Reasoning With Conditionals About Everyday and Mathematical Concepts in Primary School

摘要

A research link between conditional reasoning and mathematics has been reported only for late adolescents and adults (Attridge & Inglis, 2013; Stylianides, Stylianides, & Philippou, 2004; Durand-Guerrier, 2003), despite claims about the pivotal importance of conditional reasoning, i.e. reasoning with if-then statements, in mathematics. Secondary students’ problems with deductive reasoning in mathematics have been documented for a long time. However, evidence from developmental psychology shows that even elementary students possess some early conditional reasoning skills in familiar contexts (e.g Markovits et al., 1996). It is still an open question to what extent conditional reasoning with mathematical concepts differs from conditional reasoning in familiar everyday contexts. Based on Mental Model theories of conditional reasoning, we assume that (mathematical) content knowledge will influence the generation of models, when conditionals concern mathematical concepts. In a cross-sectional study, N=102 students in Cyprus from grade 2, 4, and 6 solved four conditional reasoning tasks on each type of content (everyday and mathematical). All four logical forms, Modus Ponens, Modus Tollens, Denial of the Antecedent, and Affirmation of the Consequent, were included in each task. Consistent with previous findings, even 2nd graders were able to make correct inferences on some logical forms. Controlling for WM, there were significant effects of grade and logical form, with stronger growth on MP and AC than on MT and DA. The main effect of context was not significant, but context interacted significantly with logical form and grade level. The pattern of results was not consistent with the predictions of MMT. Based on analyses of students’ chosen responses, we propose an alternative mechanism explaining the specific pattern of results. The study indicates that deductive reasoning skills arise from a combination of knowledge of domain-general principles and domain-specific knowledge. The study extends results concerning the gradual development of primary students' conditional reasoning with everyday concepts (Markovits & Barrouillet, 2002) to reasoning with mathematical concepts adding to our understanding of the link between mathematics and conditional reasoning in primary school. The results inspire the development of educational interventions, while further implications and limitations of the study are discussed.