This paper analyses learners' common errors in simplifying algebraic problems. 102 Grade 10 learners from three rural schools in South Africa participated in the study. Following a quantitative approach, content analysis of learners' responses to algebraic tests revealed that while learners commit several errors in algebraic problems, encoding and…

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…

In this article, we explored Grade 11 learners' algebraic and geometric connections when solving Euclidean geometry riders. A qualitative interpretive case study design was followed. Thirty Grade 11 learners from a non-fee-paying secondary school in the Capricorn North district of South Africa were conveniently sampled to participate in this…

With the system changes made in 2012 in Turkey, the fifth grade was transferred from the primary school level to the secondary school level. For this reason, secondary school teachers were forced to teach mathematics courses to a group of students they had never met before. Fifth-grade students do not deal with algebra and cannot use equations to…

Seeds of Algebraic Thinking comes from the Knowledge in Pieces (KiP) perspective of learning. KiP is a systems approach to learning that stems from the constructivist idea that people learn by building on prior knowledge. As people experience the world, they acquire small, sub-conceptual knowledge elements. When people engage in a particular…

Mathematical problem-posing and modeling are essential skills in developing students' analytical thinking and problem-solving abilities. This study aims to examine correlation between 9th-grade students' problem-posing and mathematical modeling skills within the learning domain of numbers and algebra. Additionally, it evaluates students'…

This article details an exploratory data analysis project using the Common Online Data Analysis Platform (CODAP) based on the "Guidelines for Assessment and Instruction in Statistics Education" (GAISE) four-part statistical problem-solving model. The project goal was to answer what similarities and differences exist within the school…

The use of the algebraic method for solving word problems is a challenging topic for secondary school students. Students' difficulties are usually associated with extracting the problem's network of relationships between quantities and with formalizing these relationships into algebraic language in a problem model. Both sources can coexist and…

Providing students with opportunities to build, and test and revise ideas, can help them develop critical thinking and problem-solving skills. In this article, the authors describe how core measurement and geometry concepts were embedded within a "Model It!" task. They replicate an industry-based, interdisciplinary problem, but only…

Solving word problems is a large part of algebra coursework and statewide testing. However, solving secondary mathematics word problems is difficult for most students and extremely challenging for students with specific learning disabilities (SLD). In recent meta-analyses, two problem solving strategies emerged as effective for secondary students…

The transition from arithmetic to algebra in middle school can be critical for students having persistent difficulties in mathematics. The leading perception in our project is that holistic relational thinking is an effective problem-solving tool in both arithmetic and algebra. We worked in collaboration with two teachers of special classes to…

We propose some generalizations of the classical Division Algorithm for polynomials over coefficient rings (possibly non-commutative). These results provide a generalization of the Remainder Theorem that allows calculating the remainder without using the long division method, even if the divisor has degree greater than one. As a consequence we…

Problem-solving competency is crucial for social development, especially in complex environments. In mathematics education, problem-solving enhances logic, creativity, and analytical skills, contributing to societal progress. This article identified quantitative information about important publications, authors, resources, and research trends on…

One pedagogical technique that promotes conceptual understanding in mathematics learners is self-explanation integrated with worked examples (e.g., Rittle-Johnson et al., 2017). In this work, we implemented self-explanations with worked examples (correct and erroneous) in a software-based Intelligent Tutoring System (ITS) for learning algebra. We…

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…