COGNITIVE LOAD FOR CONFIGURATION COMPREHENSION IN COMPUTER-SUPPORTED GEOMETRY PROBLEM SOLVING: AN EYE MOVEMENT PERSPECTIVE

The present study investigated (a) whether the perceived cognitive load was different when geometry problems with various levels of configuration comprehension were solved and (b) whether eye movements in comprehending geometry problems showed sources of cognitive loads. In the first investigation, three characteristics of geometry configurations involving the number of informational elements, the number of element interactivities and the level of mental operations were assumed to account for the increasing difficulty. A sample of 311 9th grade students solved five geometry problems that required knowledge of similar triangles in a computer-supported environment. In the second experiment, 63 participants solved the same problems and eye movements were recorded. The results indicated that (1) the five problems differed in pass rate and in self-reported cognitive load; (2) because the successful solvers were very swift in pattern recognition and visual integration, their fixation did not clearly show valuable information; (3) more attention and more time (shown by the heat maps, dwell time and fixation counts) were given to read the more difficult configurations than to the intermediate or easier configurations; and (4) in addition to number of elements and element interactivities, the level of mental operations accounts for the major cognitive load sources of configuration comprehension. The results derived some implications for design principles of geometry diagrams in secondary school mathematics textbooks.     

应用题相似性和图式归纳对解题迁移的影响

研究采用问题解决作业单和认知作业分析法考察了71名高中生解决学科问题时的图式归纳和迁移情况。结果表明：（1）在问题结构相同的情况下，增加问题表面相似性能促进问题解决迁移；（2）近类比条件有助于同一学科领域问题的迁移，而远类比条件可能更有助于跨学科领域问题的迁移；（3）近类比条件下，图式归纳水平对学科问题迁移的影响不大，远类比条件下，较高的图式归纳水平有助于学科问题解决的迁移。     

DEVELOPING PROBLEM SOLVING SKILLS

Some complex societal problems such as sudden changes in Eastern Europe or the problem of AIDS are very hard to handle. Even defining the problem is difficult. Managers and experts often lack the knowledge and training to handle these kinds of problem, although the problems require intensive effort. Education typically offers few opportunities for learning how to handle them. Research on Artificial Intelligence mostly focuses on problems in stable situations which have already been solved, and ignores as yet unsolved problems in rapidly changing situations. Before a problem can be solved, it has to be defined: System dynamic modelling can be a powerful tool for doing this. Defining the kind of problem discussed here also requires teamwork: Managers and experts can learn to define a complex problem in a special learning environment involving cases embedded in free form games.     

利用"华氏对称性原理"解决空间图形问题

本文从对称性原理来讨论空间图形,所用方法独特.     

发现数学问题的主要途径与数学研究的基本方法

本文介绍了发现数学问题的三种主要途径和开展数学研究的十二种基本方法．     

THE EFFECTS OF TEACHING PROBLEM SOLVING ON ACADEMIC PERFORMANCE AND RETENTION

A study of the effects of explicitly teaching a problem‐solving strategy on problem‐solving ability, course average, course success, and student retention is reported. Two classes of microeconomics principles were involved in a quasi‐experiment. The experimental class was explicitly taught the problem‐solving strategy and this strategy was then used to solve microeconomic problems in class. The control class was assigned, solved, and discussed the same problems without being taught the problem‐solving strategy. Multiple regression and analysis of variance show that while teaching problem solving did not significantly affect course average, student success in passing the course or problem solving ability, it did result in significantly higher student retention. Results indicate that teaching problem solving only affects those students with low problem solving abilities who would have dropped out of class, and that teaching this strategy helps them remain in the class and succeed.     

SELF ASSESSMENT IN THE CONTEXT OF THE McMASTER PROBLEM SOLVING PROGRAMME

Self assessment is applied to develop students' confidence in their problem solving ability in the context of a four‐course sequence in Chemical Engineering, called the McMaster Problem Solving (MPS) programme. The issues in using self assessment are explored and then illustrated in the context of the MPS programme. The criteria for assessment are public, explicit and related to the learning objectives for each of 35 separate skills, topics or Units that comprise the programme. The criteria are primarily generated by faculty, but the students can generate their own to obtain higher levels of accomplishment. Students use journal writing as the main method of providing evidence, satisfying the criteria and demonstrating achievement. The students rationalise their self assessment in an interview with the instructor. The self assessment counts for between 10 and 27% of their grade. The students receive 6 hours of training on self assessment early in the course. Self assessment is applied to all of the subsequent activities in the MPS programme.

Comparisons are given between students' summative assessments and their performance on a written final examination and their overall mark in the course. The average deviation is usually less than 10%.

