In this article, we consider the phenomenon of improvisation by small groups of middle years students while engaged in rich mathematical tasks in a classroom setting. Working from the premise that improvisation comprises a spectrum of behaviour, we propose that there is a range of improvisational behaviours that may be observed as the students…

What is a teacher to do when students share an idea with underlying mathematics that is different from that of the student contribution being discussed? Could such situations be avoided to begin with? In this article, the authors share strategies that can help teachers better keep the mathematics related to the student contribution under…

Minecraft is an open world survival computer game that was originally created in Sweden in 2011 and later purchased by Microsoft® in 2014. It is among the most popular computer games with students of all ages because it gives players a sense of ownership and opportunities for creative exploration. The game has three unique features: (1) no clear…

This study explores the relationships among students' perceived learning opportunities in school mathematics, their perceptions of self in mathematics, and their desire to learn more mathematics in the future. Data included student survey responses from eighth and tenth grade students from a state in the Southeast region of the United States.…

Internationally mathematical modeling is garnering more attention for the benefits associated with it. Mathematical modeling can develop students' communication skills and the ability to demonstrate understanding through different representations. With the increased attention on mathematical modeling, there is a need for more curricula to be…

Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…

Researchers of mathematics education have been paying attention to the affective aspect of learning mathematics for more than one decade. Different theoretical frameworks have been suggested to analyze this aspect, where we utilize in the present research the discursive framework of Evans, Morgan and Tsatsaroni. This framework enables to link…

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…

While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts,…

Technology may play a critical role in impacting student engagement, specifically within an assessment context. Using a mixed methods approach, I examined the relationship between varying degrees of technology-enhancements applied in a mathematics performance task on the outcome of student cognitive engagement. Using a counterbalanced…

This paper examines the learning by students who were participating in a project designed to promote persistence while working on mathematical tasks. We examined their learning of mathematics concepts and learning about the processes of engaging in mathematical tasks. There were substantial increases in students' knowledge of angles and also…

Within recent years, history of mathematics (HoM) has become an increasingly popular topic. Studies have shown that student reactions to it depend on the ways they use history of mathematics. The present action research study aimed to make students deduce volume rules of frustum pyramids using the dissection method. Participants were 24 grade…

The study of function transformations helps students understand the function concept which is a basic and main concept in mathematics, but this study is problematic to school students as well as college students, especially when transformations are performed on non-basic functions. The current research tried to facilitate grade 9 students'…

An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

This naturalistic case study investigates the problem posing patterns that emerge as four small groups of 12 year old students in Western Canada work collectively on a structured mathematics task. A method of data analysis is introduced that blurs the data to create transcript "tapestries" providing visual evidence of collective patterns…