Understanding and describing mathematical knowledge for teaching: knowledge about proof for engaging students in the activity of proving

This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in, mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about proof is likely to be important for teachers to have as they engage students in the activity of proving. We explain that existing research informs the knowledge about the logico-linguistic aspects of proof that teachers might need, and we argue that this knowledge should be complemented by what we call knowledge of situations for proving. This form of knowledge is essential as teachers mobilize proving opportunities for their students in mathematics classrooms. We identify two sub-components of the knowledge of situations for proving: knowledge of different kinds of proving tasks and knowledge of the relationship between proving tasks and proving activity. In order to promote understanding of the former type of knowledge, we develop and illustrate a classification of proving tasks based on two mathematical criteria: (1) the number of cases involved in a task (a single case, multiple but finitely many cases, or infinitely many cases), and (2) the purpose of the task (to verify or to refute statements). In order to promote understanding of the latter type of knowledge, we develop a framework for the relationship between different proving tasks and anticipated proving activity when these tasks are implemented in classrooms, and we exemplify the components of the framework using data from third grade. We also discuss possible directions for future research into teachers’ knowledge about proof.

Social working memory: Memory for another rat's spatial choices can increase or decrease choice tendencies

In two experiments using a radial-arm maze, pairs of rats made choices among eight maze locations, each containing a large quantity of one of two food types. The choices made by 1 rat affected the choices made by the other rat. Under most conditions, visits by 1 rat increased the tendency of the other rat to subsequently choose that maze location. However, the effect depended on the quality of the food available in a particular location. When it was possible for the rats to observe each other on the maze arms and a rat had experienced that a location contained the less preferred food type, a previous visit to that location by the foraging partner decreased the tendency to visit that location. These effects are attributed to working memory for the spatial choices of another rat, and they indicate that memory produced by a rat’s own visit to a maze location is integrated with memory for the behavior of another rat to determine spatial choice     

An Analytic Strategy to Assist Institutional Recruitment and Marketing Efforts

This article demonstrates how to fit a statistical model to historical data, test whether the model can accurately predict enrollment out-of-sample, and use the results to segment admitted students into groups so that different recruitment and marketing interventions can be applied. Conceptual and practical issues are discussed, as well as policy considerations.     

英文手机短信翻译的格式塔意象再造及审美再现

英文手机短信分为文学体和非文学体两大类。依据接受美学理论,手机短信文本的意义是一种动态生产物,具有开放性和召唤结构。收信人在阅读的具体过程中,通过发挥想象力去填补“空白”,从整体上理解接受原文的信息,在大脑中形成一个格式塔意象。译者在翻译过程中,首先应充分理解、接受原文信息,并进行格式塔意象再造,然后,最大限度地再现短信原文的韵律美、形式美、形象美、修辞美、模糊美和幽默美。     

PhD students’ work conditions and study environment in university- and industry-based PhD programmes

During the last 10 years, new models of funding and training PhD students have been established in Denmark in order to integrate industry into the entire PhD education. Several programmes have been conducted where it is possible to co-finance PhD scholarships or to become an employee as an industrial PhD in a company. An important question is what impact these new conditions will have on the PhD students’ training, work conditions and study environment. In this article, the new type of programmes will be presented together with data analysis of PhD students’ work conditions and study environment in various programmes mainly based on a research project from 2006. The results of this study show no significant difference between PhD students in a traditional university PhD programme and PhD students in an industrial programme concerning working environment. However, the study shows significant differences in the intercultural dimension, where foreign PhD students are significantly more satisfied with their study environment compared with Danish PhD students. In general the workload is very high and the environment is stressful for all PhD students.     

Spelling well despite developmental language disorder: what makes it possible?

