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1. Classroom Assessment in Japanese Mathematics Education.

Author

Nagasaki, Eizo and Becker, Jerry P.

Abstract

In Japan, assessment in classroom teaching cannot be considered apart from classroom lessons. This paper describes typical mathematics classroom situations and some of the developments in classroom assessment underway in Japan. The first section of the paper discusses classroom teaching, including whole-class instruction, discussion, objectives, and the importance of lesson plans and records. Next, assessment practices during and after lessons are discussed. Two long-term research projects to assess higher-order thinking are then considered. The Open-End Approach to Teaching Mathematics Project included three types of open-ended mathematics problems: how to find rules or relations, how to classify, and how to measure. Students' achievement was evaluated in terms of fluency, flexibility, and originality. The Developmental Treatment of Mathematics Problems Project had features similar to the Open-End project, except that students formulated or posed problems of their own. Student evaluation was conducted from three points of view: by the number of problems, by how the students formulated their problems, and by the direction of development from the given problem. Samples of lesson plans, classroom dialogue, and sample problems formulated by both teachers and students are provided throughout the document. Contains 25 references. (MKR)

Published
1993

2. Report of U.S.-Japan Cross-National Research on Students' Problem Solving Behaviors.

Author

Southern Illinois Univ., Carbondale. Dept. of Curriculum, Instruction and Media. and Becker, Jerry P.

Abstract

In 1986 the United States (U.S.)-Japan Seminar on Mathematical Problem Solving convened to compare the state of problem solving in the classroom and in research in the two countries. The data and results given in this paper are the results of research conducted in the United States in response to the 1986 seminar. The U.S. and Japanese research groups decided to collect problem solving data at the 4th, 6th, 8th, and 11th grade school levels. Problems were collected from a pool of problems submitted by both the United States and Japan. U.S. subjects were from at least two 4th-, 6th-, 8th-, and 11th-grade classes from large rural, small urban, and large urban schools in areas around Carbondale and Champaign/Urbana, Illinois; Pittsburgh, Pennsylvania; Gainesville, Florida; and Athens, Georgia. In addition to the problems, student questionnaires collected data on students' attitudes towards problem solving, their comparison of the problems to textbook problems, and their reactions to the problems. A teacher questionnaire collected information about the schools, teachers' views of their classes, their reactions to the problems, and their perceptions of how students worked on problems. These questionnaires are included in the appendix. Five research reports include the results for each of five problems developed for varying grade levels, as follows: (1) the "Marble Arrangement Problem" for grade 4 (researched by E. Silver, S. Leung, and J. Cai); (2) the "Matchsticks Problem" for U.S. students in grades 4 and 6 (M. Hart and K. Travers); (3) the "Marble Pattern Problem" for U.S. students in grades 6, 8, and 11 (K. Fouche and M. Kantowski); (4) the "Arithmogons Problems" for U.S. students in grades 8 and 11 (J. Becker and A. Owens); and (5) the "Areas of Squares Problem" for U.S. students in grade 11 (J. Wilson). (Contains 39 references, as well as references with chapters.) (MDH)

Published
1992

3. The United State-Japan Seminar on Computer Use in School Mathematics. Proceedings. (Honolulu, Hawaii, July 15-19, 1991).

Author

Southern Illinois Univ., Carbondale. Dept. of Curriculum, Instruction and Media., Becker, Jerry P., and Miwa, Tatsuro

