Analyzing the teaching of advanced mathematics courses via the enacted example space

Examples are believed to be very important in developing conceptual understanding of mathematical ideas, useful both in mathematics research and instruction (Bills & Watson in Educational Studies in Mathematics 69:77–79, 2008; Mason & Watson, 2008; Bills & Tall, 1998; Tall & Vinner, 1981). In this study, we draw on the concept of an example space (Mason & Watson, 2008) and variation theory (Runesson in Scandinavian Journal of Educational Research 50:397–410, 2006) to create a lens to study how examples are used for pedagogical purposes in undergraduate proof-based instruction. We adapted the construct of an example space and extended its application to the constructs of example neighborhood, methods of example construction, and the functions of examples. We explained how to use our new lens to analyze the collection of examples and non-examples that the students had access to. We then demonstrate our method by analyzing the collection of examples and non-examples of a mathematical group the professor of an abstract algebra class presented during lectures or assigned to students in problem sets or exams.     

The Effect of Linguistic Simplification of Science Test Items on Score Comparability

The use of accommodations has been widely proposed as a means of including English language learners (ELLs) or limited English proficient (LEP) students in state and districtwide assessments. However, very little experimental research has been done on specific accommodations to determine whether these pose a threat to score comparability. This study examined the effects of linguistic simplification of 4th- and 6th-grade science test items on a state assessment. At each grade level, 4 experimental 10-item testlets were included on operational forms of a statewide science assessment. Two testlets contained regular field-test items, but in a linguistically simplified condition. The testlets were randomly assigned to LEP and non-LEP students through the spiraling of test booklets. For non-LEP students, in 4 t-test analyses of the differences in means for each corresponding testlet, 3 of the mean score comparisons were not significantly different, and the 4th showed the regular version to be slightly easier than the simplified version. Analysis of variance (ANOVA), followed by pairwise comparisons of the testlets, showed no significant differences in the scores of non-LEP students across the 2 item types. Among the 40 items administered in both regular and simplified format, item difficulty did not vary consistently in favor of either format. Qualitative analyses of items that displayed significant differences in p values were not informative, because the differences were typically very small. For LEP students, there was 1 significant difference in student means, and it favored the regular version. However, because the study was conducted in a state with a small number of LEP students, the analyses of LEP student responses lacked statistical power. The results of this study show that linguistic simplification is not helpful to monolingual English-speaking students who receive the accommodation. Therefore, the results provide evidence that linguistic simplification is not a threat to the comparability of scores of LEP and monolingual English-speaking students when offered as an accommodation to LEP students. The study findings may also have implications for the use of linguistic simplification accommodations in science assessments in other states and in content areas other than science.     

The naked truth: disability,sexual objectification,and the ESPN Body Issue

We critically analyze four images of female Paralympians posing nude in ESPN The Magazine’s Body Issue from the years 2009, 2010, 2012, and 2014. Past literature shows that media portrayals of female Paralympians emphasize esthetically pleasing bodies, able-bodied images and asexualization. Weaving’s continuum of sexual objectification was applied to assess the varying degrees of sexual objectification showcased within each image. From a feminist perspective, discourses of heteronormativity and ableism were applied to outline the concerns with female Paralympic representation in The Body Issue. We argue that by normalizing disability and sexual objectification, woman athletes are trivialized.     

Self-directed learning characteristics: making learning personal,empowering and successful

Due to the speedy emergent investigation in self-directed learning (SDL) over the past 40 years, SDL is an education technique used progressively within tertiary institutions. SDL can be well-defined in terms of the amount of accountability the student accepts for his or her own learning. The self-directed students regarding learning take control and apply self-determination to learn what they view as imperative for themselves. The amount of control the students are keen to take over their own learning will depend on their assertiveness, aptitudes and personality characteristics. The article thus explores what individual features and characteristics can define the student who is involved in SDL; What capabilities and characteristics need to be grasped by the students who are involved in SDL? Therefore, the objective of the article was to identify characteristics of the self-directed learner in the context of teacher education. Based on our conclusion, it is clear that teacher-students should challenge themselves within this process of SDL development to participate in SDL opportunities. The characteristics of SDL teacher-students must be strengthened to promote their self-directedness with regard to learning and it is also the lecturer’s task to create a class atmosphere of SDl to inculcate and develop SDL characteristics in students.     

Education policy borrowing in China: has the West wind overpowered the East wind?

Recent education reform in China reflects the global trend of education policy borrowing from Anglophone countries such as the USA. The reform in China essentially advocates shifting from knowledge reproduction and didacticism to knowledge construction by students through a learner-centredness approach. Aware of the trend of borrowing policy from ‘Western’ countries, some educators in China use the proverb ‘the West wind has overpowered the East wind’ to describe this phenomenon. This paper examines the cultural factors that influence education policy borrowing in China by drawing upon Johnson’s metaphors of the ‘politics of selling’ and the ‘politics of gelling’. This paper argues that there exist fundamental cultural differences between Western and Chinese perspectives on the nature and transmission of knowledge that make education policy transfer in China challenging. This paper further proposes that China borrow education policy judiciously by integrating foreign and indigenous sources of knowledge, teaching and learning.     

Social justice education with Chinese characteristics: An example from Shanghai

This article analyses a Chinese approach to social justice in education using the example of Shanghai. In addressing schooling inequalities, Shanghai illustrates social justice education with Chinese characteristics, which revolves around the ideal of ‘educational balance’ (jiaoyu junheng). The ‘balance’ in question is about achieving a values-centred and all-round education in and across all schools through the cultivation of a school’s ‘inner quality’ (neihan). This Chinese formulation of social justice education is manifested through two representative policy measures: creating and strengthening ‘new high-quality schools’ and helping weak schools to level up. The Chinese characteristics of these action plans are seen in two ways: a focus on social justice between schools rather than between students; and an emphasis on the moral cultivation of students. It is argued that a Chinese model of social justice education promotes educational equity to some extent through the politics of redistribution, recognition and representation. However, a major critique is its hegemonic and top-down nature, which overlooks alternative and competitive voices—especially those of migrant children—as part of a politics of representation.     

“OUR SHARED VALUES” IN SINGAPORE: A CONFUCIAN PERSPECTIVE

In this essay Charlene Tan offers a philosophical analysis of the Singapore state's vision of shared citizenship by examining it from a Confucian perspective. The state's vision, known formally as “Our Shared Values,” consists of communitarian values that reflect the official ideology of multiculturalism. This initiative included a White Paper, entitled Shared Values, which presented pejorative assessments of the ideals of “individual rights” and “individual interests” as antithetical to national interests. Rejecting this characterization, Tan argues that a dominant Confucian perspective recognizes the correlative rights of all human beings that are premised on the inherent right to human dignity, worth, and equality. Furthermore, Confucianism posits that it is in everyone's interest to attain the Confucian ethical ideal of becoming a noble person in society through self‐cultivation. Tan concludes by highlighting two key implications for Singapore from a Confucian perspective on the Shared Values: first, schools in Singapore should place greater emphasis on individual moral development of their students, and second, more avenues should be provided for residents to contribute actively to the development of the vision of shared citizenship.