The goal of the study was to investigate the overlap between developmental language disorder (DLD) and developmental dyslexia, identified through spelling difficulties (SD), in Russian-speaking children. In particular, we studied the role of phoneme awareness (PA), rapid automatized naming (RAN), pseudoword repetition (PWR), morphological (MA), and orthographic awareness (OA) in differentiating between children with DLD who have SD from children with DLD who are average spellers by comparing the two groups to each other, to typically developing children as well as children with SD but without spoken language deficits. One hundred forty-nine children, aged 10.40 to 14.00 years, participated in the study. The results indicated that the SD, DLD, and DLD/SD groups did not differ from each other on PA and RAN Letters and underperformed in comparison to the control groups. However, whereas the children with written language deficits (SD and DLD/SD groups) underperformed on RAN Objects and Digits, PWR, OA, and MA, the children with DLD and no SD performed similarly to the children from the control groups on these measures. In contrast, the two groups with spoken language deficits (DLD and DLD/SD) underperformed on RAN Colors in comparison to the control groups and the group of children with SD only. The results support the notion that those children with DLD who have unimpaired PWR and RAN skills are able to overcome their weaknesses in spoken language and PA and acquire basic literacy on a par with their age peers with typical language. We also argue that our findings support a multifactorial model of DLD.     

Being highly internationalised strengthens your reputation: an empirical investigation of top higher education institutions

In an educational context characterised by globalisation, reputation constitutes a crucial issue for today’s higher education institutions. Internationalisation of higher education is often seen as a potential response to globalisation and, consequently, higher education has become increasingly internationalised during the past decade. In this paper, we investigate the relationship between internationalisation and reputation in top higher education institutions. Results reveal that internationalisation positively influences a university’s reputation but also moderates the relationship between the institution’s reputation and its institutional performance with regard to research quality, teaching quality and graduate employability.     

Factors influencing early adolescents’ mathematics achievement: High-quality teaching rather than relationships

This study used data from the Assessment Tools for Teaching and Learning project, which involved data on the academic performance of more than 90,000 New Zealand students in six subjects (i.e. reading, writing and mathematics in two languages). Two sub-samples of this dataset were included for detailed re-analysis to test the general applicability of the Australian model of Quality of School Life (Ainley et al. 1986) in the New Zealand context. The first sample comprised 336 year 8 students from elementary schools and the second sample consisted of 272 year 10 students from high schools. Furthermore, two structural equation models were developed and tested, expressing relationships between students’ quality of school life perceptions, students’ attitudes to mathematics, and their effects on mathematics achievement. The quality of school life questionnaires scales [Ainley and Bourke, in Res Pap Educ 7(2):107–128, 1992] were used as indicators of students’ perceptions regarding learning, teachers and peer relationships. The model proposed that perceived quality of school life would affect students’ attitudes of liking and confidence in mathematics, which would in turn affect their academic performance. After controlling for other variables in the model, students’ perception about their self-efficacy to learn mathematics was more directly related to outcomes than to perceptions of teacher quality or peer involvement. Data analyses revealed no apparent relationships of these factors to mathematics achievement. Moreover, results for both samples led to the conclusion that the perceived quality of learning is connected with ‘confidence in’ and ‘liking mathematics’, which in turn predict students’ mathematics achievement.     

澳门特区免费幼儿教育政策研究

澳门特区自2007～2008学年开始实施15年免费教育,即9年义务教育、3年高中教育和3年学前教育免费.研究者运用网络调查及访谈法,对澳门特区免费幼儿教育政策进行研究,结果发现:(1)免费幼儿教育政策只适用于6家公办幼儿园和42家加入免费教育学校系统的私立幼儿园.(2)7家未加入免费教育学校系统的私立幼儿园需缴学费、补充服务费和选择性服务费,但可获政府发放的学费津贴和书簿费.家长很满意这一政策,并表示愿意继续送孩子上收费的私立幼儿园.(3)受访园(校)长、家长及教师对澳门的免费幼儿教育政策都很满意,教师特别满意政府推出的幼儿园教师津贴.(4)免费幼儿教育政策对私立园所的影响有所不同:有些私立园所为了生存而选择加入免费教育学校系统,有些私立园所则为了校政自主而选择不加入免费教育学校系统.客观上,高收费门槛令不同阶层家庭的幼儿自然分流.