Investigating pupils' images of mathematicians

This paper describes a research project that had two goals: (1) to design and develop a tool with which to investigate pupils' images of mathematicians; and (2) to use the device to compare those images held by lower secondary pupils (ages 12–13) in five countries. We report that with small cultural differences certain stereotypical images of mathematicians are common to pupils in all of these countries and these images indicate that for pupils of this age mathematicians and the work that they do are, for all practical purposes, invisible. This revised version was published online in July 2006 with corrections to the Cover Date.     

Oral reading errors of two young beginning readers

Oral reading errors were collected from two young beginning readers (6 years old) as they read to their class teacher throughout a school year. The data were collected from the naturalistic setting of an infant classroom. The errors of substitution were analysed for graphophonic, syntactic and semantic similarity and examined to determine whether the observed response was a previously read word. The study demonstrated that the two boys frequently used a previously read word as a substitution although there was less reliance upon this source towards the end of the year. The graphophonic cue system was used throughout the year, with first letter similarity particularly in evidence. However, finer discriminations over time were also noted. The contextual constraints of syntax and semantics were in evidence throughout the year and the use of these cues had increased by the end of the year. The evidence from this in–depth case study was used to question previously postulated developmental phases of reading.     

江西籍数学家与浙江数学

有六位江西籍数学家是浙江籍数学家的得意门生,他们受到了浙江籍数学家的教育培养,成为了数学家和数学教育家。他们学成以后,都在浙江工作过,为浙江的数学研究和数学教育作出了贡献。     

Insider accounts of dyslexia from research mathematicians

Educational Studies in Mathematics - Within educational research, dyslexia and other disabilities are typically conceptualized as deficits. The theory of neurodiversity encourages researchers to...     

Investigating the impact of observation errors on the statistical performance of network-based diffusion analysis

Experiments in captivity have provided evidence for social learning, but it remains challenging to demonstrate social learning in the wild. Recently, we developed network-based diffusion analysis (NBDA; 2009) as a new approach to inferring social learning from observational data. NBDA fits alternative models of asocial and social learning to the diffusion of a behavior through time, where the potential for social learning is related to a social network. Here, we investigate the performance of NBDA in relation to variation in group size, network heterogeneity, observer sampling errors, and duration of trait diffusion. We find that observation errors, when severe enough, can lead to increased Type I error rates in detecting social learning. However, elevated Type I error rates can be prevented by coding the observed times of trait acquisition into larger time units. Collectively, our results provide further guidance to applying NBDA and demonstrate that the method is more robust to sampling error than initially expected. Supplemental materials for this article may be downloaded from http://lb.psychonomic-journals.org/content/supplemental.     

Values and norms of proof for mathematicians and students

In this theoretical paper, we present a framework for conceptualizing proof in terms of mathematical values, as well as the norms that uphold those values. In particular, proofs adhere to the values of establishing a priori truth, employing decontextualized reasoning, increasing mathematical understanding, and maintaining consistent standards for acceptable reasoning across domains. We further argue that students’ acceptance of these values may be integral to their apprenticeship into proving practice; students who do not perceive or accept these values will likely have difficulty adhering to the norms that uphold them and hence will find proof confusing and problematic. We discuss the implications of mathematical values and norms with respect to proof for investigating mathematical practice, conducting research in mathematics education, and teaching proof in mathematics classrooms.     

Factors mathematicians profess to consider when presenting pedagogical proofs

This paper concerns proof presentation at the university level. We report on a study in which we observed ten mathematicians constructing or revising proofs for pedagogical purposes. We highlight the factors that they claimed to consider when completing these tasks. We found that intended audience and medium (lecture or textbook) influenced proof presentation. We also found that, although mathematicians generally valued pedagogical proofs featuring diagrams and emphasizing main ideas, these mathematicians did not always incorporate these aspects in the proofs they constructed or revised.     

数学家的成功对数学教育的启示

我国传统的数学教育有成功的地方,也有不足之处。对基本功的过度追求,使学生没有机会自主探索感兴趣的问题,学生无法获得对数学的良好感受。本文分析了历史上数学家的成功经验,指出在数学教学中,应渗透以下教学方法;数学史和数学知识的起源介绍;启发学生进行联想;创造浓厚的交流氛围。     

Why and how mathematicians read proofs: an exploratory study

In this paper, we report a study in which nine research mathematicians were interviewed with regard to the goals guiding their reading of published proofs and the type of reasoning they use to reach these goals. Using the data from this study as well as data from a separate study (Weber, Journal for Research in Mathematics Education 39:431–459, 2008) and the philosophical literature on mathematical proof, we identify three general strategies that mathematicians employ when reading proofs: appealing to the authority of other mathematicians who read the proof, line-by-line reading, and modular reading. We argue that non-deductive reasoning plays an important role in each of these three strategies.     

