A cycle for validating a learning progression illustrated with an example from the concept of function

A learning progression, or learning trajectory, describes the evolution of student thinking from early conceptions to the target understanding within a particular domain. As a complex theory of development, it requires conceptual and empirical support. In earlier work, we proposed a cycle for the validation of a learning progression with four steps: 1) Theory Development, 2) Examination of Empirical Recovery, 3) Comparison to Competing Models, and 4) Evaluation of Instructional Efficacy. A group of experts met to discuss the application of learning sciences to the design, use, and validation of classroom assessment. Learning progressions, learning trajectories, and how they can support classroom assessment were the main focuses. Revisions to the cycle were suggested. We describe the adapted cycle and illustrate how the first third of it has been applied towards the validation of a learning progression for the concept of function.     

Connecting multiplicative thinking and mathematical reasoning in the middle years

Mathematical reasoning and problem solving are recognised as essential 21st century skills. However, international assessments of mathematical literacy suggest these are areas of difficulty for many students. Evidenced-based learning trajectories that identify the key ideas and strategies needed to teach mathematics for understanding and support these important capacities over time are needed to support teachers and curriculum developers so that they do not have to rely solely on mathematics content knowledge. Given this goal and recent evidence to suggest a relationship between the development of multiplicative thinking and mathematical reasoning, this paper explores the processes involved in developing a single, integrated scale for multiplicative thinking and mathematical reasoning using data from a four-year design-based project to establish learning and assessment frameworks for algebraic, geometrical and statistical reasoning in the middle years of schooling.     

AN SVAD ALGORITHM BASED ON FNNKD METHOD

The capacity of mobile communication system is improved by using Voice Activity Detection (VAD) technology. In this letter, a novel VAD algorithm, SVAD algorithm based on Fuzzy Neural Network Knowledge Discovery (FNNKD) method is proposed. The performance of SVAD algorithm is discussed and compared with traditional algorithm recommended by ITU G.729B in different situations. The simulation results show that the SVAD algorithm performs better.     

A learning process for fuzzy control rules using genetic algorithms

The purpose of this paper is to present a genetic learning process for learning fuzzy control rules from examples. It is developed in three stages: the first one is a fuzzy rule genetic generating process based on a rule learning iterative approach, the second one combines two kinds of rules, experts rules if there are and the previously generated fuzzy control rules, removing the redundant fuzzy rules, and the thrid one is a tuning process for adjusting the membership functions of the fuzzy rules. The three components of the learning process are developed formulating suitable genetic algorithms.     

迎接e时代的品质挑战

本文先介绍e时代来临与特质,e时代对品质的新需求，e时代的品质展开，e时代的学习曲线，以及如何应对e时代的品质挑战。     

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。