This study investigates when and how university students in first-semester introductory calculus interpret multiple representations of the same function. Specifically, it focuses on three tasks. The first task has students give their definitions of 'function sameness', the results of which suggests that many students understand a function as being…

Critical thinking is a key transversal competency of the 21st century, but some students have difficulty, especially during the transition to online learning due to the COVID-19 pandemic. This study aims to identify epistemological obstacles in critical thinking related to proof, generalization, alternative answers, and problem-solving. This…

Detailed mathematical reasoning abilities can help students to understand higher mathematical abilities, including proving, problem-solving, and critical thinking. However, based on surveys and research, students' mathematical reasoning abilities are low and require significant attention. Therefore, this study aims to gain a detailed picture of…

This paper discusses several linear algebra activities designed to help enhance students' skills in collaborating, exploring mathematics, and linking together abstract and visual ways of approaching mathematics. Most of these activities are short, accessible, engaging, and easy to incorporate into any classroom. In addition, we discuss some…

ABN (Abierto Basado en Números--Open Calculation Based on Numbers) is a method for teaching basic arithmetic operations in primary education that has become popular in recent years and that is based on the decomposition of numbers through manipulative materials that encourage mental calculation. Currently there is limited number of tools that can…

The aim of this study is to develop a theoretically sound, valid, and reliable scale to examine seventh and eighth grade students' attitudes towards so-called skill-based mathematics questions (SBMQ). The sample of the study was 820 seventh and eighth grade students at three different middle schools in Etimesgut District of Ankara Province. A…

In 2010 a mathematics curriculum was introduced in Irish second level schools entitled 'Project Maths' (PM). It aimed to refocus second level mathematics teaching and learning away from an over emphasis on procedural mathematics towards problem solving and real understanding [Department of Education and Skills (DES). (2010). "Report of the…

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…

This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

The purpose of this development research is to create a self-efficacy instrument to assist students learning mathematics that is valid, practical, and reliable. A self-efficacy questionnaire is the format of the instrument that was created. The main driving force behind this research is the scarcity of empirically validated self-efficacy surveys…

This study used the RBC+C model to reveal the abstractions of the 6th-grade students in the process of transition to the parallelogram area formula. Also, constructing parallelogram area information was employed as a teaching experiment based on the basic interpretive approach, one of the qualitative research methods. The study participants…

Researchers intending to identify the unique characteristics of dyscalculia rely upon the problematic and imprecise proxy of low mathematics achievement. Although detailed case studies of adults with dyscalculia have offered insight into its characteristics, we do not yet know if these characteristics are unique to dyscalculia and could be used to…

In this study, it was investigated whether it would be possible to observe abstraction processes of secondary school 7th graders using the Revised Bloom's Taxonomy. For this purpose, eight students participated in the study. The study was conducted at a state secondary school in Turkey. Purposeful sampling method was used in the selection of…

In mathematics education, students are repeatedly confronted with the tasks of interpreting and relating different representations. In particular, switching between equations and diagrams plays a major role in learning mathematical procedures and solving mathematical problems. In this article, we investigate a rather unexplored topic with…

Across the world, standards and practices for preparing teachers of mathematics emphasize the importance of math modeling (MM) in developing students' mathematical thinking. The aim of this research study was to develop the Mathematical Modeling Knowledge Scale (MAMKS), capable of determining preservice teachers' (PSTs') knowledge of MM. The study…