Teaching for transfer of core/key skills in higher education: Cognitive skills

This article is a result of a completed survey of the mainly cognitive science literature on the transferability of those skills which have been described variously as ‘core’, ‘key’, and ‘generic’. The literature reveals that those predominantly cognitive skills which have been studied thoroughly (mainly problem solving) are transferable under certain conditions. These conditions relate particularly to the methods and environment of the learning of these skills. Therefore, there are many implications for the teaching of key skills in higher education, which the article draws out, following a summary of the main findings of the research literature. Learning of principles and concepts facilitates transfer to dissimilar problems, as it creates more flexible mental representations, whereas rote learning of facts discourages transfer. Transfer is fostered when general principles of reasoning are taught together with self-monitoring practices and potential applications in varied contexts. Training in reasoning and critical thinking is only effective for transfer, when abstract principles and rules are coupled with examples. Transfer is promoted when learning takes place in a social context, which fosters generation of principles and explanations. Transfer improves when learning is through co-operative methods, and where there is feedback on performance with training examples. The specificity of the context in which principles are learned reduces their transfer. Transfer is promoted if learners are shown how problems resemble each other, if they are expected to learn to do this themselves, if they are aware of how to apply skills in different contexts, if attention is directed to the underlying goal structure of comparable problems, if examples are varied and are accompanied by rules or principles (especially if discovered by the learners), and if learners’ self-explanations are stimulated. Learning to use meta-cognitive strategies is especially important for transfer.     

The role of number words in preschoolers’ addition concepts and problem‐solving procedures

Preschoolers’ conceptual understanding and procedural skills were examined so as to explore the role of number‐words and concept–procedure interactions in their additional knowledge. Eighteen three‐ to four‐year‐olds and 24 four‐ to five‐year‐olds judged commutativity and associativity principles and solved two‐term problems involving number words and unknown numbers. The older preschoolers outperformed younger preschoolers in judging concepts involving unknown numbers and children made more accurate commutativity than associativity judgements. Children with conceptual profiles indicating a strong understanding of concepts applied to unknown numbers were more accurate at solving number‐word problems than those with a poor conceptual understanding. The findings suggest that an important mathematical development during the preschool years may be learning to appreciate addition concepts as general principles that apply when exact numbers are unknown.     

Case studies of teaching problem solving

Summary Some important results that relate to classroom learning and teaching of problem solving emerge from these case studies. These are now summarized as follows. In terms of the students' potential learning experiences of problem solving, it was found that the students were mainly witnessing their teachers' demonstrations of using rules or algorithms for solution to problems. Repeated practice of solving the sorts of problems that occur in examinations was also emphatically included as part of the learning experience. The students were not exposed to a range of strategies that could possibly be used to solve the same problems. There was no explicit teaching of important problem solving skills such as translation skills (comprehending, analyzing, interpreting, and defining a given problem) and linkage skills (concept relatedness between two concepts or using cues from the problem statements to associate ideas, concepts, diagrams, etc. from memory). When teachers solve problems they use, in general, several strategies to solve the same class of problems and they are very careful and explicit about translating problem statements, making relevant linkages and checking. These absences in the teachers' teaching of problem solving (and hence in the students' range of learning experiences) are particularly interesting because they are part of the teachers' own repertoire of skills. Accordingly, it may not be too difficult to get teachers to include them in their teaching. This would mean that the students' range of learning experiences for problem solving would be very much strengthened.     

新加坡科学课程普通水准教育证书考试评析

在新加坡科学课程改革中,普通水准教育证书考试起着积极的引导作用。它们具有这样一些特点:重视对科学概念原理理解、信息处理能力和解决问题能力以及实验操作技能和科学探究能力的评价;控制数学运算的分量和复杂性;尊重学习者的差异、给予充分的选择权。这些对于我国科学课程考试评价改革有着重要的借鉴意义。     

Learning 'How' Versus Learning 'When': Improving Transfer of Problem-Solving Principles

How can problem solving be improved in domains where similar principles are learned? A series of three experiments based on Ross (1987) examined how instructing learners about when to apply problem-solving principles may later improve performance. In Experiment 1, subjects studied a similar pair (combinations and permutations) or a distinct pair (combinations and conditional probability) of probability principles. Haft of the subjects received information on when to apply the principles (applicability-instructions condition), whereas other subjects received instructions that reviewed how to solve problems using the principles (procedural-review condition). Subjects who received applicability instructions made fewer confusion errors than subjects who received procedural-review instructions when learning the similar problem pair. However, this instructional manipulation had no effect when subjects were learning the distinct problem pair. Because applicability instructions affect confusion errors but not overall performance, they may improve the ability to identify when to apply a procedure but may not improve memory for the formula or the ability to instantiate it. Experiment 2 supported this notion by showing that subjects given applicability instructions did better at selecting when to use each formula. Experiment 3 tested whether giving learners the pairs of examples to review together afforded them the opportunity to learn the applicability conditions on their own. The results showed that the important differences between the principles (i.e., why the formulas apply in certain situations) must be identified in the instructional material because subjects were not likely to induce the differences on their own. The results showed that when differences between the related principles are identified in instructional material (i.e., why the formula applies in certain problems), these applicability instructions may serve to reduce confusion in noticing and selecting...     

