It's (Not) Ours To Reason Why: A Comparative Analysis of Algorithms for the Division of Fractions

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This research project takes a deep look at how division of fractions problems, known as some of the most complex to teach and learn in school mathematics, can be approached. It takes a look at the two main algorithms for division of fractions present in the literature and compares them in order to consider each algorithm's benefits and drawbacks in answering the following question: How do the common-denominator and invert-and-multiply algorithms for the division of fractions compare in terms of their algorithmic efficiency, curricular fit, and mathematical integrity? Through an analysis of efficiency based on the upper bound of the number of single-digit basic operations required to solve a division of fractions problem with each algorithm, and of the meaning and coherence based on multiple representations of the two algorithms and their grounding in the mathematics methodized by the Common Core State Standards, I found that the flip-and-multiply algorithm is more efficient because requires fewer single digit basic operation to produce an answer, but the common-denominator algorithm is more closely tied to the instructional content that typically precedes it in teaching fractions. However, this analysis also established the extent to which both algorithms have the potential to be taught with a strong grounding on mathematical ideas rather than just for the ability to give a numerical answer, which is arguably more important for learning mathematics than algorithmic efficiency.


Type of resource text
Date created May 2017


Author Cordero, Montserrat
Advisor Boaler, Jo


Subject mathematics education
Subject division of fractions
Subject fractions
Subject division
Subject efficiency
Subject honors thesis
Subject Stanford Graduate School of Education
Subject comparative analysis
Subject mathematics
Genre Thesis

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Cordero, Montserrat. (2017). It's (Not) Ours To Reason Why: A Comparative Analysis of Algorithms for the Division of Fractions. Unpublished Honors Thesis. Stanford University, Stanford CA.


Undergraduate Honors Theses, Graduate School of Education

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