Closing the Learning and Teaching Gap

Stage: 1, 2, 3 and 4
Article by Dr Merilyn Buchanan


The Third International Mathematics and Science Study[1] (TIMSS) has become one of the most referenced studies when international comparisons are made of pupils' performances. The 1995 study was one of the largest and most comprehensive ever undertaken, revealing comparative mathematics and science achievement levels for four age grades in over 40 countries. The finding that we have become most familiar with is that Asian countries repeatedly outperform Western nations at all age levels, with Singapore rating highest overall in mathematical achievement. But there are lessons to be learned by mathematics educators beyond simply knowing how individual countries rank on the world-wide league table. There are significant differences in the content and breadth of the curriculum, as well as when specific concepts are introduced and the depth of investigation those children engage in. The craft and culture of teaching also differs widely across nations. The challenge is how to use the information to close the performance gap that exists between nations.

Beyond TIMMS

Knowing the critical content and pedagogical factors of the successful programs that enable so many Asian students to flourish, should help us begin to improve our own practice and our students' achievement. These twin aspects of curriculum content and curriculum delivery have been extensively described in professional journals and the popular press. The most comprehensive analyses are in the books, The Learning Gap[2] and The Teaching Gap[3]. The seminal work of Harold Stevens and James Stigler in 1986, which measured and examined differences between one state in the U.S. and three Asian countries, not only spawned the TIMSS report, but has led to a new generation of studies. These studies continue to investigate how teaching is performed and received and why so wide a gap continues between Asian and Eastern and Western nations. The importance placed on the endeavour is indicated by the amount of funding the project has been awarded - more than 12 million US dollars.

The funding has allowed Stigler and his associates to take up residence in a former furniture store in Los Angeles that has been transformed into a state of the art facility. The 42 person team is composed of researchers, translators, transcribers, visiting scholars, and professors of psychology and education. Using over a thousand video tapes of mathematics and science lessons from Japan, Hong Kong, Germany, the Czech Republic and Australia, as well as the United States, the multi-national team is developing CD Roms for use in teacher professional development projects. Each disc contains nine lessons from various participating nations, showing how teachers transmit knowledge and assist students' concept development around specific mathematics topics. Alongside the digitised video runs a full transcript of the lesson. Viewers are able to freeze frames, to review, to examine practice - exemplary or otherwise - to watch students from around the world as they interact and engage in learning[4]. For a profession known for its solitary confinement, this is a rare opportunity to open classroom doors and look inside.

A new project being developed focuses specifically on cross-national teaching of Algebra - the strand of mathematics that is regarded in the U.S. as "the gatekeeper" to higher education. The State of California is collaborating on a teacher development initiative to raise the standard of algebra instruction and attainment at the middle school sector.

But before looking too far into the future, Professor Stigler was interviewed for NRICH readers. Here, he reflects on the gap between Japanese gifted and talented mathematics' students and their peers. It is a universal gap that teachers everywhere have to negotiate within their classrooms.

Do teachers in Asia differentiate instruction to meet the needs of pupils?

In the U.S., and in Europe, we ask, "What about the gifted kids?" In Japan - this generally applies to all Asian countries, but I'll just refer to Japan - the question is, "What can we do for the slow learner?" They are not withdrawn from class, the teacher attends to their needs outside of regular class time and they receive extra help after school. But, there are no special considerations for gifted and talented students. It's just not even considered - it's almost, "How dare they want or expect special treatment." Teachers simply don't accommodate them. There are no special 'extension' activities; they are expected to be part of the class.

What is very interesting though, having said this, is that recently a group has started to ask what should be done for gifted students, how can their talents be enhanced. The feeling is the exceptional skills of gifted students need to be developed. It will be interesting to see if changes begin to emerge.

How is the gap between the gifted and talented maths students bridged?

