Tacit Beginnings Towards a Model of Scientific Thinking

The purpose of this paper is to provide an examination of the role tacit knowledge plays in understanding, and to provide a model to make such knowledge identifiable. To do this I first consider the needs of society, the ubiquity of information in our world and the future demands of the science classroom. I propose the use of more implicit or tacit understandings as foundational elements for the development of student knowledge. To justify this proposition I consider a wide range of philosophical and psychological perspectives on knowledge. Then develop a Model of Scientific Knowledge, based in large part on a similar model created by Paul Ernest (Social constructivism as a philosophy of mathematics, SUNY Press, Albany, NY, 1998a; Situated cognition and the learning of mathematics, University of Oxford Department of Educational Studies, Oxford, 1998b). Finally, I consider the work that has been done by those in fields beyond education and the ways in which tacit knowledge can be used as a starting point for knowledge building.     

Do the Colors of Educational Number Tools Improve Children’s Mathematics and Numerosity?

This study examined how colored educational tools improve children’s numerosity (“number sense”) and/or mathematics. We tested children 6–10 years (n = 3,236) who had been exposed to colored numbers from the educational tools Numicon (Oxford University Press, 2018) or Numberjacks (Ellis, 2006), which map colors to magnitudes or Arabic numerals, respectively. In a free association task pairing numbers with colors, a subset of children spontaneously provided colors matching one of these schemas. These children, who had internalized Numicon (colored magnitude), showed significantly better numerosity but not mathematics compared to peers. There was no similar benefit from internalizing Numberjacks (colored numerals). These data support a model in which colored number tools provide benefits at different levels of numerical cognition, according to their different levels of cross-modal mappings.     

Response to 'Cautions on OECD's Recent Educational Survey (PISA)'

In his recent paper, 'Cautions on OECD's recent educational survey (PISA)' ( Oxford Review of Education , 29, 2), S.J. Prais questioned the outcomes of the Organisation for Economic Cooperation and Development's PISA survey of the reading, mathematics and science attainments of 15-year-olds. Prais suggested that methodological flaws in PISA had resulted in an apparent improvement in the attainment of British students--particularly when compared to their Swiss and German counterparts. This paper responds to Prais's criticisms, noting that when Prais's conjectures are tested with empirical data they are not supported. Further it is noted that many of Prais's criticisms are due to an incomplete understanding and knowledge of the methodology of international studies, and of PISA in particular.     

Gender and Social Inequality at Oxford and Cambridge Universities

Abstract

The academic efficiency and social justice of entry procedures at Oxford and Cambridge Universities are examined over the past quarter of a century. For each major subject the mean A‐level scores of males and females entering from state and independent schools are compared with mean final examination scores in the major subjects. In any comparison of state and independent cohorts of the same gender, within the bounds of normal statistical fluctuation, the difference in A‐level score is a good predictor of the difference in finals score. For example, when between state men and independent men the difference in A‐level score is zero, the difference between mean finals score is zero also. The origin of female under‐achievement is examined. In most subjects there is pronounced gender inequality due to the following chain of circumstances: (1) to break‐even in finals women require at entry better grades at Advanced Level than men; (2) women used to have much the better A‐levels and so, in finals a quarter of a century ago, they matched and even — in some subjects — surpassed the men; (3) the A‐levels of women entering Oxford and Cambridge Universities fell off during the 1970s; (4) today female A‐level scores are slightly worse than male A‐level scores, and so female finals scores are much worse, in most subjects, than male finals scores. The concept of an ideal subject is defined; this is a subject in which zero difference in A‐level score between male and female yields zero difference in finals score. Law at Cambridge and chemistry at Oxford are ideal subjects. Ideal subjects are rare at Oxbridge: most subjects exhibit a significant male lead in finals when male and female have equal A‐level scores. The most non‐ideal subject at Oxford is mathematics, in which zero difference in A‐level score between males and females yields a male lead in finals score of 13%: at Oxford the other non‐ideal subjects are physics (male lead at equal A‐levels 11%), philosophy, politics and economics (9%), history (8%), modem languages (8%) and English (5%). An ideal subject is a paradigm which requires even‐handedness between male and female cohorts in the following parameters: (1) efficiency of course selection from school; (2) efficiency of teaching; (3) efficiency of finals assessment; (4) latent ability. A pronounced relative decline in the A‐level scores of girls educated in state maintained schools entering English and Welsh universities occurred in the 1970s; it is attributed to the reform of the state school system, particularly the growth in mixed‐sex comprehensive schools and the decline in the number of female single‐sex grammar schools. A peculiar aspect of the admissions filters at both Oxford and Cambridge ensures that state‐school educated men gaining entry do so with A‐level scores markedly superior to those of the other three cohorts.     