Physics students' understanding of relative speed: A phenomenographic study

It is important that students of physics develop both quantitative and qualitative understanding of physical concepts and principles. Although accuracy and reliability in solving quantitative problems is necessary, a qualitative understanding is required in applying concepts and principles to new problems and in real-life situations. If students are not able to understand what underlies quantitative problem-solving procedures nor interpret the solution in physical terms, it is questionable whether they have developed an adequate understanding of physics. The research reported here is part of a larger phenomenographic study that is concerned with the assessment of physics students' understanding of some basic concepts and principles in kinematics. In this article students' understanding of the concept of relative speed is described. A variety of ways of understanding relative speed and of viewing a problem that dealt with this concept were uncovered. The results are used to suggest ways for teachers to proceed in assisting students to enhance their understanding of this concept. The teaching principles outlined concern both teaching relative speed, in particular, and teaching scientific concepts and principles, more generally.     

浅谈数学概念的教学过程

成功的概念教学 ,可以提高学生学习数学的积极性和对学习数学的兴趣 ,使整个教学过程得到事半功倍的作用     

Effects of the SOLVE Strategy on the Mathematical Problem Solving Skills of Secondary Students with Learning Disabilities

This study examined the effects of explicit instruction in the SOLVE Strategy on the mathematical problem solving skills of six Grade 8 students with specific learning disabilities. The SOLVE Strategy is an explicit instruction, mnemonic‐based learning strategy designed to help students in solving mathematical word problems. Using a multiple probe across participants design, results suggested a functional relation between explicit instruction in the SOLVE strategy and increase in strategy use and computation scores on grade level mathematical word problems for all participants. Additionally, all participants generalized the SOLVE Strategy to other mathematic topics and concepts, and the teacher and students felt the intervention was socially acceptable. Finally, limitations, implications for practice, and suggestions for future research are discussed.     

AN INQUIRY ORIENTED LABORATORY EXAMINATION

Having discussed the dearth of testing of actual performance in real situations, a variety of arguments are raised to support the need for assessment in the Practical mode, and the development and nature of an inquiry oriented laboratory examination is described. One test problem is presented in detail including materials, instructions to examinees, instructions for administration and scoring as well as sample answers. Data regarding validity and reliability are provided together with findings pertaining to the relationship between the various skills assessed by the examination. Moderation procedures for determining the individual scores in an examination in which different students perform different test problems are suggested. The author contends that the type of examination described reflects the inquiry objectives of the BSCS philosophy and provides a valid and reliable measure of problem solving ability in a practical laboratory setting.     

Predictors of well‐structured and ill‐structured problem solving in an astronomy simulation

This study compared the problem‐solving skills required for solving well‐structured problems and ill‐structured problems in the context of an open‐ended, multimedia problem‐solving environment in astronomy. Two sets of open‐ended questions assessed students' abilities for solving well‐structured and ill‐structured problems. Generalized, rubric scoring systems were developed for assessing problem‐solving skills. Instruments were also developed and administered to assess cognitive and affective predictors of problem‐solving performance. By regressing the scores on the cognitive and affective predictors onto students' scores on the well‐structured and ill‐structured problems, we concluded that solving well‐structured and ill‐structured problems require different component skills. Domain knowledge and justification skills were significant predictors of well‐structured problem‐solving scores, whereas ill‐structured problem‐solving scores were significantly predicted by domain knowledge, justification skills, science attitudes, and regulation of cognition. Implications for problem solving in science education are presented. © 2003 Wiley Periodicals, Inc. J Res Sci Teach 40: 6–33, 2003     

高等数学美学探微

本文通过高等数学中某些数学概念之间内在联系，以及某几个数学问题呈现形式及解题策略与技巧，从不同角度阐述了数学美在数学内容、数学语言、数学规律、数学思维、解题方法等方面的体现。让学生欣赏数学美、体验数学美，在美的熏陶中提高数学能力。     

