Deanne M. Adams

Using erroneous examples to improve mathematics learning with a web-based tutoring system

Middle school students learned to solve decimal problems with a web-based tutoring system.ExErr group received erroneous examples to correct and explain.PS group received problems to solve and explain.ExErr group outperformed PS group on a delayed test and on judging answer correctness.PS group reported liking the lessons better than the ExErr group. This study examines whether asking students to critique incorrect solutions to decimal problems based on common misconceptions can help them learn about decimals better than asking them to solve the same problems and receive feedback. In a web-based tutoring system, 208 middle school students either had to identify, explain, and correct errors made by a fictional student (erroneous examples group) or solve isomorphic versions of the problems with feedback (problem-solving group). Although the two groups did not differ significantly on an immediate posttest, students in the erroneous examples group performed significantly better on a delayed posttest administered one week later (d=.62). Students in the erroneous examples group also were more accurate at judging whether their posttest answers were correct (d=.49). Students in the problem-solving group reported higher satisfaction with the materials than those in the erroneous examples group, indicating that liking instructional materials does not equate to learning from them. Overall, practice in identifying, explaining, and correcting errors may help students process decimal problems at a deeper level, and thereby help them overcome misconceptions and build a lasting understanding of decimals.

To err is human, to explain and correct is divine: a study of interactive erroneous examples with middle school math students

Erroneous examples are an instructional technique that hold promise to help children learn. In the study reported in this paper, sixth and seventh grade math students were presented with erroneous examples of decimal problems and were asked to explain and correct those examples. The problems were presented as interactive exercises on the Internet, with feedback provided on correctness of the student explanations and corrections. A second (control) group of students were given problems to solve, also with feedback on correctness. With over 100 students per condition, an erroneous example effect was found: students who worked with the interactive erroneous examples did significantly better than the problem solving students on a delayed posttest. While this finding is highly encouraging, our ultimate research question is this: how can erroneous examples be adaptively presented to students, targeted at their most deeply held misconceptions, to best leverage their effectiveness? This paper discusses how the results of the present study will lead us to an adaptive version of the erroneous examples material.

Meta-analysis of action video game impact on perceptual, attentional, and cognitive skills

The ubiquity of video games in today’s society has led to significant interest in their impact on the brain and behavior and in the possibility of harnessing games for good. The present meta-analyses focus on one specific game genre that has been of particular interest to the scientific community—action video games, and cover the period 2000–2015. To assess the long-lasting impact of action video game play on various domains of cognition, we first consider cross-sectional studies that inform us about the cognitive profile of habitual action video game players, and document a positive average effect of about half a standard deviation (g = 0.55). We then turn to long-term intervention studies that inform us about the possibility of causally inducing changes in cognition via playing action video games, and show a smaller average effect of a third of a standard deviation (g = 0.34). Because only intervention studies using other commercially available video game genres as controls were included, this latter result highlights the fact that not all games equally impact cognition. Moderator analyses indicated that action video game play robustly enhances the domains of top-down attention and spatial cognition, with encouraging signs for perception. Publication bias remains, however, a threat with average effects in the published literature estimated to be 30% larger than in the full literature. As a result, we encourage the field to conduct larger cohort studies and more intervention studies, especially those with more than 30 hours of training.

Delayed Learning Effects with Erroneous Examples: a Study of Learning Decimals with a Web-Based Tutor

Erroneous examples – step-by-step problem solutions with one or more errors for students to find and fix – hold great potential to help students learn. In this study, which is a replication of a prior study (Adams et al. 2014), but with a much larger population (390 vs. 208), middle school students learned about decimals either by working with interactive, web-based erroneous examples or with more traditional supported problems to solve. The erroneous examples group was interactively prompted to find, explain, and fix errors in decimal problems, while the problem-solving group was prompted to solve the same decimal problems and explain their solutions. Both groups were given correctness feedback on their work by the web-based program. Although the two groups did not differ on an immediate post-test, the erroneous examples group performed significantly better on a delayed test, given a week after the initial post-test (d = .33, for gain scores), replicating the pattern of the prior study. Interestingly, the problem solving group reported liking the intervention more than the erroneous examples group (d = .21 for liking rating in a questionnaire) and found the user interface easier to interact with (d = .37), suggesting that what students like does not always lead to the best learning outcomes. This result is consistent with that of desirable difficulty studies, in which a more cognitively challenging learning task results in deeper and longer-lasting learning.