The beginning of decoding

It is widely agreed that children recognize their first words in a different way than they later decode. One hypothesis is that sight words are recognized as wholes, another that they are recognized by parts. Two experiments were devised to compare these hypotheses. In one, children were taught a sight word accompanied by a salient extraneous cue and then tested for recognition of the word and the cue. In the other, children were taught sight words, then tested for recognition of each half of the word. The children were found to recognize the cue but not the word; they recognized one half of the word but not the other. The results support the idea that first words are recognized by selective association.     

Children's made-up mathematics problems — a new perspective on talented mathematicians

As part of a large scale mathematics study, students were asked to make up a mathematics problem that would be difficult for a friend to solve. They were also asked to solve the problem themselves. A sub-sample of 11- to 13-year-olds was interviewed while they worked through the items in the study.The problems made up by a group of eight more able and eight less able children from this sub-sample are reported here, together with the comments the children made during the interviews about their respective problems.The results highlight features of the problems made up by the two groups of children. In general, the more able children made up problems of greater computational difficulty, with more complex number systems and with more operations than their less able peers. In addition, there is evidence to suggest that the more able students planned their problems and were able to work out the answer, while their less able peers had difficulty with both the planning and the solution of their own problems.As the substance and style of the problem made up by each child uniquely reflects that child's mathematical experiences and ideas, the made up problem is a particularly useful tool for studying mathematically talented children for whom routine tasks are usually completed quickly and accurately.     

A beginner's beginning

Seventeenth‐Century Lyrics. By Alexander Corbin Judson (Indiana University). Chicago: University of Chicago Press, 1927. Pp. xx + 413. Price, $2.50.

The Golden Trumpets. By Blanche Jennings Thompson. New York: The Macmillan Co., 1927. Pp. x + 163.

Essentials of Electrical Work. By George A. Willoughby. Peoria, Ill.: The Manual Arts Press, 1927. Pp. 242. Price, $1.60.

With the Circus. By Courtney Ryley Cooper. Boston: Little, Brown &; Co., 1927. Pp. vi + 212. Price, 75 cents.

Old Testament Stories. By Eulalie Osgood Grover. Boston: Little, Brown &; Co., 1927. Pp. x + 309. Price, 85 cents.

History of Socialist Thought. By Harry W. Laidler. New York: Thomas Y. Crowell Co., 1927. Pp. xxii + 713. Price, $3.50.

The Organisation and Administration of Playgrounds and Recreation. By Jay B. Nash. New York: A. S. Barnes &; Co., 1927. Pp. xii + 547. Price, $4.

Historical Foundations of Modern Education. By Edward H. Reisner. New York: The Macmillan Co., 1927. Pp. xvi + 513. Price, $2.60.

Algebra, Book II. By William Raymond Longley and Harry Brooks Marsh. New York: The Macmillan Co., 1927. Pp. xii + 457.

Swimming Simplified. By Lyba and Nita Sheffield (Universities of California and Columbia). New York: A. S. Barnes &; Co., 1927. Pp. xiii + 297. Price, $2.

The Reorganization of Mathematics in Secondary Education (Part I). By John Wesley Young. Boston: Houghton Mifflin Co., 1927. Pp. xiv + 181. Price, $1.20.

Principles of Secondary Education. By L. A. Williams and G. A. Rice (University of California). Boston: Ginn &; Co., 1927. Pp. xi + 339. Price, $2.

Outlines of Historical Study. By George W. Robinson (Harvard University). Boston: Ginn &; Co., 1927. Pp. vii + 375. Price, $2.40.

Human Thinking. By Arthur Cary Fleshman (Converse College). Spartanburg, S. C: Piedmont Publishing Co., 1927. Pp. 58.

The Philosophy of Education. By Herman H. Horne (New York University), Revised Edition. New York: The Macmillan Co., 1927. Pp. xvi + 329.

A First Course in the New Mathematics. By Edward I. Edgerton and Perry A. Carpenter. Boston: Allyn &; Bacon, 1927. Pp. viii + 348.

Preventive Medicine. By Mark F. Boyd. Philadelphia: W. B. Saunders Co., 1925. Pp. 429.

Football Conditioning. By Holger Christian Langmack. New York: A. S. Barnes &; Co., 1926. Pp. xi + 48. Price, $1.50.

Prehistoric Man—Life in the Old and New Stone Ages, By Mary E. Boyle. Boston: Little, Brown &; Co., 1924.

