One of the main tenets of the mental model theory is that when individuals reason, they think about possibilities. According to this theory, reasoning on what is possible from the truth of a sentence would be psychologically basic, whereas reasoning the other way round, on the truth or falsity of a sentence from a given state of affairs, would…

According to Klahr's (2000, 2005; Klahr & Dunbar, 1988) Scientific Discovery as Dual Search model, inquiry processes require three cognitive components: hypothesis generation, experimentation, and evidence evaluation. The aim of the present study was to investigate (a) when the ability to evaluate perfect covariation, imperfect covariation,…

To conceive the infinity of integers, one has to realize: (a) the unending possibility of increasing/decreasing numbers (potential infinity), (b) that the cardinality of the set of numbers is greater than that of any finite set (actual infinity), and (c) that the leap from a finite to an infinite set is itself infinite (immeasurable gap). Three…

Items commonly belong to many categories. Cross-classification is the classification of a single item into more than one category. This research explored 2- to 6-year-old children's use of 2 different category systems for cross-classification: script (e.g., school-time items, birthday party items) and taxonomic (e.g., animals, clothes). The…

This study examined the generality of the logarithmic to linear transition in children's representations of numerical magnitudes and the role of subjective categorization of numbers in the acquisition of more advanced understanding. Experiment 1 (49 girls and 41 boys, ages 5-8 years) suggested parallel transitions from kindergarten to second grade…

o complementary experiments analyzed the acquisition of text content linearization in writing, in French-speaking participants from third to ninth grades. In both experiments, a scrambled text paradigm was used: eleven ideas presented in random order had to be rearranged coherently so as to compose a text. Linearization was analyzed on the basis…

This paper examines ways in which coherent reasoning about key concepts such as variability, sampling, data, and distribution can be developed as part of statistics education. Instructional activities that could support such reasoning were developed through design research conducted with students in grades 7 and 8. Results are reported from a…