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Creators/Authors contains: "Dawkins, Paul Christian"

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  1. ; (, Journal for Research in Mathematics Education)
    This article offers the construct unitizing predicates to name mental actions important for students’ reasoning about logic. To unitize a predicate is to conceptualize (possibly complex or multipart) conditions as a single property that every example has or does not have, thereby partitioning a universal set into examples and nonexamples. This explains the cognitive work that supports students to unify various statements with the same logical form, which is conventionally represented by replacing parts of statements with logical variables p or P(x). Using data from a constructivist teaching experiment with two undergraduate students, we document barriers to unitizing predicates and demonstrate how this activity influences students’ ability to render mathematical statements and proofs as having the same logical structure. 
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  2. ; ; (, The Journal of Mathematical Behavior)
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  3. ; (, ZDM – Mathematics Education)
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  4. ; (, The Journal of Mathematical Behavior)
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  5. ; (, Proceedings of the 12th Congress of the European Society for Research in Mathematics Education)
    Based on data from a teaching experiment with two undergraduate students, we propose the unitizing of predicates as a construct to describe how students render various mathematical conditions as predicates such that various theorems have the same logical structure. This may be a challenge when conditions are conjunctions, negative, involve auxiliary objects, or are quantified. We observe that unitizing predicates in theorems and proofs seemed necessary for students in our study to see various theorems as having the same structure. Once they had done so, they reiterated an argument for why contrapositive proofs proved their associated theorems, showing the emergence of logical structure. 
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    Accepted Manuscript Full Text Available
  6. ; (, Proceedings of the 12th Congress of the European Society for Research in Mathematics Education)
    Based on data from a teaching experiment with two undergraduate students, we propose the unitizing of predicates as a construct to describe how students render various mathematical conditions as predicates such that various theorems have the same logical structure. This may be a challenge when conditions are conjunctions, negative, involve auxiliary objects, or are quantified. We observe that unitizing predicates in theorems and proofs seemed necessary for students in our study to see various theorems as having the same structure. Once they had done so, they reiterated an argument for why contrapositive proofs proved their associated theorems, showing the emergence of logical structure. 
    more » « less
    Accepted Manuscript Full Text Available