Compared with what? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving.

Researchers in both cognitive science and mathematics education emphasize the importance of comparison for learning and transfer. However, surprisingly little is known about the advantages and disadvantages of what types of things are being compared. In this experimental study, 162 seventh- and eighth-grade students learned to solve equations (a) by comparing equivalent problems solved with the same solution method, (b) by comparing different problem types solved with the same solution method, or (c) by comparing different solution methods to the same problem. Students’ conceptual knowledge and procedural flexibility were best supported by comparing solution methods and to a lesser extent by comparing problem types. The benefits of comparison are augmented when examples differ on relevant features, and contrasting methods may be particularly useful in mathematics learning. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations.

Encouraging students to share and compare solution methods is a key component of reform efforts in mathematics, and comparison is emerging as a fundamental learning mechanism. To experimentally evaluate the effects of comparison for mathematics learning, the authors randomly assigned 70 seventh-grade students to learn about algebra equation solving by either (a) comparing and contrasting alternative solution methods or (b) reflecting on the same solution methods one at a time. At posttest, students in the compare group had made greater gains in procedural knowledge and flexibility and comparable gains in conceptual knowledge. These findings suggest potential mechanisms behind the benefits of comparing contrasting solutions and ways to support effective comparison in the classroom. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Prior knowledge activation: Inducing engagement with informational texts.

Failure to engage with informational texts is a problem frequently noted at the high school level, at which students are expected to read independently. As a means of addressing this issue, a prior knowledge activation strategy (PKA) was taught to ninth-grade students in which they were encouraged to make spontaneous connections between their personal knowledge and informational texts. Students who learned to use the PKA strategy consistently outperformed students in a main idea (MI) treatment group and those in a no-instruction control group on application-level comprehension questions but not literal-level questions. A second study replicated the operations of the first study, with the addition of an MI-PKA treatment designed to combine both strategies. Both the PKA and the MI-PKA combination groups performed higher on application-level comprehension questions and demonstrated more positive attitudes toward reading than the other groups. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Long-term memory for knowledge learned in school.

Three experiments examined students' long-term retention of knowledge learned in college courses. In Exp 1 retention was measured 4 and 11 mo after the term ended. Students retained a great deal of what they originally learned, and there were no differential forgetting effects as a function of level of original learning. Exp 2 compared retention for recall test items and 3 types of multiple-choice test items: recognition, comprehension, and mental skills. Students performed poorer on recall items, but there were no differences among the multiple-choice items measuring the other types of tasks. Exp 3 analyzed retention for student tutors. Tutors retained more after 4 mo than the students they tutored. This suggests that tutoring, a type of overlearning, has positive effects that are maintained over time. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Using worked examples as an instructional support in the algebra classroom.

In 2 experiments, high school students studied worked examples while learning how to translate English expressions into algebraic equations. In Exp 1, worked examples were used as part of the regular classroom instruction and as a support for homework. In Exp 2, students in a remedial mathematics class received individual instruction. Students using worked examples outperformed the control group on posttests after completing fewer practice problems; they also made fewer errors per problem and fewer types of errors during acquisition time, completed the work more rapidly, and required less assistance from the teacher. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Academic Aptitude and Prior Knowledge as Predictors of Student Achievement in Introduction to Psychology.

Earlier research has shown that prior knowledge of psychology is positively associated with course achievement. But are these effects attributable to preexisting differences in general ability or aptitude? The authors administered 2 pretests to 353 students early in an introductory psychology course and obtained measures of general student aptitude (i.e., ACT scores), subsequent course participation, and exam performance. In regression analyses, the pretest of psychological knowledge uniquely predicted significant variance in exam scores even with the influences of ACT scores and course participation controlled. A second pretest judging the accuracy of everyday psychological concepts also positively correlated with exam performance but did not predict unique variance in the regression. Thus, beyond general ability, domain-specific prior knowledge facilitates student learning in introductory psychology. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Interest and metacognitive word knowledge.

Tested the hypothesis that students' metacognition would be enhanced on content that aroused situational interest or that was related to students' topic interests. A metacognitive evaluation procedure was used in which students estimated their word knowledge, which was then determined objectively by a multiple-choice vocabulary test. Students could then update their vocabulary knowledge by reading a passage dealing with heart disease in which all of the previously encountered words were defined explicitly or implicitly. With differences in prior knowledge controlled, nursing students, for whom the content was related to topic interests, made more accurate metacognitive judgments than did freshmen. None of the other main effects or interactions was significant. The implications of the findings for research on interest, its relationship to prior knowledge, and the assessment of metacognition are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Relations among conceptual knowledge, procedural knowledge, and procedural flexibility in two samples differing in prior knowledge.

