Learning Logic: examining the effects of context ordering on reasoning about conditionals

Abstract

Logical statements are prevalent in mathematics, the sciences, law, and many areas of everyday life. The most common logical statements are conditionals, which have the form "If H…, then C…," where "H" is a hypothesis (or condition) to be satisfied and "C" is a conclusion to follow. Reasoning about conditionals depends on four main conditional contexts (e.g., intuitive, abstract, symbolic, or counterintuitive). The purpose of this study was to test a theory about the effects of context ordering on reasoning about conditionals. Researchers developed and tested a virtual manipulative mathematics app, called the Learning Logic App. This study addressed the question: "How does the order of teaching four conditional contexts influence reasoning about conditionals?" A total of 154 participants, randomly assigned to a context ordering, interacted with the Learning Logic App online. Researchers collected data using a Conditional Logic Assessment, score logs, and participant surveys. The results suggest that context ordering does influence learners' reasoning. The most beneficial context ordering for learners' performance was symbolic-intuitive-abstract-counterintuitive. The most beneficial context ordering according to learners' perceptions was intuitive-abstract-counterintuitivesymbolic. Based on these results, researchers propose that the symbolic-intuitive-abstractcounterintuitive-symbolic ordeing may be most effective for learning about conditionals. This progression incorporates a catalyst at the beginning (symbolic) which aids the learner in reassessing prior knowledge. Next, the ordering progresses from easiest to hardest (intuitiveabstract-counterintuitive-symbolic). These findings suggest the importance of the sequencing for teaching and learning to reason about conditionals. Research Question 1: How does the order of teaching four conditional contexts using the Learning Logic App influence learners' performance on the Conditional Logic Assessment? Research Question 2: What are learners' perceptions about how the order of teaching four conditional contexts influenced their performance on reasoning about conditionals? Research Design The research design for this study was a convergent parallel mixed methods design [25] that included the collection of quantitative and qualitative data. This design was chosen to provide a more complete understanding of participants' experiences with the different context

Venues for Analytical Reasoning Problems: How Children Produce Deductive Reasoning

“…Authors such as Hoyles and Küchmann [19], Epp [17], Lee [4], Nunes et al [16], Stylianides and Stylianides [7], and Lommatsch [22], among others, have advocated an explicit teaching of deductive reasoning in school mathematics. In general, they have criticized the teaching of propositional logic as an empty unit, considering the weak transfer of that learning to mathematics and problem-solving.…”

“…Not only do they seem to encourage the use of logical structures of high complexity, they have been shown to be within reach of the students' ability to reason deductively. The results also lead to the conclusion that this is a valuable resource for the integration of logical and deductive reasoning in the school setting, especially if one embraces the view that logic can and should be driven by the curriculum in order to make it meaningful, and as a way of establishing bridges with deductive reasoning in mathematics topics and in proofs [4,[16][17][18][19]22].…”