The powers and pitfalls of algorithmic knowledge: a case study

This study examines one child's use of computational procedures over a period of 3 years in an urban elementary school where teachers were using a standards-based curriculum. From a sociocultural perspective, the use of standard algorithms to solve mathematical problems is viewed as a cultural tool that both enables and constrains particular practices. As this student appropriated and mastered procedures for addition, subtraction, multiplication and division, she could solve problems that involved fairly straightforward computations or where she could easily model the action to determine an appropriate computation. At the same time, her use of these algorithms, along with other readily available tools, such as her fingers or multiplication tables, constrained her ability to reflect on the tens-structure of the number system, an effect that had serious consequences for her overall mathematical achievement. The results of this study suggest that even when not directly introduced, algorithms have such strong currency that they can mediate more reform-oriented instruction.     

基于Web的协同学习策略及其应用

对网络教育的现状进行了分析，并针对目前网络教育中师生之间、学生之间缺乏有效的交流的缺点，提出了将协同学习策略应用在的基于Web的协同学习系统中的方法。使用多种同学习策略对协同学习过程进行控制，并且将学习评估与协同学习过程进行结合，以提高学生的学习效果。     

Analog VLSI Circuits for Competitive Learning Networks

An investigation is made concerning implementations of competitive learning algorithms in analog VLSI circuits and systems. Analog and low power digital circuits for competitive learning are currently important for their applications in computationally-efficient speech and image compression by vector quantization, as required for example in portable multi-media terminals. A summary of competitive learning models is presented to indicate the type of VLSI computations required, and the effects of weight quantization are discussed. Analog circuit representations of computational primitives for learning and evaluation of distortion metrics are discussed. The present state of VLSI implementations of hard and soft competitive learning algorithms are described, as well as those for topological feature maps. Tolerance of learning algorithms to observed analog circuit properties is reported. New results are also presented from simulations of frequency-sensitive and soft competitive learning concerning sensitivity of these algorithms to precision in VLSI learning computations. Applications of these learning algorithms to unsupervised feature extraction and to vector quantization of speech and images are also described.     

手写汉字的四角识别方案

手写汉字的本质特征的抽取是提高识别率的关键，而识别规则的生成又依赖于大量样本的归纳学习，手写汉字的四角方案就是针对这两个问题设计并实现的。实验结果证明了该方法的可行性和优越性。     

人工神经网络的容量、学习与计算复杂性

本文讨论了人工神经网络（ＡＮＮ）解决问题的能力，从广泛的角度讨论了容量问题，推广与学习问题，深入研究了ＡＮＮ通过学习解决问题的计算复杂性，以及解决实际问题时困难所在。     

正例学习的一个启发式算法

本文基于多值逻辑函数极小化提出一种正例学习问题，并对这一正例学习问题给出一个启发式学习算法。同现存的示例学习方法相比，本文算法是基于演绎推理的，可对大量信息进行保真压缩，该算法具有简单，快速和易于实现的特点，本文用两个实例一焊接工艺自动设计知识获取和布尔函数极小化，将本算法同示例式归纳学习系统ＡＱ１５和布尔函数极小化系统ＳＷＴ进行了比较。     

前馈神经网络的一种有效学习算法

本文提出了基于混合ＧＮ－ＢＦＧＳ法进行前馈神经网络学习的新算法，该算法结合ＧＮ法与ＢＦＧＳ法的特点，既利用了问题本身的特殊结构，又能取得超线性甚至二次渐近收敛率。与ＢＰ算法相比，这种算法可取得更快和更可靠的学习特性，在学习过程中利用该方法能够区分非零残量和零残量问题的特点，提出了自动调整隐单元数的方法，从而可以保证网络学习与归纳能力，示例系统的结果表明了所提方法的有效性。     

Ambiguous chance constrained problems and robust optimization

In this paper we study ambiguous chance constrained problems where the distributions of the random parameters in the problem are themselves uncertain. We focus primarily on the special case where the uncertainty set of the distributions is of the form where ρ_p denotes the Prohorov metric. The ambiguous chance constrained problem is approximated by a robust sampled problem where each constraint is a robust constraint centered at a sample drawn according to the central measure The main contribution of this paper is to show that the robust sampled problem is a good approximation for the ambiguous chance constrained problem with a high probability. This result is established using the Strassen-Dudley Representation Theorem that states that when the distributions of two random variables are close in the Prohorov metric one can construct a coupling of the random variables such that the samples are close with a high probability. We also show that the robust sampled problem can be solved efficiently both in theory and in practice. Research partially supported by NSF grant CCR-00-09972. Research partially supported by NSF grants CCR-00-09972, DMS-01-04282, and ONR grant N000140310514.     

Facilitating an Elementary Engineering Design Process Module

STEM education in elementary school is guided by the understanding that engineering represents the application of science and math concepts to make life better for people. The Engineering Design Process (EDP) guides the application of creative solutions to problems. Helping teachers understand how to apply the EDP to create lessons develops a classroom where students are engaged in solving real world problems by applying the concepts they learn about science and mathematics. This article outlines a framework for developing such lessons and units, and discusses the underlying theory of systems thinking. A model lesson that uses this framework is discussed. Misconceptions regarding the EDP that children have displayed through this lesson and other design challenge lessons are highlighted. Through understanding these misconceptions, teachers can do a better job of helping students understand the system of ideas that helps engineers attack problems in the real world. Getting children ready for the 21st century requires a different outlook. Children need to tackle problems with a plan and not shrivel when at first, they fail. Seeing themselves as engineers will help more underrepresented students see engineering and other STEM fields as viable career options, which is our ultimate goal.