Promoting active student learning in strength of materials with the aid of CAI

The objective of this paper is to discuss how active student learning is possible with the aid of a CAI package for a subject such as Strength of Materials. Multimedia is the latest innovation that can be utilized to improve learning. In this study, multimedia components such as hypertext, sound, graphics, video, and animation are implemented in a CAI package. These capabilities can capture students' attention, and can also illustrate the application of knowledge to real world problems more effectively than traditional teaching methods. The other features of this package include guided examples, theory, and application tests. Guided examples show the students problem solving techniques, and provide feedback according to their responses. The theory and application tests enable the teacher to gauge the students' understanding of the subject matter. Students who do well in the theory test are eligible to attempt the application test, which poses real-world engineering problems. The lesson that can be concluded from this study is that students' problem solving skills can be improved with the aid of CAI which emphasizes anchored instructions. However, to achieve maximum benefit, students also need to possess independent learning skills.     

Problem-solving skills of high school chemistry students

What strategies do high school students use when solving chemistry problems? The purpose for conducting this study was to determine the general problem-solving skills that students use in solving problems involving moles, stoichiometry, the gas laws, and molarity. The strategies were examined for success in problem solving for 266 students of varying proportional reasoning ability, using interviews incorporating the think-aloud technique. Data were coded using a scheme based on Polya's heuristics. Results indicated that successful students and those with high proportional reasoning ability tended to use algorithmic reasoning strategies more frequently than nonsuccessful and low proportional reasoning students. However, the majority of all students solved the chemistry problems using only algorithmic methods, and did not understand the chemical concepts on which the problems were based.     

Collaborating With a Skilled Peer: The Influence of Achievement Goals and Perceptions of Partners' Competence on the Participation and Learning of Low-Achieving Students

The authors examined whether motivational goals influenced the participation and performance of low-achieving students during collaborative problem solving with a high-achieving partner. Thirty-five pairs of 4th- and 5th-grade students were randomly assigned a set of instructions designed to induce students to adopt a learning goal or a performance goal. The following day, the students were individually given a posttest on problems similar to those worked on collaboratively. The low-achieving students given learning-goal instructions performed better on the posttest problems and perceived their partner's competence as more similar to their own than did the low-achieving students given performance-goal instructions. No differences in overall amount or level of low achievers' participation during collaborative problem solving were observed. Implications of the findings for the use of peer learning in heterogeneous classrooms are discussed.     

教育技术学——“开发取向”的教育理论探究

从学科性质、学科任务和理论内容上看,教育技术学的研究本质上属于“开发取向”。所谓教育技术学研究的“开发取向”,是指通过研究开发和设计的原理,以及各种可重用的技术来尝试解决实际的教育教学问题,并在这个过程中体验理解教育教学规律,以形成对教育教学规律的独特认识的研究取向。开发研究、描述研究、解释分析研究、假设检验研究是对等的研究取向,它们的有机结合有助于实现教育理论的合规律性和合目的性的统一。教育技术学研究的“开发取向”,使教育技术学必然成为一门通过解决教育教学问题的理论研究和实践体验达到对教育教学系统运行规律的自为性理解的学科。     

谈谈解题能力的培养

要培养学生解数学题的能力可采取多方面的措施 ,通过讲清概念、恰当举例 ,可有效地提高学生的解题能力     

论企业团队建设

进行团队建设是当代组织领导者不可或缺的技能,企业团队建设有利于增强组织灵活性,提高劳动生产率,进一步强化激励机制,优化企业内部公关,极大地提高员工素质与技能,提高信息传递的速度与质量。针对企业团队建设中的问题,提出了团队建设的原则和方法,指出了团队建设的误区。     

解题原则与解题策略刍议

众多解题理论书籍中频繁使用着解题原则、策略两个概念，但作目前尚未见到解题原则这一概念的令人满意的表述；虽有人对解题策略这一概念作过表述，但其表述不乏有令人不满意之处．在数学解题研究工作中，也不乏有对这两个概念认识模糊不清．本试图通过这两个概念的表述及比较，明晰两个概念之间的关系与区别。     

Teaching thinking: the case for principles

Abstract

This paper reviews the situation with regard to the teaching of thinking skills as part of the taught curriculum. The case is made for direct teaching of cognitive skills both to meet the particular learning difficulties of children with special educational needs and also to enhance the learning and thinking of all children. The dangers of ‘recipe’ approaches to teaching this aspect of the curriculum are discussed and a ‘principles’ approach is advocated. Some principles are then described which may be used to underpin the designing of problem‐solving activities, through which thinking skills can be taught across the curriculum.