Grounded Feedback in a Fraction Addition Tutor

• In Event: 35.030 - Multiple Representations and Multimedia: Student Learning and Instruction

Abstract

Objective
To determine when providing a second representation as feedback during problem solving enhances learning in mathematics.

Perspective
One approach to designing with multiple representations is to have the student solve a problem in a to-be-learned representation (often symbolic) and reflect the student’s actions in a second representation that supports students’ reasoning. This design pattern is termed grounded feedback: it is grounded “in the world” (the second representation) and in the student’s prior knowledge (Stampfer & Koedinger, 2012). Grounded feedback is a potentially powerful approach, as it encourages students to identify and correct their errors (Dugdale, 1992). However, few experiments have compared it to other types of support. Some found robust improvements in learning compared to problem-solving with right/wrong feedback (Mathan & Koedinger, 2005; Nathan, 1998), while others found no differences (Yerushalmy, 1991), or benefits for worked examples over grounded feedback when using three representations (Rau, Aleven, Rummel, & Rohrbach, 2012). More research is needed to identify the contexts and design strategies that make grounded feedback useful.

Methods
We experimentally compared grounded feedback to immediate, step-level right/wrong feedback in intelligent tutors for fraction addition (see figure 1). In the grounded feedback tutor, students practiced interpreting rectangle representations of fractions before being tutored on fraction addition. All components of the study were done online, and student actions were logged to DataShop (Koedinger et al., 2010). To analyze learning, we examined students pre- and post-test scores.

Data: Over four school periods, 122 fifth graders completed a pre-test, worked with their randomly-assigned tutor, and completed a counter-balanced post-test; time was controlled for each part.

Results
Both conditions improved from pre- to post-test (right/wrong feedback: 19%; grounded feedback: 23%; paired-samples t-tests show significant differences in within-condition pre- and post-test scores, p<.0005). However, an ANOVA showed that the difference in learning gains between the two conditions was only marginally significant (post-test score as dependent, pre-test score as covariate, condition and school tracking level as fixed factors; p = .063).

Significance
This study shows that grounded feedback may be just as beneficial for learning as step-level right/wrong feedback. Further, since total time with the tutors was controlled, it shows that giving students time to practice with the feedback representation does not detract from their learning of the target material. By comparing grounded feedback to a robust control, this study adds to the very limited literature on grounded feedback. Process measures and further data analysis may reveal individual differences in working with this feedback and will confirm if students interpreted the feedback effectively. Future work will use eye-tracking and think-aloud methods to measure students’ attention to the grounded feedback and how students think about problem solving when grounded feedback is available.

Authors

• Eliane Stampfer Wiese, Carnegie Mellon University

• Kenneth R. Koedinger, Carnegie Mellon University