Reviving inert knowledge: analogical abstraction supports relational retrieval of past events

We present five experiments and simulation studies to establish late analogical abstraction as a new psychological phenomenon: Schema abstraction from analogical examples can revive otherwise inert knowledge. We find that comparing two analogous examples of negotiations at recall time promotes retrieving analogical matches stored in memory—a notoriously elusive effect. Another innovation in this research is that we show parallel effects for real-life autobiographical memory (Experiments 1–3) and for a controlled memory set (Experiments 4 and 5). Simulation studies show that a unified model based on schema abstraction can capture backward (retrieval) effects as well as forward (transfer) effects.     

Use of the mathematical principle of inversion in young children

An important issue in the development of mathematical cognition is the extent to which children use and understand fundamental mathematical concepts. We examined whether young children successfully use the principle of inversion and, if so, whether they do so based on qualitative identity, length, or quantity. Twenty-four preschool children and 24 children in Grade 1 were presented with three-term inversion problems (e.g., 3+2-2) and standard problems of similar magnitude (e.g., 2+4-3). Problems were presented in three conditions to determine whether children used inversion at all and, if so, whether their decisions were based on quantitative or nonquantitative features of the problems. Both preschool and Grade 1 children showed evidence of using inversion in a fully quantitative manner, indicating that this principle is available in some form prior to extensive formal instruction in arithmetic.     

小学3-6年级学生解决比较问题的研究

本研究对465名小学3—6年级学生解决不同类型的比较问题进行了研究。结果表明：(1)小学生解决比较问题的成绩受问题类型及年级的交互影响。儿童在一致算术问题上的成绩都很好,且显著优于不一致算术问题。在不一致算术问题、一致代数问题及不一致代数问题上,存在年级差异。5、6年级学生优于4年级学生。(2)小学生在算术问题上的通过率高于代数问题,5、6年级学生的通过率高于3、4年级。除一致算术问题外,其它类型比较问题的通过率较低。(3)小学生解决比较问题的成绩无性别差异。     

Working memory and literacy as predictors of performance on algebraic word problems

Previous studies on individual differences in mathematical abilities have shown that working memory contributes to early arithmetic performance. In this study, we extended the investigation to algebraic word problem solving. A total of 151 10-year-olds were administered algebraic word problems and measures of working memory, intelligence quotient (IQ), and reading ability. Regression results were consistent with findings from the arithmetic literature showing that a literacy composite measure provided greater contribution than did executive function capacity. However, a series of path analyses showed that the overall contribution of executive function was comparable to that of literacy; the effect of executive function was mediated by that of literacy. Both the phonological loop and the visual spatial sketchpad failed to contribute directly; they contributed only indirectly by way of literacy and performance IQ, respectively.     

Learning new problem-solving strategies leads to changes in problem representation

Children sometimes solve problems incorrectly because they fail to represent key features of the problems. One potential source of improvements in children's problem representations is learning new problem-solving strategies. Ninety-one 3rd- and 4th-grade students solved mathematical equivalence problems (e.g., 3 + 4 + 6 = 3 + __) and completed a representation assessment in which they briefly viewed similar problems and either reconstructed each problem or identified it in a set of alternatives. Experimental groups then received a lesson about one or both of two solution strategies, the equalize strategy and the add–subtract strategy. A control group received no instruction. All children completed posttest assessments of representation and problem solving. Children taught the equalize strategy improved their problem representations more than those not taught it. This pattern did not hold for the add–subtract strategy. These results indicate that learning new strategies is one source of changes in problem representation. However, some strategies are more effective than others at promoting accurate problem representation.     

Fast mapping of multiple words: Insights into when “the information provided” does and does not equal “the information perceived”

A candidate process for explaining the rapid vocabulary acquisition during the preschool years is “fast mapping,” children's ability to sketch partial maps of a word's meaning after brief exposure. The present study examines this process for learning multiple words, testing the hypothesis that children's attention to the information critical for quickly mapping multiple words onto their referents depends on the alternatives available when the words are introduced. Fifty-eight 40-month-old children participated in one of two conditions. In both conditions, each trial for novel Word #1 presented a novel object and three familiar ones. The conditions differed in the object choices presented when novel Word #2 was introduced. Although the same information was available to children in both conditions, younger children showed significantly better learning of the new words in the successive condition than in the concurrent condition. Implications of this for age-related differences and for teaching strategies are discussed.     

