Supporting Algebraic Reasoning through Personalized Story Scenarios: How Situational Understanding Mediates Performance

Abstract

Context personalization refers to matching instruction to students' out-of-school interests and experiences. Belief in the benefits of matching instruction to interests is widely held in the culture of schooling; however, little research has empirically examined how interest impacts performance and learning in secondary mathematics. Here we investigate these issues with a series of problem-solving sessions where 24 Algebra I students were presented with story problems on linear functions, some of which were personalized to their interests. Our analyses focus on performance, strategy use, and mistake patterns. Results suggest that personalization supported situational reasoning (Nathan, Kintsch, & Young, 1992) about the actions and relationships in the scenario, improving performance for weaker students and on harder problems. However, personalized scenarios seemed to act as a distraction when stronger students in the sample worked on easier problems. Thus context personalization may have the potential to provide assistance and support performance as students learn new concepts.

ACKNOWLEDGMENTS

This work was supported by the Pittsburgh Science of Learning Center, which is funded by the National Science Foundation, award number SBE-0354420. Special thanks to Mitchell Nathan, Jim Greeno, and Ken Koedinger for their valuable contributions to our thinking on this study. Thanks to Jennifer Cooper for her thoughtful and detailed comments on drafts of this manuscript. A previous version of this manuscript was presented at the 2011 Annual Meeting of the American Educational Research Association, and won the “Graduate Student Research” award for Division C.

This work was supported by the Pittsburgh Science of Learning Center, which is funded by the National Science Foundation, award number SBE-0354420.

Notes

¹Readability was measured by the Flesh-Kincaid Reading Ease score.

²Only 22 of the 24 students were asked which problem was easiest.

³Two coders coded all instances of student responses, and obtained a Cohen's kappa value of 0.92.

⁴The model showed no significant interaction between problem part and problem type, so the significance level of the results is the same across all problem parts (result unknown, start unknown, and write equation). However, given the nonlinear nature of the logistic function, the sizes of the effects are different. Performance differences for result unknowns only are provided for brevity.

⁵The cell for medium-scoring student solving an easy problem is empty because only personalized problems were solved that fell into this category.

⁶This was an instance where the student did not understand a vocabulary word (“break even”) in the story of the start unknown problem part, and did not respond as a result.