A task that elicits reasoning: A dual analysis

This paper reports on the forms of reasoning elicited as fourth grade students in a suburban district and sixth grade students in an urban district worked on similar tasks involving reasoning with the use of Cuisenaire rods. Analysis of the two data sets shows similarities in the reasoning used by both groups of students on specific tasks, and the tendency of a particular task to elicit numerous forms of reasoning in both groups of students. Attributes of that task and ways that those attributes can be replicated in other domains may have implications in the teaching of early reasoning.     

水资源持续利用的多目标决策模型的建立

可持续发展战略的实施,资源的可持续利用是关键.针对日趋短缺的淡水资源,根据多目标决策理论,以同时追求经济、环境、社会效益为主要目标提出了其可持续利用的多目标决策模型,并举例说明了模型的应用,旨在为决策者提供淡水利用规划的依据.     

从一个习题到十个命题

从一道熟知的微积分习题,可以导出十个相关的命题.通过这一讨论过程,试图表明什么是创造性学习,以及如何进行创造性学习.     

MOOCs来袭 我们准备好了吗?

MOOCs正以其巨大的浪潮冲击着当今的高等教育.本文根据国内外MOOCs的发展现状,综合分析了MOOCs的优势及其对教学模式带来的影响,结合我们正在开展的大学物理MOOCs建设,提出了在课程改革中需要重点关注的四个方面,以期有助于更好地迎接MOOCs的挑战.     

Another design for sundials

Based on Kepler's laws we calculate the position of the sun as a function of the date, the local time, the latitude and longitude and use the resulting formula to construct a portable sundial which works without being adjusted to the cardinal directions (i.e. there is no need for an additional compass).     

Loop invariants,exploration of regularities,and mathematical games

Loop invariants are assertions of regularities that characterize the loop components of algorithms. They are fundamental components of computerprograms verification, but their relevance goes beyond verification—they can be significantly utilized for algorithm design and analysis. Unfortunately, they are only modestly introduced in the teaching of programming and algorithms. One reason for this is an unjustified notion that loop invariants are ‘tied to formality’, hard to illustrate, and difficult to comprehend. In this paper a novel approach is presented for illustrating on a rather intuitive level the significance of loop invariants. The illustration is based on mathematical games, which are attractive examples that require the exploration of regularities via problemsolving heuristics. Throughout the paper students' application of heuristics is described and emphasis is placed on the links between loop invariants, heuristic search activities, recognition of regularities and design and analysis of algorithms.     

Coupled spring equations

Coupled spring equations for modelling the motion of two springs with weights attached, hung in series from the ceiling are described. For the linear model using Hooke's Law, the motion of each weight is described by a fourth-order linear differential equation. A nonlinear model is also described and damping and external forcing are considered. The model has many features that permit the meaningful introduction of many concepts including: accuracy of numerical algorithms, dependence on parameters and initial conditions, phase and synchronization, periodicity, beats, linear and nonlinear resonance, limit cycles, harmonic and subharmonic solutions. These solutions produce a wide variety of interesting motions and the model is suitable for study as a computer laboratory project in a beginning course on differential equations or as an individual or a small-group undergraduate research project.     

‘It takes me longer,but I understand better’ – student feedback on structured derivations

In this article, we present the results from a qualitative study on students' initial reactions to the use of structured derivations in mathematics education. Our findings suggest that the approach increases the clarity of solutions and facilitates debugging of proofs. It also has potential to increase students' self-perceived level of understanding. Our findings indicate that the main drawbacks experienced by the students are related to time and length. Nevertheless, the overall feedback on the approach was found to be positive, thus encouraging further use of structured derivations in mathematics education.     

Mathematics students’ next steps after graduation

This article is about what happens to newly minted mathematics graduates. It explores data from the first destination statistics from the perspective of mathematics lecturers and others involved in institutions that provide a higher education in mathematics. It also looks at reasons why this issue is important to those engaged in the higher education of mathematics undergraduates. A key finding is that the employment of mathematics graduates is concentrated in the sector of the economy that includes banking, property and financial services which makes the employment prospects for new graduates in mathematics vulnerable to recession in that sector.     

Early error detection: an action-research experience teaching vector calculus

This paper describes an action-research experience carried out with second year students at the School of Engineering of the National University of Entre Ríos, Argentina. Vector calculus students played an active role in their own learning process. They were required to present weekly reports, in both oral and written forms, on the topics studied, instead of merely sitting and watching as the teacher solved problems on the blackboard. The students were also asked to perform computer assignments, and their learning process was continuously monitored. Among many benefits, this methodology has allowed students and teachers to identify errors and misconceptions that might have gone unnoticed under a more passive approach.