International comparisons of mathematics achievement were begun in 1964 by the International Association for the Evaluation of Educational Achievement (IEA). Over a period of almost four decades, the highest achieving systems have been Japan, and, as they successively joined the study, Korea, Singapore, Hong Kong and Taiwan. In 1964, Japan was virtually tied with Israel for first place and retained that rank on the Second International Mathematics Study (SIMS) in 1981, while Israel had dropped to 12th place. In 1995, on the Third International Math and Science Study (TIMSS), Japan had dropped to 3rd place and then to 5th place at the 8th grade level in 1999, 2003 and 2007. At the 4th grade level, their scores were 3rd and 4th in 2003 and 2007, respectively (4th grade was not tested in 1999).
What can account for the superior performance of Japan and the other Asian education systems? In three publications, William Schmidt has suggested that it is because their curricula, compared to those in the U.S., are focused, coherent and rigorous, (Schmidt et al 2002; Aharoni 2005, p. 11; Schmidt 2008). Focus refers to covering a small enough number of topics to learn them thoroughly in the time available; coherence denotes teaching the topics in a logical sequence (i.e., not covering advanced topics before more elementary ones have been mastered); and rigour simply means that the material covered is challenging or demanding.
In the case of Japan, rigour has nothing to do with the success of their students in mathematics. The real key is that Japanese elementary teachers have developed extremely effective teaching methods and constantly take into account the basic physical and intellectual needs of their students. In addition, they have great influence in key areas of the Japanese education system.
The Central Role of Classroom Teachers
High-quality teaching is practiced throughout Japan because experienced elementary teachers play a crucial role in the following parts of the Japanese system:
- the training of new teachers,
- the professional development of established teachers, through teacher-initiated research groups,
- classroom research leading to the discovery and implementation of much of the knowledge that those teachers acquire, and
- the writing of the elementary textbooks and teachers’ manuals that embody their pedagogical technology.
New Teacher Training
“The training of Japanese teachers is not thought to begin until they start their first teaching job, at which point they begin a long period of apprenticeship-like training in which they are supervised closely by master teachers.” (Stigler et al, 1996, p. 217). Until 1989, the practice was informal but widespread, and in that year it was formally structured by the Ministry of Education:
The in-service training system for beginning teachers is composed of two parts: apprenticeship training in a school (about seventy days a year) and lecture courses in teacher training centres (about thirty-five days a year). Both use traditional training styles. In apprenticeship training, the first-year teachers are mentored by a retired teacher or a veteran in the school in order to master teaching skills. (Sato 1992, pp. 158-159).
In-service study activities
Since the early 1950s, research, or study groups allowed for the dissemination of the knowledge base throughout the teaching corps:
[T]he national survey of the National Institute for Educational Research in 1951 indicated that over 80 percent of teachers participated in developing their own school curricula… The movement led to professional autonomy, and teachers organized innumerable voluntary study groups both inside and outside of the schools. The Japan Teachers’ Union, established in 1947, also enhanced teachers’ autonomy by promoting voluntary studies. The union held annual study meetings for teachers at national, prefectural, and local levels, in which teachers developed their professional culture by sharing their practical experience and principles with each other. (ibid., p. 161)
… Both grassroots, teacher-initiated study circles and publicly supported study groups dot Japan’s educational landscape. … ‘Research’ in this context means classroom-based efforts to improve instructional approaches,… attempting to reshape classroom instruction in keeping with [an] idea, and sharing the resulting practices with colleagues (by visiting each other’s classrooms, videotapes or reports). (Lewis & Tsuchida 1997,p. 319)
Lesson Study
The classroom-based research referred to above is known as ‘lesson study’. According to Nobuo Shimahara, it is “… a widespread popular practice embedded in the culture of teaching, an ethos that Japanese teachers cherish as a proven means to improve teaching.” (Shimahara 2002a, p. 114). The procedure involves an experimental lesson which is developed by a group of teachers over the course of the school year. It is then taught by one of the group members and is carefully observed by the other members, who make notes about how students respond to it and who also make audio and/or video recordings. After it is taught to the class, the teachers spend several hours discussing the results in detail. (Lewis & Tsuchida 1998) Depending on its success, the lesson may be redesigned and retaught, but whatever the eventual outcome, it is written up and published, either for local or wider consumption. Lesson study is such a universal practice that “…journal articles by teachers about their educational research outnumber by a third those of university educational researchers in Japan.” (Sato & McLaughlin 1992, p. 362).
