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

To 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.     

Substituting one mystery for another: the role of self-explanations in solving algebra word-problems

Explanations students provide themselves (self-explanations) in the course of learning or problem-solving have been shown to be positively associated with performance. However, the role self-explanation plays in problem solving has not been fully elaborated. This study aims to analyze the role of self-explanation in solving algebra word problems. We argue that self-explanation may function as verbal mediation that supports the transformation between different external representations of the problem. Our analysis of the problem solving protocols aims to illustrate this point through a multiple case studies design. Specifically we illustrate the way a particular kind of self-explanation (categorical explanation) mediates students' transformation from the sentential representation of the problem to the tabular one.     

Coordinating principles and examples through analogy and self-explanation

Research on expertise suggests that a critical aspect of expert understanding is knowledge of the relations between domain principles and problem features. We investigated two instructional pathways hypothesized to facilitate students’ learning of these relations when studying worked examples. The first path is through self-explaining how worked examples instantiate domain principles and the second is through analogical comparison of worked examples. We compared both of these pathways to a third instructional path where students read worked examples and solved practice problems. Students in an introductory physics class were randomly assigned to one of three worked example conditions (reading, self-explanation, or analogy) when learning about rotational kinematics and then completed a set of problem solving and conceptual tests that measured near, intermediate, and far transfer. Students in the reading and self-explanation groups performed better than the analogy group on near transfer problems solved during the learning activities. However, this problem solving advantage was short lived as all three groups performed similarly on two intermediate transfer problems given at test. On the far transfer test, the self-explanation and analogy groups performed better than the reading group. These results are consistent with the idea that self-explanation and analogical comparison can facilitate conceptual learning without decrements to problem solving skills relative to a more traditional type of instruction in a classroom setting.     

Testing the instructional fit hypothesis: the case of self-explanation prompts

Cognitive science principles should have implications for the design of effective learning environments. The self-explanation principle was chosen for the current work because it has developed significantly over the last 20 years. Early formulations hypothesized that self-explanation facilitated inference generation to supply missing information about a concept or target skill, whereas later work hypothesized that self-explanation facilitated mental-model revision (Chi, Handbook of research on conceptual change, 2000). To better understand the complex relationship between prior knowledge, cognitive processing, and changes to a learner’s representation, two classes of self-explanation prompts (gap-filling and mental-model revision) were tested in the domain of physics problem solving. Prompts designed to focus the learner on gap-filling led to greater learning and a reduction in the amount of tutoring assistance required to solve physics problems. The results are interpreted as support for the instructional fit hypothesis—the idea that the efficacy of instruction is contingent on the match between the cognitive processing that the instruction elicits, how those processes modify the underlying knowledge representations for the task, and the utility of those representations for the task or problem.     

Can learning from molar and modular worked examples be enhanced by providing instructional explanations and prompting self-explanations?

In two experiments we explored how learning from traditional molar worked-out examples—focusing on problem categories and their associated overall solution procedures—as well as from more efficient modular worked-out examples—where intrinsic cognitive load is reduced by breaking down complex solutions into smaller meaningful solution elements—can be further enhanced. Instructional explanations or self-explanation prompts were administered to increase germane cognitive load. However, both interventions were not effective for learning and prompting for self-explanations even impaired learning with modular examples. In the latter case, prompting might have forced learners to process redundant information, which they had already sufficiently understood.     

Examining the effects of combining self-explanation principles with an educational game on learning science concepts

Educational researchers have indicated that although computer games have the potential to promote students’ motivation and engagement, the work on how to design effective games that fulfil educational purposes is still in its infancy. This study aimed to examine how integration of self-explanation into a computer game affected primary schoolers’ acquisition of light and shadow concepts. The participants were randomly assigned to either an experimental group or a control group and played a computer game with or without self-explanation prompts individually as a treatment. Students’ conceptual understanding was evaluated through a pretest and a posttest administered right after the treatment. The results revealed that by controlling the pretest scores, students who played the game with self-explanation features did not outperform those who played the game without any prompts in the posttest. Further analyses of the experimental group students’ responses to the self-explanation prompts also indicated that the students with more correct responses to the prompts did not perform better than those with lower accuracy rates. The deficits in the use of self-explanation prompts are identified, and possible improvements to enhance the function of self-explanation in educational games are proposed.     

