Examining a mathematical model of mastery learning in a classroom setting

The purpose of mathematical models in any discipline is to describe accurately the relationships among significant variables of a system. The use of mathematical models is widespread in the sciences, but has rarely found its way into educational research. In developing a mathematical model for mastery learning, empirical research has shown that prior learning, motivation, and time on task are part of the significant variables that work together in some way in a determination of student achievement. A mathematical model that shows the relationship among these variables has been developed. To test the appropriateness of this mathematical model, carefully designed and controlled experiments must be conducted to collect numerical data on the significant variables. Using the model, the accuracy of its predictions can be compared with actual results. This is the technique used in testing mathematical models in the sciences and should be applicable to mathematical models of learning.     

Designing instructional strategies which facilitate learning for mastery

While early proponents of mastery learning (ML) provided operational definitions regarding appropriate teaching/learning procedures, they did not provide guidelines for developing specific instructional strategies and activities. This article aims to provide such guidelines based on theories of learning and cognition. Part 1 describes the general instructional procedures developed by early ML proponents. Parts 2–4 provide guidelines for (a) the initial group‐based instruction, including guidelines for teaching to three different types of objectives (informational, conceptual, and procedural) and for varying four different modes of presentation (lecture, dialogue, discussion, and searwork) (b) sequencing; (c) developing correctives; and (d) developing enrichment activities.     

Recent developments in mastery learning 1

Mastery learning strategies have been widely used with considerable success in increasing the proportion of students attaining the mastery criterion. Students attaining mastery do, under appropriate conditions, change in their affect about the subject and themselves. Research on time and achievement in relation to mastery learning procedures show reduction in student variability and increases in learning efficiency and learning achievement.     

End-of-course and long-term retention outcomes for mastery and nonmastery learning paradigms

Using both end-of-course achievement outcomes and long-term cognitive retention as criteria, the present study provides comparative data on the effectiveness of a mastery and nonmastery approach to instruction. Differential effects across taxonomic levels were assessed for both criteria. The results indicated that mastery students performed significantly higher than non-mastery students for end-of-course outcomes at the highest taxonomic level and equally well for knowledge, comprehension, and application level outcomes. Retention differences were found for knowledge level outcomes only, with mastery students demonstrating significantly greater retention performance. The feasibility and desirability of implementing a learning for mastery paradigm in a single course at the college level are discussed relative to the magnitude of the present results.     

Are mastery learning strategies beneficial for developing problem solving skills?

The purpose of the present study was to investigate instructional methods appropriate for developing problem solving skills (PSS) in a paramedical course. Three instructional methods were compared: Frontal Lecture Strategies (FLS), Mastery Learning Strategies (MLS) and Experiential Mastery Learning Strategies (EMLS) in which feedback corrective procedures were embedded within experiential learning situations. Results showed that FLS produced the highest scores on Lower Mental Process subtest while EMLS yielded the highest scores on all measures of problem solving skills. Several implications of this study for future research are suggested and discussed.     

对过度反应现象进行数据挖掘的数学模型

对证券市场过度反应现象的研究是行为金融学的一个重要研究方向。文章讨论了过度反应现象的数学描述，并建立了一种以研究过度反应现象的数据挖掘算法为目标的数学模型。用我国A股市场1994．1．3至2004、12．31年的全部个股数据进行实证分析的结论是：在我国股票市场，投资者的投资行为对好消息存在过度反应现象。     

A mathematical model of symmetry based on mathematical definition

Tolerance is imperative for seamless integration of CAD/CAM (Computer Aided Disign/Computer Aided Manufacture) which is just a text attribute and has no semantics in present CAD systems. There are many tolerance types, the relations between which are very complicated. In addition, the different principles of tolerance make study of tolerance difficult; and there may be various meanings or interpretation for the same type of tolerance because of the literal definition. In this work, latest unambiguous mathematical definition was applied to study, explain and clarfy: (1) the formation and representation of tolerance zone, and (2) the formation and representation of variational elements; after which, the mathematical models of symmetry of different tolerance principles and different interpretations were derived. An example is given to illustrate the application of these models in tolerance analysis. Project supported by the National Natural Science Foundation of China for Innovation Research Groups(No.60021201) and NSFC(Nos.59705022 & 69973045).     

A feedback model for data-rich learning experiences

Feedback has been identified as one of the factors with the largest potential for a positive impact in a learning experience. There is a significant body of knowledge studying feedback and providing guidelines for its implementation in learning environments. In parallel, the areas of learning analytics or educational data mining have emerged to explore how to analyse exhaustive digital trails produced by technology mediation to improve learning experiences. Current conceptualisations of feedback do not take into account the presence of these trails nor the presence of knowledge extracted through analytics techniques. This paper presents a model to reconceptualise feedback in data-rich learning experiences. It acknowledges the presence of algorithms to analyse and predict learner behaviour and proposes an integrated view between these elements as part of the feedback process and aspects conventionally present in previous models. This new conceptualisation offers instructors, designers and researchers a framework to formulate feedback processes in scenarios with comprehensive data capturing, while retaining a solid connection with well-established educational theories.     

A design model for lifelong learning networks

The provision of lifelong learning facilities is considered to be a major new direction for higher and distance teaching educational institutes catering for the demands of industry and society. ICT networks will in future support seamless, ubiquitous access to lifelong learning facilities at home, at work, in schools and universities. This implies the development of new ways of organizing learning delivery that goes beyond course and programme-centric models. It envisions a learner-centred, learner-controlled model of distributed lifelong learning. We present a conceptual model for the support of lifelong learning which is based on notions from self-organization theory, learning communities, agent technologies and learning technology specifications such as IMS Learning Design. An exploratory implementation has been developed and used in practice. We reflect on the findings and future directions.     

能源消耗回弹效应形成机理的数理模型

为揭示能源消耗回弹效应的形成机理,从三要素生产函数出发,根据一般均衡条件构建了回弹效应形成机理的数理模型,推导了短期生产和长期生产中能源消耗关于能源使用效率改善的弹性系数,进而获得用于分析回弹效应形成机理的短期回弹效应和长期回弹效应的解析式,最后根据参数的取值情况,分别对短期回弹效应和长期回弹效应进行了情景分析。结果表明:短期内回弹效应无法实现超节能的回弹情形;在长期,回弹效应不仅可表现为零回弹效应、部分回弹、全回弹、回火4种情形,还可能出现超节能的回弹情形。     

少儿古筝学习心理的把握与调适

古筝是我国传统音乐艺术宝库中最具代表性的器乐。弘扬古筝艺术，不仅是继承传统艺术的必须，也是落实民族文化大省建设，提高青少年文化素质的有效途径。少儿古筝学习热潮的掀起对艺术事业是一件好事。要提高古筝教育水平，促进这股热潮的蓬勃发展和长盛不衰，需要教学工作者孜孜不倦的热忱和深入细致的研究。科学把握和适时调整学习心理，则是这种研究工作的重要内容。