Middle School Teachers’ Use of Mathematics to Make Sense of Student Solutions to Proportional Reasoning Problems

Mathematics teacher education aims to improve teachers’ use of mathematical knowledge to support teaching and learning, an aspect of pedagogical content knowledge (PCK). In this study, we interviewed teachers to understand how they used mathematics to make sense of student solutions to proportional reasoning problems. The larger purpose was to find accurate ways of categorizing teachers’ ability to do this vital aspect of teaching and thereby to inform assessment, teacher education, and professional development. We conjectured that teachers’ PCK for proportional reasoning could be reliably described in terms of attention to quantitative meanings in story problem contexts and in terms of understanding naïve forms of proportional reasoning. Instead, our findings reveal that individual teachers used a variety of means to make sense of (1) cognitively similar student solutions to different tasks and (2) mathematically related steps of a student solution within a single task. These findings illustrate the complexity of PCK for the topic of proportional reasoning and suggest the limits of what can be inferred about teacher knowledge from teachers’ evaluations of student solutions. We discuss implications for teacher education and assessment.     

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.     

Systems biology

Systems biology seeks to study biological systems as a whole, contrary to the reductionist approach that has dominated biology. Such a view of biological systems emanating from strong foundations of molecular level understanding of the individual components in terms of their form, function and interactions is promising to transform the level at which we understand biology. Systems are defined and abstracted at different levels, which are simulated and analysed using different types of mathematical and computational techniques. Insights obtained from systems level studies readily lend to their use in several applications in biotechnology and drug discovery, making it even more important to study systems as a whole.     

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.     

Projectile motion with quadratic damping in a constant gravitational field

The motion of a projectile in a constant gravitational field is an age-old problem. If there is no resistive force, the problem is simple. However, with the intoduction of resistive forces, the complexity of the problem increases. Recently, there has been a growing interest in the problem of projectile motion under a resistive force proportional to the square of velocity. The problem for resistive force proportional to vv cannot be solved in closed analytical form. A series solution of the equation leads to divergent series for x (t) and y (t) for reasonable values of the initial speed and angle of projection. However, we demonstrate that by inverting the series for x (t), i.e., expressing t in terms of x, and substituting this in y (t) one can express y in terms of x which is a highly convergent series and one can obtain the path of projectile with a few terms of the series. We further demonstrate that one can obtain the path even with a few terms of the divergent series for x (t) and y (t) by using extrapolation methods.     

What’s new in computers

Lately there has been a lot of excitement about disruptive forms of ‘money’ — cryptocurrencies. This article traces the evolution of cryptocurrencies focusing on the enabling technologies and some theoretical foundations. We shall also explore the challenges they pose to well-established monetary systems.     

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.     

From inactivity to encouragement: the contribution of Lord Elphinstone to the educational development of the Madras Presidency (1837–1842)

In light of the focus placed on English education by the colonial government, and the petition signed by 70,000 local inhabitants of the Madras Presidency, Lord John Elphinstone, the Governor, made efforts to disseminate English education during his governorship (1837–1842). Spurred on by the petition, Elphinstone wrote two fundamental educational minutes, in 1839 and 1841, and established Madras High School. Later, the School was transformed into Presidency College and became the first home of the University of Madras. Elphinstone’s planning led to the first systematic effort by the Madras government to impart English education. Subsequently, Elphinstone emphasised the dissemination of secular education and inclusion of native people in educational administration. Against this background, this paper discusses the contribution of Elphinstone to the educational development of Madras. It also questions the historiographical neglect of Elphinstone and challenges the established post-colonial discourse that the establishment of English institutions was a ‘colonialist’ imposition.