Unsuccessful Solvers Research Articles

A Pilot Study on Investigating Primary School Students’ Eye Movements While Solving Compare Word Problems

Abstract One of the most difficult types of arithmetic word problems in primary school is compare problems. Among these problems, the most problematic are those in which the relational term is not consistent with the arithmetic operation required for the solution. This study investigates how 10–11-year-old primary school pupils’ read and interpret compare word problems. The consistency effect and the differences between successful and unsuccessful problem solvers are mainly studied using eye-tracking technology. The results show that students are more successful in solving consistent language (CL) problems than inconsistent language (IL) problems. Regarding eye movements during reading and solving the problems, fixation duration on the relational sentence and numbers is longer in the case of IL problems than in the case of CL problems. Compared to successful problem solvers, unsuccessful solvers fixate longer on the relational term, the pronominal reference word, and the statement and relational sentence of IL problems, but not on numbers.

The Role of Motor Activity in Insight Problem Solving (the Case of the Nine-Dot Problem).

Attempts to estimate the contribution made by motor activity to insight problem solving is hindered by a lack of detailed description of motor behavior. The goal of this study was to develop and put to the test a novel method for studying the dynamics of insight problem solving based on a quantitative analysis of ongoing motor activity. As a proper problem model, we chose the nine-dot problem (Maier, 1930), in which solvers had to draw a sequence of connected line segments. Instead of using the traditional pen-and-paper way of solving the nine-dot problem we asked participants to use their index finger to draw line segments on the surface of a tablet computer. We are arguing that successful studying of the role of motor activity during problem solving requires the distinction between its instrumental and functional role. We considered the functional role on the motor activity as closely related to the on-line mode of motor planning. The goal of Experiment 1 was to explore the potential power of the method and, at the same time, to assay the patterns of motor activity related to on-line and off-line modes of motor planning. Experiments 2 and 3 were designed to uncover the potential impact of preliminary motor training on the motor output of successful and unsuccessful problem solvers. In these experiments, we tested hypotheses on how preliminary motor training, which presumably played a functional role in Experiment 2 and an instrumental role in Experiment 3, affects the motor activity of a problem solver and hence their effectiveness in solving the problem. The three experiments showed consistent results. They suggest that successful solving of the nine-dot problem relies upon the functional role of motor activity and requires both off-line and on-line modes of motor planning, with the latter helping to overcome the perceptual constraints imposed by a spatial arrangement of the nine dots. The method that we applied allows for systematic comparison between successful and unsuccessful problem solvers based on the quantitative parameters of their motor activity. Through it, we found new specific patterns of motor activity that differentiate successful and unsuccessful solvers.

Feelings-of-Warmth Increase More Abruptly for Verbal Riddles Solved With in Contrast to Without Aha! Experience.

When we are confronted with a new problem, we typically try to apply strategies that have worked in the past and which usually lead closer to the solution incrementally. However, sometimes, either during a problem-solving attempt that does not seem to lead closer to the solution, or when we have given up on problem-solving for the moment, the solution seems to appear out of nowhere. This is often called a moment of insight. Whereas the cognitive processes of getting closer to the solution are still unknown for insight problem-solving, there are two diverging theories on the subjective feeling of getting closer to the solution: (1) One that states that an intuitive feeling of closeness to the solution increases slowly, but incrementally, before it surpasses the threshold to consciousness and becomes verbalizable (=insight) (continuous approach), and (2) another that proposes that the feeling of closeness to the solution does not increase before it exceeds the threshold to consciousness (discontinuous approach). Here, we investigated the subjective feeling of closeness to the solution, assessed as feeling-of-warmth (FoW), its relationship to solving the problem versus being presented with it and whether a feeling of Aha! was experienced. Additionally, we tested whether Aha! experiences are more likely when the problem is solved actively by the participant or presented to the participant after an unsuccessful problem-solving attempt, and whether the frequency of Aha! experiences correlates with problem difficulty. To our knowledge, this is the first study combining the CRAT with FoW assessments for the named conditions (solved/unsolved, three difficulty levels, Aha!/no Aha!). We used a verbal problem-solving task, the Compound Remote Associates Task (CRAT). Our data revealed that Aha! experiences were more often reported for solutions generated by the participant compared to solutions presented after unsuccessful problem-solving. Moreover, FoW curves showed a steeper increase for the last two FoW ratings when problems were solved with Aha! in contrast to without Aha!. Based on this observation, we provide a preliminary explanation for the underlying cognitive process of solving CRA problems via insight.

