On the Existence of Balanced Chain Rule Task Sets
Haile Gilroy

TL;DR
This paper uses graph decomposition techniques to construct balanced calculus task sets that effectively assess understanding of the Chain Rule in mathematics education.
Contribution
It extends existing graph decomposition results to create balanced, mixed-topic calculus task sets focused on derivative computation and the Chain Rule.
Findings
Constructed balanced task sets for calculus derivative problems
Extended graph decomposition methods to educational task set design
Provided a systematic approach for assessing the Chain Rule
Abstract
In mathematics education research, mathematics task sets involving mixed practice include tasks from many different topics within the same assignment. In this paper, we use graph decompositions to construct mixed practice task sets for Calculus I, focusing on derivative computation tasks, or tasks of the form "Compute of the function [elementary function]." A decomposition of a graph is a collection of nonempty subgraphs such that for some nonempty subset of , and is a partition of . We extend results on decompositions of the complete directed graph due to Meszka and Skupie\'n to construct balanced task sets that assess the Chain Rule.
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Taxonomy
TopicsFormal Methods in Verification · Fuzzy Logic and Control Systems · AI-based Problem Solving and Planning
