Child, Developmental & Lifespan Psychology books

How do children understand reasoning by mathematical induction? Mathematical induction - Poincare's reasoning by recurrence - is a standard form of inference with two distinctive properties. One is its necessity. The other is its universality or inference from particular to general. This means that mathematical induction is similar to both logical deduction and empirical induction, and yet is different from both. In a major study 40 years ago, Inhelder and Piaget set out two conclusions about the development of this type of reasoning in advance of logical deduction during childhood. This developmental sequence has gone unremarked in research on cognitive development. This study is an adaptation with a sample of 100 hundred children aged five-seven years in school years one and two. It reveals evidence that children can reason by mathematical induction on tasks based on iterative addition and that their inferences were made by necessity. According to the study the main educational implication is clear: young children can carry out iterative actions on actual objects with a view to reasoning about abstract objects such as numbers.

This volume is a sympathetic but analytical and critical view of social constructivist teaching, considering both its affordances (what it offers to students when implemented well in situations for which it is well suited) and its constraints (enabling conditions; situations in which these conditions are absent and other forms of teaching are more appropriate). Contributors were asked to explain what social constructivist teaching means in the areas of teaching in which their scholarly work has concentrated, to describe the forms that such teaching takes and the rationale for using them, assess their strengths/areas of applicability and their weaknesses/areas of irrelevance or limited applicability, and talk about how the approaches would need to be adjusted from their usual forms in order to match the affordances and limitations of certain students, instructional situations, etc. The authors focus on theory and research relating to social constructivist teaching, not merely social constructivist ideas about epistemology or learning. Taken together, the contributions encompass most grade levels and school subjects and include attention to small-group as well as whole-class settings and to selection of learning activities as well as scaffolding of discourse. Most currently available scholarly writing on social constructivist teaching is limited to consideration of propositional knowledge (defining it and identifying its key characteristics) and procedural knowledge (describing its implementation in detail). This volume also includes much-needed conditional knowledge (specification of when and why it would or would not be used).

This volume revisits a number of themes that have appeared in earlier "Advances" publications, including "Social Contexts of Early Development" and "Education and Reconceptualizing Play". New social contexts for early education and care often require that we aim our inquiry at social conditions that have not existed in the past, as well as elaborating long-standing concerns. Studies of some of the social contexts of early education point to how many of the needs of the field are unique, depending on where and when we do our work, and with whom we work. "Reconceptualizing Play" points to the multiple perspectives that teachers, researchers, parents, and children bring to our understanding of play. Culture, policy, belief, and values prove to be worthy lenses for enhancing our developmental views of childhood play and practice. Our hope is that others will build on some of these reconceptualizations, to assist teachers and families to improve the lives of children in their programs.