In this paper, we present data from two iterative teaching experiments involving students' constructions of four basic counting problems. The teaching experiments were designed to leverage the generalizing activities of relating and extending to provide students with opportunities to reflect on initial combinatorial activity when constructing…

Computational activity is increasingly relevant in education and society, and researchers have investigated its role in students' mathematical thinking and activity. More work is needed within mathematics education to explore ways in which computational activity might afford development of mathematical practices. In this paper, we specifically…

A striking characteristic of human thought is that we form representations about abstract kinds (Giraffes have purple tongues), despite experiencing only particular individuals (This giraffe has a purple tongue). These generic generalizations have been hypothesized to be a cognitive default, that is, more basic and automatic than other forms of…

Computational Thinking is considered a universal competence, which should be added to every child's analytical ability as a vital ingredient of their school learning. In this article we further elaborate on what Computational Thinking is and present examples of what needs to be taught and how. First we position Computational Thinking in Papert's…

Educators often use concrete objects to help children understand mathematics concepts. However, findings on the effectiveness of concrete objects are mixed. The present study examined how two factors--perceptual richness and established knowledge of the objects--combine to influence children's counting performance. In two experiments, preschoolers…

The study examined the effectiveness of a program to improve the cognitive skills of 91 hearing impaired college students. Experimental students received systematic cognitive instruction focusing on specific generalizable skills during the experimental period, several times per week, in the contexts of their regular college classes. Instructors of…