以“科学和工程实践”视角分析高中化学教科书

以“科学和工程实践”的8大环节和学习者主体性2个维度建立模型,分析上海科学技术出版社出版的高中化学教科书中的实践活动。发现此教科书中的实践十分注重分析环节,能较好发挥学生主体性的环节有：科学实践中的分析解释数据环节;工程实践中的建模、计划、实施调查等环节。但总体上工程实践不足,无论科学实践还是工程实践,在提出问题、设计步骤这2个环节上学生过于被动。据此认为,在化学教科书实践活动的修改或教学优化上,应增强学生的主动性,除了要开展科学探究活动,也要适当增加工程设计等活动。     

The Interplay Between Fairness and Randomness in a Spatial Computer Game

This article describes how children use an expressive microworld to articulate ideas about how to make a game seem fair with the use of randomness. Our aim in this study is to disentangle different flavours of fairness and to find out how children used each flavour to make sense of potentially complex behaviour. In order to achieve this, a spatial computer game was designed to enable children to examine the consequences of their attempts to make the game fair. The study investigates how 23 children, aged between 5.5 and 8 years, engaged in constructing a crucial part of a mechanism for a fair spatial lottery machine (microworld). In particular, the children tried to construct a fair game given a situation in which the key elements happened randomly. The children could select objects, determine their properties, and arrange their spatial layout in the machine. The study is based on task-based interviewing of children who were interacting with the computer game. The study shows that children have various cognitive resources for constructing a random fair environment. The spatial arrangement, the visualisation and the manipulations in the lottery machine allow us gain a view into the children’s thinking of the two central concepts, fairness and randomness. The paper reports on two main strategies by which the children attempted to achieve a balance in the lottery machine. One involves arranging the balls symmetrically and the other randomly. We characterize the nature of the thinking in these two strategies: the first we see as deterministic and the latter as stochastic, exploiting the random collisions of the ball. In this article we trace how the children’s thinking moved between these two perspectives.

Measuring pre-service teachers’ self-efficacy in tutoring children in primary mathematics: an instrument

This article reports on the use of Rasch modelling to develop and validate an instrument measuring self-efficacy in tutoring children in primary mathematics (SETcPM). In response to the literature on teacher efficacy, the 20-item instrument aims to inform teacher educators, and is designed for novice pre-service teachers (nPSTs) preparing to teach mathematics in primary school (grades 1–7, ages 6–13). To ensure that the tasks of teaching are imaginable for nPSTs, the instrument targets the core activity of teaching mathematics: helping a generic child with mathematics tasks. We propose that SETcPM is measurable for the intended population and represents a central part of self-efficacy in teaching mathematics (SETM). Understanding the initial SETcPM of novices and mapping its development over the course of their training programme can contribute to a better understanding of SETM, and allow teacher educators to tailor their support.     

Developing flexible procedural knowledge in undergraduate calculus

Mathematics experts often choose appropriate procedures to produce an efficient or elegant solution to a mathematical task. This flexible procedural knowledge distinguishes novice and expert procedural performances. This article reports on an intervention intended to aid the development of undergraduate calculus students’ flexible use of procedures. Two sections of the same course were randomly assigned to treatment and control conditions. Treatment students completed an assignment on which they resolved derivative-finding problems with alternative methods and compared the two resulting solutions. Control students were assigned a list of functions to differentiate. On the post-intervention test, treatment students were more likely to use a variety of solution methods without prompting than the control. Moreover, the set of treatment section solutions were closer to those of a group of mathematics experts. This study presents evidence that not only is flexible procedural knowledge a key skill in tertiary mathematics, it can be taught.     

Investigating the geometry curriculum in Palestinian textbooks: towards multimodal analysis of Arabic mathematics discourse

ABSTRACT

The analytical scheme used in the project The Evolution of the Discourse of School Mathematics (EDSM) was developed to analyse the change over time in examination texts. An adapted version of the EDSM scheme has been deployed to analyse the nature of mathematics construed in Palestinian schools’ textbooks and the mathematical activity expected of students in the geometry textbooks for students aged 10 to 16 years. The adaptation includes adding further tools for analysing visual components of texts, as well as accounting for some differences between English and Arabic. This article outlines these adaptations and illustrates the use of the adapted scheme with a different genre of texts from those studied in the EDSM project. Some of the challenges in the adaptation process in relation to Arabic mathematics discourse are discussed.     

数学建模对高职院校数学教师专业发展推动作用的研究——以海南省公办和民办高职院校比较为例

通过问卷调查了解数学建模对海南省高职院校数学教师专业发展推动作用,利用Spss软件将公办、民办教师反馈的相关信息做对比分析,探讨这两个类型学院教师的参与度情况、推动成效、师资培训力度等方面的差异,调研数学建模对高职院校数学教师专业发展的推动成效.     

基础化学综合实验中学生“自主设计”的教学实践

在基础化学综合实验中,教师只提出主要原料和欲制备的产品大类,学生通过查找资料自主设计,用不同的方法、途径制备出所要求产品,并分析几种方法在操作过程、经济及环保等方面各自的优缺点,从而达到培养学生自主创新能力的目的.     

Post-primary students’ images of mathematics: findings from a survey of Irish ordinary level mathematics students

A questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination – the final examination for students in second-level or post-primary education. At the time this study was conducted, ordinary level mathematics students constituted approximately 72% of Leaving Certificate students. Students were aged between 15 and 18 years. A definition for ‘image of mathematics’ was adapted from Lim and Wilson, with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. A questionnaire was composed incorporating 84 fixed-response items chosen from eight pre-established scales by Aiken, Fennema and Sherman, Gourgey and Schoenfeld. This paper focuses on the findings from the questionnaire survey. Students’ images of mathematics are compared with regard to gender, type of post-primary school attended and prior mathematical achievement.     

Generating the patterns of variation with GeoGebra: the case of polynomial approximations

In this paper, we report a teaching experiment regarding the theory of polynomial approximations at the university mathematics teaching in Sweden. The experiment was designed by applying Variation theory and by using the free dynamic mathematics software GeoGebra. The aim of this study was to investigate if the technology-assisted teaching of Taylor polynomials compared with traditional way of work at the university level can support the teaching and learning of mathematical concepts and ideas. An engineering student group (n = 19) was taught Taylor polynomials with the assistance of GeoGebra while a control group (n = 18) was taught in a traditional way. The data were gathered by video recording of the lectures, by doing a post-test concerning Taylor polynomials in both groups and by giving one question regarding Taylor polynomials at the final exam for the course in Real Analysis in one variable. In the analysis of the lectures, we found Variation theory combined with GeoGebra to be a potentially powerful tool for revealing some critical aspects of Taylor Polynomials. Furthermore, the research results indicated that applying Variation theory, when planning the technology-assisted teaching, supported and enriched students’ learning opportunities in the study group compared with the control group.