Search results for "Elementary University Mathematics"
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Automated Checking of Flexible Mathematical Reasoning in the Case of Systems of (In)Equations and the Absolute Value Operator
2021
We present an approach and a tool for automatically providing feedback on solutions that involve complicated reasoning patterns. Currently the tool supports linear systems of equations and inequations that may also contain the absolute value operator and a restricted form of rational functions. This suffices for designing problems that are laborious to solve with standard mechanical procedures, but much easier using short-cuts that students may find by creative thinking. Earlier research has found that struggling with important mathematics promotes conceptual development. Our goal is to encourage students to such struggling. A crucial feature is to give them great freedom to choose the path…
Adapting Formal Logic for Everyday Mathematics
2022
Although logic is considered central to mathematics and computer science, there is evidence that teaching logic has not been a great success. We identify three issues where what is typically taught conflicts with what is needed by those who are supposed to apply logic. First, what is taught about the notion of implication often disagrees with human intuition. We argue that in some cases human intuition is wrong, and in some others teaching is to blame. Second, the formal concepts of logical consequence, logical equivalence and tautology are not the similar concepts that everyday mathematicians and computer scientists need. The difference is small enough to go unnoticed but big enough to cau…