The integration of artificial intelligence (AI) into mathematical problem-solving has shown significant potential to enhance student learning and performance. However, while AI tools offer numerous benefits, they are prone to occasional conceptual and arithmetic errors that can mislead users and obscure understanding. This research examines such…

Undergraduate students are expected to produce and comprehend constructive existence proofs; yet, these proofs are notoriously difficult for students. This study investigates students' thinking about these proofs by asking students to validate two arguments for the existence of a mathematical object. The first argument featured a common structural…

This qualitative case study, grounded within the interpretive paradigm, analyzed the errors and misconceptions made by 11th-grade learners when tackling the tangent-chord theorem task in Euclidean geometry. Studying Euclidean geometry helps learners develop critical thinking skills, such as constructing arguments and applying logical reasoning.…

Two problems, both from Gaspar Nicolas' "Tratado da Prática d'Arismética", published in 1519 are considered in this study. The tasks were carried out using pencil, paper and students from Portuguese schools. The aim was to explore the following students' performances: 1. The students were able to recognize the "error",…

The aim of this study is to examine the ability of pre-service mathematics teachers to detect errors made in solving questions about matrices. The study particularly focused on revealing the internalization of the teachings such as the meanings and relational dimensions of concepts and operations about matrix. The study was conducted with 26…

Several studies have shown that children do not only erroneously use additive reasoning in proportional word problems, but also erroneously use proportional reasoning in additive word problems. Traditionally, these errors were contributed to a lack of calculation and discrimination skills. Recent research evidence puts forward an additional…

We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

Over the years, we have noticed our students constructing proofs that commutativity is preserved by isomorphism that do not explicitly use the fact that the isomorphism is surjective. These proofs are typically valid otherwise. However, such proofs are invalid because they would prove the false claim that commutativity is preserved by any…

This study targets to 1) describe students' mathematical reasoning skills in terms of guardian personality type; 2) knowing the causes of student mistakes in answering questions. This type of study is descriptive qualitative. The subjects in this study were students of class XI MIPA four Wanasaba 1 Senior High School in East Lombok in the…

The purpose of this research is to examine fourth grade students' ability to solve mathematical problems which have the same solutions but are given in three different formats as "symbolic, numerical and story (word) problem" and which require four operations. Within this frame, the students' solutions in different formats, their…

This qualitative study examines the gifted students' self-reflections about the mathematical problems in an elaborated way. The participants of the study were three gifted students in 10th grade and 10 problem solving sessions were carried out with these participants. According to findings, the gifted students did not take into account the…

This is a study of my dramatized narrative based on a true story of what took place in a mathematics class in an international school setting. My narrative includes the exploration of a mathematical "mistake" and the discovery of newly emergent problems. The drama, commentary, and reflections provide a close examination of the conduct…

The aim of this study is to examine the mistakes made by students in the use of logical connectives while simplifying algebraic equations and inequalities, and the extent to which teachers are aware of these mistakes and how they assess them. The study was conducted among 50 ninth grade students and 63 practicing teachers of mathematics. The data…

Research in psychology and in mathematics education has documented the ubiquity of "intuition traps" -- tasks that elicit non-normative responses from most people. Researchers in cognitive psychology often view these responses negatively, as a sign of irrational behaviour. Others, notably mathematics educators, view them as necessary…

As algebra teachers, the authors explore the following question in this article: "How can algebra 1, algebra 2, and precalculus teachers support students to develop algebraic reasoning and understanding of structure that can serve them in day-to-day algebraic computation?" The article shows how the algebraic identity "(a +…