What Can Be Learned from the Survey of Mathematics and Science Opportunities (SMSO)?
SMSO researchers have helped develop new research tools, hypotheses, and approaches. These include methodologies for comparative studies of curriculum and context-sensitive methods of developing survey instruments and observation guides. In addition, SMSO offers ideas about international differences in curriculum and some preliminary observations about how instruction may vary across countries. These ideas are valuable for what they show about the complexities of making cross-national comparisons. At the same time, the SMSO preliminary findings point to the value of probing those comparisons carefully and illustrate what can be learned from the similarities and differences. SMSO was not intended to provide conclusive analyses about international differences and should not be read in that way.
This section is divided in two parts, one focused on insights that SMSO reports from investigating the six countries' intended curriculum in mathematics and science and the second on what emerged from their observations of instructional practices. Our purpose here is to highlight the types of issues that can be pursued with international comparisons. References to specific countries are provided to illustrate broad comparative statements, not to make generalizations about those countries.
What Does SMSO Say about Intended Curriculum?
Discussion of intended curriculum in SMSO is based on data gathered about curriculum guides and texts using the TIMSS curriculum frameworks, 19 as well as on information from the countries about the structures and authority for curriculum decision-making and guidance. We briefly highlight three provisional findings reported by SMSO: one about the mathematics and science content included in the intended curriculum across the six countries, one about differences between the mathematics and science curriculum across the six countries, and one about how the intended curriculum is determined in these different countries.
• What does the curriculum analysis reveal about the content of mathematics and science curriculum frameworks and textbooks across the six SMSO countries?
There are many ways in which one might expect curricula in different countries to vary. Prominent dimensions in curriculum include the number of topics to be covered each year, topic sequence, topic development, and depth and breadth of the curriculum.
When they considered the number of topics to be covered, SMSO researchers found that some countries, such as Japan, and Spain, aim for a smaller number of mathematics topics each year and that, in contrast, Norway, France, and the United States cover many more mathematics topics per
year. Science textbooks examined in France, Japan, and Norway appear to include more detail on fewer topics than do the textbooks examined in the other countries.
SMSO found that, in the intended curricula of some countries, particular topics are emphasized and developed with concentration and focus and then are sustained over several years. In contrast, topics appear in the curriculum in other countries over and over but never seem to receive a sustained emphasis. For example, the materials examined from Japan emphasized "equations and formulas" in virtually every grade, while materials from Norway and Spain did not emphasize this topic in any grade. In France, the analysis indicated that "chemical properties of matter" is introduced to students at age 13 and emphasized at ages 15, 16, and 17, while in Norway, the same topic is introduced to students at age 10 and addressed each year thereafter but never emphasized. In science, Switzerland's pattern generally showed relatively late introduction and focus emphasis for most topics.
The SMSO study also found differences in when a topic first appears in the intended curriculum, as well as when it is dropped. For example, the Japanese curriculum introduces some algebra topics to students as early as age 8, while in Spain those topics are not introduced to students until age 12. Science topics such as "reproduction of organisms" and "earth building and breaking processes" are introduced in the U.S. several years earlier in the curriculum than they are in Japan. In other science topic areas, such as "organs and tissues,'' coverage in the typical American text ends the year after it is first introduced in Swiss texts. In the U.S., there also is a tendency to address a given topic repeatedly over a period of several grades. In Japan, it is more common for a topic to be dealt with entirely within a grade or two. Understanding these large variations in many dimensions of the intended curriculum is critical to understanding differences in educational practice and achievement across countries.
Variations also are found in the expectations of and demands on students in the intended curriculum. Japanese science textbooks for 13-year-olds are characterized in SMSO as emphasizing "understanding complex and thematic information" more than "simple information." French and Spanish textbooks for this age group exhibit a similar emphasis but to a lesser extent. Differences in emphasis are evident also in mathematics textbooks for this age group. For example, texts in Switzerland and Norway devote more than 50% of their space to "whole number operations." "Properties and meanings of whole numbers'' (a more complex topic) occupies 20% of the space in French texts as compared to 2% of the space in Swiss texts and 8% of the space in Norwegian texts. These differences in emphasis and coverage between simple and complex topics suggest substantial differences in performance expectations across the six countries. Even for a topic such as whole number operations for 9-year-olds, the curricula of different countries call for different levels of complexity, which is likely to produce differences student performance.
• In looking cross-nationally, are there important differences between the mathematics curriculum and the science curriculum?
As they examined the intended curriculum across countries, SMSO researchers found that the mathematics curriculum and the science curriculum have different characteristics. For example, science curriculum frameworks and textbooks in the six countries were found to contain many more topics than the curriculum frameworks and texts for mathematics. In their report, researchers noted that this is true at both the 9-year-old and 13-year-old levels. A second difference is evident in the volume of content to be taught in mathematics and science. In SMSO countries, although the number of mathematics topics to be taught increases for 13-year-olds, the increase is more dramatic in science. A third difference is that there are more similarities in the mathematics curriculum across countries than in the science curriculum. Clearly, there are important questions to be asked about the differences in the ways that science and mathematics are viewed and taught in different countries. These differences also may have implications for student performance differences in mathematics and science.
• How is the intended curriculum specified in each country?
Another salient difference across countries lies in the ways in which the intended curriculum is determined. Decisions about what should be taught and with what priority are made in very different ways across countries. Communication about these different priorities, and the extent to which teachers are expected to follow centralized curriculum guidelines, also vary considerably. The degree of alignment of textbooks with centralized curriculum goals also varies. These issues are not about the actual curriculum encountered in classrooms by students but about how the aims and means of the intended curriculum are articulated.