自我解释的研究述评

自我解释是指学习者向自身做出解释,以理解新信息的一种认知活动。研究表明,在学习过程中,自我解释的学习者对学习材料的理解更好,这种现象称为“自我解释效应”。文章从自我解释效应的影响因素,促进自我解释和自我解释的心理机制三个角度出发,回顾了以往关于自我解释的研究。最后,提出了三个有待进一步研究的问题。     

Exploring the effects of integrating self-explanation into a multi-user game on the acquisition of scientific concepts

The purpose of this study was to examine the impacts of embedding collaboration into a game with a self-explanation design for supporting the acquisition of light and shadow concepts. The participants were 184 fourth graders who were randomly assigned to three conditions: a solitary mode of the game with self-explanation, a collaborative mode with self-explanation, or the control condition of a single-user game without integrating self-explanation. Students' conceptual understanding was measured through an immediate posttest and a retention test with a three-week delay. Further, students' engagement in answering the prompts was also investigated. The findings showed that having students collaboratively play science-based games with a self-explanation design embedded was not sufficient to help them learn the science concepts. Rather, it was the level of engagement in responding to the self-explanation prompts that mattered.     

The consistency effect depends on markedness in less successful but not successful problem solvers: An eye movement study in primary school children

This study examined the effects of consistency (relational term consistent vs. inconsistent with required arithmetic operation) and markedness (relational term unmarked [‘more than’] vs. marked [‘less than’]) on word problem solving in 10–12 years old children differing in problem-solving skill. The results showed that for unmarked word problems, less successful problem solvers showed an effect of consistency on regressive eye movements (longer and more regressions to solution-relevant problem information for inconsistent than consistent word problems) but not on error rate. For marked word problems, they showed the opposite pattern (effects of consistency on error rate, not on regressive eye movements). The conclusion was drawn that, like more successful problem solvers, less successful problem solvers can appeal to a problem-model strategy, but that they do so only when the relational term is unmarked. The results were discussed mainly with respect to the linguistic–semantic aspects of word problem solving.     

Problem Solving and Teaching How to Solve Problems in Technology-Rich Contexts

ABSTRACT

Problem solving is perhaps the key characteristic that makes us human. Given the kinds of problems that we face in a competitive economy and society, the new generation of learners is ever more required to have problem-solving abilities. By drawing from the literature on technological pedagogical content knowledge, design thinking, general and specific methods of problem solving, and role of technologies for solving problems, this article highlights the importance of problem solving for future teachers and discusses strategies that can help them become good problem solvers and understand the requirements of teaching their students problem solving in technology-rich contexts. This article consists of two main parts. Part 1 focuses on strategies required to help preservice teachers to be better problem solvers, and Part 2 summarizes approaches to introduce preservice teachers to the methods of teaching problem solving. The strategies reviewed provide a tangible guidance for teacher education programs regarding how to promote future teachers’ problem-solving skills.     

对自我解释研究的分析

自我解释是学生在学习过程中自己向自己解释学习内容的知识获得过程。该文解释了“自我解释”的含义、总结了自我解释的类型、比较了几种自我解释产生的认知机制、归纳了影响因素,从而提出了关于自我解释需要进一步研究的未来问题。     

An Empirical Analysis of Children's Thinking and Learning in a Computer Game Context

This study explored ways to analyse gains in children's cognitive skills through playing computer games. Eighty-seven children aged from 7 to 10 years participated in a computer game called 'Find the Flamingo', one of Safari Search series (O'Brien, 1985). The game consisted of a set of rules, given with affirmative and negative if-then statements. Development, individual differences and learning were found in children's inferential game play. It was also found that there were already different play patterns from the beginning of the games between the good problem solvers and the random guessers. Discussions were made on the methods for analysis of computer game activity.     

An Activity Analysis of Secretarial Duties as a Basis for an Office Practice Course

The cognitive processes used by children during problem solving have received considerable attention in recent years. The identification of the processes used by both successful and unsuccessful problem solvers has been hampered by the difficulties involved in making accurate observations of mental processes which may or may not have physical manifestations during problem solving. In addition, problem solvers themselves often are unaware of many of the thought processes they use while attempting to solve problems. The most popularly used methods for studying problem solving processes are not sufficiently reliable or valid. This study explored the potential effectiveness of a new procedure for identifying and studying certain of the cognitive processes used during problem solving. In addition, the procedure was used to categorize the types of conceptual thinking problem solvers employ, to study the use of trial and error behavior, and to investigate problem solvers’ abilities to coordinate multiple bits of information. It appears that the procedure has application for generating hypotheses about cognitive processes problem solvers use.     

加工水平对具有广义抽象关系数学问题迁移的影响

解题者对靶题与源题之间的共性意识及加工水平对解题迁移的影响已经得到了验证,其中靶题与源题之间存在着广义抽象关系.结果表明:(1)当靶题是低难度或高难度问题时,解题者对靶题与源题之间共性关系的意识及加工水平对解题迁移的影响没有显著差异;(2)当靶题是中难度问题时,解题者对靶题与源题之间共性关系的意识及加工水平对解题迁移的影响有显著差异.     

