Cognitively demanding tasks have been shown to support students' understanding of mathematics. How a task is launched, or introduced, determines how students engage with the task, as well as the type of work the teacher engages in during the task implementation. The authors designed a unit focused on launching a task where prospective teachers…

When it comes to choosing tasks, values can have a significant impact. This study explores teachers' values as they choose one task from among three that they believe will have the most potential to occasion mathematical creativity in the classroom. Participants' analyses of each task, as well as their reasons for choosing one task as most…

A one-degree angle would certainly be difficult to draw accurately, especially without the aid of other tools like a protractor. However, mentally making a one-degree angle in visualized imagination is not only possible, but it is important for students' emergent understandings of angular measure. When students begin learning about length,…

A clear relationship exists between the consistent selection and implementation of cognitively demanding tasks and students' conceptual understanding of mathematics. However, mathematics teachers often struggle to maintain the cognitive demand of implemented tasks, with a number of factors identified as contributing to this decline. As many…

Self-efficacy, the beliefs learners hold about what they can do, develops largely from whether learners perceive and interpret their experiences as successful (i.e., perceived mastery). In mathematics, the relationship between perceived mastery and self-efficacy has been well established. Less is known about the factors that may influence…

The COVID-19 pandemic provided students a rare opportunity to use their mathematical knowledge to make sense of a top-of-mind crisis. Based on a report in a major regional newspaper, we designed tasks that require an understanding of infection rates and an interpretation of a misleading claim made in the newspaper. Our analysis of 91 undergraduate…

This book argues that mathematical challenge can be found at any level and at every age and constitutes an essential characteristic of any mathematics classroom aimed at developing the students' mathematical knowledge and skills. Since each mathematics classroom is heterogeneous with respect to students' mathematical potential, quality…

The purposes of this study were to evaluate the effects of an auditory-distractor stimulus and vocal-blocking task on performance on a math task and measures of overt verbal operants. College students served as participants, and they were instructed to solve an arithmetic problem while continuously emitting overt verbal behavior. The overt verbal…

We investigated the cognitive demand of the exercise problems that middle school students from Nepal are expected to complete. The middle school (grades 6, 7, and 8) mathematics textbooks examined in this study were published and distributed by the government of Nepal. Our data set consisted of textbooks that are currently in use in public schools…

Drawing on a larger, cross-institutional study that examines equitable elementary mathematics education, this article reports initial findings related to tensions that emerged for preservice teachers (PSTs) related to trusting students with open-ended, challenging mathematics tasks. Data composed of 194 PSTs' written responses to a survey…

Let's say you are a Grades 3-5 teacher in search of an activity sheet on different fraction notations. A search in May 2022 on the popular resources sharing site TeachersPayTeachers (TpT) yielded 2,832 results, 105 of which were free. With so many options, how would you go about choosing a resource for your students? What would factor into your…

This study examined the quality and types of mathematical tasks used for classroom instruction in an upper secondary school -- gymnasium. All the mathematical tasks presented in nine different school classrooms during the first semester of the school year 2018/2019 were analysed against a 5D analytical framework. The dimensions of the individual…

We report on and validate a system for ranking the cognitive demand of mathematical tasks. In our framework, task rankings are determined by the sequences of units and unit transformations students might use to solve each task. Using this framework, we ranked a set of 10 fractions tasks. We then interviewed 12 pre-service teachers to assess the…

Educational mathematics researchers and educationists emphasise teaching for understanding. However, does it influence students' mathematical learning behaviour? The purpose of this study was to explore late adolescent students' views on mathematical learning behaviour in teaching-for-understanding classes. Content analysis of secondary data from…

Generalizing patterns is an important feature of algebraic reasoning that is accessible to students across grade-levels because it connects their numerical reasoning to algebraic reasoning. In this article, the authors describe how teachers can use the game Crack the Code to introduce generalizing to their students or can extend students'…