This research investigates errors and misconceptions among learners in algebraic education by utilizing Koch's error analysis method alongside the Structure of the Observed Learning Outcome (SOLO) taxonomy. The primary aim of the investigation is to discern the kinds of errors and cognitive stages demonstrated by Grade 9 students when engaged in…

This study aims to examine the relation between spatial ability and creativity in Geometry. Data was collected from 94 ninth graders. Three spatial abilities were investigated: spatial visualization, spatial relations and closure flexibility. As for students' creativity, it was examined through a multiple solution problem in Geometry focusing on…

Sixty (35 girls) ninth graders were assessed on measures of algebraic reasoning and usage of visual and symbolic representations (with a prompt for visual use) to solve equations and inequalities. The study grouped visual representations into two categories: arithmetic-visual, which entailed the use of real-world objects to represent specific…

This study was conducted to examine whether newly enrolled 9th grade students were ready to directly engage in the theoretical discursive process from the perspective of Duval's Cognitive Model. The sample of the study was comprised of 51 newly enrolled 9th grade students between the ages of 14 and 15, who had not received any prior geometry…

Investigations of differences between gifted and nongifted students have examined cognitive abilities, including intelligence quotient (IQ) differences, higher order thinking skills, and divergent thinking (DT). However, little is known about differences in problem finding (PF). Moreover, previous works on gifted students have never explored…

The relation between academic achievement and various measurements of cognitive abilities, problem-solving skills and self-managed learning has been established in the research before the COVID-19 pandemic and distance learning. The aim of the current research was to analyze the extent to which these aspects predicted the educational achievement…

The purpose of this study was to explore geometry spatial mathematical reasoning in Grade nine Annual National Assessments, South Africa. Conceptual Blending was the guiding theory. Document analysis within the exploratory case study was used to explore available data, the 2014 Annual National Assessment learners' scripts (n=1250). Results…

Schematic chunks denote patterns, schemes, or sophisticated rules and knowledge stored in the long-term memory in the form of chunks. We investigated whether schematic chunking is effective in improving the performance of students with math difficulties (MD) and students at risk of math failure, and how the complexity level of geometry problems…

We report on the construction, validation, and implementation of an instrument for measuring students' strategic knowledge about drawing for geometry modelling problems, namely, the "strategic knowledge about drawing scale." We conducted a qualitative study and a quantitative study to validate the proposed construction and interpretation…

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…

The Australian Curriculum: Mathematics calls for the concurrent development of mathematical skills and mathematical reasoning. What are the big ideas of mathematical reasoning and is it possible to map their learning trajectories? Using rich assessment tasks designed for middle-years students of mathematics, this symposium reports on the…

This study aims to determine the ability of algebra students who have 3 levels van Hiele levels. Follow its framework Dindyal framework (2007). Students are required to do 10 algebra shaped multiple choice, then students work 15 about the geometry of the van Hiele level in the form of multiple choice questions. The question has been tested levels…

This case study contrasts the strategies used by two students in solving bilateral symmetry and reflection tasks, based on the differential properties they attended to. The ninth grader focussed on congruence of sides as the main property of reflection whereas the eighth grader focussed on perpendicularity and equi-distance, as is the normative…

We conducted a qualitative research of case studies based on think-aloud protocols. The aim was to carry out in-depth analyse secondary students' cognitive difficulties appearing in early stages of transfer processes in problem-solving. The task was to relate several source problems to a target problem, in order to solve it effectively. Source and…

This study investigated how question prompts and feedback influenced knowledge acquisition and cognitive load when learning Newtonian mechanics within a web-based multimedia module. Participants were one hundred eighteen 9th grade students who were randomly assigned to one of four experimental conditions, forming a 2 x 2 factorial design with the…