A comparison of updating processes in children good or poor in arithmetic word problem-solving

This study examines the updating ability of poor or good problem solvers. Seventy-eight fourth-graders, 43 good and 35 poor arithmetic word problem-solvers, performed the Updating Test used in Palladino et al. [Palladino, P., Cornoldi, C., De Beni, R., and Pazzaglia F. (2002). Working memory and updating processes in reading comprehension. Memory and Cognition, 29, 344–354.]. The participants listened to wordlists, each comprising 12 words referring to objects or animals of different sizes. At the end of each list participants were asked to recall the 3 or 5 words denoting the smallest objects/animals in the list. Results show that poor problem-solvers recalled fewer correct words and made more intrusion errors (recall of non-target words) than good problem-solvers. Results support the hypothesis that the ability to select and update relevant, and suppress irrelevant information, is related to problem-solving, even when the influence of reading comprehension is controlled for. With reference to Baddeley's, and other recent WM models [Miyake, A., and Shah, P. (Eds.), (1999). Models of working memory: Mechanisms of active maintenance and executive control. New York: Cambridge University Press.], our results point to the idea that problem-solving relies on the central executive for processing and updating information contained in the problems.     

Learning by self-explaining causal diagrams in high-school biology

Understanding scientific phenomena requires comprehension and application of the underlying causal relationships that describe those phenomena (Carey 2002). The current study examined the roles of self-explanation and meta-level feedback for understanding causal relationships described in a causal diagram. In this study, 63 Korean high-school students were randomly assigned to one of three conditions: instructional explanation, self-explanation, and meta-level feedback. Results showed that self-explaining a causal diagram was as effective as studying instructional explanations. Furthermore, the effectiveness of self-explaining a causal diagram was enhanced by meta-level feedback that prompted students to reflect on their own explanations by comparing them with instructional explanations. We identified three main difficulties that high-school students experienced when explaining a causal diagram to themselves: one-sided explanation, erroneous explanation, and the lack of inference. Implications of the study were discussed in regard to the improvement of self-explanation and the design of causal diagrams in science education.     

样例学习中自我解释效应的研究

在样例学习过程中,学习者对样例的知识内容进行自我解释,会导致样例学习成绩提高,这就是自我解释效应。Chi等人最初对自我解释效应所进行的研究发现,自我解释效应的影响因素包括先行知识、一般能力和个体差异。对自我解释效应的三种理论解释是:间隙—填充(gap—filling)、图式—结构(schema formation)和相似增强(analogical enhancement)。未来对自我解释效应研究的关注点是:自我解释效应的机制、人为设定自我解释提示能否改进学习效果,以及建构性活动与样例学习效果之间的关系。     

Analysing cognitive or non‐cognitive factors involved in the process of physics problem‐solving in an everyday context

Recently, the importance of an everyday context in physics learning, teaching, and problem‐solving has been emphasized. However, do students or physics educators really want to learn or teach physics problem‐solving in an everyday context? Are there not any obstructive factors to be considered in solving the everyday context physics problems? To obtain the answer to these questions, 93 high school students, 36 physics teachers, and nine university physics educators participated in this study. Using two types of physics problems—everyday contextual problems (E‐problems) and decontextualized problems (D‐problems)—it was found that even though there was no difference in the actual performance between E‐problems and D‐problems, subjects predicted that E‐problems were more difficult to solve. Subjects preferred E‐problems on a school physics test because they thought E‐problems were better problems. Based on the observations of students' problem‐solving processes and interviews with them, six factors were identified that could impede the successful solution of E‐problems. We also found that many physics teachers agreed that students should be able to cope with those factors; however, teachers' perceptions regarding the need for teaching those factors were low. Therefore, we suggested teacher reform through in‐service training courses to enhance skills for teaching problem‐solving in an everyday context.     

The effects of self-explanation training on students' problem solving in high-school mathematics

The performance of a group of grade 9 mathematics students trained to use a self-explanation procedure during study of a new theorem in geometry was compared with that of students who used their usual study procedures. The processing activities used by the students during the study session and those used in a subsequent problem-solving test were observed. The focus of analysis on both occasions was on the knowledge access, knowledge generation, management and elaboration activities used by students. The self-explanation group showed more frequent use of each type of activity and also obtained higher scores on the problem-solving test. The difference in post-test performance of the groups was greatest on a set of far-transfer items. These items required the students to extend their use of the newly learned theorem to problem types that were substantially different from those presented in the original study material. Of particular note was the carryover effect of self-explanation training to students' processing in the subsequent problem-solving session. The relationships among the processing activities, students' beliefs, prior knowledge and post-test performance were examined using a partial least-squares path analysis procedure. Use of the self-explanation method had an indirect effect on performance, this effect being mediated by associated knowledge access and knowledge generation activity. There was no direct effect of method on performance. The strongest predictor of performance was the level of knowledge generation activity during which students showed evidence of making novel connections, either within the newly presented study material or between parts of that material and their existing geometry knowledge. In the final path model derived from the analysis of student performance, the students' prior knowledge measure had both a weak direct on their problem-solving performance and an effect on that performance that was mediated by relationships with the knowledge access and knowledge generation variables in the model.