共查询到20条相似文献，搜索用时 539 毫秒
1.
Peter Kernel 《Higher Education Quarterly》1988,42(2):119-133
This paper addresses three questions: (i) How has the role of central government in higher education evolved? (ii) What have been the main concerns of government? (iii) How should government canny out its role? The first two questions are examined by looking at the historical record in Australia. Australia's experience does not differ greatly from that of Britain. 相似文献
2.
Let R be a ring, a ,b ∈ R, ( D , α ) and (G , β ) be two generalized derivations of R . It is proved that if aD ( x ) = G ( x )b for all x ∈ R, then one of the following possibilities holds: (i) If either a or b is contained in C , then α = β= 0 and there exist p , q ∈ Qr ( RC) such that D ( x )= px and G ( x )= qx for all x ∈ R;(ii) If both a and b are contained in C , then either a = b= 0 or D and G are C-linearly dependent;(iii) If neither a nor b is contained in C , then there exist p , q ∈ Qr ( RC) and w ∈ Qr ( R) such that α ( x ) = [ q ,x] and β ( x ) = [ x ,p] for all x ∈ R, whence D ( x )= wx-xq and G ( x )= xp + avx with v ∈ C and aw-pb= 0. 相似文献
3.
Shivam Kumar 《Resonance》2007,12(9):25-39
Are there perfect squares which on division by 7 leave remainder 3? Are there perfect squares which on division by 3 leave
remainder 7? (A “remainder of 7” on division by 3 is the same as a remainder of 1.) The answers: ‘NO’ and ‘YES’, respectively.
These facts are stated by number theorists as follows: 3 is a quadratic non-residue modulo 7; 7 is a quadratic residue modulo 3. The notion of quadratic residue is far reaching, and the key theorem here is the Law of Quadratic Reciprocity, first stated
by Euler in 1783, but without proof, and first proved by Gauss, in 1796. The theorem is easy to state but is mysterious, as
it reveals a connection between two questions that appear unconnected. Let p, q be distinct odd primes; then the questions are: “Is p a quadratic residue modulo q?” and “Is q a quadratic residue modulo p?” Gauss had a high regard for this result and called it Theorema Aureum, the Golden Theorem. Though it has been proved in many different ways, it retains its mystery. In this two part article we
give three proofs of the theorem. The first one, described in this part, is based on group theory. 相似文献
4.
Gabriel J. Stylianides Andreas J. Stylianides George N. Philippou 《Journal of Mathematics Teacher Education》2007,10(3):145-166
There is a growing effort to make proof central to all students’ mathematical experiences across all grades. Success in this goal depends highly on teachers’ knowledge
of proof, but limited research has examined this knowledge. This paper contributes to this domain of research by investigating
preservice elementary and secondary school mathematics teachers’ knowledge of proof by mathematical induction. This research
can inform the knowledge about preservice teachers that mathematics teacher educators need in order to effectively teach proof to preservice teachers. Our analysis is based
on written responses of 95 participants to specially developed tasks and on semi-structured interviews with 11 of them. The
findings show that preservice teachers from both groups have difficulties that center around: (1) the essence of the base
step of the induction method; (2) the meaning associated with the inductive step in proving the implication P(k) ⇒ P(k + 1) for an arbitrary k in the domain of discourse of P(n); and (3) the possibility of the truth set of a sentence in a statement proved by mathematical induction to include values
outside its domain of discourse. The difficulties about the base and inductive steps are more salient among preservice elementary
than secondary school teachers, but the difficulties about whether proofs by induction should be as encompassing as they could
be are equally important for both groups. Implications for mathematics teacher education and future research are discussed
in light of these findings.
相似文献
| George N. PhilippouEmail: |
5.
In this paper, it is proved that the radial pth mean body RpK（p 〉 0） is homothetic to the difference body DK when K is a simplex, Furthermore, the equality Rp（Rq） = Rq（Rp） is established when p 〉 0 and q 〉 0. It is also proved the Brunn-Minkowski inequality of radial pth mean body of simplex and uniqueness property. 相似文献
6.
When a liberal arts college decides to include computer science as one of its academic disciplines, a number of questions arise. What is an appropriate curriculum? What sort of laboratory support does this new discipline need? How does a small liberal arts school attract, retain, and evaluate faculty in this area? Do computer science faculty become a separate department or remain joined with mathematics or some other discipline? In short, what must be done to put computer science on equal footing with mathematics and other scientific disciplines? This paper addresses these questions. 相似文献
7.
