We report a randomised controlled trial evaluation of an intensive one-to-one numeracy programme--"Numbers Count"--which formed part of the previous government's numeracy policy intervention--"Every Child Counts." We rigorously designed and conducted the trial to CONSORT guidelines. We used a pragmatic waiting list design to…

Previous studies have suggested that both automatic and intentional processes contribute to the learning of grammar and fragment knowledge in artificial grammar learning (AGL) tasks. To explore the relative contribution of automatic and intentional processes to knowledge gained in AGL, we utilized dual-task methodology to dissociate automatic and…

Theories of psychology and mathematics education recommend two instructional approaches to develop students' mental representations of number: The "exact" approach focuses on the development of exact representations of organized dot patterns; the "approximate" approach focuses on the approximate representation of analogue magnitudes. This study…

The First Grade Pre-Screening is designed to be used at the start of the first grade school year so that teachers can obtain information about their incoming students. This information is intended to give teachers insight about what math and reading skills a student may or may not have at the beginning of the year. The information can aid teachers…

This study sought to review literature pertinent to difficulties encountered by students in the learning and usage of mathematical terminology. The need to carry out this study arose from the concern by the Kenya National Examinations Council, and the general public, over the poor annual results in mathematics. Therefore, the objective of this…

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 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 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…