Oxford House: deaf-affirmative support for substance abuse recovery

Deaf individuals seeking substance abuse recovery are less likely to have access to treatment and aftercare services because of a lack of culturally and linguistically specific programs and insufficient information about existing services. Previous research indicates that Oxford House, a network of resident-run recovery homes, serves a diverse group of individuals in recovery. However, research has not addressed the experiences of Deaf Oxford House residents. The present study found no significant differences between Deaf and hearing men living in Oxford House in terms of sense of community and abstinence self-efficacy. However, while most of the hearing participants were employed, none of the Deaf Oxford House members were. The study's findings indicate that Oxford House may be a promising Deaf-affirmative alternative for individuals seeking recovery from substance abuse. However, since Oxford Houses are self-supporting, Oxford Houses designed for the Deaf community may face unique economic challenges.     

Events in learning mathematics: Insights from research in classrooms

In this paper, it is contended that in order to understand individual student's learning in the complexity of the mathematics classroom it is necessary to examine the events that occur before, during, and after learning. To illustrate, the process by which two children each construct new mathematical meanings is examined in this manner. The detailed analyses of each of these events provides insight into the processes by which individual students construct mathematical meanings in classroom settings. The investigation also reveals that the underlying social norms differ from those found in traditional classes, and that this creates different opportunities for learning. It is contended that it is the differences in the norms that have been established in their respective classes that distinguishes between the events in learning for the two children.Preparation of this paper was supported by the National Science Foundation (RED 9254939) and while the author was the Snodgrass Scholar in the School of Education Purdue University. The final draft was completed at the Mathematics Education Research Centre, Oxford University. All opinions are those of the author.     

牛津大学教育理念与研究生教育

牛津大学是一所古老而现代的大学。它因历史悠久、大师云集、人才培养和学术成就卓著、国际化程度高而享誉世界,它在国家乃至世界政治、经济、文化、科技生活中均发挥了重要的作用,一直保持世界一流大学的地位而不动摇。牛津大学的研究生教育坚守的是自由教育和精英教育传统,在研究生培养上固守培养世界一流顶尖人才为目标,在学科设置上注重跨学科的交叉,其特点对我国研究生教育有很好的借鉴意义。     

Social constructivism and the <Emphasis Type="Italic">Believing Game</Emphasis>: a mathematics teacher’s practice and its implications

The study reported here is the third in a series of research articles (Harkness, S. S., D’Ambrosio, B., & Morrone, A. S.,in Educational Studies in Mathematics 65:235–254, 2007; Morrone, A. S., Harkness, S. S., D’Ambrosio, B., & Caulfield, R. in Educational Studies in Mathematics 56:19–38, 2004) about the teaching practices of the same university professor and the mathematics course, Problem Solving, she taught for preservice elementary teachers. The preservice teachers in Problem Solving reported that they were motivated and that Sheila made learning goals salient. For the present study, additional data were collected and analyzed within a qualitative methodology and emergent conceptual framework, not within a motivation goal theory framework as in the two previous studies. This paper explores how Sheila’s “trying to believe,” rather than a focus on “doubting” (Elbow, P., Embracing contraries, Oxford University Press, New York, 1986), played out in her practice and the implications it had for both classroom conversations about mathematics and her own mathematical thinking.     

牛津大学导师制的传播意义

牛津大学导师制是牛津大学本科教学的核心和基础,也是其卓越教学质量得以保障的关键因素。牛津大学导师制不仅对英国高等教育产生了重要影响,而且在世界诸多国家广为传播。尽管很少有国家能够实施牛津大学式的导师制,但是其独特的教学理念已为很多大学所接受。各国借鉴导师制的经验足以为我国推进本科导师制改革,提高大学教学质量提供有益的启示。     

A CASE STUDY IN THE EXAMINATION OF SYSTEMS ANALYSIS Robert

This article describes an approach to the teaching and examining of systems analysis as a final year and MSc subject in a university department of computing mathematics.

One of the chief functions, if not the chief function of our University, is to prepare young Men — partly by the personal influence of those who have charge of them, and partly by the influence they exercise on one another — for the business of life.

(This needs to be specially borne in mind in connection with the assumption, so constantly made in this controversy, that the sole meaning of the BA Degree is that it guarantees the possession of a large amount of knowledge.)