CHRISTOPHER DUBBS 《Journal of Philosophy of Education》2020,54(3):521-540
The philosophical branch of ethics is foundationally concerned with the question of right or wrong, benevolent or harmful, and ultimately what is proper conduct. The present inquiry addresses two related questions: (1) How have theories of ethics been applied to mathematics education research? and (2) What alternatives have not been considered? What might the implications be if these alternative formulations were considered? To answer the first question, I offer a review of the philosophy of mathematics education literature, considering those articles which discuss ethics and mathematics education together. The ethical perspectives adopted within the literature span normative and non-normative, modern and postmodern orientations towards ethics. To answer the second question, I explored philosophy literature to identify which philosophical perspectives of ethics have (not) been adopted by philosophers of mathematics education research. The structure of this paper parallels these two questions: the first part considers the philosophy of mathematics education research and how researchers have defined ethics while the second part discusses additional philosophical approaches to ethics and puts those approaches into conversation with those identified in part one. I conclude by intertwining these two strands into my central thesis: ethics per se is construed too narrowly in the philosophy of mathematics education literature and considering additional ethical perspectives from philosophy can be generative of new ideas. 相似文献
8.
To understand the relationship between social background and sex in schooling, we use Bourdieu’s theory of social reproduction and a feminist perspective of gender as practice. We pose two questions: (1) What is the relationship between economic and cultural capital and achievement for 4th-grade females versus males studying in Germany? (2) Is the relationship between school composition and student achievement different for 4th-grade females versus males? We report no differences between females and males in the relationships between social background and achievement (p > 0.05). However, the relationship between class-aggregated social background and achievement is halved in female-majority mathematics classrooms (β = -12.6, p < 0.05). 相似文献
9.
数学证明的教育价值是数学证明教育研究中要探讨的首要问题,人们数学证明教育观的转变主要依赖于对数学证明做出的教育价值判断.对于数学证明的教育价值问题,以下几方面有待研究:数学证明有哪些重要的教育价值,实证性的量化研究,影响数学证明教育价值实现的因素. 相似文献
10.
Lani Florian 《British Journal of Special Education》2008,35(4):202-208
In this article, Lani Florian, Professor of Social and Educational Inclusion at the University of Aberdeen, examines the relationships between ‘special’ and ‘inclusive’ education. She looks at the notion of specialist knowledge among teachers and at the roles adopted by staff working with pupils with ‘additional’ or ‘special’ needs in mainstream settings. She explores the implications of the use of the concept of ‘special needs’– especially in relation to attempts to implement inclusion in practice – and she notes the tensions that arise from these relationships. She goes on to ask a series of questions: How do teachers respond to differences among their pupils? What knowledge do teachers need in order to respond more effectively to diversity in their classrooms? What are the roles of teacher education and ongoing professional development? How can teachers be better prepared to work in mixed groupings of pupils? In seeking answers to these questions, Lani Florian concludes that we should look at educational practices and undertake a thorough examination of how teachers work in their classrooms. She suggests that it is through an examination of ‘the things that teachers can do’ that we will begin to bring meaning to the concept of inclusion. 相似文献
11.
Juan Pablo Mejia-Ramos Evan Fuller Keith Weber Kathryn Rhoads Aron Samkoff 《Educational Studies in Mathematics》2012,79(1):3-18
Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research
on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper,
we address these issues by presenting a multidimensional model for assessing proof comprehension in undergraduate mathematics.
Building on Yang and Lin’s (Educational Studies in Mathematics 67:59–76, 2008) model of reading comprehension of proofs in high school geometry, we contend that in undergraduate mathematics a proof is
not only understood in terms of the meaning, logical status, and logical chaining of its statements but also in terms of the
proof’s high-level ideas, its main components or modules, the methods it employs, and how it relates to specific examples.
We illustrate how each of these types of understanding can be assessed in the context of a proof in number theory. 相似文献
12.
智障学生的数学学习兴趣现状如何呢？哪些因素影响了数学学习兴趣？怎么样才能提高智障学生的数学学习兴趣呢？这些问题一直困扰着培智学校的多数教师。通过对智障学生的数学学习兴趣现状进行调查研究,我们可以总结出需要通过哪些方法和途径提高智障学生的学习兴趣,可以有针对性地进行下一步的课题研究,建构一个适合智障学生的＂乐学课堂＂。 相似文献
13.
Kathleen Nolan 《Journal of Mathematics Teacher Education》2009,12(3):205-216
The current push to marry off mathematics with social justice compels one to ask such critical questions as “What is social justice?” and “How does (or can) mathematics look and act when viewed in/through the lenses of social justice?” Taking a critically reflective approach, this article draws the reader into a discussion of what is amiss in the currently promoted picture-perfect marriage of mathematics and social justice, presenting perspectives on both the content and context of mathematics teaching and learning. In this article, the author’s account of her experience in teaching a mathematics curriculum course for prospective middle years' teachers highlights a call to re-imagine the relationship between mathematics and social justice as more than a perfunctory integration of a “statistics and figures” approach. The author’s reflections acknowledge the complexity and potentiality of the relationship while challenging current status quo practices and paradigms in mathematics education. 相似文献
14.
