The subgoal learning model: Creating better examples so that students can solve novel problems.

Learners have great difficulty solving problems requiring changes to solutions demonstrated in examples. However, if the solution procedures learners form are organized by subgoals, then they are more successful. Subgoal learning is hypothesized to be aided by cues in example solutions that indicate that certain steps go together. These cues may induce a learner to attempt to self-explain the purpose of the steps, resulting in the formation of a subgoal. Across 4 experiments it was found that a label for a group of steps in examples helped participants form subgoals as assessed by measures such as problem-solving performance and talk aloud protocols. Abstract labels were more likely than superficial labels to lead participants to form subgoals with fewer ties to surface features. Subgoals guide problem solving by helping learners focus on the steps to modify in novel problems that involve the same subgoals but require new steps to achieve them. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Acquisition of a problem-solving skill: Levels of organization and use of working memory.

We examined the acquisition of a problem-solving skill at three levels of organization—strategy, subgoal, and operator—and investigated changes in temporary storage, manipulation of information, and coordination of multiple representations. 6 college students practiced minimizing the simulated cost of solving diagnostic problems with digital electronic circuits for approximately 50 hr (347 problems). Ss were tested on declarative knowledge, inferential skills at the subgoal level, and ability to solve problems during working memory tasks. The working memory tasks required retention of a preload, concurrent processing, or integration of displayed information with the contents of working memory. The data support the view that restructuring is goal sensitive and strategic. The results suggest a multiple-level analysis of skill acquisition in which practice allows strategic restructuring of cognitive processes at 3 levels of organization. Implications for models of skill acquisition and working memory are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Cognitive sequence knowledge: What is learned?

In 4 experiments, participants performed running-arithmetic tasks. These tasks involved a sequential ordering of individual operations and a structure of subgoals that defined how calculations fit together in purpose. Consistent transitions between adjacent steps facilitated performance only when subgoal structures were relatively simple. When subgoal structures were more complex, consistent mapping of operations to serial locations produced a slight benefit. Consistently of subgoal structure produced a substantial benefit in both speed and accuracy, and some knowledge of subgoal structure integrated with knowledge of the sequence of operations. Apparently, a task's subgoal structure imposes demands that either facilitate or obscure benefits of sequence consistencies. The benefits are attributed to increase deficiency in using working memory. (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)     

Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive-load approach.

Studied 4 computer-based training strategies for geometrical problem solving in the domain of computer numerically controlled machinery programming with regard to their effects on training performance, transfer performance, and cognitive load. A low- and a high-variability conventional condition, in which conventional practice problems had to be solved (followed by worked examples), were compared with a low- and a high-variability worked condition, in which worked examples had to be studied. Results showed that students who studied worked examples gained most from high-variability examples, invested less time and mental effort in practice, and attained better and less effort-demanding transfer performance than students who first attempted to solve conventional problems and then studied work examples. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

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)     

Ingredients for a theory of instruction.

Analyzes the steps involved in deriving an optimal teaching strategy for instructional situations where a model-theoretic account of the learning process can be given. 2 examples derived from the author's research are considered: optimizing primary-grade instruction in initial reading, and optimizing 2nd-language learning by college students. In both cases, the optimal model-theoretic strategy yields large gains when compared with other strategies in widespread use in the schools. It is stated that these examples illustrate the relationship between a theory of learning and its corresponding theory of instruction. (22 ref.) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Self-monitoring of attained subgoals in private study.

Compared 3 conditions of self-monitoring of private study for their effects on academic performance and intrinsic motivation. Ss were 240 1st-yr college students who were divided among high, moderate, and low achievers. Within each group, Ss were assigned to 1 of 4 study conditions: self-monitor subgoal condition, self-monitor time-on-study condition, self-monitor distal-goal condition, and control condition. In end-of-year examinations, Ss who self-monitored subgoals outperformed Ss who self-monitored either time or study or distal goals on the target course of the investigation. Furthermore, although Ss who self-monitored duration of study actually spent significantly longer on study, their examination performance was not significantly better than that of control Ss. Besides the beneficial effects on learning, subgoal self-monitoring enhanced intrinsic interest in the target course, as evidenced from Ss' ratings. Requiring Ss to turn in samples of study notes did not have an impact on examination performance; however, this requirement interacted with study condition in its effect on intrinsic interest. (29 ref) (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)     

Learning and transfer: A general role for analogical encoding.

Teaching by examples and cases is widely used to promote learning, but it varies widely in its effectiveness. The authors test an adaptation to case-based learning that facilitates abstracting problem-solving schemas from examples and using them to solve further problems: analogical encoding, or learning by drawing a comparison across examples. In 3 studies, the authors examined schema abstraction and transfer among novices learning negotiation strategies. Experiment 1 showed a benefit for analogical learning relative to no case study. Experiment 2 showed a marked advantage for comparing two cases over studying the 2 cases separately. Experiment 3 showed that increasing the degree of comparison support increased the rate of transfer in a face-to-face dynamic negotiation exercise. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving.