Charles L. Dodgson Christ Church College Oxford 7 March 1896(1)

     

牛津大学的发展历程、教育理念及其启示

牛津大学是一所古老而现代的大学.在长达800多年的发展过程中,牛津始终坚守着人才培养和学术研究的优良传统,致力于造就有教养的绅士,培养精英人才,人文教育与科学教育相融合以及国际化教育.牛津大学的先进教育理念和成功经验对我国高等教育改革,尤其是世界一流大学的建设有重要的启示作用.     

一场对“大学自治、学者治校”的深入反思： 2004-2006年牛津大学治理改革案例分析

近四十多年来,为了在激烈的国际竞争和广泛的社会变革中保持世界一 流,牛津深入反思了大学的宗旨和原则——“学术卓越”和“民主自治”,并 对治理体制进行了一系列的改革探索。2004-2006年的牛津治理改革大讨论是 现代大学治理模式在学术与行政权力之间的一场激烈冲突。牛津的改革努力激 励着世界的其他大学反思自身的办学之道,反思大学的本质和未来。本文系统 分析了这场改革的背景、过程、特点和影响。     

关联日常数学与学校数学--现代数学教育一个重要的理论与实践课题

日常数学是当前数学教育研究的一个热点问题.日常数学与学校数学具有一定的相容性和互补性,关联日常数学与学校数学是数学教育研究的一个重要的理论与实践课题.在数学教育中,我们应做到以下几个方面:显化含于具体情境之中的日常数学,揭示日常数学和学校数学之间的联系,利用日常数学促进学校数学教学,重建数学教学的理论和实践.     

高校教师视角下的人文社会科学国际发表及其激励制度

在学术国际化和中国哲学社会科学"走出去"的背景下,越来越多的高校对教师发表SSCI和A&HCI论文进行激励。激励制度主要体现在物质奖励和学术评价两个层面。从对国内某研究型大学文科教师深度访谈的情况来看,高校教师对人文社会科学国际发表及其激励制度持不同意见,虽一般不反对对国际发表进行物质奖励,但他们对国际发表在学术评价中的地位的认识存在较大分歧。高校在实施人文社会科学国际发表激励制度的过程中应理解和尊重差异性的存在,关注国际化与本土化的平衡。     

牛津大学与牛津城--传统大学与社区间互动的一个经典个案分析

本文从牛津大学与牛津城间的历史冲突分析入手,解析这一系列冲突事件对彼此所发生的影响,以及冲突在大学史中的意义和价值.从而,试图通过这样的一个经典案例的分析,为我们探索传统大学与它所在社区间互动的性质提供些许启发.     

A-Level考试成绩在牛津大学本科招生中的作用——以专业与科目的匹配为中心

牛津大学本科招生是对申请者A-Level成绩、AS成绩、GCSE成绩、个人陈述、推荐信、书面作品、入学考试、面试等因素的综合评价。作为衡量申请者学术能力的重要依据,牛津大学在招生过程中对A-Level考试成绩格外重视。牛津大学不同专业对A-Level考试科目及成绩提出了明确的等级要求,根据专业与科目的相关性设置了必选科目、建议科目、辅助科目三种科目类型,部分专业还对考试科目设定了模块要求。牛津大学本科招生极其注重A-Level考试科目与专业的匹配性,体现了科目设定详细、主次关系明显、专业与科目关联性强三个特点。     

Book Reviews

Book reviewed in this article: The Oxford Companion to Twentieth Century Art HAROLD OSBORNE (ED) The Oxford Dictionary of Art IAN CHILVERS, HAROLD OSBORNE & DENNIS FARR (EDS) Art Education and Multiculturalism RACHEL MASON Double Harness ROBIN TANNER Design and Applied Arts Index     

浅析多元化数学的教育价值及其实现途径

数学史作为数学文化的重要载体,其教育价值是数学教育研究中的热点问题,在关注数学史成为数学教育结构中构成要件的同时,还应该重视数学史中多元化数学在当今文化教育中的价值。本文在介绍了数学史、数学文化和数学史中多元化数学的基础上,从理解多元文化、扩宽世界视野,探索不同思想方法与培养创造性思维的教育理念出发,对多元化数学的教育价值及实现途径进行了行之有效的探讨。     

数学观的嬗变及其对数学教育的启示

数学观是人们对数学的总体看法。数学观是不断演变的。数学观的发展经历了从绝对主义数学观到可误主义数学观以及建构主义数学观三个阶段。数学观的演变给数学教育极大的启示,在数学教育中,我们应该把握数学观的深刻内涵,领悟数学是一种文化,理解数学知识的本质,把握数学思想方法,鉴赏数学美和追求数学精神。