On the Role of Situational Stressors in the Disruption of Global Neural Network Stability during Problem Solving.

When individuals are placed in stressful situations, they are likely to exhibit deficits in cognitive capacity over and above situational demands. Despite this, individuals may still persevere and ultimately succeed in these situations. Little is known, however, about neural network properties that instantiate success or failure in both neutral and stressful situations, particularly with respect to regions integral for problem-solving processes that are necessary for optimal performance on more complex tasks. In this study, we outline how hidden Markov modeling based on multivoxel pattern analysis can be used to quantify unique brain states underlying complex network interactions that yield either successful or unsuccessful problem solving in more neutral or stressful situations. We provide evidence that brain network stability and states underlying synchronous interactions in regions integral for problem-solving processes are key predictors of whether individuals succeed or fail in stressful situations. Findings also suggested that individuals utilize discriminate neural patterns in successfully solving problems in stressful or neutral situations. Findings overall highlight how hidden Markov modeling can provide myriad possibilities for quantifying and better understanding the role of global network interactions in the problem-solving process and how the said interactions predict success or failure in different contexts.

Capturing students’ abstraction while solving organic reaction mechanism problems across a semester

Students often struggle with solving mechanism problems in organic chemistry courses. They frequently focus on surface features, have difficulty attributing meaning to symbols, and do not recognize tasks that are different from the exact tasks practiced. To be more successful, students need to be able to extract salient features, map similarities to problems seen previously, and extrapolate while solving problems. In short, students must be able to recognize and generate abstractions. To help students in learning to solve problems, we need a better understanding of the nature of students’ capacity for abstraction. Building upon an exploratory study (Sevian H., Bernholt S., Szteinberg G. A., Auguste S. and Pérez L. C., (2015), Use of representation mapping to capture abstraction in problem solving in different courses in chemistry,Chem. Educ. Res. Pract., 16(3), 429–446), we applied the representation mapping model of Hahn and Chater (1998a) to characterize the abstraction employed by students while solving mechanistic problems in organic chemistry, and to measure students’ growth in abstraction capacity across a semester. This model operationalizes abstraction by considering (a) the ways in which students match existing knowledge to new instances (abstracting) and (b) the level of abstractness of students’ representations. We describe characteristic indicators of abstracting and abstractness. Trends were observable in the abstraction present in the reasoning of successful and unsuccessful problem solvers. Students who proposed plausible solutions used both strict or partial matching, but students who proposed implausible solutions tended to use strict matching. Students who proposed plausible solutions utilized higher levels of abstractness. This indicates that flexibility in abstraction processes may be important to successfully solve problems. The findings have implications for developing instructors’ assessment practices in ways that build students’ abstraction capacity.

ДВИЖЕНИЯ В СТРУКТУРЕ РЕШЕНИЯ ИНСАЙТНЫХ ЗАДАЧ (НА МАТЕРИАЛЕ ЗАДАЧИ 9 ТОЧЕК)

Existing data about the effect of concomitant or preceding motor activity on the process of insight problem solving conflicts with modern theories of insight. Therefore, it requires more detailed research of motor activity in the insight problem solving. This study investigates the regular changes of motor activity in the process of solving a classical insight problem “9 dots” (nine-dot problem). To register the motor activity parameters (length of the motor units, velocity of implementation of the motor units, duration of the pauses between the motor units) and to present conditions of the problem a tablet was used. As a result, persistent differences in the motor activity were found between successful and unsuccessful solvers in the initial and final stage of the problem solution. It turned out that successful solvers demonstrated a greater length of motor units (especially at the final stage of the solution) than unsuccessful ones. At the same time, differences in the duration of pauses between the motor units atthe initial and final stages of the solution were not found. Subjects who did and did not solve the problem do not differ in the duration of pauses between the motor units. It was found that at the final stage the frequency of the “fast” lines increases which can be associated primarily with the “offline” planning of motor activity that is the planning preceding the activity itself, rather than proceeding in parallel with it.

Integrating eye trackers with handwriting tablets to discover difficulties of solving geometry problems

AbstractTo deepen our understanding of those aspects of problems that cause the most difficulty for solvers, this study integrated eye‐tracking with handwriting devices to investigate problem solvers' online processes while solving geometry problems. We are interested in whether the difference between successful and unsuccessful solvers can be identified by employing eye‐tracking and handwriting. Sixty‐two high school students were required to complete a series of geometry problems using pen tablets. Responses, including eye movement measures, wrote/drew trace, perceived cognitive load and questionnaires concerning the source of difficulties, were collected. The results suggested that the technique could enhance methods to diagnose difficulties by differentiating between successful and unsuccessful solvers. We considered mental rotation could be a primary obstacle in the integrating stage of diagram comprehension. The technique can be extensively applied in various instructional scenarios. Educational implications for problem solving are discussed.

