Studies on math education and weak trigraph homomorphisms

Date

2024-01-03

Authors

Mullin, Freddie

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Abstract

This thesis is comprised of two parts: (i) a study of homomorphisms of weak trigraphs and (ii) an analysis of the effectiveness of the University of Victoria (UVic) Department of Mathematics and Statistics’ Pretest. In the first part of the thesis, we study homomorphisms of weak trigraphs. Results analogous to those for graph homomorphisms are developed. In particular, we determine the complexity of decid- ing whether there is a weak trigraph homomorphism of a weak trigraph G to a weak trigraph H, the complexity of deciding whether a given weak trigraph has a weak trigraph homomorphism to a proper subgraph (the complexity of deciding whether it is not a core) and describe an efficient algorithm based on consistency checking that determines whether there is a weak trigraph homomorphism from a given cactus weak trigraph to a fixed weak trigraph H. In the second part of the thesis, we analyze the effectiveness of the UVic Pretest. First we compare the current online pretest with the past paper pretest in terms of their respective effectiveness in identifying students who are ready for Calculus I. We also analyze the current online pretest in greater detail, to identify which precalculus skills are most likely to predict success on that test itself. Finally, we use odd ratios to categorize each question on the online pretest and identify questions that are particularly useful to the test.

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Keywords

Math Education, Weak Trigraph, Homomorphisms, University of Victoria, UVic, Calculus Readiness, Pretest, Trigraph, Weak Trigraph Homomorphism

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