This article models how to plan and facilitate implementing the same task in two sixth-grade classrooms with two different learning goals using the Five Practices structure.

These educators share the "how" and "why" behind their use of open middle tasks in the classroom. In this article, the authors share a type of mathematics task, called Open Middle, that exhibits the characteristics outlined above. The authors frequently use Open Middle tasks in their classrooms because they teach students that…

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…

In this article, the role of digital feedback that was provided in an outdoor mathematics education setting is taken into consideration. Using the app MathCityMap (2020) in the context of a mathematics trail, the influence of positive and/or negative feedback is examined in relation to how it influences the processes of verification and…

This paper reports on an experiment involving 108 sixth-grade French students in which the history of Chinese numeration was used in mathematics education. The aim of this study is to evaluate the relevance of using ancient number systems in mathematics education, which is common in French textbooks. In the experiment a pre-test with usual…

In our multi-method study, feedback levels derived from the well-known feedback model of Hattie and Timperley were used in conjunction with feedback that was related to subject-specific content; here, mathematical reasoning tasks in primary school. Feedback needs to be aligned with the learning process; in the beginning, more task feedback is…

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'…

This study examined a game-based teaching activity on "Factors and Multiples" designed for the 6th grade students. The game aims to create a differentiated and enriched learning environment targeted the curriculum standard "The students determine prime numbers using their properties. The students find prime numbers using the…

To learn mathematical practices, students need opportunities to engage in them. But simply providing such opportunities may not be sufficient to support all students. Simultaneously, explicitly teaching mathematical practices could be problematic if instruction becomes prescriptive. This study investigated how teachers might make mathematical…

This study came to characterize the features of mathematical models built by mathematics pre-service teachers for a model eliciting activity. Fourteen groups participated in building the models. We used a combination of deductive and inductive content analysis to characterize the pre-service teachers' elicited models, taking into account features…

In this paper, we trace the development of our theorizing about students' mathematical understanding, showing how the adoption of an enactivist perspective has transformed our gaze in terms of the objects of our studies and occasioned for us new methods of data analysis. Drawing on elements of Pirie-Kieren (P-K) Theory for the Dynamical Growth of…

Having an answer to "When are we ever going to use this in real life?" is important to middle school mathematics teachers. The activity described in this article awakened sixth graders' understanding of how artists use mathematics. By exploring ratio and proportionality in different paintings, students realized the use of proportional…

This article describes a project that focuses on how a Society and Environment unit could develop required numeracy. This is more of an integrated unit organised around a theme rather than a Society and Environment unit that required specific aspects of numeracy. Suggested data sources for examining students numeracy development included (1) a…

Values education is crucial since it is one of the factors to reach success in education in broader sense and in mathematics education in particular sense. It is also important for educating next generations of societies. However, previous research showed that expected importance for values education was not given in Mathematics courses. In a few…

This article presents results of a case study of a math circle designed for low income, minority students from an inner city middle school. The students were 6th, 7th and 8th grade African American and Hispanic males enrolled in a science, technology, engineering and mathematics focused charter school. The study focused on the impact of…