Children's sense of numbers before formal education is thought to rely on an approximate number system based on logarithmically compressed analog magnitudes that increases in resolution throughout childhood. School-age children performing a numerical estimation task have been shown to increasingly rely on a formally appropriate, linear…

The international debate about experimental approaches to the teaching and learning mathematics is very current. While number theory lends itself naturally to such approaches, elementary geometry can also provide interesting starting points for creative work in class. This article shows how simple considerations about right triangles and the…

Deaf students often lag behind hearing peers in numerical and mathematical abilities. Studies of hearing children with mathematical difficulties highlight the importance of estimation skills as the foundation for formal mathematical abilities, but research with adults is limited. Deaf and hearing college students were assessed on the…

Young children spontaneously engage in a variety of one-to-one correspondence activities during play. The present study tested whether one of these activities--pairing objects with containers--supported the development of numerical equivalence judgments. Three-year-olds were given sets of toys to take home. In one condition, the toys were…

In this article, a simple exercise for finding groups isomorphic to the symmetry group of the real line is presented. A mechanism for producing metrics on the real line is used to construct the group elements, and these transformations, by construction, are isometries with respect to the generating metric.

The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…

This paper aims to describe how students develop understanding of one-digit decimals. To achieve the aim, Local Instruction Theory (LIT) about the process of learning decimals and the means designed to support that learning are developed. Along with this idea, the framework of Realistic Mathematics Education (RME) is proposed. Based on the aim,…

In this article, the authors illustrates techniques for integrating diverse learners in shared mathematical contexts while providing differentiated support or challenge, as necessary. The techniques described were developed for a curriculum project entitled Learning Mathematics through Representations (LMR). A premise of LMR is that students'…

Incorporating the use of children's literature when teaching mathematics to young children is a developmentally appropriate practice: "Literature … provides a means for children to encounter mathematical concepts and vocabulary in the context of something familiar, a story" (Fogelberg et al. 2008). Moreover, introducing culturally…

Motivating middle school students to learn can be challenging. One proven method for doing so is through an integrated curriculum. Educational philosophers and curriculum theorists have long noted the benefits of an integrated curriculum, which recognizes that the subject areas within the curriculum are connected to one another and to the real…

Do concrete learning materials promote strong learning outcomes, or do they simply make learning tasks more initially accessible? Although concrete materials may offer an intuitive foothold on a topic, research on desirable difficulties suggests that more challenging tasks facilitate greater retention and transfer. In the approach introduced here,…

The general purpose of this article is to shed some light on the understanding of real numbers, particularly with regard to two issues: the real number as the limit of a sequence of rational numbers and the development of irrational numbers as a continued fraction. By generalizing the expression of the golden ratio in the form of the limit of two…

Studies reveal that students as well as teachers have difficulties in understanding and learning of decimals. The purpose of this study is to investigate students' as well as pre-service teachers' solution strategies when solving a question that involves an estimation task for the value of a decimal number on the number line. We also examined the…

In this study, using ADDIE instructional design model, it is aimed to prepare English language educational material for 4th grade primary students to teach them numbers. At the same time, ARCS model of motivation's attention, relevance and satisfaction phases are also taken into consideration. This study also comprises of Design Based Research…

This paper was born out of combinatorics. It defines a level of utility which, though it cannot be measured, can be preferred to another in each specific combination of goods. In turn, each combination defines a menu, meaning that there will be as many menus as there are combinations of goods. In this manner, we have a menu and a utility for each…