The task shared in this article provides geometry students with opportunities to recall and use basic geometry vocabulary, extend their knowledge of area relationships, and create area formulas. It is characterized by reasoning and sense making (NCTM 2009) and the "Construct viable arguments and critique the reasoning of others"…

We present a design study developed in an Italian school. Taking inspiration from the work of the Russian psychologist V. V. Davydov, we have reformulated some activities of his curriculum for the first grade, in order to adapt them to a didactic project for a fifth grade class. In the paper we firstly expose our theoretical assumptions and the…

We study here an aspect of an infinite set "P" of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of probability "P" for which every element may be expressed as a finite sum of squares of real…

In this article, the authors describe how a theoretical framework--the modeling cycle of Bliss, Fowler, and Galluzzo (2014)--came to life in their classroom as students struggled with an open-ended modeling task. The authors share their high school students' work--warts and all. They explain how they used their students' ideas and errors to help…

Mathematics itself is a living and creative act (Boaler, 2008), and mathematicians themselves often collaborate in their work (Burton, 2004). What, then, is holding school mathematics back? Are educators so conditioned to expect the act of mathematizing in school to proceed in a certain abstract, formalized way that they are neglecting other means…

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…

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…

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…

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.

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…

In many mathematics curricula, the notion of limit is introduced three times: the limit of a sequence, the limit of a function at a point and the limit of a function at infinity. Despite the use of very similar symbols, few connections between these notions are made explicitly and few papers in the large literature on student understanding of…

Every day, 27,000 trees are used to make bathroom tissue. Americans use an average of 23.6 rolls per person per year, and more than 7 billion rolls of toilet paper are sold yearly in the United States alone. Perhaps the amount of bathroom tissue used can be reduced by changing the dimensions of the paper or the core. This brief article presents…

Technology integration in K-12 mathematics has received increased attention in the last decade as new mathematical technologies have been developed and implemented more often. There is a need for further research on these technologies and for effective implementation practices of technology in mathematics education in general. in practice,…

Our goal in this article is to discuss the importance of problems in early childhood education for the child's development and engagement with the mathematics existing in childhood culture. Our assumption is that an important task for young children's education is to create a democratic and critical environment, in which multiplicity of…

Elementary school children (ages 7-11) struggle to understand mathematical equivalence, a foundational prealgebraic concept. Some manipulations to the learning environment, including well-structured nontraditional arithmetic practice alone, have been shown to improve children's understanding; however, improvements have been modest. The goal of…