Competence in many domains rests on children developing conceptual and procedural knowledge, as well as procedural flexibility. However, research on the developmental relations between these different types of knowledge has yielded unclear results, in part because little attention has been paid to the validity of the measures or to the effects of prior knowledge on the relations. To overcome these problems, we modeled the three constructs in the domain of equation solving as latent factors and tested (a) whether the predictive relations between conceptual and procedural knowledge were bidirectional, (b) whether these interrelations were moderated by prior knowledge, and (c) how both constructs contributed to procedural flexibility. We analyzed data from 2 measurement points each from two samples (Ns = 228 and 304) of middle school students who differed in prior knowledge. Conceptual and procedural knowledge had stable bidirectional relations that were not moderated by prior knowledge. Both kinds of knowledge contributed independently to procedural flexibility. The results demonstrate how changes in complex knowledge structures contribute to competence development. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

On warm conceptual change: The interplay of text, epistemological beliefs, and topic interest.

The aim of this study was to go further than considering only cognitive factors to extend the understanding of the complex, dynamic underlying knowledge revision processes. Fifth graders were assigned to 2 reading conditions. Participants in 1 condition read a refutational text about light, whereas participants in the other read a traditional text. Within each reading condition, students had more or less advanced beliefs about scientific knowledge (complex and evolving vs. simple and certain), as well as high or low topic interest. Overall findings from pretest to immediate and delayed posttests showed that knowledge revision was affected by several interactions among the variables examined. Students who attained the highest scores at both the immediate and delayed posttests were those who had read the refutational text and had high topic interest, as well as more advanced beliefs about scientific knowledge. In particular, the refutational text was more powerful in prompting a restructuring of alternative conceptions about 2 of the 3 light phenomena examined. In addition, students preferred the innovative text to the traditional textbook text. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Does a Clinical Psychology Education Moderate Relationships Between Personality or Emotional Adjustment and Performance As a Clinical Psychologist?

Does an education in clinical psychology affect relationships between personality or emotional adjustment and clinical knowledge or clinical practice ability? Two groups were assessed at the beginning of their professional development and 1 year later. The 1st group was studying clinical psychology, and the 2nd group was obtaining training under a workplace supervision model. At pretest, measures of defensiveness were correlated with practice ability, and participants who had emotional adjustment problems obtained lower practice ability scores. At posttest, neither pretest personality nor emotional adjustment was correlated with clinical performance. An interaction between education group and problem group suggests that a clinical education enhances the performance of students with emotional problems at the onset of their education. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Schema training in analogical reasoning.

In 3 experiments, college students learned how to solve 20 verbal analogy problems and took transfer and memory tests. Ss learned from worked-out examples that emphasized relational terms such as "part-to-whole" or under 3 other instructional conditions that required responding to examples or that excluded mention of relational terms. The former Ss were more accurate and faster then other Ss on solving new problems involving the same relations but less accurate in recognizing words from previous problems. This pattern is inconsistent with active responding theory, which predicts students learn best by generating answers and receiving feedback to problems, and is consistent with active learning theory, which predicts that students learn best by inducing schemas for particular problem types. Results indicate that schema induction is maximized when the schemas are made salient and the cognitive system is not overloaded. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Profiling the differences in students' knowledge, interest, and strategic processing.

The purpose for this research was threefold: to determine whether distinct and informative student profiles would emerge from knowledge, interest, and strategy measures specific to educational psychology; to compare these profiles with prior studies; and to explore changes in student profiles across an academic semester. As a result of cluster-analytic procedures, 3 distinct groups of participants emerged at pretest, and 4 emerged at posttest. One of the profiles that remained fairly consistent from pretest to posttest was the Learning-Oriented cluster. Students fitting this profile began the semester with the highest means in interest and strategic processing and with a moderate level of domain knowledge. By the end of the semester, this cluster obtained the highest means also on the domain knowledge test. Yet, the largest cluster at posttest seemed unable or unwilling to learn from demanding exposition. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Visual argument: Graphic organizers are superior to outlines in improving learning from text.

Most research on graphic organizers (i.e., figural organizations of text information) has failed to simulate actual classroom learning. Typically, studies have used short, poorly organized text, single graphic organizers, and immediate tests measuring only factual knowledge. Also, there is no convincing evidence that graphic organizers are better than outlines. Two experiments were conducted that represented attempts to address these problems in answering the question, "What types of text information do graphic organizers and outlines help college students learn?" Results revealed that when given enough time, students studying graphic organizers learned more hierarchical and coordinate relations, and as a result, they were more successful in applying that knowledge and in writing integrated essays than students studying outlines or text alone. These findings are discussed in terms of efficient indexing through visual argument. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Multimedia Learning in an Interactive Self-Explaining Environment: What Works in the Design of Agent-Based Microworlds?

Students learned about electric motors by asking questions and receiving answers from an on-screen pedagogical agent named Dr. Phyz who stood next to an on-screen drawing of an electric motor. Students performed better on a problem-solving transfer test when Dr. Phyz's explanations were presented as narration rather than on-screen text (Experiment 1), when students were able to ask questions and receive answers interactively rather than receive the same information as a noninteractive multimedia message (Experiments 2a and 2b), and when students were given a prequestion to guide their self-explanations during learning (Experiment 3). Deleting Dr. Phyz's image from the screen had no significant effect on problem-solving transfer performance (Experiment 4). The results are consistent with a cognitive theory of multimedia learning and yield principles for the design of interactive multimedia learning environments. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Signaling as a cognitive guide in multimedia learning.

