On mathematical understanding: perspectives of experienced Chinese mathematics teachers

Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers’ views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result of continuous connection making. However, in contrast to the popular view which separates understanding into conceptual and procedural, Chinese teachers prefer to view understanding in terms of concepts and procedures. They place more stress on the process of concept development, which is viewed as a source of students’ failures in transfer. To achieve mathematical understanding, the Chinese teachers emphasize strategies such as reinventing a concept, verbalizing a concept, and using examples and comparisons for analogical reasoning. These findings draw on the perspective of classroom practitioners to inform the long-debated issue of the meaning of mathematical understanding and ways to achieve mathematical understanding.     

略论数学建模教育与高校数学教学方式改革

本文阐述了数学建模教育与高校数学教学方式改革的相关理论问题,分析了当前高校数学建模教育中存在的问题,并就完善数学建模教育方式提出了相关建议。     

The mathematical vitality of secondary mathematics graduates and prospective teachers: A comparative study

This article links two areas of contemporary interest in mathematics education. These are respectively; mathematical characteristics of prospective teachers, and the notion of levels of understanding.The study reported here considered questions relating to the mathematical appreciation of successful students at both senior secondary (university entrance) and tertiary level. The tertiary students were graduates embarking upon a post-graduate course of teacher-training.It was found that response patterns were stable across a variety of institutions, geographical regions (Australian States), and education systems. Mathematical malfunctions present among secondary graduates were found to exist in substantially the same proportions among the graduate teacher trainees. It was found that the type of understanding sought in this study was not enhanced merely by taking more mathematics courses. The problem of recycling of attitudes and mathematical misconceptions within the secondary teaching structure is addressed, and the question of the approach to the study of mathematics at both secondary and tertiary level is raised as a matter of continuing concern.     

Stability of educational goal orientations held by teachers

This study assesses the temporal stability of teacher goal orientation and identifies factors associated with change. Seventy-four elementary teachers responded to questionnaires and interviews over a 4-year period. Teacher goal orientation was found to be a relatively stable construct, as few teachers made major and enduring shifts in goal orientation. Subjects identified a variety of factors as contributing to change in goal orientation, with student behavior emerging as a primary impetus for change. Contrary to expectation, shifts in goal orientation were most often exhibited by the more highly experienced teachers in the study. Implications are discussed.     

Factor analysis and psychometric evaluation of the mathematical modeling attitude scale for teachers of mathematics

Journal of Mathematics Teacher Education - The effective teaching and learning of mathematics through mathematical modeling and connecting mathematics to the real world has gained rapid growth at...     

Degrees held by the presidents of state teachers colleges

Curriculum Development: Theory and Practice. By Hilda Taba. (New York: Harcourt, Brace &; World, Inc., 1962. Pp. 529. $6.95.)

The Education of the Secondary School Teacher. Edited by Ernest Stabler. (Middletown, Conn.: Wesleyan University Press, 1962. Pp. 239. $5.00.)

Psychology in the Making: Histories of Selected Research Problems. Edited by Leo Postman. (New York: Alfred A. Knopf, 1962. Pp. 785. $9.00.)

Supervision: A Synthesis of Thought and Action. By William H. Lucio and John E. McNeil. (New York: McGraw‐Hill, 1962. Pp. 282. $6.50.)

Soviet Education: Anton Makarenko and the Years of Experiment. By James Bowen. (Madison, Wis.: The University of Wisconsin Press, 1962. Pp. 232. $5.00.)

Teacher Education: A Reappraisal. Edited by Elmer R. Smith. (New York: Harper and Row, 1962. Pp. 213. $4.00.)     

A capstone mathematics course for prospective secondary mathematics teachers

This article describes an innovative capstone mathematics course that links college mathematics with school mathematics and pedagogy. It describes how college juniors in a secondary mathematics teacher preparation program engage in leadership experiences that enable them to learn mathematics for teaching while developing student-centered pedagogical and assessment strategies. Examples show how students teach the class, complemented by excerpts from student journals containing students?? perceptions of their learning. Preliminary research indicates the effectiveness of this course for preparing future mathematics teachers.     

