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\contentsline {figure}{\numberline {5.2.1}{\ignorespaces Conceptualizations found for what a proof is\relax }}{49}
\contentsline {figure}{\numberline {5.3.1}{\ignorespaces Student Conceptualizations of How to Comprehend a Proof\relax }}{51}
\contentsline {figure}{\numberline {5.4.1}{\ignorespaces Conceptualizations about why to study proofs\relax }}{55}
\contentsline {figure}{\numberline {5.8.1}{\ignorespaces Conceptualizations about validity of proofs\relax }}{62}
\contentsline {figure}{\numberline {5.10.1}{\ignorespaces Themes from interview data\relax }}{65}
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\contentsline {figure}{\numberline {6.1.1}{\ignorespaces Categories of Student Conceptualizations of Proof by Induction that Recursion Works\relax }}{83}
\contentsline {figure}{\numberline {6.7.1}{\ignorespaces Conceptualizations found for what a proof is\relax }}{112}
\contentsline {figure}{\numberline {6.8.1}{\ignorespaces Conceptualizations of how to comprehend a proof\relax }}{113}
\contentsline {figure}{\numberline {6.9.1}{\ignorespaces Conceptualizations about why to study proofs\relax }}{115}
\contentsline {figure}{\numberline {6.13.1}{\ignorespaces Conceptualizations about validity of proofs\relax }}{118}
\contentsline {figure}{\numberline {6.15.1}{\ignorespaces Themes from interview data\relax }}{124}
\contentsline {figure}{\numberline {.0.1}{\ignorespaces Equation (1)\relax }}{134}
\contentsline {figure}{\numberline {.0.2}{\ignorespaces Equation (2)\relax }}{134}
\contentsline {figure}{\numberline {.0.3}{\ignorespaces \relax }}{136}
\contentsline {figure}{\numberline {.0.4}{\ignorespaces \relax }}{136}
\contentsline {figure}{\numberline {.0.5}{\ignorespaces First\relax }}{137}
\contentsline {figure}{\numberline {.0.6}{\ignorespaces Second\relax }}{137}
\contentsline {figure}{\numberline {.0.7}{\ignorespaces \relax }}{142}