Tacit models,treasured intuitions and the discrete—continuous interplay

We explore conditions for productive synthesis between formal reasoning and intuitive representations through analysis of college students’ understanding of the limit concept in the definition of the derivative. In particular, we compare and contrast cognitive processes that accompany different manifestations of persistence of intuitions and tacit models that coexist with students’ logical reasoning. The students are highly trained in mathematics. We encounter expressions of the persistence and impact of intuitions and tacit pictorial models as described by Fischbein. But we also observe some new characterization of persistence of tacit models in which the tacit pictorial model continues to interfere in the student’s reasoning process, coexists with a logical reasoning but does not prevent the student from reaching a feeling of logical consistency. The empirical analysis and the theoretical discussion offered in the present paper permit us to highlight this very special integration of the formal and the intuitive components of the reasoning process.     

Exploring the phase space of a system of differential equations: different mathematical registers

We describe and analyze a situation involving symbolic representation and graphical visualization of the solution of a system of two linear differential equations, using a computer algebra system. Symbolic solution and graphical representation complement each other. Graphical representation helps to understand the behavior of the symbolic solution. Together with it, the symbolic solution and its analysis are needed to understand the graphical representation and to overcome the limiting constraints of the CAS. The study described in this paper points out the importance of flexibility in building connections between different mathematical registers, together with the fact that the balance between the usage of symbolic representations and of graphical representations can be very different from one student to the other. Research supported by Israel Science Foundation, grant number 1340/05.     

Children’s Appraisals of Gender Nonconformity: Developmental Pattern and Intervention

Gender-nonconforming (GN) children are often perceived less positively, which may harm their well-being. We examined the development of such perceptions and an intervention to modify them. Chinese children’s appraisals were assessed using multiple measures (verbal responses, sharing, and rank order task) after viewing vignettes of gender-conforming (GC) and GN hypothetical peers. In Study 1, children (N = 210; 4-, 5-, 8-, and 9-year-olds) were less positive toward GN than GC peers, especially if they were older or if the peers were boys. In Study 2 (N = 211, 8- and 9-year-olds), showing children exemplars of GN peers who displayed positive and GC characteristics subsequently reduced bias against gender nonconformity. These findings inform strategies aimed at reducing bias against gender nonconformity.     

Boys Outperforming Girls: an 8‐year cross‐sectional study of attainment and self‐esteem in Year 6

This 8‐year cross‐sectional study measured the self‐esteem, reading and mathematical attainments of eight cohorts of Year 6 children. A total of 1488 children (737 boys, 751 girls) in five randomly selected primary schools within one Local Education Authority (LEA) comprised the sample to which the Lawseq questionnaire (Lawrence, 1982), Mathematics 11 (NFER, 1985) and the Primary Reading Test Level 2 (France, 1981) were administered. Differences in attainment related to gender were found in mathematics, but not in reading, with boys significantly outperforming girls (at the 5% level). The percentage of boys who scored significantly above the mean in mathematics and significantly below the mean in reading contrasted with the girls’ more compressed scores in the middle range. The national test data for Cohorts 7 and 8 followed the national pattern with girls outperforming boys. Boys had significantly higher self‐esteem than the girls (at the 0.1% level). Correlation coefficients between Lawseq and mathematics and reading mean scores for boys and girls were all significant at the 0.1% level. The findings are discussed in relation to the current debate concerning the low performance of boys.     

A Systematic Review of Whole School Improvement Models

This article presents a review of widely implemented, externally developed whole school improvement models. The models serve elementary, middle, and high schools and schools operated by education service providers. A systematic review of the research was conducted using rigorous evidence standards. Across models, the whole school improvement approach demonstrates promising results, with the majority of the evidence pertaining to elementary school models. However, there is relatively little research evidence that the majority of the models reviewed positively impact student academic achievement. For the majority of the models, most of the core components (i.e., practices or strategies) are linked to empirical evidence. An examination of the models' designs and materials revealed that model providers offer a range of services and supports for successful implementation. The use of research evidence in conjunction with other considerations is discussed.     