A Computer-Based Game that Promotes Mathematics Learning More than a Conventional Approach

Excitement about learning from computer-based games has been papable in recent years and has led to the development of many educational games. However, there are relatively few sound empirical studes in the scientific literature that have shown the benefits of learning mathematics from games as opposed to more traditional approaches. The empirical study reported in this paper provides evidence that a mathematics educational game can provide superior learning opportunities, as well as be more engaging. In a study involving 153 students from two middle schools, 70 students learned about decimals from playing an educational game-Decimal Point-whereas 83 students learned the same content by a more conventional, computer-based approach. The game led to significantly better gain scores in solving decimal problems, on both an immediate d =.43 and delayed d =.37 posttest and was rated as significantly more enjoyable d =.95. Low prior knowledge students especially benefitted from the game. This paper also summarizes the games design characteristics.

Effects of Mental and Manual Rotation Training on Mental and Manual Rotation Performance

Abstract: Previous research has shown that training can improve mental rotation performance and has found connections between mental and manual rotation. Here we examine how practice in mental or manual (virtual) rotation, affects performance on mental and manual rotation tasks, compared to a control condition. Experiment 1 examined improvement on a mental rotation task following practice in mental or manual rotation. Both mental and manual rotation practice led to more efficient posttest performance. Experiment 2 examined improvement on a manual rotation task. Practice in manual but not mental rotation led to improved performance. Analyses of the manual rotation trajectories revealed no evidence of strategy differences. These results suggest that manual rotation may require additional processes outside of those needed for mental rotation. In terms of training effects, manual rotation training improved both manual and mental rotation performance, whereas mental rotation only significant improved mental rotation performance.

Erroneous Examples as Desirable Difficulty

Erroneous examples, an unusual and challenging form of learning material, are arguably a type of desirable difficulty for students that could lead to deeper learning. In a series of studies we have done over the past three years involving web-based math instruction, the learning benefits of erroneous examples we have observed occured on delayed tests, as occurs in the desirable difficulties literature. This short paper briefly reviews the literature, summarizes our results, and speculates on how an adaptive version of our materials could better leverage desirable difficulties theory and lead to deeper student learning.

Uncovering Gender and Problem Difficulty Effects in Learning with an Educational Game

A prior study showed that middle school students who used the educational game Decimal Point achieved significantly higher gain scores on immediate and delayed posttests of decimal understanding than students who learned with a more conventional computer-based learning tool. This paper reports on new analyses of the data from that study, providing new insights into the benefits of the game. First, females benefited more than males from the game. Second, students in the game condition performed better on the more difficult intervention problems. This paper presents these new analyses and discusses why the educational game might have led to these results.

Evaluating the Cognitive Consequences of Playing "Portal" for a Short Duration.

Learning physics often requires overcoming common misconceptions based on naïve interpretations of observations in the everyday world. One proposed way to help learners build appropriate physics intuitions is to expose them to computer simulations in which motion is based on Newtonian principles. In addition, playing video games that require spatial processing may also facilitate the development of spatial skills that have been associated with learning in science, technology, engineering, and mathematics areas. Two studies were conducted to examine whether playing the first-person perspective puzzle game Portal causes improvements in physics intuitions and spatial cognition skills. In Experiment 1, college students played Portal, the two-dimensional puzzle game Tetris, or the anagram game TextTwist for 75 minutes. There were no significant differences on measures of naïve physics reasoning (selected from the Force Concept Inventory) or measures of spatial cognition (mental rotation and perspective taking). To determine whether Portal could influence formal physics learning, in Experiment 2 participants viewed a brief lesson on Newton’s laws of motion after playing one of the three games for 1 hour. The groups did not differ on subsequent tests of physics learning. This study shows that Portal was not successful in priming intuitions about motion or spatial abilities related to physics learning.