The more mathematically capable children are catered for within the context of the lesson. Rich problems by their nature have something for all; they are designed to accommodate a variety of levels. Solutions can be reached by counting strategies or algebraic reasoning. Students are asked to find other ways of solving the complex problems, to extend they're thinking, to develop multiple ways to reach solutions. The attitude of teachers (in Japan) is that the gifted child needs to persuade others, to explain and describe ideas and solutions and convince the rest of the students of his or her point of view.

Is there any setting, tracking, within or across classes so those children with similar skills have the opportunity to work together?

We (the U.S.), and Europe seems to be the same, we aim to meet children's needs by tracking them early on. It is done across age levels and within classrooms. This is not the case in Japan. Children's needs are met by engaging their thinking. Otherwise, low achieving students miss the opportunity of having students, other than ones with similar learning difficulties, model for them alternate ways to solve problems. High achieving students in mixed ability groupings have to find ways of interacting, and communicating ideas, and this really benefits them.

This is not to say there is no tracking or setting of students. Asian countries delay tracking. In Japan, up until 10th grade, classes are heterogeneous. This allows for different rates of the developmental trajectory. It's what we all know and talk about but don't do much about! We see it all the time, children who don't get it one day and then suddenly they take off. We over emphasise academic intelligence, we have a one dimensional view of gifted and talented. The Japanese system allows for individual differences, different types of achievement - leadership, communication skills etc.

Is there a significant difference in classroom structure, management and teaching style as students move into the secondary phase of schooling?

There is remarkable continuity in practice right up to the eighth grade. There is no gap between the levels. The curriculum flows, the classrooms look the same just more crowded (with bigger bodies, dressed in uniforms). Look at this lesson on this C. D.

The lesson shown on the disc is very similar in structure to those video taped in fourth grade classrooms (Year 5) for an earlier study. It opens with the teacher posing a problem to the class. There is an opportunity to collaborate with classmates. The room is noisy. Students are out of their seats, huddled in small groups discussing possible ways to solve the given problem. The teacher circulates, carefully selecting the groups who share their solutions. A representative of each chosen group uses manipulatives or displays visuals that the group has made to demonstrate their thinking. The strategies represented on the board range from least to most sophisticated in a very organised way. All methods are left on the board and at the end of the presentations students evaluate and comment on the various strategies and solutions. They comment on effectiveness, on efficiency, they look for discrepancies and lack of logic, and applaud when to acknowledge success and/or effort. The teacher uses mistakes as teaching opportunities, if students have not referred to an error then the teacher will guide their attention. The lesson does not just 'end' with the command, "Put your books away." The pupils summarise the day's lesson, often generating a mathematical 'rule'. The teacher records the definition on the board and students copy it into their notebooks for reference. Learners have ownership over a rule that is expressed in their own words and it is more meaningful to them.

Is your goal to identify best practice and define a formula to close the teaching gap?

No. A really important point that I can't emphasise enough is that different teaching methods are appropriate to different student groups. This depends on whether (the groups) are homogeneous or heterogeneous, and on different contexts, then different methods are more or less effective. Teaching is a cultural activity. Any suggestion of trying to transplant a system outside its cultural context has to be treated cautiously. Teaching is also a private activity; there is a lack of shared language to describe it. Teaching is a complex system; no dimension of it is universal. (Teaching) is hard to see - it is hard to change. Teachers themselves think they are doing one thing, such as changing their practice, but their actions are very different from their mental picture.

There are three ways to improve teaching:

  • to improve teachers (quality control of the profession)
  • to improve teachers' competency (knowledge base)
  • to improve teaching methods.

By examining the practice of others, teachers reflect upon their own practice and also have alternatives to consider. Teaching can only be improved from inside the classroom. To do this, teachers need time for quality reflection and planning, only then can they produce quality programs.


[1] Third International Mathematics and Science Study (TIMSS), (1995). National Academy Press

[2] Stevenson, H. & Stigler, J. (1992). The Learning Gap . New York: Summit Books.

[3] Stigler, J. & Heibert J. (1999) The Teaching Gap . New York: Simon & Schuster

[4] Steve Olson, Candid Camera: Can videotaping classrooms uncover essential truths about teaching? , Teacher Magazine, May /June 1999