One of the most significant steps in learning algebra is understanding the change in the role of letters in mathematical expressions from unknowns to variables. We describe the historical development of this change in usage, starting with the ancient use of mathematical unknowns, detailing several important changes in practice that allowed for the…

Students often complain that the rules of mathematics are being changed. A short conversation between a professor and a class of college algebra students dramatizes this in the realm of complex numbers and the legal realm of speed limits.

We summarize the most important facts about the Steiner point of a triangle and find formulas for its distance to each vertex in terms of the side-lengths of the triangle.

Algebraic notation has been bedazzling learners for generations, yet despite research, learned papers, comparative studies, and a great deal of hard work on the part of classroom practitioners the situation remains a stubborn constant. In this article some small-scale research has highlighted some issues that might find a resonance in many…

Calculators with computer algebra systems (CAS) are powerful tools when working with equations and algebraic expressions in mathematics. When calculators are allowed to be used during assessments but are not available or provided to every student, they may cause bias. The CAS calculators may also have an impact on the trustworthiness of results.…

The Peer Enabled Restructured Classroom (PERC) is an instructional innovation developed to address gaps in science, technology, engineering, and math (STEM) in urban high schools. The PERC model changes instruction from teacher led to peer led by bringing peer students into the classroom to lead small-group work. Our study sought to provide…

Number sense is one's ability to understand what numbers mean, perform mental mathematics, and look at the world and make comparisons. Researchers show instruction that teaches children how to classify numbers, put numbers in sequence, conserve numbers effectively, and count builds their number sense skills. Targeted instruction that teaches…

How does teacher-guided whole-class interaction contribute to expanding students' potential for making and exchanging mathematical meanings? We address this question through an interpretative analysis of a whole-group conversation in a sixth grade class taught by an experienced teacher in a school in Southern Argentina. The extended interaction…

A college mathematics placement test with 25 basic algebra items and 15 calculus readiness items was administered to 1572 high school seniors, and first college mathematics course grades were obtained for 319 of these students. Test results indicated that more than two thirds of the high school graduates were not college ready, and the test…

These proceedings contain the papers and posters of the 22nd International Conference on e-Society (ES 2024) and 20th International Conference on Mobile Learning (ML 2024), organised by the International Association for Development of the Information Society (IADIS) in Porto, Portugal, during March 9-11, 2024. The e-Society 2024 conference aims to…

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…

Students' attitudes and approaches to physics problem solving can impact how well they learn physics and how successful they are in solving physics problems. Prior research in the U.S. using a validated Attitude and Approaches to Problem Solving (AAPS) survey suggests that there are major differences between students in introductory physics and…

The use of handheld CAS technology in undergraduate mathematics courses in Australia is paradoxically shrinking under sustained disapproval or disdain from the professional mathematics community. Mathematics education specialists argue with their mathematics colleagues over a range of issues in course development and this use of CAS or even…

How teachers make sense of new academic standards significantly shapes the implementation of those standards. Professional development organized around the analysis of mathematical tasks has potential to prepare teachers for standards implementation by helping them develop common understandings of standards and how to help students meet ambitious…

Between 2003 and 2013, the proportion of California 8th graders enrolled in Algebra or a more advanced course nearly doubled to 65 percent. In this paper, we consider the organizational processes that accompanied this curricular intensification. Facing a complex set of accountability, institutional, technical/functional, and internal political…