Action planning in sequential skills: Relations to music performance

The hypothesis that planning music-like sequential actions involves anticipating their auditory effects was investigated in a series of experiments. Participants with varying levels of musical experience responded to each of four colour-patch stimuli by producing a unique sequence of three taps on three vertically aligned keys. Each tap triggered a tone in most experimental conditions. Response–effect (key-to-tone) mapping was either compatible—taps on the top, middle, and bottom keys triggered high, medium, and low pitched tones, respectively—or incompatible—key-to-tone mapping was scrambled, reversed, or neutral (taps on different keys triggered the same tone). The results suggest that action planning was faster with compatible than with incompatible mappings (and faster than with no tones). Furthermore, the size of this compatibility effect grew with increasing musical experience, which suggests that improvements in auditory imagery ability that typically accompany musical training may augment the role of anticipatory auditory-effect representations during planning.     

Stability and change in children's division strategies

Age-related changes in children's performance on simple division problems (e.g., 6/2, 72/9) were investigated by asking children in Grades 4 through 7 to solve 32 simple division problems. Differences in performance were found across grade, with younger children performing more slowly and less accurately than older children. Problem size effects were also found in that children were faster and more accurate on small problems than on large problems. Two strategies changed across age, with children in Grade 4 relying heavily on the strategy of "addition" (adding the divisor until the dividend was reached) to solve the problems and children in Grades 5 through 7 relying primarily on the strategy of "multiplication" (recasting the division problem as a multiplication problem) to solve the problems. Surprisingly, the frequency of direct retrieval (retrieving the answer directly from memory) did not increase across grade and never became the dominant strategy of choice. Reasons for why retrieval use remains infrequent and age invariant are discussed. Overall, the results suggest that division is a unique operation and that the continued study of division may have implications for further understanding of how procedural and conceptual knowledge of arithmetic develops.     

A Test of the Testing Effect: Acquiring Problem‐Solving Skills From Worked Examples

The “testing effect” refers to the finding that after an initial study opportunity, testing is more effective for long‐term retention than restudying. The testing effect seems robust and is a finding from the field of cognitive science that has important implications for education. However, it is unclear whether this effect also applies to the acquisition of problem‐solving skills, which is important to establish given the key role problem solving plays in, for instance, math and science education. Worked examples are an effective and efficient way of acquiring problem‐solving skills. Forty students either only studied worked examples (SSSS) or engaged in testing after studying an example by solving an isomorphic problem (STST). Surprisingly, results showed equal performance in both conditions on an immediate retention test after 5 min, but the SSSS condition outperformed the STST condition on a delayed retention test after 1 week. These findings suggest the testing effect might not apply to acquiring problem‐solving skills from worked examples.     

Rumination and social problem-solving in depression

We tested the hypothesis that impaired social problem solving in depression is a consequence of state-oriented rumination, which can be ameliorated by improving awareness of mental processes. 32 currently depressed, 26 recovered depressed, and 26 never depressed participants completed the Means Ends Problem Solving Test while randomly allocated to no questions, state-oriented ruminative questions, (e.g. focusing on why you have a problem) or process-focused questions (e.g. focusing on how you decide to solve a problem). In the no question condition, the currently depressed group was significantly impaired at problem solving compared to the never depressed and recovered depressed groups, which did not differ from each other. As predicted, the process-focused questions significantly improved social problem solving in depressed patients, compared to no questions and state-oriented questions, which did not differ from each other. As predicted, compared to the process-focused questions, the state-oriented questions significantly impaired social problem solving in the recovered depressed group. These results are consistent with recent theories and treatment developments which suggest that increased awareness of mental processes can shift people away from ruminative thinking, thereby, reducing depressive relapse.     

Deconstructing the tower: Parameters and predictors of problem difficulty on the Tower of London task

The Tower of London (TOL) task has been widely used in both clinical and research realms. In the current study, 104 healthy participants attempted all possible moderate- to high-difficulty TOL problems in order to determine: (1) optimal measures of problem solving performance, (2) problem characteristics, other than the minimum moves necessary to solve the problem, that determine participants’ difficulty in solving problems successfully, quickly, and efficiently, and (3) effects of increased task experience on which problem characteristics determine problem difficulty. A factor analysis of six performance measures found that, regardless of task experience, problem difficulty could be captured well either by a single factor corresponding to general quality of solution or possibly by three subordinate factors corresponding to solution efficiency, solution speed, and initial planning speed. Regression analyses predicting these performance factors revealed that in addition to a problem’s minimum moves three problem parameters were critical in determining the problem difficulty: goal position hierarchy, start position hierarchy, and number of solution paths available. The relative contributions of each of the characteristics strongly depended on which performance factor defined performance. We conclude that TOL problem performance is multifaceted, and that classifying problem difficulty using only the minimum moves necessary to solve the problem is inadequate.     

