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…

This study analysed first-year preservice teachers' understanding of trigonometric equations at a South African university in the Eastern Cape province. We employed the Action-Process-Object-Schema (APOS) framework to analyse the mental constructions made by preservice teachers in solving trigonometric equations. A qualitative case study design…

This study aims to examine the construction process of the square root concept of secondary school students in Realistic Mathematics Education (RME) based environment. The study was carried out in an 8th-grade classroom with 16 students from a secondary school in a city in the Black Sea Region. The research was designed qualitatively as a case…

The aim of this study is to determine the distribution of the questions in an 8th grade mathematics textbook in terms of the categories (mathematical content, mathematical literacy contexts, mathematical processes, PISA mathematics proficiency scale levels, and item types) within the PISA mathematics literacy framework. Investigation of the…

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…

The article presents one of the possible ways of overcoming the misconception that is one of the myths about mathematics, which says that teaching mathematics is based only on the transfer of mathematical knowledge in the finished form -- often in the form of certain algorithms. The newly proposed method of access to mathematics teaching is…

To improve students' mathematics achievement, their errors should be treated as an opportunity to stimulate conceptual and procedural understanding. Using a teaching scenario, this study investigated 40 high school teachers' analyses of and responses to a student error(s) in solving a quadratic equation by using the factoring method. The teachers'…

This paper proposes an experimental path aimed at guiding upper secondary school students to overcome that discontinuity, often perceived by them, between learning geometry and learning algebra. This path contributes to making students aware of how the algebraic language, formalized in the most powerful form by Descartes, grafts itself onto the…

The present study explored 285 11th-grade students' preconceptions, misconceptions, and errors in solving mathematics tasks by graphical method. A descriptive-explorative study design was adopted. Cluster sampling was used to select students from sampled secondary schools in eastern and central Uganda. Students' paper and pen solution sketches…

Conceptual understanding is one of the main concerns of mathematics education. Numerous research have discussed student understanding of algebraic concepts, linear equations in particular. This research was drawn upon in order to develop a new approach for teaching and learning linear equations based on the equivalence concept, one that aims to…

Problem solving is an important aspect of the mathematics classroom and teachers should work to promote problem solving in their classrooms. The purpose of this explanatory mixed-methods study was to examine mathematics preservice teachers' (PSTs) problem-solving performance and connect it with their K-12 and tertiary education problem-solving…

In order to interpret students' attitudes about mathematics, Vesife Hatisaru asks: What do students find necessary or useful in learning mathematics? And what are the connections between their perceived needs for mathematics and their attitudes, views and feelings about mathematics? In this article, she provides evidence on these critical issues…

Researchers and instructors have only recently embraced the role of errors as vehicles for learning in the algebra classroom. Studying a mixture of correct and incorrect worked examples has been shown to be beneficial relative to correct worked examples alone. This study examines the effectiveness of having students generate, or anticipate, errors…

In this study, we investigate students' ways of understanding graphing tasks involving quantitative relationships in which time functions as an implicit variable. Through task-based interviews of students ages 14-16 in a summer mathematics program, we observe a variety of ways of understanding, including thematic or visual association, pointwise…

The current study aimed to reveal the changes to the identities of two tenth graders in mathematics learning at a Japanese high school during the COVID-19 pandemic from the perspective of learning from home versus learning in the classroom. The following research questions are raised: How has the pandemic situation affected and changed Japanese…