Learning Logic

Examining the Effects of Context Ordering on Reasoning About Conditionals

Christina Lommatsch, Patricia S. Moyer-Packenham

Research output: Contribution to journalArticle

Abstract

Logical statements are prevalent in mathematics, science and everyday life. The most common logical statements are conditionals, ‘If H … , then C … ’, where ‘H’ is a hypothesis and ‘C’ is a conclusion. Reasoning about conditionals depends on four main conditional contexts (intuitive, abstract, symbolic or counterintuitive). This study tested 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.

A total of 154 participants, randomly assigned to a context ordering, interacted with the Learning Logic App. Researchers collected data using a Conditional Logic Assessment, score logs and surveys. The results suggest that context ordering influences learners’ reasoning. The most beneficial context ordering for learners’ performance was symbolic–intuitive–abstract–counterintuitive, but according to learners’ perceptions it was intuitive–abstract–counterintuitive–symbolic. Based on these results, researchers propose the symbolic–intuitive–abstract–counter intuitive–symbolic ordering. This progression incorporates a catalyst at the beginning (symbolic) which aids the learner in reassessing prior knowledge. Next, it progresses from easiest to hardest. These findings suggest the importance of sequencing for learning to reason about conditionals.
Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalInternational Journal of Mathematical Education in Science and Technology
DOIs
Publication statusE-pub ahead of print - 13 Jun 2019

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Reasoning
Logic
Application programs
mathematics
learning
Catalysts
everyday life
science
Catalyst
Progression
Prior Knowledge
Sequencing
knowledge
performance
Context
Learning
Intuitive

Cite this

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title = "Learning Logic: Examining the Effects of Context Ordering on Reasoning About Conditionals",
abstract = "Logical statements are prevalent in mathematics, science and everyday life. The most common logical statements are conditionals, ‘If H … , then C … ’, where ‘H’ is a hypothesis and ‘C’ is a conclusion. Reasoning about conditionals depends on four main conditional contexts (intuitive, abstract, symbolic or counterintuitive). This study tested 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.A total of 154 participants, randomly assigned to a context ordering, interacted with the Learning Logic App. Researchers collected data using a Conditional Logic Assessment, score logs and surveys. The results suggest that context ordering influences learners’ reasoning. The most beneficial context ordering for learners’ performance was symbolic–intuitive–abstract–counterintuitive, but according to learners’ perceptions it was intuitive–abstract–counterintuitive–symbolic. Based on these results, researchers propose the symbolic–intuitive–abstract–counter intuitive–symbolic ordering. This progression incorporates a catalyst at the beginning (symbolic) which aids the learner in reassessing prior knowledge. Next, it progresses from easiest to hardest. These findings suggest the importance of sequencing for learning to reason about conditionals.",
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