In this commentary, we briefly review the collective effort of design researchers to weave theory with empirical results, in order to gain a better understanding of the processes of learning. We seek to respond to this challenging agenda by centring on the evolution of one sub-field: namely that which involves investigations within a…

In this interview, biologist, artist, and shiatsu healer Artemis Papert describes how computational thinking can help people organize their thoughts in a more formal way. She discusses TurtleArt, a software that allows both children and adults to create two-dimensional static art images using geometry and coding as a medium. TurtleArt not only…

The authors of this article strongly advocate for a change to the current Australian model of primary education in order to, among other things, establish the concrete practicalities of systematic mathematics thinking thereby limiting the "re-teaching" time required of secondary school mathematics teachers; bring a clear focus to the…

Humans can learn to organize many kinds of domains into categories, including real-world domains such as kinsfolk and synthetic domains such as sets of geometric figures that vary along several dimensions. Psychologists have studied many individual domains in detail, but there have been few attempts to characterize or explore the full space of…

It is of deep interest to both linguists and psychologists alike to account for how young children acquire an understanding of number words. In their commentaries, Barner and Butterworth both point out that an important question highlighted by the work of Syrett, Musolino, and Gelman, and one that remains highly controversial, is where number…

As an undergraduate in the 1960s, the author mostly used a slide rule for calculations and a Marchant-brand motor-operated mechanical calculator for statistics. This was after an elementary education replete with learning multiplication tables and taking speed and accuracy tests in arithmetic. Times have changed and assuming even basic calculation…

Probability is an essential tool for understanding heredity and modern genetics, yet many students have difficulty with this topic due to the abstract and quantitative nature of the subject. To facilitate student learning of probability in genetics, we have developed a set of hands-on, cooperative activities that allow students to determine…

Examines some of the issues that underlie the conceptual structure of the computational approach to cognition. Finds that this approach construes symbolization too narrowly, thereby blocking more adequate treatments of learning and acquisition of skills. Discusses the notion of symbol and symbolization and suggests an alternative approach to the…

Examines Kolers and Smythe's 1984 paper on the computational approach to cognition. Considers: (1) five specific criticisms of the computational approach, (2) their analysis of the conceptual basis of symbolization, and (3) their proposed alternative approach. Summarizes their position and discusses its shortcomings. (SED)

Discusses Kolers and Smythe's 1984 paper on the computational approach to cognition. Suggests some factors that support the continued emphasis on the analytic approach of the psychological representation of knowledge, but also acknowledges that they have provided a useful set of distinctions and at least one vocabulary for describing them. (SED)

Discusses the limitations in the explain-practice and active learning methods of teaching mathematics. Proposes that problem-centered learning is a teaching method that encourages student reflection, and presents examples demonstrating that encouraging reflection results in greater mathematics achievement. (MDH)

Experiments in strategy instruction for mathematics have been conducted using three models (direct instruction, self-instruction, and guided learning) applied to the tasks of computation and word problem solving. Results have implications for effective strategy instruction for learning disabled students. It is recommended that strategy instruction…

This article discusses how children learn to understand the decimal system in very concrete ways, while having fun using beads. When counting the beads, the children learn 5,491 is not simply "five thousand four hundred and ninety-one" but actually 5 thousands, 4 hundreds, 9 tens, and 1 unit. They begin to understand that as they get 10 units,…

Students should be encouraged to focus on a big mathematical idea and to look for connections between problems and solution strategies. This unified view suggests that the students are developing computational fluency with fractions.

The history of mathematics is full of rich examples that can help students to see the place of the discipline within our cultural heritage. Valuable as this can be, it also has the unfortunate side-effect of making students think that all the math has already been done and they do not get a sense that the subject is dynamic and growing.…