Problem solving and classical genetics: Successful versus unsuccessful performance

Expert-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.     

Successful and unsuccessful problem solving in classical genetic pedigrees

Using 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.     

Analysing probem solving behaviour of successful and unsuccessful statistics students

The present study investigated problem-solving behaviour in statistics by documenting differences between successful and unsuccessful students. Two methodological approaches were used. The first, based on studies by Chi, Glaser and Rees (1982), required students to identify key structural features of common problems. The second, based on further work by Chi, Bassok, Lewis, Reimann & Glaser (1989), used verbal protocol procedures to examine the processes employed when Good and Poor statistics students solve an ANOVA problem. It was expected that findings obtained by these earlier researchers in the domain of Physics would also apply in Statistics. Two groups of students in an undergraduate Psychology course were selected for the study. The first group (N=8) had performed well in a statistics unit, the second group (N=6) had failed that unit. In the first part of the study, no differences were found between groups on the task of identifying key structural features of common problems. In the second part of the study, protocol analyses showed that the Good students engaged in more concept-oriented solution behaviour, displayed more monitoring/judging behaviour, and asked more questions about the problem itself. These findings are similar to those obtained in other abstract knowledge domains such as Physics and Mathematics and indicate quite fundamental differences in the way in which competent and incompetent Statisics students solve Statistics problems.     

Problem solving and transfer

Problem solving is an important yet elusive educational goal. This article briefly reviews the research on the components of problem solving and two mechanisms for fostering the transfer of problem-solving strategies--low-road transfer and high-road transfer. The interactions between these two mechanisms and two types of content (domain-specific knowledge and higher order thinking) are then discussed. Exploratory research on one of the interactions (low-road transfer of higher-order thinking) is summarized, with a particular focus on the performance of students with disabilities. Finally, some implications for curriculum and instruction are outlined.     

解决问题与创新意识的培养

培养学生解决问题 ,尤其是创造性地解决问题的能力是当前中小学数学教育的一个重要目标 ,但目前在解决问题的教学上还远远未取得它应该取得的效果。为此 ,本文试图从方法论的角度对解决问题的教学加以探讨 ,以寻求建立一个促进学生主动参与、探索式地解决问题的教学环境。     

"问题解决"与创新素质培养

“问题解决”国际数学教育界较为流行的一种教学模式。数学学科重视“问题解决”教学 ,有利于培养学生的创新意识 ,训练学生的创新思维 ,发展学生的创新个性 ,锻造学生的创新品质     

Problem solving in science and technology education

Both science and technology education have a commitment to teaching process; investigations or scientific method in science, design in technology, and problem solving in both areas. The separate debates in science and technology education reveal different curricular emphases in processes and content, reflecting different goals, and pedagogic and educational research traditions. This paper explores these differences and argues that each curriculum area can learn from the other. Despite the interest in processes, problem solving remains neglected in each area, particularly with respect to empirical accounts of student problem-solving activities and the supporting pedagogy. This paper draws on the situated learning and social constructivist literature to provide insights into problem solving in technology education. The research reported here, gives accounts of the problem-solving strategies of English secondary school students. These strategies represent their responses to technology activities and the learning environment created by teachers.     

Problem solving beyond the logic of things: contextual effects on understanding and solving word problems

Arguments are put forward in this paper that classroom word problem solving is more-and also less-than the urgent analysis of a factual structure, in the sense that it is essentially a species of a social-cognitive activity. Word-or story-problems, presented in classroom contexts, represent textual and pragmatic patterms of a certain grammaticality. To present a problem verbally to a student means to organize a fact in some way for the attention of a problem solver. There is not only the structure of the problem text itself by which situations are denoted, but there is also the stimulative nature of the social-pragmatic context which shapes the student's textbook-problem solving behavior over a long period of time.The present paper discusses the results of several studies showing, for example, that subject matter related attitudes towards a problem frequently do not play an important part in the problem solving efforts; that students often solve problems correctly without understanding them; and that false contextual expectations can lead to abstruse errors of understanding and to peculiar solution attempts.The studies indicate that students can become sensitive and skilful in perceiving and capitalizing on subtle textual and contextual signs pointing to the solution and anticipating its pattern. It seems that usual textbook problems let students get accustomed to certain courses of processing where a simple fact, like whether an equation works out evenly or does not, can stop the process or push it further. It is argued that the deeper reason for the observed textual and contextual influences on understanding and problem solving lies in a fundamental weakness of the student's epistemic control behavior. The psychological and instructional significance of the studies is discussed.     

