Search

This study was aimed to analyze how students’ mathematical ideas emerged through a flow of lesson in mathematics classroom using Lesson Study and Open Approach. A context of the study was the Open Approach as a teaching approach and the Lesson Study as a way to improve the quality of teaching (Inprasitha, 2015a). The flow of lesson, likewise, is considered to be a tool for accessing to students’ ideas when the students are involved in problem solving and connection between students’ real world and mathematical real world (Inprasitha, 2017b). Ethnographic study was employed as a research methodology in this qualitative study by using a participative research design to form a lesson study team for collaborative designing of lesson plans guided by Thai version of Japanese mathematics textbooks. Research results were shown that the students’ mathematical ideas emerged, through the flow of lesson, when the students’ ideas of a problem solving were mathematized as follows: 1) the mathematical ideas were extended through representations of real world, 2) the mathematical ideas were extended and generalized through semi-concrete aids, and 3) the mathematical ideas were generalized through representations of mathematical world. The processes of mathematization (Isoda & Katagiri, 2012), furthermore, were accomplished when the students’ mathematical ideas become “how to” or tools for learning for the next lessons.

This research aims to analyze how and what teachers learn in community of implementing mathematics textbooks with Lesson Study and Open Approach about addition in number and operations for first grade. The participants were 2 teachers who use the textbook in the classroom using Lesson Study and Open Approach. The mathematics textbooks for this study were Japanese mathematics textbooks (Thai version), and consist of mathematics activities, flow of lesson, and students’ mathematical ideas (Inprasitha, 2015b). The data were collected in October 2015 by interview and classroom observation with video recording. The data were analyzed based on communities of practice (CoP) from Wenger, McDermott, & Snyder (2002), and Shulman & Shulman (2004). The result of this research found that how and what teachers learned in community of implementing mathematics textbooks with Lesson Study and Open Approach, are 2 aspects: 1) teachers learned about the content of mathematics from their sharing on the textbook and students’ ideas together, and 2) teachers learned how to teach the content, through using the textbook for sharing anticipating students’ ideas, observing students’ ideas, and reflecting by using evidence from students’ ideas that appeared in classroom.

This study examines the difficulty level of mathematics textbooks in junior secondary schools in China, the USA, South Korea, Singapore, and Japan. The analysis uses a novel framework which focuses on content breadth, content depth, difficulty level of worked examples, and difficulty level of exercises. Based on the analysis of five selected topics—numbers and calculation, equations, triangles, solids, and statistics—China has the most difficult textbooks, followed by South Korea and Singapore. The US difficulty levels are quite similar to those in Japan, which has the easiest textbooks. In addition, the selected Chinese mathematics textbook seems to value “shapes and geometry” most significantly among the five nations, whereas the selected US textbook seems to emphasize “numbers and calculation.” Furthermore, it is found that the selected Japanese mathematics textbook series involves the least amount of mathematics, and also shows a lack of statistics.

Mathematics education community in Japan has continuously and extensively developed 'mathematical thinking' as an educational value. In this paper, the historical review was conducted on mathematical thinking in terms of its evaluation and educational method, textbook change, and research on treatment of diversified mathematical thinking. This approach can provide methodologically an important perspective to grasp, clarify and make relative the values in mathematics education in different times of each culture. Values here mean those attitudes which lay at the back of the intention, judgment, and selection of teaching-learning activity exhibited by primary teachers. As a result of this research, it is learnt that the theme in mathematics education research does reflect values held by the primary mathematics teachers. They, in turn, have held central ideas and value utilizing children's diversified mathematical thinking, letting them subjectively and extensively construct mathematical ideas in the lesson. The major characteristics of Japanese Mathematics education is the open-ended approach, which has been developed as an evaluation and educational method of mathematical thinking. This is available as translated version of 'The Open-Ended Approach: A New Proposal for Teaching Mathematics' (The original version (Shimada) is in Japanese published in 1977).

