The impact of spurious correlations on students' problem-solving

2001

How does detection of correlational structure affect mathematical thinking and learning? When does correlational information lead to erroneous problem solving? Are experienced students susceptible to misleading correlations? This work attempts to answer these questions by examining a source of systematic errors termed the spurious-correlation effect. This effect is hypothesized to occur when a student perceives a correlation between an irrelevant feature in a problem and the algorithm used for solving that problem and then proceeds to execute the algorithm when detecting the feature in a different problem. In this research, we investigated whether students encode spurious correlations in memory and exhibit them during the learning process leading to ineffectual problem solving. Findings suggest that even experienced students rely on surface-structural feature-algorithm correlations for solving new problems. Implications for teaching are discussed.

Educational Psychology Review, 2015

Robust knowledge serves as a common instructional target in academic settings. Past research identifying characteristics of experts’ knowledge across many domains can help clarify the features of robust knowledge as well as ways of assessing it. We review the expertise literature and identify three key features of robust knowledge (deep, connected, and coherent) and four means of assessing these features (perception, memory, problem solving, and transfer). Focusing on the domains of math and science learning, we examine how four instructional techniques—practice, worked examples, analogical comparison, and self-explanation—can promote key features of robust knowledge and how those features can be assessed. We conclude by discussing the implications of this framework for theory and practice.

1989

This study, involving 65 undergraduates at the Georvia Institute of Technology (Atlanta); explores a scheme for representing problem-solving knowledge and predicting transfer as a function of problem-solving subgoals acquired from examples. A subgoal is an unknown entity (numerical or conceptual) that needs to be found in order tc achieve a higher level goal of a problem. Subjects studied three algebraic word problems dealing with work. Twenty-three subjects studied examples in which the representations for each worker's rate and time were provided, as well as the actual solution; 21 subjects studied examples in which only an explicit representation for each worker's rate and the solution were provided; and 21 subjects studied examples in which only an explicit representation for each worker's time and the solution were given. Results indicate that learners who had read examples illustrating certain subgoals did a better job of achieving those subgoals in novel test problems requiring new representations compared to subjects who had not been exposed to those subgoals in their examples. It is contended that if researchers can determine subgoals for solving problems in a domain, particularly from a novice's viewpoint, they can develop examples that are more likely to teach those subgoals. Four sample word problems are included. (11,1H)

1989

AIP Conference Proceedings, 2007

We examine the effect of misconceptions about friction on students' ability to solve problems and transfer from one context to another. We analyze written responses to paired isomorphic problems given to introductory physics students and discussions with a subset of students. Misconceptions associated with friction in problems were sometimes so robust that pairing them with isomorphic problems not involving friction did not help students fully discern their underlying similarities.

Transfer of learning is an important objective of education. However, students usually have difficulties in solving physics transfer tasks even after having solved similar problems previously. We investigated if instruction provided using videos containing detailed explanations of previously solved problems will improve students' performance in tackling near and far transfer tasks. We also investigated whether the combination of visual cues followed by video solutions yields further enhancement of students' performance. N=33 students in an algebra-based physics class participated in an interview containing two problem sets each with one initial task, a training session, and a near and far transfer task. For the training, students either received visual cues only, visual cues and a video or only videos, depending on the condition. We compare students' correctness rate on near and far transfer tasks in the three conditions.

1977

This research was based on the assumption that the teaching of broadly generalizable cognitive skills should be a primary goal of education--that students can be taught to be better insight problem solvers outside of school by training in school and that they can be given the skills necessary for efficient disCovery learning. The subjects were 116 students of introductory educational psychology at the University of Texas, Austin. The students were divided into siill groups and exposed to an insight problem solving training procedure for approximately one hour. Following this training, each individual worked on a test booklet containing 11 insight prohlems for 50*minutes. Four of the groups received experimental training: dual training, visualization training, practice, or control. Comparision of adjusted scores for all groups indicated that dual training yielded the highest scores. These results lend support to-theGestal-t-vi-ew-of-insight-problems-e-t6-the--------. possibility that students can be trained to perform better on such problem:J, and to the suggestion that it may be necessary to combine practice and instruction to teach generalized skills. (EM)

2006

Fifth-graders' results from a category learning experiment suggest that inferring stimulus properties given the category membership leads to better acquisition of category knowledge than classifying stimulus items. Fifth-graders liked better and learned more properties of the shark categories acquired through inference than those acquired through classification. Classification promoted learning of only the property that was most diagnostic in discriminating among categories. Inference facilitated learning of all properties associated with each category, including properties not queried during training. Seven to 33 days after training, fifth-graders who inferred still had more information about properties of each category than fifthgraders who classified. Classroom teaching should emphasize reasoning from the category to multiple properties rather than from a set of properties to the category.

Memory & Cognition, 1994

People often memorize a set of steps for solving problems when they study worked-out examples in domains such as math and physics without learning what domain-relevant subgoals or subtasks these steps achieve. As a result, they have trouble solving novel problems that contain the same structural elements but require different, lower-level steps. In three experiments, subjects who studied example solutions that emphasized a needed subgoal were more likely to solve novel problems that required a new approach for achieving this subgoal than were subjects who did not learn this sub goal. This result suggests that research aimed at determining the factors that influence subgoal learning may be valuable in improving transfer from examples to novel problems. A number of studies have indicated that learners rely heavily on worked-out examples when trying to solve novel problems (e.g., LeFevre & Dixon, 1986; Pirolli & Anderson, 1985). Unfortunately, in a domain, novices have great difficulty separating the features of the examples that are necessary to the solution procedure from those that are incidental (Ross, 1987, 1989). In addition, learners have difficulty generalizing solutions from examples to structurally similar, but nonisomorphic, problems (Reed, Ackinclose, & Voss, 1990; Reed, Dempster, & Ettinger, 1985). Although certain training manipulations have succeeded in improving transfer from examples to novel problems to some degree (

2007 Annual Conference & Exposition Proceedings

He has published 29 books and hundreds of articles, papers, and reports on text design, task analysis, instructional design, computer-based learning, hypermedia, constructivist learning, cognitive tools, and technology in learning. He has consulted with businesses, universities, public schools, and other institutions around the world. His current research focuses on the cognitive processes engaged by problem solving and models and methods for supporting those processes during learning. Sanjay Rebello, Kansas State University Sanjay Rebello is Associate Professor of Physics at Kansas State University. His research interest is in transfer of learning and how learners activate and coordinate their small-grain-size conceptual resources to make sense of new situations. He is particularly interested in the application of transfer of learning to problem solving in introductory undergraduate physics courses for both structured and ill-structured problems.