The consistency effect depends on markedness in less successful but not successful problem solvers: An eye movement study in primary school children

This study examined the effects of consistency (relational term consistent vs. inconsistent with required arithmetic operation) and markedness (relational term unmarked [‘more than’] vs. marked [‘less than’]) on word problem solving in 10–12 years old children differing in problem-solving skill. The results showed that for unmarked word problems, less successful problem solvers showed an effect of consistency on regressive eye movements (longer and more regressions to solution-relevant problem information for inconsistent than consistent word problems) but not on error rate. For marked word problems, they showed the opposite pattern (effects of consistency on error rate, not on regressive eye movements). The conclusion was drawn that, like more successful problem solvers, less successful problem solvers can appeal to a problem-model strategy, but that they do so only when the relational term is unmarked. The results were discussed mainly with respect to the linguistic–semantic aspects of word problem solving.     

Manipulatives and number sentences in computer aided arithmetic word problem solving

In this study we investigated the relative contribution of two main components often used in the instruction of arithmetic word problem solving to first-grade children and children with learning problems, external representation with manipulatives and formal mathematical representation with number sentences. Four computer aided treatments were developed along these dimensions. Furthermore, an assessment control group was formed.It was shown that performance improved significantly after treatment in comparison to the performance of the assessment control group. Comparison of the different training conditions showed that a number sentence treatment was the most effective training component. However, this effect was only present with the relatively high competent children and not with the relatively low performing children.     

Perspectives on educational psychology

As a background, the views are presented of Jean Jacques Rousseau, Johann Heinrich Pestalozzi, Friedrich Froebel, and Johann Friedrich Herbart, who had a five-step proposal for teaching. I then review briefly the new psychology of G. Stanley Hall and William James, followed by trends in psychology and education in the early twentieth century. The influences of psychoanalysis and Gestalt psychology are addressed, as well as the development of educational psychology textbooks and the growth of instructional psychology.     

New findings for concreteness and imagery effects in written composition

This experiment investigated the effects ofword concreteness and either imagery, verbal,or control strategy instructions on thecomposition of written definitions. Resultsrevealed significant effects of wordconcreteness on several quantity and qualityvariables, but no significant effect ofstrategy instructions or interaction betweenconcreteness and strategy instructions. Results of self-ratings of strategies actuallyused in composing revealed that a mentalimagery strategy was used with concrete wordsand a verbal strategy was used with abstractwords regardless of strategy instructions. Findings replicated the results of Tirre,Manelis and Leicht [(1979) Journal of ReadingBehavior 11, 99–106] in the production ofwritten composition on word relationships, andpartially replicated the results of Sadoski,Kealy, Goetz and Paivio [(1997) Journal of EducationalPsychology 89, 518–526] in the timedwritten production of word definitions. Results are interpreted from Dual Coding Theoryand levels of processing perspectives.     

A Semiotic Perspective of Mathematical Activity: The Case of Number

A semiotic perspective on mathematical activity provides a way of conceptualizing the teaching and learning of mathematics that transcends and encompasses both psychological perspectives focussing exclusively on mental structures and functions, and performance-focussed perspectives concerned only with student' behaviours. Instead it considers the personal appropriation of signs and the underlying meaning structures embodying relationships between signs. It is concerned with patterns of sign use and sign production, including individual creativity in sign use, and the underlying social rules and contexts of sign use. It is based on the concept of a semiotic system, comprising signs, rules of sign production, and an underpinning meaning structure. This theorisation is applied to the learning of number, from counting to calculation. Historical, foundational and developmental (i.e., learning) perspectives are explored and contrasted. It is argued that in each of these domains, the dominant significant activity concerns the production of sequences of signs.