Abstract

The purpose of a seminar attended by mathematics educators from the United States and Japan was to explore ways that use of technology in teaching problem solving can improve student learning. The following presentations were made: (1) "A Report of U.S.-Japan Cross-cultural Research on Students' Problem-Solving Behavior," (T. Miwa and T. Fujii); "Results of U.S.-Japan Cross-cultural Research on Students' Problem-Solving Behaviors" (J. Becker); (3) "An Overview of Computer Use for Mathematical Problem Solving in Japanese Schools" (T. Miwa); (4) "Calculators, Computers, and Algebra" (J. Fey); (5) "Using Construction Programs in the Teaching of Geometry" (J. Choate); (6) "On the use of Software in Mathematics Classrooms in Japan" (Y. Sugiyama, T. Kaji, and Y. Shimizu); (7) "Graphing in the K-12 Curriculum: The Impact of the Graphing Calculator" (F. Demana); (8) "A Study of Problem Solving with Cabri-Geometry in Secondary School Mathematics" (N. Nohda); (9) "Some Examples of Mathematics Instructional Software in Japanese Classrooms" (S. Sakitani and S. Iida); (10) Software Demonstrations by the Japanese Delegation (Y. Morimoto); (11) "Where Do Functions Come From? Data Analysis in Secondary Mathematics" (D. Teague); (12) "The Use of Computers in Schools: Some Findings From National and International Surveys" (T. Sawada); (13) "The Use of Computers in Schools: The State of Using Computers in Mathematics Classrooms in Japan" (K. Kumagai); (14) "Presentation of the Hawaii Geometry Learning Project to the U.S. Japan Seminar" (W. G. Martin) (handout provided at seminar); (15) "Computer Use in Teaching Mathematical Problem Solving--Pre-Service Teacher Education at Yokohama National University" (Y. Hashimoto); (16) "Graphical Reasoning for New Approaches to Topics in Mathematics" (S. Dugdale); (17) Software Demonstration by U.S. Delegation (J. Choate and D. Teague); (18) "Mathematical Visualization in Problem Solving Facilitated by Computers" (J. Wilson); (19) "Mathematical Education in a High-Technological Information Oriented Society--What Should It Be?" (T. Uetake); (20) Summary of Seminar (T. Miwa and J. Becker). A delegates list, opening and closing statements, proposed topics for further study, descriptions of software, and a list of supplementary papers are included. (MDH)

Published
1992

5. Preservice Teachers’ Conceptual and Procedural Knowledge of Fraction Operations: A Comparative Study of the United States and Taiwan

Author

Lin, Cheng-Yao, Becker, Jerry, Byun, Mi-Ran, Yang, Der-Ching, and Huang, Tsai-Wei

Abstract

This study examined (a) the differences in preservice teachers’ procedural knowledge in four areas of fraction operations in Taiwan and the United States, (b) the differences in preservice teachers’ conceptual knowledge in four areas of fraction operations in Taiwan and the United States, and (c) correlation in preservice teachers’ conceptual knowledge and procedural knowledge of fractions in Taiwan and the United States. Participants were preservice teachers ("N" = 49) in a teacher education program in the United States and comparable Chinese preservice teachers ("N" = 47). Results indicated that Chinese preservice teachers performed better in procedural knowledge on fraction operations than American preservice teachers. No significant differences were found for conceptual knowledge on fraction division. Further, the correlation in this study showed that for Chinese and American preservice teachers, the relationship between conceptual and procedural knowledge of fraction operations was weak. (Contains 4 tables and 1 figure.)

Published
2013
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6. Foreign and Domestic Journals in Mathematical Education. Revised Edition.

Author

National Council of Teachers of Mathematics, Inc., Reston, VA. and Becker, Jerry P.

Abstract

This document lists periodicals devoted to mathematics education which are published throughout the world. One hundred sixty-eight journals from 61 countries, and four journals of international organizations concerned with mathematics education are included. Each listing provides the journal title, an address from which information is available, and the language in which it is published. Brief descriptions are provided for many of the journals. (SD)

Published
1976

7. Proceedings of the U.S.-Japan Seminar on Mathematical Problem Solving (Honolulu, Hawaii, July 14-18, 1986).

Author

Southern Illinois Univ., Carbondale., Becker, Jerry P., and Miwa, Tatsuro

Abstract

The main purposes of the seminar were to examine the present status of school mathematics problem solving; to explore classroom practice and what is known about research; to compare the situations appearing in textbook word problems; and to make plans for cross-cultural research in both countries. A paper from each country was presented during the eight sessions. The session topics were: (1) "The Present States of Problem Solving in the U.S. and Japan"; (2) "Classroom Practice of Problem Solving"; (3) "Comparison of Achievement"; (4) "Comparison of Situations Appearing in Word Problems"; (5) "Typical Word Problem Solving"; (6) "Pattern Finding"; (7) "Non-Routine Problem Solving"; and (8) "Mathematical Modelling." The closing session was an open discussion on the formulation of the seminar and joint cross-cultural research and the formation of a joint study group. A discussion of the findings and proposals is given, and an appendix includes examples of problems in mathematics for the entrance examinations to national and private universities in Japan. (YP)