Of the six SMSO countries, the U.S. has the least centralized control of curriculum. In France, Japan, Norway, and Spain, national curriculum frameworks are developed under the control of centralized government agencies. These frameworks specify curricular goals to be implemented by regions and schools. There is no comparable national curriculum framework for Switzerland or the U.S. In Switzerland, recommended curriculum frameworks do exist within each canton, and in the U.S., most states and many local districts do have curriculum frameworks. However, in the U.S., there is no single pattern of curriculum specification. 20
Considerable variation also exists in the ways in which textbooks are produced and selected. In virtually all SMSO countries, textbooks are produced by commercial publishers, not by government agencies. In four of the six countries, textbooks must adhere to national guidelines. 21 Selection of
textbooks varies across the countries: in some cases, it is the responsibility of individual teachers, while in others, it is the responsibility of schools, school districts, or states. In Norway, textbooks are selected by the national government.
What Does SMSO Say about the Implemented Curriculum and Instructional Practices?
Through observations of 127 classrooms, SMSO researchers also investigated the implemented curriculum—how content is actually taught—in the six countries. To draw conclusions about national trends in instructional practice from SMSO classroom data would be unwarranted. However, the differences that emerged are interesting and raise useful questions about the connections of instructional practice to the cultures in which it is embedded. Such questions might help guide examination of the TIMSS achievement data as it is released over the next several months.
One of the most dramatic messages from SMSO is the extraordinary diversity of educational systems and practices and of conceptionalizations of fundamental elements of the educational process. Although the teaching of mathematics and science content is held by some professionals to transcend cultural boundaries, the teaching of mathematics and science appears to be strongly influenced by and reflective of its cultural setting. For example, SMSO researchers not from the U.S. were unfamiliar with the common American practice of having students exchange and check one another's homework papers. The size of classes, the role of teachers, the kinds of academic tasks assigned to students—these "basics" all seemed deeply embedded in culture as researchers examined teaching in one another's countries.
In order to develop instruments sensitive enough to study teaching across cultural contexts, SMSO researchers devised a framework to guide examination of a few lessons in each country. The framework elements were content complexity and representation, content presentation, and classroom discourse. For content complexity and representation, the researchers focused on how content was modeled and represented by teachers. Content presentation refers to the strategies used to engage students in the content. Discourse was the term used to refer to how students and teachers interacted with one another about content.
Practices in one country often were unfamiliar to those from other countries. However, the SMSO team found that simply focusing on specific differences in practice did not seem to capture the larger, recurrent patterns in pedagogical style and classroom approach that seemed to characterize all the observations within a country. The SMSO report provides illustrations of these sorts of recurrent patterns in both mathematics and science.
What follows are some prominent recurrent features of these patterns, which the researchers noted in the lessons they observed in each country. The anecdotes are based on a few observations and cannot be taken to describe the characteristic practices of any of the six countries. The points raised below are meant therefore to illustrate only the notion that styles and patterns of teaching science and mathematics may be culturally rooted. The larger TIMSS data set will provide opportunities to probe the durability and consistency of this notion.
In the science and mathematics lessons they observed in France, SMSO researchers reported a consistent tendency for the teachers to make formal presentations of complex subject matter. They saw teachers emphasizing formal definitions, laws, and principles and observed students engaged in theoretical reasoning and problem solving. Many of the lessons observed in Spain shared these features. In addition, the small set of Spanish teachers observed seemed to seek to link theoretical principles to practical everyday applications. Textbooks also seemed more central in the Spanish lessons observed in SMSO. A great deal of emphasis also seemed to be placed in Spain on use of homework.
In contrast, the set of mathematics and science lessons in Norway seemed more often to center on helping students develop factual knowledge. The content did not seem as complex or as formal from a disciplinary perspective as what was evident in the French lessons observed. In the judgment of the SMSO research team, the Norwegian teachers sought to engage students in learning activities in both individual and small group work in ways that seemed more child-centered than what was observed in the other countries. Compared to the French and Spanish teachers observed, the Norwegian teachers also spent less time lecturing. It should be noted that observers saw little classroom discussion in these lessons.
The Japanese lessons were quite different from those in France, Norway, and Spain. Observers from SMSO noted an active engagement with the content by both teachers and students. They cited notable emphasis on multiple representations and methods, as well as a considerable amount of complex, content-focused discussion. Some of the discussion in the Japanese lessons seemed to be guided quite strongly by the teacher and focused on eliciting complex ideas rather than on facts or simple understanding.
The Swiss lessons were similar to those in Norway and emphasized student responsibility for learning through teacher-prepared demonstrations and activities. Lessons tended to be structured around a single subject matter idea and covered a small amount of content. Textbooks seemed to play a smaller role than in some other countries observed.
In lessons observed in the U. S., teachers often seemed to be the central figures in the classroom. Frequently, they functioned as transmitters of information. In their report, researchers note that the teachers appeared to be more involved with subject matter content than the students were, although, in some lessons, little actual topic content was observed. The lessons observed tended to be organized, structured, and directed by the teacher, and definitions and vocabulary were emphasized.
The SMSO study of instructional practice raises the important issue of the extent to which mathematics teaching and science teaching are embedded in culture. Although the lessons that the researchers observed across countries shared characteristics, and lessons within countries showed variation, SMSO researchers were able to identify what they believe to be pervasive and recurrent patterns by country. In the report, they employ the term characteristic pedagogical flow (CPE) as a way to capture the notion of a cluster of culturally embedded classroom relations, practices, and