Students' and teachers' explanations of chemical equilibrium

Specializations: cognitive processes in science learning and teaching.     

On the chemical equilibrium concept: Constrained word associations and conception

The use of the method of constrained word associations to gain knowledge on the conception of the chemical equilibrium concept is reported. The analysis provides information on:

• (a) A general indication of change in the cognitive structure of students associated with chemical comprehension.
• (b) The comparison of clusters of concepts at pre- and postinstruction indicating the associated concepts.
• (c) A graphical representation of the links among concepts which resulted from instruction.

The results obtained by this technique were similar to those obtained by the method of free sorting of a set of concepts. As the latter was found to correlate with problem-solving ability, it is argued that the method of constrained word associations is a reliable tool for mapping certain aspects of cognitive structure concerned with understanding.     

Behaviour theory in the nursery school: Problem solving and teacher training

The present study reports an attempt to develop a training programme for nursery school teachers with reference to new developments in behaviour theory. The underlying aim of the training programme is to develop a general problem-solving strategy simple and flexible enough to be used in new problem situations in the four social fields of teacher-child interactions, teacher-teacher interactions, teacher-parent interactions, and the interactions between nursery school and community. The problem-solving strategy is a behavioural sequence which consists of the following stages: problem analysis, selection of goals, selection of modification procedures, application of modification procedures, and evaluation. The training of teachers to solve social problems in the nursery school can also be structured by means of these five steps. The training programme has been developed in close cooperation with the teachers of a nursery school. Some experiences concerning this cooperation and the application of the problem-solving paradigm are discussed.

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Zusammenfassung Diese Studie berichtet über einen Versuch, ein Ausbildungsprogramm für Erzieher im Hinblick auf die Entwicklungen in der Verhaltenstheorie zu konstruieren. Dem Ausbildungsprogramm liegt die Absicht zugrunde, eine allgemeine Problemlösungs-Strategie zu entwickeln, die einfach und flexibel genug ist, um in neuen Problemsituationen auf den sozialen Gebieten der Erzieher-Kind, Erzieher-Erzieher und Erzieher-Eltern Beziehungen sowie auf dem der Beziehungen zwischen Kindergarten und Gemeinschaft angewandt werden zu können. Die Problemlösungs-Strategie ist eine Verhaltensfolge und besteht aus den folgenden Phasen: Problemanalyse, Auswahl von Zielen, Auswahl von Abänderungsverfahren, Anwendung der Abänderungsverfahren und Evaluation. Gemäss diesen vier Stufen kann auch die Ausbildung der Erzieher in der Lösung sozialer Probleme im Kindergarten strukturiert werden. Das Ausbildungsprogramm wurde in enger Zusammenarbeit mit den Erziehern an einem Kindergarten entwickelt. Einige Erfahrungen aus dieser Zusammenarbeit und der Anwendung des Problemlösungs-Paradigmas werden besprochen.

