While scholars have proposed incorporating the study of complex phenomena such as chaotic systems in high school and undergraduate-level curricula, the literature on this topic is scant and has focused mostly on the analysis of mathematical models--and often only on certain populations, such as gifted students. We report in this manuscript an…

This study explored 54 preservice elementary teachers' identification and modification of mathematical tasks in raising cognitive demand and examined the features of their modified tasks. The study collected data using a three-phase activity: (a) identifying the level of cognitive demand of the given task, (b) modifying the low cognitive demand…

We investigated the relations between self-reported math anxiety, task difficulty, and pupil dilation in adults and very young children during math tasks of varying difficulty levels. While task difficulty significantly influenced pupillary responses in both groups, the association between self-reported math anxiety and pupil dilation differed…

Although culturally responsive mathematics teaching is important, post-secondary education for preservice teachers (PTs) does not typically lead to learning opportunities for them to use mathematics to recognize the roles of social agents. To address this issue, we created a culturally responsive mathematical modeling task in which we invited PTs…

The aim of the study was to examine how students generate problems about the concept of series, and how they evaluate and solve these problems. The difficulties experienced by the students while posing problems and their perceptions of the posing-evaluating-solving approach were also explored. In the first stage, 46 second-year university students…

In recent decades, research has stressed the prominence of mathematics classroom discussions in productive instructional practices in mathematics instruction. In this context, problem-solving activities have been a common focus of research. Research shows that teachers need to deal with prerequisites and challenges such as norms, design of tasks,…

The present study adds to an ongoing debate about third spaces in teacher education, spaces where theory and practice come together. One third space is constituted by the written tasks from practicum. Yet research has shown only modest emphasis on theory in such tasks. Tasks from two versions of a programme are used to represent two different…

This article reports on results from a design research project that implements a formative assessment practice with support from a classroom response system (CRS). Cumulatively building on earlier research and drawing on iteratively generated data from secondary schools in Sweden, the article elaborates on design principles and task types for…

In this article, the goal is to describe students' mathematical reasoning in the context of different settings of problem-solving tasks. The core of the tasks are real objects, which are presented to the students with the help of photos, a 3D model or in the environment itself. With reference to the experiential learning theory and relations to…

Spanish educational curriculum adopts a mathematical process-based approach, which encompasses problem solving, reasoning and proof, communication, connections and representation. A fundamental role in the integration of these processes in mathematics teaching is played by teachers' professional practice of designing tasks. According to this, our…

In this study, the relationships between task value, self-efficacy and mathematics anxiety in everyday life in secondary school students were investigated. In addition, the mediating role of self-efficacy in the relationship between task value and mathematics anxiety in daily life was examined. 203 secondary school students participated in the…

Students are more likely to obtain correct solutions in solving derivative problems. Even though students can complete it correctly, they may not necessarily be able to explain the solution well. Cognition and communication by the students will greatly affect the subsequent learning process. The aim of this study is to describe students'…

Assessing students' conceptions related to independence of events and determining probabilities from a sample space has been the focus of research in probability education for over 40 years. While we know a lot from past studies about predictable ways students may reason with well-known tasks, developing a diagnostic assessment that can be used by…

This study adopts a holistic single-case design to explain the task design processes of mathematics student teachers (MSTs) regarding History, Theory, Technology, and Modeling (HTTM). A criterion sampling method was used to select nine MSTs who had successfully completed "algorithms and programming" course. Video analyses, written answer…

A selection of secondary school mathematics textbooks from twelve countries on five continents was analysed to better understand the support they might be in teaching and learning mathematical problem solving. Over 5700 tasks were compared to the information provided earlier in each textbook to determine whether each task could be solved by…