Solving systems of linear equations is a core concept in linear algebra and a wide variety of problems found in the sciences and engineering can be formulated as linear equations. This study sought to explore undergraduate students' development of the schema for solving systems of linear equations. The triad framework was used to describe the…

Recognizing, building, describing, extending, and analyzing patterns are key components of algebraic reasoning. Oftentimes pattern-based instruction is used to support the understanding of functions and variables. In this study, elementary preservice teachers (n = 23) were asked to explore, extend, explain, create equations for, and analyze…

This study's purpose was to analyse the relationship between geometric thinking skills with self-regulated learning and with students' basic geometry skills. Furthermore, analyze student errors in solving geometry problems based on their self-regulated learning to determine the optimal geometry learning environment for geometry thinking skills.…

Euclidean geometry provides an opportunity for learners to learn argumentation and develop inductive and deductive reasoning. Despite the significance of Euclidean geometry for developing these skills, learner performance in mathematics, particularly geometry, remains a concern in many countries. Thus, the current study examined the nature of…

This study offers a comprehensive investigation of 14-15-year-old students' comprehension of non-Euclidean geometries, with a specific focus on the assessment of their understanding through a 15-itemed test. The primary objective of this research is to assess the current state of students' knowledge and proficiency in non-Euclidean geometries and…

Problem-solving is the essence of mathematics and is the main goal in learning mathematics. Many students did not have good problem-solving skills based on the field observations. The problems grew up because the students were not used to solving the problems and the problem-solving stages. They did not include issues with high complexity, such as…

Fraction arithmetic facility is fundamental to learning more advanced math topics. However, attaining the ability to add and subtract fractions is hard for many students. The present longitudinal study examined students' growth on simple addition and subtraction word problems between fourth and sixth grades (N = 536). Latent class growth analyses…

Whole number computations are a critical skill that serves as a foundation upon which higher-order concepts in mathematics are taught to children. To facilitate their instruction, educators often use multiple representations to support a child's cognition. Representations with physical manipulatives are widely studied through a graduated…

The adverse influence of the presence of an irrelevant number and language inconsistency in a word problem is well known. Our study focused on the combination of these two variables and on the position of the irrelevant number in the word problem for Grade 6 pupils. The study has a mixed design. Item Response Theory was used to make equally able…

The research aimed to analyze the students' abilities in solving realistic mathematics problems using "What-If"-Ethnomathematics Instruments with content focused on plane and space materials. The "What-If"-Ethnomathematics instruments are instruments that enable educators to analyze various errors and obstacles experienced by…

The present study investigates the understanding of the equals sign among middle school students. The study data were gathered from a total of 433 middle school students (111 in the fifth grade, 106 in the sixth grade, 95 in the seventh grade and 121 in the eighth grade) using a ten-item equals sign test developed by the researcher. The study…

Children need support in the early elementary grades to construct a deep, formal understanding of foundational prealgebraic concepts. In this article, the authors share recommendations for teaching one such foundational concept--mathematical equivalence. First, they define mathematical equivalence and discuss research supporting the benefits of…

This study aimed to reveal the common errors in fractions, the associated thinking strategies among 5th graders, and the persistence of these errors. A quantitative method was applied in this study through calculating the percentages of every type of error the students made in the diagnostic test, The qualitative part was performed through…

Thinking is a tool to construct knowledge in learning mathematics. However, some college students have not been fully aware of the importance of constructing their knowledge. Therefore, this study aims to explore students' thinking processes in completing mathematical proofs through assimilation and accommodation schemes. This research was…

Multiplicative thinking is widely accepted as a critically important 'big idea' of mathematics that underpins much mathematical understanding beyond the primary years. It is therefore important to ensure not only that children can think multiplicatively, but that they can do so at a conceptual rather than procedural level. This paper reports on a…