Abstract
A research link between conditional reasoning and mathematics has been reported only for late adolescents and adults, 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. 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 Theory (MMT) 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, 102 students in Cyprus from grades 2, 4, and 6 solved four conditional reasoning tasks on each type of content (everyday and mathematical). All four logical forms, modus ponens (MP), modus tollens (MT), denial of the antecedent (DA), and affirmation of the consequent (AC), were included in each task. Consistent with previous findings, even second graders were able to make correct inferences on some logical forms. Controlling for Working Memory (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. It extends results concerning the gradual development of primary students’ conditional reasoning with everyday concepts 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.
Highlights
The ability to make valid deductions is considered of central importance for scientific reasoning, hypotheses generation, and evaluation (Kuhn et al, 1988), as well as for mathematical thinking (Moshman, 1990; Markovits and Lortie-Forgues, 2011) and learning and success (Nunes et al, 2007; Morsanyi and Szücs, 2014). Crombie (1994) puts forward mathematical deduction as one of six styles of scientific reasoning, which Kind and Osborne (2017) propose as a framework for science education
We focus on deductive reasoning with mathematical concepts as an important mode of scientific reasoning, which extends and complements research on other scientific styles, such as experimentation
Definite conclusions are possible for modus ponens (MP; minor premise “p is true” or “we have two numbers that have an odd sum” in the example) and modus tollens (MT; minor premise “q is false” or “we have two numbers that do not have an even product”)
Summary
The ability to make valid deductions is considered of central importance for scientific reasoning, hypotheses generation, and evaluation (Kuhn et al, 1988), as well as for mathematical thinking (Moshman, 1990; Markovits and Lortie-Forgues, 2011) and learning and success (Nunes et al, 2007; Morsanyi and Szücs, 2014). Crombie (1994) puts forward mathematical deduction as one of six styles of scientific reasoning, which Kind and Osborne (2017) propose as a framework for science education. Kind and Osborne (2017) argue that an exclusive focus of psychological and science education research on a restricted set of scientific reasoning styles, such as experimentation, offers students an “impoverished account of scientific thinking.” In this contribution, we focus on deductive reasoning with mathematical concepts as an important mode of scientific reasoning, which extends and complements research on other scientific styles, such as experimentation. Mathematical concepts are characterized by specific properties, which often have the form of conditional statements (e.g., “If the sum of two whole numbers is odd, their product is even”). Making inferences with such statements requires conditional reasoning skills. Conditional statements are a central part of mathematical discourse, but they occur frequently in everyday language and communication, for example, as with rules such as “If you have a fever, you will have to stay in bed.”
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