Mathematics can be viewed as complex structures comprising intricate and profoundly useful webs of relationships. Students can experience mathematics in this way when working on mathematical tasks such as problem-solving, modelling, investigations or problem posing. Yet these kinds of tasks are seldom implemented in many upper-secondary and…

The way in which mathematics is communicated and represented in schools (including the written language, symbols and diagrams of mathematics textbooks and the verbal/spoken classroom interaction itself) constructs particular views of the nature of mathematics and expectations about students' participation in mathematical activity. In a previous…

We report on five-year professional development collaboration with a group of middle-school mathematics teachers during which their views of what constitutes a productive classroom statistical activity changed. The teachers' statistics instruction was initially typical in the US context and focused on producing calculations and following…

The purpose of the current article is to test and revise the hypothetical learning trajectory designed for teaching quadrilaterals by reporting the classroom mathematical practices emerged in a social learning environment developing preservice middle school mathematics teachers' understanding of quadrilaterals. Ten preservice teachers participated…

An exploratory study was conducted to investigate the use of magic activities in a math course for prospective middle-school math teachers. This research report focuses on a lesson using two versions of math magic: (1) the "5-4-3-2-1-½ Magic" involves having students choose a secret number and apply six arithmetic operations in sequence…

Issue 41 of Bank Street's Occasional Paper Series features a collection of papers by authors with a shared affinity for the work of critical mathematical inquiry (CMI). Essays in this issue include: (1) Teaching for Social Justice through Critical Mathematical Inquiry (Steven Greenstein and Mark Russo); (2) Re-designing Mathematics Education for…

When students are working together, some off-task conversations actually smooth the way to working together more effectively. While many assume that off-task talk is unproductive, our study revealed that students used off-task talk predominantly for productive purposes. We found that off-task talk supported student access to collaboration, and…

This article describes a project in which students investigate the question: What dihedral angles between pairs of mirrors in a kaleidoscope result in perfectly symmetric images? The unit culminates with students building their own kaleidoscopes. This content aligns with parts of the Common Core's standards for fifth grade (classify…

As part of the CBAL® learning and assessment initiative in mathematics, we developed a hypothesized learning progression (LP) for geometrical measurement in 1, 2, and 3 dimensions based on a synthesis of empirical literature in this field and through expert review. The geometrical measurement LP is intended to represent a developmental progression…

Two simple discrete-time models of mutation-induced cannibalism are introduced and investigated, one linear and one nonlinear. Both form the basis for possible classroom activities and independent investigative study. A range of classroom exercises are provided, along with suggestions for further investigations.

This case study investigated how three teachers developed mathematical modelling activities integrated with content standards through participation in a course on mathematical modelling. The class activities involved experiencing a mathematical modelling activity, reading and rating example mathematical modelling activities, reading articles about…

The introduction to general topology represents a challenging transition for students of advanced mathematics. It requires the generalization of their previous understanding of ideas from fields like geometry, linear algebra, and real or complex analysis to fit within a more abstract conceptual system. Students must adopt a new lexicon of…

Integrating multiple theoretical frameworks, the authors examined rising first- to fourth-grade students' mathematics utility conceptions--their knowledge and beliefs about the usefulness of mathematics, home-based mathematics engagement, and grade-level differences in mathematics utility conceptions and home engagement. Most children viewed…

Functional near-infrared spectroscopy (fNIRS) is an easy to use neuroimaging technique that is portable and maintains a liberal tolerance to movement. As such, fNIRS represents an ideal tool to observe children's neural activity as they engage in real-world classroom activities, such as the interaction with digital math apps on an iPad. Here, we…

If teachers have a deeper comprehension of their students' reading ability, it may lead to students' improved literacy and understanding of the subject. The account presented in this article of the author's growing interest in mathematical literacy specifically involves mathematical reading. This shift in interest began with a six-week…