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Résumé Cette étude rend compte d'une tentative de développement d'un programme de formation des enseignants des écoles maternelles, compte tenu des nouveaux développements de la théorie du comportement. Le but sous-jacent du programme de formation est de développer une stratégie générale de résolution des problèmes qui soit suffisamment simple et souple pour être utilisée dans les nouvelles situations problématiques, dans les quatre domaines sociaux des interactions enseignant-enfant, enseignant-enseignant, enseignant-parent, et école maternelle-collectivité. La résolution des problèmes est un enchaînement du comportement qui comprend les stades suivants: analyse du problème, choix des objectifs, choix des procédés de modification, application des procédés de modification, évaluation. La formation des enseignants les entraînant à résoudre les problèmes sociaux à l'école maternelle peut aussi être structurée en ces cinq phases.Le programme de formation a été élaboré en étroite coopération avec les enseignants d'une école maternelle. Quelques expériences relatives à cette coopération et concernant l'application du paradigme de résolution des problèmes sont discutées dans cette étude.

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The authors may be contacted at the Staatsinstitut für Frühpädagogik, Arabellastr. I/II, D-8000 München 81, F.R.G.     

The King Alfred's College Maths Game: Problem solving and mathematical activity

The paper describes the use, with primary school maths teachers on an in-service course, of a problem-solving activity in a game format known as the King Alfred's College Maths Game. The game, a variant of a more generalised problem-solving activity, is described in some detail, and the responses of teachers to this are discussed. Use of the game demonstrates to teachers that approaches to problem-solving need to be developed through structured learning experiences which provide material for reflection, and that this reflection requires the teacher to act as questioning agent.     

Problem solving in the rat: Piecemeal acquisition of cognitive maps

The purpose of this experiment was to compare the problem-solving performance of rats allowed to explore either one or two tables of Maier’s three-table-problem apparatus on successive days. The feeding experience and test trial were administered on the day after all tables and runways had been explored in this piecemeal fashion. No rat that explored only one table and runway per day was able to solve the problem, whereas 60% of the rats that explored two tables and their interconnecting runways did solve the problem. All rats that explored the entire apparatus on each exploratory day were able to solve the problem. These data support the notion that animals can conceptually link objects experienced successively into cognitive representations which specify the constant relationships existing between those objects. The existence of such an absolute spatial mechanism makes it unnecessary for an organism to depend upon relative spatial mechanisms such as routes or cues.     

Problem solving in mathematics: the significance of visualisation and related working memory

The importance of educational psychologists’ (EPs’) skills to the formulation of evidence-based educational strategies, as well as in response to learning difficulties, is demonstrated here in relation to mathematical problem solving. Initiatives to improve the link between mathematical skills from school to everyday life have drawn significantly on problem solving tasks. Through critical evaluation of research, the relevance of visualisation methods and working memory to problem solving is considered within this article. Studies suggest that differences exist in the effectiveness of particular visualisation methods, but that training can improve their utility and thereby problem solving performance. Additionally, differences between individuals and contexts can influence visualisation use, and some pupils experience specific difficulties in this area. Recommendations are made to enhance the teaching of visualisation as a strategy for problem solving, and to support those pupils with specific difficulties.     

Problem solving strategies and mathematical resources: A longitudinal view on problem solving in a function based approach to algebra

This study is an attempt to analyze students' construction of function based problem solving methods in introductory algebra. It claims that for functions to be a main concept for learning school algebra, a complex process that has to be developed during a long period of learning must take place. The article describes a longitudinal observation of a pair of students that studied algebra for 3 years using a function approach, including intensive use of graphing technology. Such a long observation is difficult to carry out and even more difficult to report. We watched for three years classrooms using the ‘Visual-Math’ sequence, and sampled students that exhibited various levels of mathematics achievement. The analysis method presented here is a non-standard case study of a pair of lower achievers students and their work is often juxtaposed to the work of other pairs participating in the study. The students' attempts to solve a linear break-even problem is analyzed along three interviews which present the development of the use of mathematical resources and the patterns of problem solving at different learning phases. Beyond describing solving attempts, the article offers terms for describing and explaining what and how do learners appreciate and make out of solving introductory school algebra problems over a three years course. This revised version was published online in July 2006 with corrections to the Cover Date.