We provide a gentle alert that the standard definitions of basic algebraic structures--such as that of a group--contain aspects that may be questionable to students, and discuss what instructors could do to minimise the questionability.

Simplifying equations via assumptions is integral to the "engineering method." Algebraic scaling helps in teaching the engineering skill of making good assumptions. Algebraic scaling is more than a pedagogical tool. It can create a solution where one was not possible before scaling. Scaling helps in engineering proper design…

The purpose of this study is to conduct a bibliometric analysis of the research published in the field of mathematics misconception from 1947 to 2023, to determine the general knowledge structure and participation in research publication. An analytical approach was used based on Scopus database data. This study used mixed methods; quantitative…

With feedback gathered from townhall meetings at the start of 2025, Kentucky's education leaders are revising the state's assessment and accountability framework to give districts more choice in how they assess student mastery of content and skills and to give their communities full rein to design local school accountability systems tied to their…

Initial algebra is a critical stage in the teaching of algebra and occurs when students are transitioning from arithmetic to algebra. Irish mathematics education at post-primary level has undergone a period of major reform beginning in 2010, which encompassed a radical change in the methods for teaching algebra. Despite this reform evidence…

Students often instrumentally use variables and unknowns without considering the variational thinking behind them. Using parameters to modify the coefficients or unknowns in equations or systems of linear equations (without altering their structure) involves consciously incorporating variational thinking into problem-solving. We will test the…

This study analyzes the mathematical knowledge to teach early algebra exhibited by pre-service early childhood education teachers, from the perspective of the Mathematical Knowledge for Teaching (MKT) model. The research adopts a mixed exploratory-descriptive methodological approach, based on the application of the MKT-early algebra questionnaire…

Developing both conceptual and procedural knowledge is important for students' mathematics competence. This study examined whether U.S. Grade 9 general education mathematics teachers' self-reported use of concept-focused instruction (CFI) and procedure-focused instruction (PFI) were associated differently with ninth graders' algebra achievement…

This study used the Motivated Strategies for Learning Questionnaire (MSLQ) to assess the motivation and learning strategies of students in a self-paced developmental mathematics class. A total of 194 undergraduate students participated in this study. Descriptive statistics, correlation coefficients, and regression analysis were conducted to assess…

Background: Many students face difficulties with algebra. At the same time, it has been observed that fraction understanding predicts achievements in algebra; hence, gaining a better understanding of how algebra understanding builds on fraction understanding is an important goal for research and educational practice. Objectives: However, a wide…

The notion of function is central in all of the secondary curriculum, and indeed functional models appear in almost all higher education that is based on mathematics. However, in secondary education, functions usually appear in restricted and somewhat sterile forms. In this (mostly theoretical) paper, we present a proposal -- exemplified by a…

This study aims at elaborating a well-established theoretical framework that distinguishes three modes of thinking in linear algebra: the analytic-arithmetic, the synthetic-geometric, and the analytic-structural mode. It describes and analyzes the bundle of signs produced by an engineering student during an interview, where she was asked to recall…

Large language models (LLMs) have significantly advanced smart education in the artificial general intelligence era. A promising application lies in the automatic generalization of instructional design for curriculum and learning activities, focusing on two key aspects: 1) customized generation: generating niche-targeted teaching content based on…

Meaningful collaborative interactions in asynchronous online mathematics teacher professional development (PD) may provide teachers with valuable opportunities to learn. We studied collaborative interactions in online teacher PD activities that involved embedded videos, prompts, discussions, and multiple online tools. Analysis of teacher responses…

This paper describes the design, implementation, and results of a training action with prospective primary education teachers, focusing on the creation of problems involving proportional and algebraic reasoning. Prospective teachers must solve a proportionality problem using both arithmetic and algebraic procedures, and then vary it to motivate…