Influence of cooperative problem solving on students’ control and help-seeking strategies during mathematical problem solving

15.00 Developing problem solving is one of the main goals of school education. A self-regulated learner have more success in problem solving, as developing self-regulated learning skills should be an important goal of school education. A teacher, in order to be able to develop their pupils’ self-regulated learning skills, should master these skills. Thus developing these skills should be an essential goal of teacher education. In this paper two important skills of a self-regulated learner are studied: control and help-seeking behavior during problem solving. The article presents a research on the influence of the cooperative problem solving strategies on students’ self-control and self-monitoring during problem solving, and their help seeking strategies in case of unsuccessful problem solving. The results show that students’ control decrease when using cooperative problem solving; cooperative problem solving helped students to realize the importance of asking for help when solving problems; and cooperative problem solving prevent increasing the giving up rate in case of non-routine problems. Normal 0 false false false EN-US X-NONE X-NONE

Tracking eye movements when solving geometry problems with handwriting devices

The present study investigated the following issues: (1) whether differences are evident in the eye movement measures of successful and unsuccessful problem-solvers; (2) what is the relationship between perceived difficulty and eye movement measures; and (3) whether eye movements in various AOIs differ when solving problems. Sixty-three 11th grade students solved five geometry problems about the properties of similar triangles. A digital drawing tablet and sensitive pressure pen were used to record the responses. The results indicated that unsuccessful solvers tended to have more fixation counts, run counts, and longer dwell time on the problem area, whereas successful solvers focused more on the calculation area. In addition, fixation counts, dwell time, and run counts in the diagram area were positively correlated with the perceived difficulty, suggesting that understanding similar triangles may require translation or mental rotation. We argue that three eye movement measures (i.e., fixation counts, dwell time, and run counts) are appropriate for use in examining problem solving given that they differentiate successful from unsuccessful solvers and correlate with perceived difficulty. Furthermore, the eye-tracking technique provides objective measures of students’ cognitive load for instructional designers.

Using Students’ Representations Constructed during Problem Solving To Infer Conceptual Understanding

The differences in the types of representations constructed during successful and unsuccessful problem-solving episodes were investigated within the context of graduate students working on problems that involve concepts from 2D-NMR. Success at problem solving was established by having the participants solve five problems relating to material just encountered within a computer-based tutorial. The results indicate that representations constructed during successful problem-solving episodes tend to be more accurate and more complete, but not as abstract as those constructed during unsuccessful problem-solving episodes. When more than a single representation was constructed, however, the additional representations associated with successful problem solving tended to be more abstract than those constructed during unsuccessful problem solving. The authors contend that the constructs of accuracy, abstractness, and completeness are useful for characterizing the differences in the representations constructed during successful and unsuccessful problem-solving episodes, and may serve as useful indicators of the degree of conceptual understanding the individual brings to the problem-solving event.

Visual attention for solving multiple-choice science problem: An eye-tracking analysis

This study employed an eye-tracking technique to examine students’ visual attention when solving a multiple-choice science problem. Six university students participated in a problem-solving task to predict occurrences of landslide hazards from four images representing four combinations of four factors. Participants’ responses and visual attention were recorded by an eye tracker. Participants were asked to think aloud during the entire task. A 4 (options) × 4 (factors) repeated measures design, two paired t-tests and effect sizes analyses were conducted to compare the fixation duration between chosen and rejected options and between relevant and irrelevant factors. Content analyses were performed to analyze participants’ responses and think aloud protocols and to examine individual’s Hot Zone image. Finally, sequential analysis on fixated LookZones was further utilized to compare the scan patterns between successful and unsuccessful problem solvers. The results showed that, while solving an image-based multiple-choice science problem, students, in general, paid more attention to chosen options than rejected alternatives, and spent more time inspecting relevant factors than irrelevant ones. Additionally, successful problem solvers focused more on relevant factors, while unsuccessful problem solvers experienced difficulties in decoding the problem, in recognizing the relevant factors, and in self-regulating of concentration. Future study can be done to examine the reliability and the usability of providing adaptive instructional scaffoldings for problem solving according to students’ visual attention allocations and transformations in a larger scale. Eye-tracking techniques are suggested to be used to deeply explore the cognitive process during e-learning and be applied to future online assessment systems.