Comparing multiple examples typically supports learning and transfer in laboratory studies and is considered a key feature of high-quality mathematics instruction. This experimental study investigated the importance of prior knowledge in learning from comparison. Seventh- and 8th-grade students (N = 236) learned to solve equations by comparing different solution methods to the same problem, comparing different problem types solved with the same solution method, or studying the examples sequentially. Unlike in past studies, many students did not begin the study with equation-solving skills, and prior knowledge of algebraic methods was an important predictor of learning. Students who did not attempt algebraic methods at pretest benefited most from studying examples sequentially or comparing problem types, rather than from comparing solution methods. Students who attempted algebraic methods at pretest learned more from comparing solution methods. Students may need sufficient prior knowledge in a domain before they benefit from comparing alternative solution methods. These findings are in line with findings on the expertise-reversal effect. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The role of learning from examples in the acquisition of recursive programming skills.

Presents an analysis and simulation model of the verbal protocols of 2 college students and 1 8-yr-old S learning to program recursive functions. The model is formalized as a production system capable of acquiring new production rules based on problem-solving experience. The model and protocols suggest that (a) problem solving by analogy to worked-out examples is frequent in initial attempts by novices to write recursive functions; (b) different representations of examples are used to guide problem solving by analogy; and (c) performance on later problems reflects the particular representations used in problem solving by analogy on earlier problems. The protocols and simulations also suggest that learning is facilitated by using abstract representations of the structure of recursion examples to guide initial coding attempts. (French abstract) (25 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The relationships among students' future-oriented goals and subgoals, perceived task instrumentality, and task-oriented self-regulation strategies in an academic environment.

The authors performed path analysis, followed by a bootstrap procedure, to test the predictions of a model explaining the relationships among students' distal future goals (both extrinsic and intrinsic), their adoption of a middle-range subgoal, their perceptions of task instrumentality, and their proximal task-oriented self-regulation strategies. The model was based on R. B. Miller and S. J. Brickman's (2004) conceptualization of future-oriented motivation and self-regulation, which draws primarily from social-cognitive and self-determination theories. Participants were 421 college students who completed a questionnaire that included scales measuring the 5 variables of interest. Data supported the model, suggesting that students' distal future goals (intrinsic future goals in particular) may be related to their middle-range college graduation subgoal, to their perceptions of task instrumentality, and to their adoption of proximal task-oriented self-regulation strategies. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

When less is more in cognitive diagnosis: A rapid online method for diagnosing learner task-specific expertise.

Rapid cognitive diagnosis allows measuring current levels of learner domain-specific knowledge in online learning environments. Such measures are required for individualizing instructional support in real time, as students progress through a learning session. This article describes 2 experiments designed to validate a rapid online diagnostic method that was inspired by experimental procedures applied in classical cognitive studies of chess expertise. With the described rapid verification method, learners are required to rapidly verify suggested steps at various stages of a problem solution procedure. In this study involving 33 university students, a high degree of correlation was found between rapid testing scores and results of in-depth cognitive diagnosis based on observations of problem-solving steps using video recordings and concurrent verbal reports in the domains of kinematics (vector addition motion problems) and mathematics (transforming graphs of linear and quadratic functions). The article discusses possible applications of the suggested method in adaptive learning environments. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Generalizing from the use of earlier examples in problem solving.

Novices often are reminded of earlier examples during problem solving. Four experiments examine the hypothesis that the use of earlier examples promotes generalizations about problem types, thereby influencing what is learned about the domain. Subjects studied four probability principles with word problems and then tried to solve two test problems for each principle. For half of the first tests, cues indicated which study problem might be used. All second tests were uncued. Experiments 1 and 2 showed that the first-test cuing led to an advantage on second-test performance for both the access and the use of relevant information. Experiments 3 and 4 demonstrated that this cuing benefit is due to some generalization induced from using the study problem to solve the first-test problem. Discussion focuses on the distinctions about how problem comparisons are used in learning and the implications of the view that remindings lead to generalizations. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Further studies of the Tower of Hanoi problem-solving performance of retarded young adults and nonretarded children.

12 retarded Ss (mean CA 20.19 yrs; mean MA 10.23 yrs) and 36 nonretarded kindergartners and 1st–4th graders were given 4–7 step Tower of Hanoi problems that differed in type of goal state. Overall performance levels of the kindergarten, 1st-grade, and retarded groups were the same, but were reliably below the performance level of 3rd and 4th graders. Performance differences were related to the minimum number of steps needed for a problem's solution and to the depth of search required for a problem's initial subgoal. The propensity of the older nonretarded Ss to search 2 moves ahead, while the members of the other groups limited themselves primarily to a 1-move search, contributed importantly to the group differences. Degree of constraint concerning which disk should be the first to be transferred to its goal peg also played a role in producing task and group differences, as did Ss' particular choice of strategies. All groups improved slightly. (16 ref) (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)     

Teacher influences on student achievement.

Reviews research that indicates that students achieve more when their teachers emphasize academic objectives in establishing expectations and allocating time, use effective management strategies to ensure that academic learning time is maximized, pace students through the curriculum briskly but in small steps that allow high rates of success, and adapt curriculum materials based on their knowledge of students' characteristics. Qualitative research also indicates that teachers differ in how they perform such instructional behaviors as giving information, asking questions, and providing feedback. Context-specific effects are noted with respect to grade level, socioeconomic status (SES), ability and affect, and teacher intentions. It is concluded that any attempt to improve student achievement must be based on the development of effective teaching behavior. (66 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)