This article presents an instructional model (inclusively responsive instruction) that takes advantage of student diversity in order to differentiate student learning while maintaining high expectations. In the history of U.S. education, diversity and academic rigor were often considered at odds, and educators tried to emphasize one at the expense of the other. This article uses a detailed set of examples from Japanese mathematics education to illustrate how diverse ideas, as important resources, can drive classroom instruction. Teaching and learning supports are described that are essential to helping all teachers balance group and individual learning in classrooms. Current U.S. instructional approaches and the model of inclusively responsive instruction are compared in terms of balancing diversity and academic expectations.

This study aims to capture similarities and differences in teachers’ questioning in German and Japanese mathematics classrooms, specifically focusing on the stage of introducing new mathematical content. The author analyzed consecutive mathematics classes taught by experienced teachers in Germany and Japan, who were recruited based on their locally defined “teaching competence” in the Learner’s Perspective Study. The results revealed that even questions that required students to recall previously learned content or provide the results of a calculation, which were regarded as lower cognitive questions in previous studies, played key roles at the stage of introducing new mathematical content in both German and Japanese classrooms. Further, distinctive patterns in the sequences of teachers’ questioning were identified. These differences suggest what is valued as quality mathematics teaching in each educational system.

A book entitled ‘University Students who Cannot Calculate Fractions’ published at the end of 1990s in Japan (edited by Okabe k. et. al, 1999) aimed to disclose the mathematical level of Japanese University Students by testing them with primary and secondary school level math quizzes. The 20% of them could not even solve fraction questions that children learn at primary school. This fact is indeed problematic for them to study Economics in higher education. Our study thus investigated how Japanese mathematics education has improved after 20 years of this book publication by testing university students with the same math questions used in the previous survey. The results were indifferent from the previous ones proving that the mathematics education in Japan was not innovated in these 20 years. Our paper explored what kinds of mathematical knowledge would disturb the current Japnese university students for understanding fundamental subjects such as Macro and Micro Economics. The results clarified the mathematical components they felt difficulty for understanding as well as their feelings of dislike for math. They are in the category of basic mathematical knowledge used in Economics, meaning that the education of this field is not sufficient and adequate for Japanese university students. This category is characteristic for Japanese university`s curriculum,called Economic Mathematics. Our paper pointed out that the education of mathematical knowledge for understanding Economics including curriculums must be drastically developed. By doing so, students who do not even understand primary level fractions should be able to adequately understand Economics in higher education. As a result, our original textbook based upon the research outcomes will be created.

Previous research gives evidence that Japanese mathematics teachers “may have a more detailed and widely shared theory about how to teach effectively” when compared to their U.S. counterparts (Jacobs & Morita, 2002). This study explores the conceptions and cultural scripts of a group of Japanese mathematics teachers by analyzing the conversations between cooperating teachers and student teachers. It describes 6 principles of high-quality instruction that arose in at least half the conversations we analyzed. Each of these principles is examined in detail. Finally, some advantages of having a strong, shared conception of high-quality instruction and focusing on widely applicable instructional principles are presented.

This study was designed to determine the perceptions of five concerned groups about the outcomes for the elementary school mathematics curriculum in Japan. The outcomes and a Likert-type scale were submitted to the following concerned groups: (a) elementary school mathematics teachers; (b) elementary school principals; (c) mathematics educators; (d) professors of education; and (e) scientists, mathematicians, and engineers. The list of outcomes contained 71 statements of outcomes expected to result from the study of mathematics. These were based on the four major headings of (a) general skills; (b) attitude, interests, and appreciations; (c) knowledge; and (d) intellectual abilities and skills. The ordinal ranks were determined by mean ratings of each outcome for each group. Nine outcomes were ranked by all concerned groups in the first quartile. Twenty-three other outcomes were ranked by one or more concerned groups in the first quartile. The correlation of perceptions between each pair of the c...