The overarching interest of this study concerns how to outline learning opportunities and support in early childhood education (ECE) without losing its play-based character. More specifically, the study reports an empirical investigation into the evolving activity of a 6.5-year-old child and an adult conversing about the child’s drawing of ‘Numberland’. What the child’s drawing and his discussion about it with the adult tell us about his emergent mathematics skills is analysed. How the child shifts between speaking and enacting as if and as is, and how the adult supports his mathematics understanding through entering into the play-frame are analysed. How imaginary, play-based activities like this can provide the means for ECE and what this implies for the teacher are discussed. 相似文献
15.
Ahmad Faiz 《上海大学学报(英文版)》1998,2(2):108-111
The diagonal Padé approximants for exp (x), tan x and tanh x are obtained in a simple manner by using the property of Legendre polynomials that on [−1,1] P
r1(x) is orthogonal to every polynomial of lower degree. Gauss’s quadrature formula is used to find the denominators of some functions. 相似文献
16.
S M Srivastava 《Resonance》2007,12(2):59-70
In 1931, the great Austrian mathematician Kurt Gödel proved “all consistent axiomatic formulations of number theory include undecidable propositions”. This discovery of Gödel and its proof had enormous repercussions in mathematics and computer science. The proof hinged upon the writing of a self-referential mathematical statement, in the same way as the liar’s paradox — I am lying — is a self-referential statement. In this three-part article, we describe Gödel’s discovery and his famous proof. 相似文献
17.
《Early childhood research quarterly》2004,19(1):159-166
Big Math for Little Kids, a comprehensive program for 4- and 5-year-olds, develops and expands on the mathematics that children know and are capable of doing. The program uses activities and stories to develop ideas about number, shape, pattern, logical reasoning, measurement, operations on numbers, and space. The activities introduce the mathematical ideas in a coherent, carefully sequenced fashion, and are designed to promote curiosity and excitement about learning and doing mathematics. The program produces playful but purposeful learning of deep mathematical ideas, and encourages children to think about and express their mathematical thinking. Throughout the program, great emphasis is placed on the development of mathematical and mathematics-related language. Our observations suggest two broad questions for future research: What kinds of competence can children develop in the context of a rich mathematics environment? In what ways can mathematics learning promote language and literacy? 相似文献
18.
This article contends that over a long period of time there was growing support for a student loan scheme. In the event, the Thatcher Government adopted proposals which failed to consolidate that emerging consensus. What was it about the Government's legislation that achieved this political own goal? How can such politically maladroit behaviour be explained? What elements should the legislation have contained if the consensus were to be firmed up and enhanced? These are the key questions which we attempt to answer in this article. 相似文献
19.
Andreas J. Stylianides Gabriel J. Stylianides George N. Philippou 《Educational Studies in Mathematics》2004,55(1-3):133-162
Literature suggests that the type of context wherein a task is placed relates to students' performance and solution strategies. In the particular domain of logical thinking, there is the belief that students have less difficulty reasoning in verbal than in logically equivalent symbolic tasks. Thus far, this belief has remained relatively unexplored in the domain of teaching and learning of mathematics, and has not been examined with respect to students' major field of study. In this study, we examined the performance of 95 senior undergraduate mathematics and education majors in symbolic and verbal tasks about the contraposition equivalence rule. The selection of two different groups of participants allowed for the examination of the hypothesis that students' major may influence the relation between their performance in tasks about contraposition and the context(symbolic/verbal) wherein this is placed. The selection of contraposition equivalence rule also addressed a gap in the body of research on undergraduate students' understanding of proof by contraposition. The analysis was based on written responses of all participants to specially developed tasks and on semi-structured interviews with 11 subjects. The findings showed different variations in the performance of each of the two groups in the two contexts. while education majors performed significantly better in the verbal than in the symbolic tasks, mathematics majors' performance showed only modest variations. The results call for both major- and context- specific considerations of students' understanding of logical principles, and reveal the complexity of the system of factors that influence students' logical thinking. 相似文献
20.
Aiko Oshiro Agneta Pihl Louise Peterson Niklas Pramling 《International Journal of Early Years Education》2019,27(1):82-94
This study reports an analysis of how children in a Japanese kindergarten are scaffolded when facing the challenge of collaboratively retelling a kitsune story they have been told. What is referred to as a kitsune story is an example of a trickster tale with foxes as anthropomorphised animals. The participants were ten 5-year-old children and their teacher. Told a story by their teacher, the children were asked later to collaboratively retell it. How this retelling activity is supported – theorised in terms of the metaphor of scaffolding – is analysed on the basis of recordings. The findings show the nature of this evolving process. The conclusion is that the metaphor of scaffolding may require some contextual specification to remain a functional conceptual – and in extension, pedagogical – tool in activities fundamentally different from the activity studied in Wood, Bruner and Ross’ founding 1976 study. 相似文献