In 3 experiments, students received a short science lesson on how airplanes achieve lift and then were asked to write an explanation (retention test) and to write solutions to 5 problems, such as how to design an airplane to achieve lift more rapidly (transfer test). For some students, the lesson contained signals, including a preview summary paragraph outlining the 3 main steps involved in lift, section headings, and pointer words such as because or as a result. The signaling did not add any additional content information about lift but helped clarify the structure of the passage. Students who received signaling generated significantly more solutions on the transfer test than did students who did not receive signaling when the explanation was presented as printed text (Experiment 1), spoken text (Experiment 2), and spoken text with corresponding animation (Experiment 3). Results are consistent with a knowledge construction view of multimedia learning in which learners seek to build mental models of cause-and-effect systems. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Prior knowledge and correlational structure in unsupervised learning.

Prior knowledge has been shown to facilitate both supervised and unsupervised category learning, but questions remain about how this facilitation occurs. This article describes two experiments that investigate the effects of prior knowledge on unsupervised learning, using the exemplar-memory task of Clapper and Bower (2002). Experiment 1 demonstrates that prior knowledge facilitates learning in this task, as expected, and that this facilitation extends to both knowledge-relevant and knowledge-irrelevant features of the new categories. Experiment 2 shows that knowledge facilitates learning not only by increasing the probability that people will discover separate categories, but also by making the features of different categories seem less interchangeable, thereby reducing interference and confusion among them. Taken together, these experiments demonstrate that prior knowledge has multiple effects on unsupervised learning and suggests that the exemplar-memory task may provide a useful procedure for disentangling and investigating these effects. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Improving Green Building Education by Addressing the Learning Style and Prior Knowledge of Students

Green building education requires successful teamwork of students from different disciplines to solve challenging problems. Team performance depends on both team process behavior and team cognition. There have been many studies on team process behavior such as communication. However, establishing a common understanding of a team, i.e., the essential part of team cognition, still lacks adequate research. To gain this common understanding, concept learning is critical. A concept learning process can be improved when factors affecting it are addressed. This paper discusses the results of an empirical study addressing the relationship between the concept learning process and such a factor, the learning style of students, in a multidisciplinary team context. An experiment was conducted comparing two groups of students in terms of acquiring knowledge about certain concepts in green building. One group learned concepts by using a conventional method, and the other group was given concepts customized to their learning styles. Tests were conducted at various stages, and the results were statistically analyzed. The findings indicate that, in general, the group that was given customized study materials showed significantly more improvement in their concept learning than the group who learned concepts through conventional materials. This initial finding is based on a small group of students. Additional studies on the impact of other factors such as thinking style need to be conducted in the future.     

Gender differences in solution of algebraic word problems containing irrelevant information.

In the 1st experiment, 219 boys and 217 girls in 10th grade classified algebraic word problems in terms of whether the problems contained missing, sufficient, or irrelevant information for solution. Among students with similar levels of general mathematical ability, girls were less likely than boys to identify missing or irrelevant information within problems. More girls than boys perceived irrelevant information within the text of a problem as being necessary for solution. In the 2nd experiment, 11th-grade girls (n?=?234), who were as able as boys (n?=?287) to solve algebraic word problems containing sufficient information, had lower solution rates than did boys on problems containing irrelevant information. On the latter problems, the girls more often incorporated the irrelevant information into their attempted solution than did the boys. The results point to differences between boys and girls in knowledge of problem structure. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effects of prior knowledge on the generation advantage: Calculators versus calculation to learn simple multiplication.

Elementary school children learned simple multiplication by generating (i.e., computing the answers) or reading (i.e., reading the answers from a calculator display). The children were given a pretest, read or generate training, a posttest, and a retention test after 2 weeks. Read training involved approximately half as much training time compared with generate training and was moderately effective. In terms of accuracy, generate training effectiveness depended on children's prior knowledge of multiplication. It was highly effective for low-knowledge children and ineffective for high-knowledge children. In terms of test time, read children showed a loss in efficiency after the 2-week delay compared with the generate children who showed no loss. The results are explained in terms of a procedural account of the generation advantage, and instructional applications are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

An evaluation of the relative effectiveness of NCTM standards-based interventions for low-achieving urban elementary students.

The effects of 2 instructional methods, problem solving and peer collaboration, were evaluated for enhancing mathematics achievement, academic motivation, and self-concept of 104 low-achieving 3rd and 4th graders. Students were assigned randomly to 1 of 4 conditions: control, problem solving, peer collaboration, and problem solving?+?peer collaboration. Students in all conditions met twice weekly for 30-min mathematics sessions over a 7-week period. Results indicate that problem-solving students performed significantly higher than their counterparts who did not receive problem solving on measures of computation and word problems and reported higher levels of academic motivation, academic self-concept, and social competence. Students who participated in peer collaboration scored higher on measures of computation and word problems and reported higher levels of academic motivation and social competence than did students who did not participate in peer collaboration. No significant interaction effect was found. (PsycINFO Database Record (c) 2010 APA, all rights reserved)