Using technology to explore mathematical relationships: a framework for orienting mathematics courses for prospective teachers

The technological revolution that has finally permeated K-12 education has direct implications for modern teacher educators whose “Hippocratic oath” is to best prepare future teachers for twenty-first-century classrooms. The goal of this article is to suggest that the heart of sound technological implementation is to encourage students to use whatever tools are available to explain the mathematical relations that underlie what they observe on the screen. We suggest ways in which Mishra and Koehler’s construct of Technological Pedagogical Content Knowledge may be customized to provide a framework for guiding prospective teachers’ efforts to develop and assess lesson plans that use technology in novel and effective ways. Data are presented in the form of two contrasting case studies to illustrate the differing degrees to which prospective mathematics teachers leveraged technology to teach themselves and their future students to explain the mathematics behind various topics.     

Preparing teachers for realistic mathematics education

A shift in mathematics education in the Netherlands towards the so-called realistic approach made it necessary to prepare prospective teachers for a type of curriculum different from what they experienced as pupils. This article describes the characteristics of a preservice programme aiming at this goal and presents an analysis of the development of the student teachers' views of mathematics and mathematics education during the programme as well as their classroom behaviour. This analysis is based on two research studies. The first was a longitudinal study in which the student teachers were followed during years by means of questionnaires and interviews. The second was a study in which graduates from this programme were compared with graduates from a more traditional preparation programme by means of two teacher questionnaires and a pupil questionnaire, the latter measuring the pupils' perceptions of the actual teaching behaviour of the graduates. The teacher education programme appeared to be successful in changing the student teachers' views of mathematics education, especially in the direction of a more inquiry oriented approach, and in promoting effective teacher behaviour in the classroom. As far as their facilitating role as a teacher is concerned, the student teachers seemed to go through a two-stage learning process. Most of them reached the first stage, in which they realize that pupils have different preferences for learning and that a variety of possible explanations for problems should be offered. However, only a small number of student teachers seem to reach the second stage, in which they recognize the principle of building on pupils' own constructions, an important feature of realistic mathematics education. Possible explanations for the low impact of the programme, as well as solutions are discussed.     

数学教师专业化与高师数学教育专业课改

数学教师专业化是世界数学教师教育的发展潮流,其内涵包括:数学教师数学专业化、数学教师教育专业化和数学教师专业情意.当前高师数学教育在课程设置上不适应数学教师专业化要求,改革重点是构建合理的课程体系.     

Training mathematics teachers at a distance

This article describes the development, with the help of international aid, of a distance education course for secondary school teachers located in a number of Caribbean countries. The course was designed to cover both content and teaching methods, and was able to introduce difficult and challenging ideas with some degree of success. The author of the course, and of this paper, Paul Ernest, is now at the University of Exeter.     

过年忙 忙过年

小寒大寒,立春过年。日子过得就是这么快,转眼间又要过年了。按理说,“年”是一个节日,是一个可以休息和娱乐的假期,其实不然。有人曾经问我过年是什么感觉,我说就是一个字：忙!年味是忙出来的,大家都在忙着过年,越忙年味就越浓。     

Concerns of new university teachers

Eighty-one newly appointed university teachers at the University of Copenhagen were interviewed about their concerns in connection with their forthcoming class-room début. It appeared that most of them had some previous teaching experience. Only one out of four had never taught before. Primary among their concerns ranked problems with their personal subject matter adequacy and with organizing and verbally presenting subject matter in an adequate form. A comparison of their chief concerns with the content components that are most frequently included in education courses for University staff, suggests that some of the latter have little relevance for specifically beginner teachers. A particular analysis of inexperienced new teachers relative to those with ample previous experience unequivocally supports the assumption that inexperienced new teachers are primarily ego-centered in their concerns whilst their more experienced colleagues are primarily teaching- or student-centered in their concerns about teaching. The implications for the design of training programmes for university staff are discussed.     

Images of the limit of function formed in the course of mathematical studies at the university

The paper is based on extensive research carried out on students of mathematics who had completed a university course of calculus. The basic purpose of the research was to determine the students' images of the concept of limit, that is to find out their associations, conceptions and intuitions connected with limits and to determine the degree of their efficiency and the sources of their formation. To achieve the objectives an expanded set of selected problems — simple but not quite standard — and various other research instruments were used. Several classes of images of the limit concept have been identified and described, according to their main foci: neighborhoods, graph approaching, values approaching, being defined at x₀, limit of f atx₀ equals f(x₀), and algorithms.