Joint activity, or interaction, can be the basis for understanding how language use organizes both social activity as well as individual thought. These interactions can be a useful unit of analysis for studying how students use language to make sense of mathematical concepts and how students learn to appropriate specific mathematical language…

Recent solar eclipses provide relevant real-world contexts for learning about the scientific phenomena of the lunar phases. News coverage of the phenomenon may have raised questions such as, "Why does the Moon look different at different times, and sometimes as if it is not there?," and "What patterns can be found in the lunar…

This study examines the solutions of 34 kindergarten children as they create equal groups from n bottle caps, where n was equal to 8, 9, 22, and 23. For each n, children were asked to find as many different solutions as possible. The number of solutions they found, i.e., children's fluency, as well as the strategies used to create equal groups,…

On the surface, the number line may seem like a basic tool with obvious applications. However, using a number line is not always intuitive for students. Students may not recognize significant features such as the size of the unit, how units are represented by iterated equal lengths, or that the accumulation of iterated units is a magnitude of…

We discuss student conceptions of improper integrals and infinity in the context of a second-semester calculus course (in a three-course sequence). Our observations stem from a sequence of activities used in an online course over a three-day period. Throughout the enactment of these activities, students are challenged to develop conceptions of…

We explore how the concept of abstraction, which is central to mathematical activity, can lead to detachment or attachment to land, nature, culture, language, and heritage in Indigenous contexts. We wonder if students detach themselves from mathematics because they feel mathematics asking them to detach themselves from people and places to whom…

Beginning a mathematics lesson involving a challenging task with a carefully chosen preliminary experience is an effective means of activating student cognition. In this article, the authors highlight a variety of preliminary experiences, each with a different structure and form, all designed to support students to more successfully engage with…

The relationship between surface area and dynamics of processes can be demonstrated by adding iron at room temperature to liquid nitrogen. The rate at which the liquid nitrogen boils to produce gas is related to the surface area of the iron. Adding iron in the form of consistent units that have measurable sizes can be readily connected to…

"Assumptions" play a fundamental role in disciplinary mathematical practice, especially concerning the relativity of truth. However, much is still unclear about ways to help students recognize key aspects of this role. In this paper, we propose a set of principles for task design to introduce students to the role of assumptions in…

Students encounter difficulties in understanding integral because the concept of integral requires the usage of theorems, formulas, daily life practices, and interdisciplinary approaches. From this point of view, in this study we examine the effects of a teaching process consisting of modelling activities on understanding the definite integral…

Get a deeper understanding of teaching functions, 9-12 with our concise and comprehensive Go-To Guide. Based on "Developing Essential Understanding of Functions 9-12" and "Putting Essential Understanding of Functions into Practice 9-12," this summary distills the key concepts and ideas into a quick-reference guide that's…

Math educators must engage students in deep learning and talk spanning shorter, medium, and longer time frames to offer both the structures and language so that secondary English learners can participate fully alongside their classmates. In this article, the authors present: (1) "structure and language" to facilitate full participation…

This paper reports on the design, implementation, and evaluation processes of an activity that focused on the comparison meaning of the subtraction of integers and included the number line model as the primary representation. Finding the answer and determining the sign of the answer in the subtraction questions were targeted as the learning…

The purpose of this study is to implement an a-didactical activity relating to the acquisition of the triangle inequality, prepared within the framework of the "Didactic Situations Theory" (TDS), and to report the experiences of the students during the implementation process. The study employs a case study method based on a qualitative…

Research focusing on the home mathematics environment has shown mixed results across age groups. Using data from a large online survey, we explored parents' perceptions of the age appropriateness of home mathematics activities for their children. Children's ages ranged from one to 6 years old (N = 958). Activities spanned multiple domains of early…