Research addressing the effectiveness of feedback for learning has focused on many dimensions of feedback, including the timing (Kulik & Kulik, 1988), type (Mory, 2004), and amount of available information (Dempsey et. al, 1993). Much of the feedback research in education has tacitly assumed that the available information is perceived, and any learning or difficulties occur in the internal processing of that information. In contrast, the thesis presented here is that a good deal of learning involves coming to see the structure of the feedback itself (Gibson, 1969). This claim is defended by an analysis of quantitative and qualitative data from two studies of fourth grade students interacting with a mathematics simulation targeting multiplicative reasoning, and one study of adults using a similar, though more complex, mathematical simulation. In Study 1, 24 fourth grade students interacted with a simulation environment developed by the author to target the mathematical concept of grouping as it relates to place value (Blair et al., 2008). Students interacted with the simulation under two feedback conditions. In one condition, students saw the implications of their input choices play out in the simulation ("implication feedback"). In the other, students were told the correct answer as feedback, and the simulation always ran using the correct values ("corrective feedback"). Among the high performing students, the implication feedback condition yielded slightly, though not significantly, faster times to master all levels of the simulation environment. For the low performing students, however, students in the implication feedback condition mastered fewer levels in the environment than those in the corrective feedback condition. Observations of the low performing students in the implication feedback condition suggested that one reason the students struggled is that they did not perceive important quantitative information in the feedback. Analyses revealed four levels of feedback perception, which increased in the amount of quantitative structure perceived. (1) Correct/incorrect information: Students perceived only that there was a discrepancy between the outcome of their answer in the simulation and the desired goal state. (2) Direction information: Students perceived the direction of that discrepancy (too big or too small). (3) Approximate magnitude information: Students perceived the approximate size of that discrepancy. (4) Exact magnitude: Students perceived the precise countable size of the discrepancy. A computer program was developed to generate a visual representation of students' responses to feedback, based on their log files. Over time, many students exhibited a statistically significant trajectory through the feedback perception levels. Students who did not were unable to learn from their mistakes and made little progress in the environment. Study 2 found similar patterns of feedback perception for adults who interacted with a more complex mathematical simulation. Some progressions were attributable to the adults' search strategy for identifying relations between input and output. Yet, like the fourth grade children, the adult data also clearly demonstrated differential feedback perception. Learning to perceive feedback is not only an issue for young children. Study 3 returned to a fourth-grade population to further demonstrate the significance of coming to perceive feedback structure. An experimental study examined whether scaffolding feedback perception would improve performance, as compared to a condition that reduced working memory demand and a baseline condition. Limitations in the design of the scaffolding materials led to inconclusive results. However, a qualitative analysis, which considered students' gestures, counting moves, and comments, supported the interpretation that the improvements in performance were due to improved feedback perception. Further evidence supporting changes in feedback perception included data from a drawing-from-memory task and correlations between performance and theoretically motivated covariates. Understanding the effects of feedback on learning, particularly in quantitative domains, requires researchers to consider not only what information is "available" in the feedback, but also what information students actually "perceive". Implications for feedback research and instructional design, including how to help students perceive the feedback generated by interactive environments, are discussed. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]