Social problem solving and autobiographical memory in posttraumatic stress disorder

This study investigated the relationship between overgeneral autobiographical memory and social problem solving in posttraumatic stress disorder (PTSD). Civilian trauma survivors with and without PTSD (N=41) provided autobiographical memories of events in response to positive and negative cue words. Participants also completed the means-end problem-solving (MEPS) procedure. PTSD participants reported more overgeneral memories, regardless of cue valence, than non-PTSD participants. Individuals with PTSD also displayed poorer problem solving than those without PTSD. Overgeneral autobiographical memory was strongly associated with deficits in problem solving. This study suggests that deficient problem solving in PTSD is associated with impaired retrieval of specific autobiographical memories.     

Inhibition and language pragmatic view in redundant data problem solving

The present study concerns redundant data problems, defined as problems in which irrelevant data is provided. This type of problem provides a misleading context [Pascual-Leone, J. (1987). Organismic process for neo-Piagetian theories: A dialectical causal account of cognitive development. International Journal of Psychology, 22, 531–570] similar to the Piagetian class inclusion task. The two experiments performed showed that adding the a-pragmatic cue ‘in total’ to the final question of redundant data problems increased both 7- and 9-year-old children's failure rate, without modifying the structure of the problem. This indicates that a non-structural linguistic cue can bias children towards failure by enhancing the lack of inhibition of the ordinary adding schema.     

Eye movements reveal solution knowledge prior to insight

In two experiments, participants solved anagram problems while their eye movements were monitored. Each problem consisted of a circular array of five letters: a scrambled four-letter solution word containing three consonants and one vowel, and an additional randomly-placed distractor consonant. Viewing times on the distractor consonant compared to the solution consonants provided an online measure of knowledge of the solution. Viewing times on the distractor consonant and the solution consonants were indistinguishable early in the trial. In contrast, several seconds prior to the response, viewing times on the distractor consonant decreased in a gradual manner compared to viewing times on the solution consonants. Importantly, this pattern was obtained across both trials in which participants reported the subjective experience of insight and trials in which they did not. These findings are consistent with the availability of partial knowledge of the solution prior to such information being accessible to subjective phenomenal awareness.     

Consultant Problem Understanding as a Function of Training in Interviewing to Promote Accessible Reasoning

The focus of this article is on how consultants develop a “high-quality” understanding of a teacher's presenting problem situation from interviewing them. A longitudinal quasi-experimental study was conducted with 10 graduate students enrolled on an accredited training program in school psychology in which interviewing and problem-solving skills were taught and practiced. Eight individuals who had been selected for the same training program but who had not enrolled acted as a comparison group to measure possible practice effects. The results indicated that following training consultant use of statements designed to reveal their reasoning to the teacher significantly increased, and was highly correlated with the quality of their subsequent written analyses of the teacher's problem situation.     

Insight problem solving in individuals with high versus low schizotypy

Insight problem solving requires restructuring of a problem space by stepping out of the framework provided by the commonly activated cognitive schemas and acquiring a new perspective on the problem. Schizotypy has been linked with loosened associative and overinclusive thinking that may be advantageous for this process. The present study tested this hypothesis and found that individuals with a high degree of schizotypy show better performance on a set of insight problems relative to individuals with low schizotypy, but not on a set of incremental problems that required focused goal-related thinking. Results support the notion that schizotypy is associated not only with enhanced abilities in creative processes involved in divergent thinking but also in creative operations during analytical problem solving.     

How great apes perform on a modified trap-tube task

To date, neither primates nor birds have shown clear evidence of causal knowledge when attempting to solve the trap tube task. One factor that may have contributed to mask the knowledge that subjects may have about the task is that subjects were only allowed to push the reward away from them, which is a particularly difficult action for primates in certain problem solving situations. We presented five orangutans (Pongo pygmaeus), two chimpanzees (Pan troglodytes), two bonobos (Pan paniscus), and one gorilla (Gorilla gorilla) with a modified trap tube that allowed subjects to push or rake the reward with the tool. In two additional follow-up tests, we inverted the tube 180° rendering the trap nonfunctional and also presented subjects with the original task in which they were required to push the reward out of the tube. Results showed that all but one of the subjects preferred to rake the reward. Two orangutans and one chimpanzee (all of whom preferred to rake the reward), consistently avoided the trap only when it was functional but failed the original task. These findings suggest that some great apes may have some causal knowledge about the trap-tube task. Their success, however, depended on whether they were allowed to choose certain tool-using actions. Electronic Supplementary Material Supplementary material is available for this article at