Proof image

The emergence of a proof image is often an important stage in a learner’s construction of a proof. In this paper, we introduce, characterize, and exemplify the notion of proof image. We also investigate how proof images emerge. Our approach starts from the learner’s efforts to construct a justification without (or before) attempting any formal argument, and it focuses on the process by which a complete but not necessarily communicable image of that justification becomes available to the learner and provides explanation with certainty. We consider the interplay between the learner’s intuitive and logical thinking and, using the theoretical framework of Abstraction in Context, we trace the construction of knowledge that results from and enables progress of this interplay. The existence and identification of proof images and the nature of the processes by which they emerge constitute the theoretical contribution of this paper. Its practical value lies in the empirical analyses of these processes and in the potential to apply them to the design of tasks that support students in constructing their own proofs images and proofs. We believe that such processes are likely to considerably enrich students’ mathematical experience.     

Chinese-style pragmatic objectivity in war reporting

China plays an increasing role in the wars and conflicts around the world with its expanding political and economic interests overseas and its diplomatic role in international affairs. More and more Chinese journalists go to the frontlines overseas to cover distant conflicts for domestic audiences. Based on semi-structured in-depth interviews with 16 Chinese correspondents who have covered conflicts outside China, this study examines Chinese journalists' perceptions and reflections on objectivity in the war zones. The author adopts a term of Chinese-style pragmatic objectivity to mean that objectivity is a convenient approach for Chinese journalists to do war journalism in the field. At the level of objectivity-as-a-value, objectivity is defined as a pragmatic value and a practical ritual for Chinese journalists to do news within the scope they can reach, to protect themselves from criticisms, and to justify their version of the truth. It promotes allegiance and patriotism. At the level of objectivity-as-a-practice, objectivity in war coverage is compromised by China's foreign policies, military constraints, the press's political orientations and editorial polices, and journalists' personal experiences and values. Chinese journalists use Chinese-style objectivity to negotiate their roles in the power struggle with the state, foreign militaries, the newsroom, and journalists.     

Athletes in transition: German immigrants to Mandatory Palestine – between integration and segregation*

The Brit Maccabim Atid sport club was founded by immigrants from Germany who came to Palestine during the 1930s. The circumstances surrounding this organisation’s establishment differed from those of the sports organisations operating in Palestine until then. We consider sports culture as a tool for analysing immigrant absorption processes. Our discussion is based on the claim that sports served as a means of social integration for German Jews. In Palestine, sports served as an arena of conflict between the political camps in the Jewish settlement. In response to this political reality, immigrants from Central Europe began organising to establish separate sports clubs along political and ethnic lines, thus responding to the needs of immigrants identifying with German cultural circles. Brit Maccabim Atid constitutes a test case for the social and cultural changes in the meaning of sports in the move from one country to another. The paper describes two sociological models, each of which examines the impact of involvement in sports on the extent to which immigrants become integrated into society. Our findings indicate that sports participation in an immigrant society can be a unifying and assimilative factor and at the same time a segregating factor.     

Morning and afternoon nursery sessions: can they be equally effective in giving children a positive start to school?

This paper analyses the effects of gender, attendance period and age on children's adjustment to nursery classes as measured by the teachers using the Child at School Schedule. The sample consisted of 820 children in sixteen nursery classes attached to primary schools in one Local Education Authority. Within the sample three age groups were distinguished: Oldest (4:3 — 4: 8 years); Middles (3:9 — 4:2: years); Youngest (3:1 — 3:8 years). The results of a three‐way analysis of variance showed that boys and afternoon attenders were perceived to be less well‐adjusted to school than girls and morning attenders (at 1% level). In addition, the oldest children were perceived as better adjusted than younger ones: with the exception of three items the youngest were perceived as the least well adjusted. Strategies to help boys and afternoon attenders to experience as positive a start to nursery education as girls and morning attenders are discussed. The key role of the adults in helping children to develop personal and social skills is highlighted as is the need for home/school partnership. The implications of gender for play and classroom organisation are also considered.