Like terms are usually defined for variables with numerical coefficients. While the definition is sufficient to combine polynomial terms, it does not help the students to combine radical, logarithmic, or trigonometric terms. The purpose of this paper is to propose a lesson that introduces a broader definition of like terms and trialed with a group…

The purpose of the present article is to investigate the definition of matrix multiplication as a central issue in linear algebra courses. Applying both historical and pedagogical approaches, it focuses on the philosophy of generating the usual matrix multiplication, as a special binary operation, with its partly unexpected form compared with the…

This report proposes a framework for describing student analogical reasoning activities in abstract algebra that moves beyond the traditional literature-based treatment of analogical mapping. The Analogical Reasoning in Mathematics (ARM) framework captures the activities that students engage in when anticipating, creating, and reasoning from…

Our field has generally reached a consensus that active-learning approaches improve student success; however, there is a need to explore the ways that particular instructional approaches affect various student groups. We examined the relationship between gender and student learning outcomes in one context: inquiry-oriented abstract algebra. Using…

The mathematics curricula of countries such as the United States, Singapore, Australia and New Zealand have started to incorporate the teaching of algebra in early childhood education. From this perspective, our study has two objectives: (a) to design a learning trajectory and teaching itinerary introducing patterns for children between the ages…

Low levels of literacy and numeracy skills are associated with a range of negative outcomes later in life, such as reduced employment, earnings and health. This review examines the effects of a broad range of school-based interventions targeting students with, or at risk of, academic difficulties on standardised tests in reading and maths.…

Financial literacy and financial capacity of schoolchildren should be developed to meet the requirements of the rapidly developing society and increasingly complicated financial system of the Russian Federation. The authors focused on the financial education of schoolchildren who represent a special target group in financial relations. The main…

In this study, differential prediction of student outcomes by race and teacher traits relative to the certification levels of novice teachers was assessed. Overall, algebra achievement was higher for students who were taught by teachers with standard certificates relative to students who were taught by novice teachers with nonstandard…

Understanding related to fraction concepts is a critical prerequisite for advanced study in mathematics such as algebra. Therefore, it is important that elementary students form conceptual and procedural understanding of fractional numbers, allowing for advancement in mathematics. The concrete-representational-abstract (CRA) instructional sequence…

When designing an instructional tool and using it in pedagogical activities, it is essential that designers and users understand what pedagogical affordances and constraints the tool provides to support its successful integration into targeted pedagogical activities. Toward this end, we developed "Pedagogical Affordance Analysis (PAA)."…

The present study focused on the lack of knowledge of the double use of brackets in arithmetic expressions and the difficulty in the operatively of expression for mathematics application at the school level. Learning the other rules and formulas of mathematics involves learning the use of a bracket. Binding is useful in both arithmetic and…

Math fact fluency involves the quick, accurate retrieval of basic arithmetic combinations and the ability to use this fact knowledge efficiently. Math fact retrieval is typically considered fluent when performed accurately within 2 to 3 seconds, and "efficiency" refers to students' ability to apply fact knowledge to more complex…

As K-12 mathematics standards shift toward emphasizing both conceptual and procedural knowledge in secondary courses such as algebra and geometry, the struggles for students with disabilities become more pronounced. To address these challenges, research has commonly explored the use of technology to aid in the teaching of students with…

Competence in fractions is important in achieving advanced mathematics such as algebra and calculus. To foster students' understanding of fractions, intervention studies have found number lines to be an effective representational tool. Yet, it is unclear whether or not number lines are equally effective regardless of the ways in which they are…

During this action research study of Algebra I teachers at a high school in the Dallas/Fort Worth Metroplex, I have presented information related to the implementation of inquiry-based learning (IBL) and the findings from classroom observations and a focus group interview. The purpose of this study was to identify the effect of IBL instructional…