The approaches taken in this MPS programme are compared with those of others. Suggestions for development and improvement are noted.     

THE POWER OF PERFORMANCE IN DEVELOPING PROBLEM SOLVING AND SELF ASSESSMENT ABILITIES

Students of Alverno College develop problem solving as one of eight abilities they are required to demonstrate in order to graduate. They must also demonstrate self assessment ability as an important part and over‐riding outcome of their educational process.

In ongoing studies, the research staff of the college found that students show increasing sophistication in their performance of these abilities and identify them as significant aspects of their education. Faculty contribute to their own developing educational theory and practice by analysing student performance and judging it by criteria they have articulated to describe expert performance. In requiring students to integrate self assessment into their problem solving process, faculty have found that students show increasing understanding of inter‐relationships of ability, content, and context. Students take responsibility for their learning as a dynamic, continuing process. They gradually internalise their practice of both problem solving and self assessment ability.     

THEORETICAL AND PHILOSOPHICAL PERSPECTIVES TO PROBLEM SOLVING

No abstract available for this article.     

DEVELOPING CREATIVE PROBLEM SOLVING IN CIVIL ENGINEERING

The development of creative problem solving in a civil engineering degree course since the late 1960s is outlined. It is shown that prior to the Finniston Report, Middlesex Polytechnic had begun to educate civil engineers to meet an ever changing world.

The results of a psychological testing programme confirm that it is possible to increase the creative ability of students during a civil engineering degree course. An attempt is made to predict the performance of students on examinations and current lines of research are indicated.     

DESIGN, DEVELOPMENT AND VALIDATION OF A MODEL OF PROBLEM SOLVING FOR EGYPTIAN SCIENCE CLASSES

Educators and policymakers envision the future of education in Egypt as enabling learners to acquire scientific inquiry and problem-solving skills. In this article, we describe the validation of a model for problem solving and the design of instruments for evaluating new teaching methods in Egyptian science classes. The instruments were based on an established model for problem solving and were designed to assess seventh grade students’ problem solving, experimental strategy knowledge, achievement and motivation towards science. The test for assessing students’ knowledge has been developed based on the topic, density and buoyancy which will be taught in seventh grade in a later intervention study. The instruments were partly self-developed and partly adapted from newly performed studies on strategy knowledge and problem solving in Germany. All instruments were translated into Arabic; the translation process and quality control are described. In order to determine the quality of the instruments, 44 students in Egypt completed the questionnaires and tests. The study’s aim to develop and validate the instruments did require an ad hoc and typical sample which was drawn from an accessible population. Accordingly, the characteristics of the sample are described. Data were analysed according to the classical test theory, but to underpin the results, the instruments were additionally analysed using the even stronger Rasch model. The findings demonstrated the reliability of the items and aspects of validity. In addition, this study showed how test items can be successfully developed and adapted in an international study and applied in a different language.     

求一维方势阱问题数值解的两种新方法

本文给出两种数值求解一维方势阱问题的新方法.同文献中可见的节点法比较,这两种方法具有简捷、方便、且计算速度快等优点.     

PERFORMANCE IN MATHEMATICAL PROBLEM SOLVING AS A FUNCTION OF COMPREHENSION AND ARITHMETIC SKILLS

Many factors influence a student’s performance in word (or textbook) problem solving in class. Among them is the comprehension process the pupils construct during their attempt to solve the problem. The comprehension process may include some less formal representations, based on pupils’ real-world knowledge, which support the construction of a ‘situation model’. In this study, we examine some factors related to the pupil or to the word problem itself, which may influence the comprehension process, and we assess the effects of the situation model on pupils’ problem solving performance. The sample is composed of 750 pupils of grade 6 elementary school. They were selected from 35 classes in 17 Francophone schools located in the province of Quebec, Canada. For this study, 3 arithmetic problems were developed. Each problem was written in 4 different versions, to allow the manipulation of the type of information included in the problem statement. Each pupil was asked to solve 3 problems of the same version and to complete a task that allowed us to evaluate the construction of a situation model. Our results show that pupils with weaker arithmetic skills construct different representations, based on the information presented in the problem. Also, pupils who give greater importance to situational information in a problem have greater success in solving the problem. The situation model influences pupils’ problem solving performance, but this influence depends on the type of information included in the problem statement, as well as on the arithmetic skills of each individual pupil.     

电学方法对扩散问题求解的启示

本文介绍了电磁学中常见的镜像法在扩散问题中的应用,说明可以借助于电学模拟方法,并进行电量的测量,为相类似的扩散问题寻得解答。