Zeigarnik effect in Insight problem solving: Hemi-spheric difference in brain activities following problem solving and during hint presentation

People tend to exhibit enhanced memory performance for the unfinished tasks relative to the finished ones, which known as the Zeigarnik effect. Consistently, the impasse state in insightful problem solving were believevd to play an important role in maintaining the problem in one’s mind and in catching the critical clue to overcome the main obstacles. More importantly, through hemi-visual field presentation technology, studies on insight found the keynotes for the unsolved puzzle could be more efficient in catalyzing a breakthrough when presented to the left-visual field (i.e., the right hemisphere) than to the right-visual field, especially when there was a temporal delay between the disappearance of the puzzle and the presentation of keynotes. This observation implied that the right hemisphere, relative to the left one, might play a more important role in keeping the information of the unsolved problem online and might be more ready in processing the related clue for that problem. In order to testify this hypothesis, we compared the Event-Related Potentials (ERPs) between the solved and unsolved insightful chunk decomposition problems during (a) the moment when the subjects pressed a key to indicate whether or not they could solve the problem by themselves before seeing any external hint, and (b) the moment when subjects were given the hint. The ERPs results showed that, during the moment of subjects’ confirmation of their successful or unsuccessful problem solving, the unsolved problems were accompanied with a more positive P150 over the right frontal cortex, whereas the solved ones exhibited a more positive P150 over the left side. Consistently, during the moment of hints presentation, the hints to the unsolved problems also elicited a more positive P2 over the right hemisphere, whereas the the hints to the solved problems elicited a more positive P2 over the left side. These results confirmed the hypothesis that, after the failure in insight problem solving, the right hemisphere might be more positive in preserving the unsolved problem in mind and be more responsive to the external hint for problem solving.

Socially mediated metacognition: creating collaborative zones of proximal development in small group problem solving

This paper reports on a three year study of patterns of student-student social interaction that mediated metacognitive activity in senior secondary school mathematics classrooms. Transcripts of small group problem solving were analysed to determine how a collaborative zone of proximal development could be created through interaction between peers of comparable expertise, and to investigate conditions under which such interaction led to successful or unsuccessful problem solving outcomes. Unsuccessful problem solving was characterised by students' poor metacognitive decisions exacerbated by lack of critical engagement with each other's thinking, while successful outcomes were favoured if students challenged and discarded unhelpful ideas and actively endorsed useful strategies. In reconceptualising metacognition as a social practice, the study contributes to the growing body of research applying sociocultural theories to understand learning in mathematics classrooms.

How Problems are Solved: Reconsidering the Phase Theorem

The literature on problem-solving is dominated by the phase theorem. The descriptive facet of the theorem suggests that problem solvers follow a certain sequence of phases. Its prescriptive facet suggests that problem solvers are more likely to succeed if they follow a certain sequence of phases. Despite the ubiquity of the phase theorem, there is no empirical support for either its descriptive or its prescriptive validity. This study tested the descriptive and prescriptive validity of a six-phase probabilistic problem-solving model in seventy-five pairs of retrospective reports of successful and unsuccessful problem-solving in organizational settings. In both types of cases, the location of phases in the problem-solving process was consistent with the sequence prescribed by the model, and the order of consecutive phases, irrespective of location in the sequence, was also consistent with the model. Differences between success and failure processes were found in frequency of diagnosis, the compatibility of diagnosis and action, and the extent to which diagnosis preceded action. The results suggest that, contrary to received opinion, the descriptive validity of the phase theorem is still unresolved. Further research is required to establish whether the descriptive and prescriptive models suggested by these results reflect actual problem-solving processes, or implicit schemata of how problems are, and should be, solved.

Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers.

