Learning Fractions by Splitting: Using Learning Analytics to Illuminate the Development of Mathematical Understanding

The struggle with fraction learning in kindergarten through Grade 12 in the United States is a persistent problem and one of the major stumbling blocks to succeeding in higher mathematics. Research into this problem has identified several areas where students commonly struggle with fractions. While...

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Bibliographic Details
Published in:The Journal of the learning sciences 2015-10, Vol.24 (4), p.593-637
Main Authors: Martin, Taylor, Petrick Smith, Carmen, Forsgren, Nicole, Aghababyan, Ani, Janisiewicz, Philip, Baker, Stephanie
Format: Article
Language:English
Subjects:
Cluster analysis
Concept Formation
Data Analysis
Data Collection
Distance Education
Educational Games
Elementary School Mathematics
Elementary School Students
Fractions
Grade 3
Grade 5
Learning
Learning Analytics
Mathematical Aptitude
Mathematical Concepts
Mathematics
Mathematics Instruction
Multivariate Analysis
Pretests Posttests
Secondary school students
Teaching Methods
Transfer of Training
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Summary:The struggle with fraction learning in kindergarten through Grade 12 in the United States is a persistent problem and one of the major stumbling blocks to succeeding in higher mathematics. Research into this problem has identified several areas where students commonly struggle with fractions. While there are many theories of fraction learning, none of the research on these theories employs samples large enough to test theories at scale or nuanced enough to demonstrate how learning unfolds over time during instructional activities based on these theories. The work reported here uses learning analytics methods with fine-grained log data from an online fraction game to unpack how splitting (i.e. partitioning a whole into equal-sized parts) impacts learning. Study 1 demonstrated that playing the game significantly improved students' fraction understanding. In addition, a cluster analysis suggested that exploring splitting was beneficial. Study 2 replicated the learning results, and a cluster analysis showed that compared to early game play, later game play showed more optimal splitting strategies. In addition, in looking at the types of transitions that were possible between a student's early cluster categorization and later cluster categorization, we found that some types of transitions were more beneficial for learning than others.
ISSN:1050-8406
1532-7809
DOI:10.1080/10508406.2015.1078244