Studies have found that some teacher professional development programs that are based on Cognitively Guided Instruction (CGI) can increase student mathematics achievement. The mechanism through which those effects are realized has been theorized, but more empirical study is needed. In service of this need, we designed a novel measure of…

In this article, the authors examine the mathematical thinking and experiences that are unique to infants, toddlers, and 2-year-olds. They identify the four precursor mathematical concepts of attribute, comparison, pattern, and change and explore them in terms of why it is so important to attend to them, what makes them inherently mathematical and…

Schools seem firmly rooted in the emphasis on computational mastery, and seldom seem to have time to develop other areas of mathematical thinking, such as real-world problem solving and the application of mathematical concepts. All too often, children seem to do well in math in the early grades because they easily memorize the facts and the…

This paper offers an account of what early mathematics education could look like in an age of young digital natives. Each "Tubby," as the tablets are called, presents Nicole (our generic little child) with stimulating mathematics microworlds, from which, beginning at age 3, she can learn basic math concepts, as well as methods of…

Presents a short biography of one of the winners of the American Psychological Association's Award for Distinguished Scientific Early Career Contributions to Psychology (2012). Thomas L. Griffiths won the award for bringing mathematical precision to the deepest questions in human learning, reasoning, and concept formation. In his pioneering work,…

Developing critical numeracy is important in a society where mathematics plays a particular and significant role. One way of helping learners to develop the level of numeracy required to participate in society is by exploring ideas embedded in rich, accessible tasks. These can be linked to contexts that have relevance in their lives. One…

This article describes some aspects of Piaget's Theory of Cognitive Development. It highlights the importance of giving young children specific access to explore conservation in measurement, which will give students invaluable experiences in measurement that in years to come will be regarded as their prior knowledge of the concept. This is…

The theory of conceptual fields is a developmental theory. It has two aims: (1) to describe and analyse the progressive complexity, on a long- and medium-term basis, of the mathematical competences that students develop inside and outside school, and (2) to establish better connections between the operational form of knowledge, which consists in…

Algebra is a gateway to expanded opportunities, but it often poses difficulty for students with learning disabilities. Consequently, it is essential to identify evidence-based instructional strategies for these students. The authors begin by identifying three areas of algebra difficulty experienced by students with disabilities: cognitive…

Formal mathematical methods remain, for most high school students, mysterious, artificial and not a part of their regular intuitive thinking. The authors develop some themes that could lead to a radically new approach. According to this thesis, the teaching of programming languages as a regular part of academic progress can contribute effectively…

Evert Willem Beth (1908-1964) was a Dutch logician, mathematician and philosopher, whose work mainly concerned the foundations of mathematics. Beth was among the founders of the Commission Internationale pour l'Etude et l'Amelioration de l'Enseignement des Mathematiques and was a member of the Central Committee of the International Commission on…

Children's thinking follows natural developmental paths in learning math. When teachers understand those paths and offer activities based on children's progress along them, they build developmentally appropriate math environments. The authors explain math learning trajectories and why teaching math using the trajectories approach is effective. A…

One of most notable features of existing body of research in transition seems to be the absence of a theoretical model. The suggestion we present in this paper--to view and understand the high school to university transition in mathematics as a modern-day rite of passage--is an attempt at defining such framework. Although dominantly reflecting…

The developmental psychology of mathematical thinking and the clinical interview method can make major contributions to education by transforming the process of formative assessment--the attempt to use information concerning student performance, knowledge, learning potential, and motivation to inform instruction. The clinical interview is a…

Mathematics and science are important for success in school, but learning mathematics and science can be a difficult task to some students. Efforts to improve students' learning of school mathematics and science have led to reform efforts in curriculum and instruction over the past decades (e.g., National Council of Teachers of Mathematics [NCTM],…