It is proposed that when solving an arithmetic word problem, unsuccessful problem solvers base their solution plan on numbers and keywords that they select from the problem (the direct translation strategy), whereas successful problem solvers construct a model of the situation described in the problem and base their solution plan on this model (the problemmodel strategy). Evidence for this hypothesis was obtained in 2 experiments. In Experiment 1, the eye fixations of successful and unsuccessful problem solvers on words and numbers in the problem statement were compared. In Experiment 2, the degree to which successful and unsuccessful problem solvers remember the meaning and exact wording of word problems was examined. Why are some students successful in solving word problems whereas others are unsuccessful? To help answer this question, we begin with the well-established observation that many students from kindergarten through adulthood have difficulty in solving arithmetic word problems that contain relational statements, that is, sentences that express a numerical relation between two variables (Hegarty, Mayer, & Green, 1992; Lewis & Mayer, 1987; Riley, Greeno, & Heller, 1983; Verschaffel, De Corte, & Pauwels, 1992). For example, Appendix A shows a successful and an unsuccessful solution to a two-step word problem containing a relational statement about the price of butter at two stores. We refer to this as an inconsistent version of the problem because the relational keyword (e.g., less) primes an inappropriate arithmetic operation (subtraction rather than addition), whereas in a consistent problem, the relational term in the second problem statement primes the required arithmetic operation (e.g., more when the required operation is addition). A substantial proportion of college students, who could be called unsuccessful problem solvers, use the wrong arithmetic operation on inconsistent problems but perform correctly on consistent problems (Hegarty et al., 1992; Lewis, 1989; Lewis & Mayer, 1987; Verschaffel et al., 1992). We interpret this finding as evidence that problem comprehension processes play an important role in the solution of arithmetic word problems.

Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers.

Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers.

Problem solving and chemical equilibrium: Successful versus unsuccessful performance

AbstractThe purpose of this study was to describe the problem‐solving behaviors of experts and novices engaged in solving seven chemical equilibrium problems. Thirteen novices (five high‐school students, five undergraduate majors, and three nonmajors) and ten experts (six doctoral students and four faculty members) were videotaped as they individually solved standard chemical equilibrium problems. The nature of the problems was such that they required more than mere recall or algorithmic learning and yet simple enough to provide the novices a reasonable chance of solving them. Extensive analysis of the think‐aloud protocols produced 27 behavioral tendencies that can be used to describe and differentiate between successful and unsuccessful problem solvers. Successful solvers' perceptions of the problem were characterized by careful analysis and reasoning of the task, use of related principles and concepts to justify their answers, frequent checks of the consistency of answers and reasons, and better quality of procedural and strategic knowledge. Unsuccessful subjects had many knowledge gaps and misconceptions about the nature of chemical equilibrium. Even faculty experts were sometimes unable to correctly apply common chemical principles during the problem‐solving process. Important theoretical concepts such as molar enthalpy, heat of reaction, free energy of formation, and free energy of reaction were rarely used by novices in explaining problems.

Successful and unsuccessful problem solving in classical genetic pedigrees

AbstractUsing the think‐aloud interview technique, 16 undergraduates and 11 genetics graduate students and biology faculty members were asked to solve from 1 to 3 classical genetics problems which require pedigree analysis. Subjects were classified as either successful or unsuccessful and the performances of these groups were analyzed from videotaped recordings of the interviews. A number of previously reported findings were corroborated. Additional observations are discussed in terms of genetic knowledge, use of production rules, strategy selection, use of critical cues, hypothesis testing, use of logic, understanding of issues of probability, and the thinking process itself. Taken collectively, these findings evidence a remarkable similarity between the successful solution of pedigree problems and the processes of medical diagnosis and scientific investigation. This convergence of research findings suggests a qualitative advance in the understanding of problem solving. Based on this understanding, recommendations for classroom instruction are presented.

Thinking Aloud: Analysing Students' Mathematics Performance

Psychologists, teachers and researchers have a common interest in understanding how students solve mathematics problems. We want, and need, to understand how solutions to problems are developed so that interactions with both successful and unsuccessful problem-solvers can become more effective. In order to build a more sophisticated understanding of problem-solving we must consider a number of major factors — the instructional setting, the nature of the problem-solver, the resources available, the structure of the mathematical content and the student's understanding of that, and the processes used in the solution. Also needed is a technique for identifying those processes in samples of students' mathematics performance. What we learn from using the technique influences the design of future instruction.

Problem solving and classical genetics: Successful versus unsuccessful performance

AbstractExpert‐novice problem‐solving research is extended in this study to include classical genetics. Eleven undergraduates (novices) and nine graduate students and instructors (experts) were videotaped as they solved moderately complex genetics problems. Detailed analysis of these “think aloud” protocols resulted in 32 common tendencies that could be used to differentiate between successful and unsuccessful problem solvers. Experts perceive a problem as a task requiring analysis and reasoning and they tend to use a knowledge‐development (forward‐working) approach. They make frequent checks on the correctness of their work, use accurate and detailed bookkeeping procedures, and have a broader range of heuristics to apply to the problem. It is clear that studying problem solving using the expert/novice design requires that the problems be difficult enough to require more than more recall and yet simple enough to allow novices a chance for solution. Applying elementary probability concepts seemed to be the most difficult aspect of many of the genetics problems, even for the experts.