Since lesson study involves designing, testing and evaluating methods of teaching content to students in the classroom, it has produced extremely effective techniques for teaching each topic.It has been applied to the order in which topics are taught and the ages at which students can best learn them. Because Japanese teachers have determined the time necessary for the activities used to teach each topic, they know the maximum number that can be addressed in a given time period. This, plus the correct sequence of topics, give their curriculum its characteristic focus and coherence.
Teacher authorship of elementary texts and teachers’ manuals
Because experienced teachers have developed and maintained the Japanese teaching knowledge base, they are hired by publishing companies as the principle authors of elementary textbooks. This is reflected in the statements of the informants in a study by Catherine Lewis et al (2002):
Interviewer: Are the people who actually write it more often classroom teachers or university professors?
Mr. Hajime: Classroom teachers. Unless you are a classroom teacher, you can’t write it, can you? … University professors might be good at writing, and might be able to write textbooks for junior high or high school, but not textbooks for elementary school. That’s why it is important that elementary teachers participate in the process. // Yet another Japanese author commented: “It’s actual teachers who are central,and university professors who are secondary in the textbook writing.” (p. 57)… in the words of one interviewee, “There is a recognition on the part of the national government that teachers are essential to the creation of textbooks. You can’t make textbooks without teachers.” (p.58)
Similar teacher involvement prevails in regard to Japanese teachers’ manuals:
…The manuals, usually written by expert teachers in a user-friendly format, provide a coherent body of subject-matter knowledge and specific pedagogical suggestions for teaching the textbook content. These suggestions often involve activities from research lessons or regular classes that demonstrate their effectiveness in guiding students tomeet the particular lesson goals. (Lee & Zusho 2002, pp. 68-69)
Reservoir of Teaching Technology
The four features of the Japanese system delineated above demonstrate that the knowledge base of teaching technology, i.e., of the math content appropriate for children at a given age, its correct sequencing and the best methods for teaching it, resides among classroom teachers, not university researchers. The training of Japanese elementary teachers is not characterised by advanced coursework in mathematics or teaching methods. In 1997 less than 5% of elementary teachers had master’s degrees. (Shimahara 2002b, p.57). The primary source of their knowledge of mathematics and methods for teaching is not college coursework, but their teachers’ manuals (Lee & Zusho 2002, pp. 79-81) and interaction with veteran teachers.
The Illusion of Rigour
Rigour was identified as a characteristic of the curricula of high-achieving systems because“…[I]n the middle grades, the rest of the world is teaching algebra and geometry. The U.S. is still, for most children, teaching arithmetic…[O]ther countries outperform us in the middle and upper grades [1995] because their curricular expectations are so much more demanding, so much more rigorous.” (Schmidt 2008, p. 23). The reality is, however, that rigour plays no part. For the Japanese the preparation for geometry in the eighth grade began in the first grade and continued at levels appropriate for the students’ developmental stages throughout elementary school. Not surprisingly, they outperformed the U.S. in the fourth grade, too, ranking 3rd against our 12th place. In the 8th grade the rankings were 3rd and 28th, respectively. There is clearly a difference between our systems, but it has nothing to do with rigour.
There are features of Asian instruction which generally enhance the effectiveness of their education by their distinct lack of rigour. These are 1) a marked lack of pressure on students during their classes, and 2) frequent, substantial periods of vigorous physical activity between classes. Regarding the first, James Stigler noted that “…Japanese classrooms appeared to move at a more relaxed pace than American classrooms. Only teachers in Japan were ever observed to spend an entire forty-minute lesson on one or two problems… Understanding takes time, and perhaps spending that time at an early stage will lead to future benefits..” (Stigler, 1988, p.29). The frequency of recesses was noted by Stevenson and Lee: “The school day was highly structured in Taipei [Taiwan] and Sendai [Japan], with 40-45 minutes of class followed by a 10-15 minute break…. [There were an] average of four recesses at the first grade in Sendai and Taipei and of eight at the fifth grade in Taipei and five in Sendai.” (Stevenson and Lee 1990,p. 31)
Such general considerations of the needs of children are matched by the actual pace of instruction by Japanese teachers. This is reflected in the number of pages of text covered in a period, which may range from one half to one page in the first grade, to from one to one and a half pages from grades two through six (MCLSG, 2009). This strikingly low rate is intended to ensure the understanding of all students, who are taught in mixed ability classrooms using whole class instruction. (Stevenson 2002, p. 104; Stevenson and Lee, 1997, p. 36).