This brief report compared the lesson on addition and subtraction of signed whole numbers in three seventh-grade Japanese mathematics textbooks with the corresponding lesson in four U.S. mathematics textbooks. The results indicated that Japanese books contained many more worked-out examples and relevant illustrations than did the U.S. books, whereas the U.S. books contained roughly as many exercises and many more irrelevant illustrations than did the Japanese books. The Japanese books devoted 81% of their space to explaining the solution procedure for worked-out examples compared to 36% in U.S. books; in contrast, the U.S. books devoted more space to unsolved exercises (45%) and interest-grabbing illustrations that are irrelevant to the lesson (19%) than did the Japanese books (19% and 0%, respectively). Finally, one of the four U.S. books and all three Japanese books used meaningful instructional methods emphasizing (a) multiple representations of how to solve worked-out examples using words, symbols, and pictures and (b) inductive organization of material beginning with familiar situations and ending with formal statements of the solution rule. The results are consistent with classroom observations showing that Japanese mathematics instruction tends to emphasize the process of problem solving more effectively than does U.S. mathematics instruction ( Stevenson and Stigler, 1992 ).

This report deals with U.S.-Japan cross-national mathematics achievement results and problem solving and creativity of U.S. and Japanese students. It addresses U.S. misconceptions about Japanese mathematics education and responds to “explanations” for low U.S. mathematics achievement. Various factors accounting for superior Japanese achievement are presented and discussed, including social, cultural, and mathematical education factors such as the “open approach” to teaching. U.S.-Japan cross-national research results on students’ problem solving behaviors are also reported. The paper concludes with some observations concerning what can be learned from the Japanese.

The theme of the International Commission on Mathematical Instruction study ‘What Is Research in Mathematics Education, and What Are Its Results?’ has also been of increasing concern among Japanese mathematics educators. One reason is a gap in interests between researchers and mathematics teachers. Mathematics teachers tend to expect direct and specific prescriptions to solve the problems they experience in their classrooms, whereas researchers tend to address problems raised in research communities that are not always directly related to teachers’ concerns.

Japan's stature as an economic and political power worldwide has caused growing interest in the country's culture and. more specifically, its system of educating its youth. International comparisons of mathematics achievement highlight Japanese students' unquestioned superiority in mathematical performance. Factors that contribute to the relatively high performance include the nature of Japanese schools, the professional stature of teachers, the homogeneity of the school population, the high parental expectations for the educational success of their children, the abundance of jukus (special cram schools), and heavy reliance on entrance and qualifying examinations.

This article describes a novel assessment method used to examine Japanese and American teachers’ ideas about what constitutes effective mathematics pedagogy. Forty American and 40 Japanese teachers independently evaluated either an American or Japanese mathematics lesson captured on videotape. Their comments were classified into over 1600 idea units, which were then sorted into a hierarchy of categories derived from the data. Next, the authors hypothesized underlying ideal instructional scripts that could explain the patterns of responses. Whereas the U.S. teachers were supportive of both traditional and nontraditional elementary school mathematics instruction and had different scripts for the two lessons, the Japanese teachers had only one ideal lesson script that was closely tied to typical Japanese mathematics instruction. The findings suggest that U.S. teachers may have more culturally sanctioned options for teaching mathematics; however, Japanese teachers may have a more detailed and widely shared theory about how to teach effectively.

In December 1979 Izaak Wirszup, Professor of Mathematics at the University of Chicago, submitted a memorandum to the U.S. National Science Foundation outlining recent changes in science and mathematics education programs of the Soviet Union. Based on his extensive studies of Soviet technical and educational literature, Wirszup concluded that graduates of Soviet secondary schools now receive so much more mathematical and scientific training than U.S. students that the gap poses a formidable challenge to American national security. Wirszup’s report soon circulated widely; it was noted by science journalists, and led to major news stories in many cities. These ominous reports of foreign progress in education exacerbated the continuing public criticism of U.S. education, re-awakened memories of earlier studies showing superb performance of Japanese mathematics students but only modest achievement of U.S. young people, and sent many American mathematics educators to the Fourth International Congress on Mathematics Education with a mixture of curiosity and concern about our national effort in mathematics teaching.