# Toward Sense Making with Grounded Feedback

In STEM domains, robust learning includes not only fluency with procedures, but also recognition and application of the conceptual principles that underlie them. Grounded feedback is one instructional approach proposed to help students integrate conceptual knowledge into their learning of procedures. Grounded feedback functions primarily by having students take an action in the target domain (often symbolic) and receiving feedback in a representation that is easier to reason with. This thesis defines grounded feedback and evaluates its effectiveness. I define grounded feedback with four characteristics: (1) The feedback reflects students’ inputs according to rules that are inherent to the topic of study. For example, an inputted equation with two variables may be shown as a graph. (2) The feedback facilitates selfevaluation - by examining the feedback, students can evaluate for themselves if their answers are correct or not. (3) Students do not directly manipulate the feedback representation. Instead, the inputs are in a format that matches the domain learning goals. (4) The feedback conveys information about the nature of errors, not just that a particular action was incorrect. For example, the feedback may indicate the direction or magnitude of the error. Some prior experiments on systems with the four characteristics of grounded feedback found greater learning of target procedures (Nathan 1998) and greater transfer (Mathan & Koedinger 20015), relative to robust controls. Over four studies with 4th and 5th graders, this thesis explores three tutor designs for fraction addition that incorporate visualizations of magnitude, including grounded feedback. Two studies of grounded feedback show effects of robust learning relative to correctness feedback, including greater future learning (in study 2) and transfer (in study 3). Another study found little difference between grounded feedback with and without correctness. In the last study, relative to correctness feedback, two implementations of dynamically linked concrete representations (variations on grounded feedback) showed greater robust learning (pre-test to delayed test). The correctness feedback tutor, used in three of these studies, is a high-bar control, including immediate step-level correctness feedback and adaptive on-demand hints. Indications of more robust learning with the grounded feedback tutor are promising, though not conclusive. Grounded feedback is intended to leverage concrete representations to elicit students’ prior knowledge of relevant concepts. Over two Difficulty Factor Assessments, 5th graders demonstrated difficulty incorporating magnitude information when evaluating fraction addition equations. In particular, students could generally evaluate an equation correctly when it was represented with fraction bars. However, including symbols with the bars interfered with students’ evaluations by triggering incorrect transfer from whole-number addition. Students also did not fully grasp that when two positive fractions are added, the resulting sum is bigger than each addend alone. These findings may help explain why the benefits of grounded feedback are not as strong as proponents of concrete representations might hope. Namely, the target population may not be able to take full advantage of the magnitude visualization because they lack pre-requisite knowledge of how fraction addition involves magnitude.