Published
1987

8. Mathematics Teaching in Japanese Elementary and Secondary Schools--A Report of the ICTM Japan Mathematics Delegation (1988).

Author

Illinois Council of Teachers of Mathematics, Carbondale. and Becker, Jerry P.

Abstract

A delegation of 22 mathematics educators sponsored by the Illinois Council of Teachers of Mathematics visited Japan September 23-October 11, 1988. The group included teachers from elementary through university levels. The group visited 16 schools, 2 teacher training colleges, a scientific university, and 2 juku schools in the four major population centers of Tsukuba, Tokyo, Nagoya, and Osaka. Visits also included bookstores, factories, and cultural sites. School visits included briefing, classroom visits, and discussions with teachers. Similarities and differences between Japanese and American societies and education are identified. The Japanese mathematics curriculum content for grades 1 through 12 is described. Other topics included are Japanese educational change, uses of technology, and implications for mathematics teaching in the United States. Four tables and 22 references are included. (DC)

Published
1989

9. Integrating Problem Solving into Mathematics Teaching. Summaries of Problem Solving Teaching Units.

Author

Becker, Jerry P. and Foland, Neal E.

Abstract

These units were developed during the summer of 1987 as one component of a project on "Integrating Problem Solving Into Mathematics Teaching." Each unit has the objective of developing students' thinking abilities in mathematics. These units have been revised subsequent to field try-outs prior to dissemination. The summaries of 56 different teaching units, organized by levels (K-3, 4-6, 7-9, 10-12), are provided in this document. Each includes a title, a brief description, and the author's name. A list of author names and addresses is appended. (CW)

Published
1989

10. Research in the Teaching and Learning of Mathematics.

Author

Becker, Jerry P. and Rogers, Lloyd V.

Abstract

This paper is a report of a symposium on research in mathematical learning and teaching held during the annual meeting of the California Mathematics Council in 1966. Speakers and their topics were: Professor Frederick J. McDonald - "The Teaching of Mathematics"; Dr. John E. Coulson - "The Learning of Mathematics"; Professor Zoltan P. Dienes - "Research and Evaluation in Mathematics Learning". Introductory remarks were made by Dr. Jerry P. Becker. (Author/FL)

Published
1969

31. Politics of California School Mathematics, The The Anti-Reform of 1997- 99

Author

Becker, Jerry P. and Jacob, Bill

Subjects
Universities and colleges -- Curricula, Educators -- Beliefs, opinions and attitudes, Schools -- Management -- California, Mathematicians -- Beliefs, opinions and attitudes, Education -- Standards, Mathematics -- Study and teaching, Education, Company business management, Management, Beliefs, opinions and attitudes, Curricula, Standards, Study and teaching
Abstract

The authors tell the story of a powerful group of parents and mathematicians in California who manipulated information and played off of the public's perception of our 'failing schools' to [...]

Published
2000

36. The role of technology in the cognitive development of mathematics learners

Author

Ipke Wachsmuth and Becker, Jerry P.

Abstract

This article reports on information disseminated and discussions and recommendations elaborated in the theme group on "Technology and Cognitive Development" at the Fifth International Congress on Mathematical Education (ICME 5) which took place in Adelaide, Australia, August 1984. In a four-session working program, the group focused on three questions around which this report is organized: 1. The use of technology to further the cognitive development of learners of mathematics; 2. The use of technology to achieve a better understanding of the processes involved in the development of children's cognitive structures relevant to mathematics; 3. Possible disadvantages connected with the use of technology.

Published
1986

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