But the single factor which best explains the high achievement and uniform progress of Japanese students is extremely effective teaching methods which are a product of the same classroom-based teacher research that has produced the focus and coherence of their curriculum.Lesson study, and the research groups that ensure the dissemination of its findings, began being carried out almost 140 years ago, from the establishment of the Japanese national education system. In his recently published book The History of Modern Japanese Education: Constructing the National School System, 1872-1890, Benjamin Duke recounts events that mark the beginning of activities which are the essence of present-day study groups and classroom lesson research. (Duke 2009, pp. 248-249). By the turn of the 20th century there were numerous journals disseminating the findings of lesson study (Sakar Arani et al 2010, p. 179, 181), and by 1930, the practice of lesson study had developed to the level at which it exists today (ibid., p.186).
With so long a history of such involved professional activity, it is no surprise that the quality of Japanese teaching has reached such a high level. This results in the appearance that the curriculum is challenging or demanding because Japanese children are able to learn material that would indeed be so for our students. But if they began in first grade and had the same learning experiences, they could learn the same material as well as the Japanese. The illusion of rigour is simply an artefact of very effective teaching practices.
The Knowledge Base
Age-appropriate subject matter, its optimum sequence, and the best methods to teach it are embodied in Japanese elementary math textbooks. Because they must conform to the Course of Study developed by the Ministry of Education, “…even though several companies produce textbooks in Japan, the books they produce are almost identical throughout the country.” (Stigleret al, 1996, p. 215). The aspects that are identical are the topics in each grade, the interconnection of topics between grades, and the activities and examples used to teach them. Textbooks from different publishers contain examples that have been found to be effective in developing an understanding of a concept, and dispelling confusion that students often display in connection with it. Two examples occur in treating the subject of area.
Area is introduced formally for the first time in the fourth grade. In an instance of spending an entire period on a single problem (see Stigler 1988 above), students are asked “Which is larger, the square or the rectangle?”, after being given sheets containing a 4cm x 4cm square and a 3cm x 5cm rectangle. They are asked to think about how they could answer the question, and since they already know about perimeter, some try to measure that aspect of the figures to answer the question. They immediately observe that the perimeters are both 16cm and learn from this clear demonstration that in this case that quantity cannot be used to describe the size of a geometric figure. These dimensions were deliberately chosen, based on teachers’ past observations of children’s mistaken assumption that perimeter is an indication of the size of an object, and serve to eliminate this misconception. (Hironaka & Sugiyama 2000, 4B, p. 24; Kyôiku Shuppan 1993, pp. 32-33).
Another issue that has often been observed to be a source of confusion is the use of square units (e.g., the cm2) to express the areas of non-rectangular shapes. Leaving nothing to chance, both texts give specific exercises in figuring out the areas of shapes other than squares or rectangles. (ibid., p. 25;ibid., p. 34)
Specific features such as these and many others, from the carefully graded sequences of topics,to the interconnections between them in different grades, to concrete activities designed to foster interest and understanding in children, are all explained in the accompanying teachers manuals,and make up the knowledge base of Japanese elementary mathematics instruction.
Conclusion
Japanese mathematics education is so effective because at the elementary level it operates on the assumption that learning something with understanding takes time and a consideration of children’s physical and intellectual needs. The very moderate pace of progress through the textbook and numerous activities involving concrete materials combine with intermittent periods of vigorous physical activity to produce optimal conditions for learning.
In addition to consistently meeting the basic needs of children, the teaching methods themselves are products of many years of classroom research by teachers. They have evolved into a carefully graded system of interconnected learning experiences which have coherence between, as well as within, the lessons, and become part of the textbooks, which are written by teams of experienced teachers. The development of concepts that may be addressed in detail at later levels is begun intuitively in very early grades. It extends throughout elementary school and into middle school, where the work in geometry gives the impression of such rigour.
But it is clearly not the mere choice to give children a “demanding” or “challenging” curriculum that develops their ability to do such work; it is the knowledge of ingenious methods to teach them effectively. Such methods, developed by experienced teachers who over many years, have produced a meticulously constructed system resulting in a high level of achievement in the average student. Instead of trying to make things more difficult by requiring more rigorous material for our students, we would do much better to prepare our teachers to use the techniques, materials, and the rational curriculum that are the products of Japanese elementary teachers’ classroom research.
Author: Daniel M. Stamm
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