Background and Context: Multiple studies report that experienced instructors lack consensus on the difficulty of programming tasks for novices. However, adequately gauging task difficulty is needed for alignment: to select and structure tasks in order to assess what students can and cannot do. Objective: The aim of this study was to examine…

In this study, the authors investigate the ways in which young students demonstrate their critical mathematical thinking (CMT). Students aged 5-6 who are beginning their first formal year of education participated in the study. Data is presented from individual clinical interviews undertaken with 16 students. These interviews were analysed using…

In this exercise, participants create a fictional business based on a set of randomly generated words. This challenge requires participants to exercise creativity, while reinforcing the business concepts learned in class. The exercise has four steps: (1) generating a prompt of three random words, (2) designing a fictional business based on this…

Teaching algorithmic thinking enables students to use their knowledge in various contexts to reuse existing solutions to algorithmic problems. The aim of this study is to examine how students recognize which algorithmic concepts can be used in a new situation. We developed a card sorting task and investigated the ways in which secondary school…

Completion of an escape room activity requires participants to work as a team to find hidden clues and solve challenging puzzles to escape before time expires. The use of escape rooms for active learning may produce a positive classroom environment by improving teamwork skills, encouraging engagement with course materials, fostering intellectual…

Mendelian genetics are essential for students seeking to comprehend the complexities of inheritance; although fundamental, these biology concepts are difficult for students to understand. This study examined the effectiveness of task-based learning (TBL) in enhancing the students' conceptual understanding of the Patterns of Mendelian Genetics. A…

Coordination class theory has proven to be a useful theoretical framework for describing processes of conceptual change in certain physical and mathematical concepts. Its development throughout different studies has allowed us to understand numerous mechanisms of conceptual learning by individual subjects. There have been attempts to implement…

A digital wall is a tool for students to structure and register their online work on mathematical problem-solving activities that involve the coordinated use of digital technologies. How could students use such digital wall to understand mathematical concepts and to develop problem-solving competencies? The aim of this study is to analyze and…

This paper focuses on pre-service mathematics teachers' geometrical construction processes while using a duo of artefacts, namely the paper-and-pencil environment (PPE) and a dynamic geometry system (DGS). The participants of this case study were two pre-service mathematics teachers, who had limited DGS experiences in solving geometry tasks. The…

In this article we present an overview of four studies investigating Greek secondary students' conceptual and procedural knowledge of fractions. We discuss the problem of defining conceptual and procedural knowledge, and the implications of adopting one particular definition over others. We draw on the studies and their results to discuss the…

Perseverance, or initiating and sustaining productive struggle in the face of obstacles, promotes making sense of mathematics. Yet, engaging in struggle can be grueling and is avoided for some students. I investigate the effect of scaffolding mathematics tasks on student perseverance. The results show how prompting secondary students to…

The emergence of new technological innovations in classroom has brought about greater changes in pedagogy especially in concepts related to abstraction such as Geography. Geography teaching and learning particularly elements of physical Geography, is mostly approached in a conventional pedagogical manner even as the concept consist abstractions.…

Mathematicians use example generation to test and verify mathematical ideas; however, the processes through which undergraduates learn to productively generate examples are not well understood. We engaged calculus students in a teaching experiment designed to develop skills in productively generating examples to learn novel concepts. This article…

Learning about heredity is important across the K-12 continuum. However, these ideas may be challenging for students. We examined third-grade students' ideas about heredity in the context of a new, six-week, model-based science unit that uses corn as a model organism to support students' ideas about heredity. We analyzed data collected during…

We report here on students' views of example generation tasks assigned to them in two first year undergraduate Calculus courses. The design and use of such tasks was undertaken as part of a project which aimed to afford students opportunities to develop their thinking skills and their conceptual understanding. In interviews with 10 students, we…