Creative Education. By Henry Fairfield Osborn (President, American Museum of Natural History). New York: Charles Scribner's Sons, 1927. Pp. xiv + 360. Price, $2.50.

Children's Stories That Never Grow Old. Adapted by Mary Stone. Chicago: The Reilly &; Lee Co. Pp. 248. Price, $1.50.

Skeezix at the Circus. By Frank King. Chicago: The Eeilly &; Lee Co., 1926. Pp. iii + 106. Price, $1.

Children's Poems That Never Grow Old. Compiled by Clement F. Benoit. Chicago: The Reilly &; Lee Co., 1922. Pp. xxii + 298.

Recitations for Younger Children. Compiled and edited by Grace Gaige. New York: D. Appleton &; Co., 1927. Pp. xviii + 215. Price, $2.

Nature Study and Health Education. By Alice Jean Patterson. Normal, Ill.: McKnight &; McKnight. Fourth Year, xii + 131 pp.; Fifth Year, 192 pp.; Sixth Year, 224 pp.     

Why and how mathematicians read proofs: further evidence from a survey study

In a recent paper (Weber & Mejia-Ramos, Educational Studies in Mathematics, 76, 329–344, 2011), we reported findings from two small-scale interview studies on the reasons why and the ways in which mathematicians read proofs. Based on these findings, we designed an Internet-based survey that we distributed to practicing mathematicians working in top mathematics departments in the USA. Surveyed mathematicians (N?=?118) agreed to a great extent with the interviewed mathematicians in the exploratory studies. First, the mathematicians reported that they commonly read published proofs to gain different types of insight, not to check the correctness of the proofs. Second, they stated that when reading these proofs, they commonly: (a) appeal to the reputation of the author and the journal, (b) study how certain steps in the proof apply to specific examples, and (c) focus on the overarching ideas and methods in the proofs. In this paper, we also report findings from another section of the survey that focused on how participants reviewed proofs submitted for publication. The comparison of participant responses to questions in these two sections of the survey suggests that reading a published proof of a colleague and refereeing a proof for publication are substantially different activities for mathematicians.     

最牛的开篇

我们经常会在各种媒体上听到有人引用类似“这是最美好的时代，这又是……”这样的句子，感觉这简直是绝妙的修辞：把一个难以形容的，复杂而又充满活力的激荡时代呈现在我们面前，自己身处何处，如何理解，全由听者去回味。     

Between end and beginning

2002 is marking the epoch as considered here. It is still within the interval Freudenthal once made predictions for, rather provocative predictions, I must confess. I quote a lecture from 1975: ‘What to predict now? How mathematics education will look like in the year 2000? The answer is simple. There will be no mathematics education anymore in the year 2000. It will be gone. There will be no subject, called mathematics anymore, no mathematics lesson on the schedule, no textbook to teach from. Don't call me ‘this devil's advocate’, I àm the devil'. In the present contribution Freudenthal's predictions will be both confirmed and refuted. This means mathematics education is underway to getting integrated in other subjects to some extent, but on the other hand.... After an example of geometry from a new program, which is on blind spots captains of ships have to deal with while navigating, the arguments justifying the renewal of mathematics programs in secondary education are considered. Then the essentials of the olds will be characterised globally. However, what is left then, are the problems of implementation. The problems for the teachers evolve from the decisive differences between the old-fashioned rules and routines oriented programs and the new, problem oriented programs, containing a wealth of situations embedded in all kinds of interesting contexts. Differences in structure, in goals, in teaching, in tests and exams pas the review. Modern technology and its possibilities and promises are of my concern in the next chapter. Finally some conditions to be created by policy makers, are elaborated which to some extent would guarantee some sound development of mathematics education up to the year 2002. One of Freudenthal's predictions seems to come through: In the year 2000 pupils in general, secondary education will pick up more mathematics than ever before, or so it seems.     

Mathematical experiences and parental involvement of parents who are and who are not mathematicians

Previous studies suggest that parental involvement in children’s mathematics education is more established for parents who feel competent in mathematics. This qualitative study aimed to gain an in-depth insight into the experiences of parental involvement of two different groups of parents: those who are mathematicians and those who are not. Data were collected through narrative interviews with parents. A thematic analysis of the data revealed findings within two distinct but interrelated themes: parents’ mathematical experiences and parental involvement in their children’s mathematics education. The findings indicated that the two groups of participating parents differ in their own experiences of mathematics as well as in their parental involvement. The main difference in parental involvement was indicated in the area of children’s school mathematics, since mathematician parents, compared to non-mathematician parents, according to their narratives almost never get involved in their children’s mathematics homework. In addition, the data revealed a large gap in the coverage and content of the mathematical activities that parents in both groups provided to their children.