ERIC Number: EJ1431370
Record Type: Journal
Publication Date: 2024
Pages: 20
Abstractor: As Provided
ISBN: N/A
ISSN: ISSN-1947-7503
EISSN: EISSN-2472-7466
Units Coordination, Combinatorial Reasoning, and the Multiplication Principle: The Case of Ashley, an Advanced Stage 2 College Student
Erik Tillema; Joseph Antonides
Investigations in Mathematics Learning, v16 n3 p243-262 2024
The multiplication principle (MP) is foundational for combinatorial problem-solving. From a units-coordination perspective, applying the MP with justification entails establishing unit relationships between the number of options at each independent stage of a counting process and the total number of combinatorial outcomes. Existing research literature, however, has not captured, generally, how students establish these unit relationships. We provide a second order model of an advanced stage 2 college student, Ashley, who had no prior combinatorics instruction, as she engaged in solving combinatorics problems that we considered to involve the MP. Our findings suggest that Ashley began by interpreting combinatorics problems using her whole number iterative units coordination scheme. Through engagement with the teacher-researcher, Ashley constructed combinatorial composites using a pairing operation, units coordination, and units simplification. We also found that Ashley was able to create a three-level-of-unit structure in activity, and to use notation that she produced to re-instantiate the reasoning that produced this unit structure. Doing so provides novel insights into how advanced stage 2 students, especially those at the college level, can use notation to manage complex unit relationships.
Descriptors: Multiplication, Mathematical Logic, Mathematics Instruction, Problem Solving, Computation, College Mathematics, Undergraduate Students
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Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education; Postsecondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A