistry students. Since successful chemistry education is based on different mathematical contents, it is important to be proficient in both mathematical and chemistry concepts as well as interconnections…

The purpose of this research is to develop a hands-on spatial geometry learning system to facilitate the learning of geometry. The development of this system was based on Duval's four critical elements of geometric learning: perceptual apprehension, sequential apprehension, operative apprehension, and discursive apprehension. The system offers…

In this study, the effectiveness of worked examples that emphasizes problem features (data type, number of groups, purpose of analysis) associated with specific problem types (t-test, chi-square, correlation) were examined on students' construction of problem schemata compared to traditional solution-only worked examples. A sample of 96 students…

A fundamental question in human cognition is how people reason about space. We use a computational model to explore cross-cultural commonalities and differences in spatial cognition. Our model is based upon two hypotheses: (1) the structure-mapping model of analogy can explain the visual comparisons used in spatial reasoning; and (2) qualitative,…