The construction of abstract units in geometric and numeric settings

The main thesis of this paper is that the construction and coordination of abstract units is central to mathematical activity in both numerical and geometric settings. Data were gathered from students in grade three through six, with four students being observed over a three year period. A consistent parallel was found in the sophistication of the types of units constructed in a geometric setting (tiling the plane) with their numeric activity. The tiling activity of the students was analyzed for evidence of the construction and coordination of units. Some students constructed rather sophisticated abstract composite units to facilitate their tiling with a particular shape while others had difficulty making a covering. Students who constructed abstract composite units in tiling did so also in adding and subtracting whole numbers. Evidence of unitizing and coordinating the units constructed was associated with advances in mathematical thinking. Unitizing seems to be a fundamental mental operation in coming to act mathematically. As mathematics activities are planned, it is important to provide opportunities for students to construct abstract composite units in both geometric and numeric settings. Emphasis on prescribed procedures such as subtracting with two-digit numerals may inhibit this construction process.     

Scaling and Sustaining Effective Early Childhood Programs Through School–Family–University Collaboration

We describe the development, implementation, and evaluation of a comprehensive preschool to third grade prevention program for the goals of sustaining services at a large scale. The Midwest Child–Parent Center (CPC) Expansion is a multilevel collaborative school reform model designed to improve school achievement and parental involvement from ages 3 to 9. By increasing the dosage, coordination, and comprehensiveness of services, the program is expected to enhance the transition to school and promote more enduring effects on well‐being in multiple domains. We review and evaluate evidence from two longitudinal studies (Midwest CPC, 2012 to present; Chicago Longitudinal Study, 1983 to present) and four implementation examples of how the guiding principles of shared ownership, committed resources, and progress monitoring for improvement can promote effectiveness. The implementation system of partners and further expansion using “Pay for Success” financing shows the feasibility of scaling the program while continuing to improve effectiveness.     

REJOINDER

In this paper, we explore the influence of the teacher on the language games being played in a Grade 3 mathematics classroom. The kinds of listening strategies used by the teacher seemed to have an impact on the kind of language game being played as a small group of students engaged in a problem‐solving activity. Understanding classroom conversation from a language‐games perspective is used to explore the kinds of sense‐making, student engagement, and new understandings evolving through classroom discourse. Language games may also be important for encouraging students to extend and transform their understandings. We describe how learning to ‘teach etcetera’ as a way of helping students ‘see‐as’ and move beyond narrowly defined predetermined content may entail playing more open‐ended language games and learning how to ‘listen’.     

Helping Taiwanese Graduate Students Help Themselves: Applying Corpora to Industrial Management English as a Foreign Language Academic Reading and Writing

Lack of knowledge in the conventional use of vocabulary and multiword patterns in one's respective field of expertise causes Taiwanese students to produce academic writing that is markedly “non-nativelike.” This is because Taiwanese students are first and foremost second language readers and often have difficulty “picking up on” the regularly encountered language patterns found in scholarly texts. As one step in determining a solution to this problem, this article reports on a pilot implementation encouraging graduate Taiwanese students for whom English is a foreign language to use self-editing techniques in their own field-specific academic writing by use of a corpus tool. Classroom interviews, draft comparisons, and individual stimulated recall interviews showed a difference in acceptance and success after using the corpus tool (StringNet Navigator) as an aid to self-editing academic English writing. The corpus tool's functions, results of its use by industrial management graduate students for self-editing academic writing, and pedagogical implications are described.     

Social justice and school linkages in teacher education programmes

This paper investigates current research into the role of education in combating social injustice, assembles this research to indicate key features of a teacher education programme that would assist education for social justice, and links these features to one innovative university teacher education programme to ascertain some of the practical difficulties in establishing such a programme. The research indicated key approaches that would enhance the probability that graduates from teacher education programmes will be able to pursue social justice initiatives.     

线性时态逻辑的决策问题复杂性

不同的时态逻辑能够适应不同的推理任务.为了符合应用,关于时间的模型从离散的自然数和整数,延伸到稠密的线性实数,甚至扩展到区间代数和树代数.如果简单的时态连接词的表达力已经足够,就只需使用这些简单的时态连接词来构造的时态逻辑.在能够承担降低运算速度的风险下,我们可以为实现更强的表达力而使用更多的连接词,也可以加上度量信息或者固定点.作者近期提出了一个令人惊讶的结论:建立在实数时间上的具有足够表达力的语言和基于自然数离散时间流的传统简单算子,它们推理的计算复杂性是一样的.在这篇论文中,作者试图对建立在标准时态连接词和线性时间流的普通类上的时态逻辑中所有决策问题的计算复杂性作新的说明.尤其是,文中指出,所有标准逻辑在PSPACE中都存在决策问题.     

Embryonic auditory experience and maternal call recognition

Peking duck embryos respond selectively to the maternal call of their species on the day before hatching, given normal embryonic auditory experience (the sounds emanating from their siblings and themselves which begin late on Day 24 of development). Groups of Peking embryos were subjected to recordings of either the mallard or the Burmese red jungle fowl maternal call beginning on Day 21 of incubation. Responses to these calls were tested on the day before hatching to determine the effects of the prenatal auditory experience. The responses of those birds exposed to the mallard maternal call were neither attenuated nor enhanced (as compared to the controls) when presented that call; those subjects which were exposed to the jungle fowl maternal call later failed to respond to that call or the mallard maternal call.     

The effectiveness of simulated robots for supporting the learning of introductory programming: a multi-case case study

This work investigates the effectiveness of simulated robots as tools to support the learning of programming. After the completion of a systematic review and exploratory research, a multi-case case study was undertaken. A simulator, named Kebot, was developed and used to run four 10-hour programming workshops. Twenty-three student participants (aged 16–18) in addition to 23 pre-service, and 3 in-service, teachers took part. The effectiveness of this intervention was determined by considering opinions, attitudes, and motivation as well as by analysing students’ programming performance. Pre- and post-questionnaires, in- and post-workshop exercises, and interviews were used. Participants enjoyed learning using the simulator and believed the approach to be valuable and engaging. The performance of students indicates that the simulator aids learning as most completed tasks to a satisfactory standard. Evidence suggests robot simulators can offer an effective means of introducing programming. Recommendations to support the development of other simulators are provided.     

Countering the Critics: Responses to Recent Criticisms of School Effectiveness Research

Criticisms of school effectiveness research (SER) from recent books are addressed. Fourteen criticisms are presented, followed by counterpoints, including: (1) many criticisms are based on simplistic/skewed readings of SER; (2) there is a wide diversity in SER; no single viewpoint prevails, as implied by critics; (3) many SER researchers have reported the direct/indirect impact of social class on student achievement, instead of ignoring it as implied by critics; (4) SER researchers believe schools have an impact beyond that of social class, and educators should influence what they can in their schools/classrooms; critics pessimistically focus on the social class/student achievement relationship; (5) pragmatism is a valid paradigm for studying schools; indeed, it has advantages over “critical” theory employed by other commentators. Resolution of these issues is unlikely given differences in commentators' world views.