This study explores the effectiveness of GeoGebra in enhancing students' understanding of vectors in mathematics education. The research compares traditional teaching methods with the application of GeoGebra to determine its impact on conceptual and procedural knowledge acquisition. Vectors are often challenging for students to grasp due to their…

Previously defined profiles for using a computer algebra system (CAS) describe prototypical uses of such a tool. When students use a dynamic geometry environment (DGE), however, new opportunities arise for transitions within and beyond the DGE. In this article, CAS profiles are used to explore students' uses of a DGE. Four cases of students, all…

Studies across a variety of educational fields have shown the efficacy of feedback on student performance and learning. Web-based homework is a common feature of secondary and collegiate mathematics courses to provide such feedback. While web-based homework provides often instantaneous feedback to students as they complete assignments, the…

This paper reports changes in the extent to which a group of Year 11 students used a Computer Algebra System (CAS), pen-and-paper (P&P), or a combination of both, when solving routine problems across seven months in four different topics. Comparing the frequency of CAS use across topics shows students made greater use of CAS in the topics of…

Taking as its point of departure, situations arising in classrooms exposed to a heavy use of CAS, exemplified by the Danish upper secondary school mathematics program, the paper discusses the use of "old" cognitive frameworks of mathematics education as an alternative to more recent theoretical developments in the field. The paper draws…

Gaming the system is a persistent problem in Computer-Based Learning Platforms. While substantial progress has been made in identifying and understanding such behaviors, effective interventions scarce. This study uses a method of causal moderation known as Fully Latent Principal Stratification to explore the impact of two types of interventions --…

Gaming the system is a persistent problem in Computer-Based Learning Platforms. While substantial progress has been made in identifying and understanding such behaviors, effective interventions remain scarce. This study uses a method of causal moderation known as Fully Latent Principal Stratification to explore the impact of two types of…

This paper reports the multimodal resources that attached to students' reasoning in the reinvention of specific geometric linear transformations (like reflections according to the axes, projections onto axes and composition of reflections) in a dynamic geometry environment. Following the design heuristics of Realistic Mathematics Education, we…

In the study reported on here, we investigated the effects of the use of dynamic geometry software (DGS) (i.e., GeoGebra) on learners' learning and a teacher's beliefs. The learners and teacher involved in the study were from a high-poverty, rural high school in South Africa. We compared grade 11 learners (N = 56) who used GeoGebra in the context…

This study explores the effects of a computer algebra system on students' mathematical thinking. Mathematical thinking is identified with mathematical thinking powers and structures. We define mathematical thinking as students' capacity to specialize and generalize their previous knowledge to solve new mathematical problems. The study was…

Algebra has long been a gatekeeper to more advanced mathematics and to tertiary education. International assessments, such as PISA, have also shown that this trend extends beyond borders, making the topic of when algebra should be learned quite political. Many reforms have been instituted since the early 1990s to infuse algebraic thinking into…

Opportunities matter when it comes to students' math attitudes and performance. Over two semesters, across treatment sections of college algebra students, we implemented a set of dynamic computer activities linking animations and graphs. Across all sections, we administered a fully online survey of students' attitudes toward math. Using mixed…

Linear algebra is a crucial part of mathematical training for engineering students and there are many problems in the application of this subject in engineering, physical, and even mathematical disciplines. In this scope, a study on the sustainability of learning this subject and how it can be improved is considered necessary. This article aims to…

This article addresses the didactical effects of CAS assisted proofs in Danish upper secondary mathematics textbooks as a result of the 2005 reform that introduced CAS as a part of the upper secondary level curriculum (and examinations). Based on a reading of 33 upper secondary school mathematics textbooks, 38 instances of CAS assisted proofs are…

Inspired by the entering of computer algebra systems (CAS) in the Danish upper secondary school mathematics program, this article addresses, from a theoretical stance, what may happen when traditional procedures are outsourced to CAS. Looking at the commands "solve" and "desolve," it is asked what happens when such CAS…