A r c h i v e d  I n f o r m a t i o n

What is the Context for Teaching and Learning Math in the FiW Consortium?
(Part 1 of 2)

This section offers some possible explanations that might account for the differences in math achievement between the FiW and the U.S. that cannot be attributed to home factors.

Drawing on data from the TIMSS teacher surveys, an analysis of textbooks done by researchers at Michigan State University, and anecdotal information based on visits to FiW schools, this section discusses differences in the contexts for teaching and learning between the FiW Consortium and the U.S.

Where international data are readily available, comparisons are also made between the contexts for teaching and learning in the FiW and those in countries with high math achievement to point out similarities or differences where they exist.

In order to simplify the analysis, the section concentrates only on the differences in the contexts for learning math. An examination of differences in the contexts for learning science may show different results.

In addition, the section only looks at the contexts for learning math in the fourth and eighth grades. These grades were selected because of the rich data available from TIMSS for analyzing math instruction at these levels.¹⁹

The findings presented in this section should be viewed as an exploration of some possible reasons for the high achievement in the FiW Consortium. This report is a first attempt to identify factors that may play an important role.

Further analysis may reveal other factors that might explain the differences in achievement between the FiW and the U.S. In addition, the paper does not investigate possible causal links between the factors discussed and the achievement gaps.

Finally, because of data limitations, this paper points only to interesting differences in patterns between the contexts for learning in the FiW, U.S. and, when data are available, other high performing countries.²⁰

Drawing on data from TIMSS, this section looks at differences in four key areas that are commonly thought to have a large impact on achievement levels:

• Curriculum. In particular, differences in instructional topic coverage and the coverage of different topics by textbooks are explored.

• Classroom instructional practices. The report looks at both student and teacher reports on the most frequently used class activities and classroom organizational methods.

• Teacher engagement. Four factors are examined: the time spent by teachers on school-related activities during personal time, frequency of teacher meetings, teacher influence over key school decisions, and teacher familiarity with key curricular and assessment documents.

• Teaching environment. Finally, teacher reports on the factors that limit their teaching ability are compared.

Each of these areas is discussed in more detail in the next section.

Curriculum

It is a common sense conclusion that what is taught in classrooms around the world has an impact on what is learned. Accordingly, differences in the math curriculum covered in the FiW and the U.S. may account for some of the variations in achievement between the FiW and U.S. students.

In particular, differences in the organization and sequence of topics, the level and depth of coverage, and the timing of topic introduction may reflect important differences in the opportunities for FiW and U.S. students to master math and science material.

The textbooks and other curricular materials used may also play a potentially important role, if they are found to be more closely aligned with the curriculum of high achievement nations. This section presents data on teacher reports on instructional topic coverage and textbook content and use.

Instructional Topic Coverage

One of the first insights from the TIMSS data has been the lack of rigor in the U.S. math curriculum. Many educational researchers and policymakers have expressed concern that U.S. students are not being taught the concepts and skills needed to achieve world class standards.

Accordingly, one possible explanation for differences in math achievement between the FiW and the U.S. might be variations in instructional topic coverage, i.e., what content teachers cover in class.

Differences in both the number and type of math topics covered throughout the school year may indicate that fourth-and eighth-grade FiW students are exposed to more advanced material than their U.S. counterparts.

According to TIMSS data, FiW students are more likely than their U.S. peers to be introduced to relatively more advanced math topics in earlier grades. This pattern is reflected in data reported by math teachers in the fourth and eighth grade.

Exhibit 1 presents detailed data on instructional topic coverage for 21 math topics in fourth grade math.²¹ In a number of key subject areas, all or nearly all FiW and U.S. students are introduced to these subjects by the end of the fourth grade, according to their math teachers.

Some of these students cover these topics in their entirety in earlier grades (indicated on the exhibit as "learned earlier"), others begin topics in earlier grades and receive reinforcement on the material during fourth grade (indicated as "reinforced information"), while still others are first introduced to the material in fourth grade (indicated as "new information").

In topic areas where these three categories sum to 100, teachers report that all fourth grade math students will have been introduced to these subjects prior to, or during, the current year.

All, or nearly all, FiW and U.S. fourth grade math students are introduced to the following five basic concepts prior to, or during, fourth grade, according to teacher reports (that is, the percentage of students in "learned earlier", "reinforced information" and "new information" sum to 100 or near 100):

(1) whole numbers;

(2) common and decimal fractions;

(3) estimation and number sense;

(4) measurement units and processes; and

(5) data representation and statistics.

In all of these subjects, FiW students were more likely to have been exposed to the topic earlier than their U.S. counterparts. For example, 75 percent of FiW students had either learned whole numbers prior to fourth grade (e.g., covered it in grade three or earlier and were no longer spending time on this concept) or were receiving reinforcement.

In contrast, less than half of U.S. students (43 percent) had been exposed to this material earlier, according to their teachers.

FiW students are also more likely than their U.S. fourth-grade counterparts to be introduced to two more difficult math concepts during or prior to fourth grade:

(1) percentages, and

(2) number sets and concepts.

Seventy-seven percent of FiW students have been introduced to percentages prior to or during fourth grade (calculated by adding the three categories indicating when topics are introduced: e.g. "learned earlier" , "reinforced information" , "new information").

This compares to only 47 percent of their U.S. peers. Sixty-three percent of FiW students have been introduced to number sets and concepts prior to or during fourth grade, compared to only 32 percent of their U.S. peers.

As illustrated in exhibit 2, according to teacher reports, all or nearly all eighth grade FiW and U.S. students had been introduced to the following eleven math topics²²:

(1) whole numbers;

(2) common and decimal fractions;

(3) percentages;

(4) number sets and concepts;

(5) number theory;

(6) estimation and number sense;

(7) measurement units and processes;

(8) perimeter, area, and volume;

(9) basics of one- and two- dimensional geometry;

(10) ratio and proportion; and

(11) equations, inequalities and formulas.

However, as in the fourth grade, FiW students are more likely than their U.S. counterparts to have been exposed to most of these basic math concepts in preceding grades. As a result, FiW students are more likely to either not cover these topics again in the eighth grade or spend time reinforcing these concepts.

For example, according to their teachers, eighth-grade FiW math students were much more likely than their U.S. counterparts to have covered whole number operations and meaning in earlier grades and moved beyond this material. Forty percent of FiW students covered this material in earlier grades; while only 16 percent of U.S. students covered this material earlier and were not covering it in eighth grade according to their teachers.

For the other ten subjects, FiW students were much more likely than U.S. students to have been exposed to the material in prior grades and to spend time in their eighth grade math classes reinforcing this material.

Eighth-grade students in the FiW were also more likely than their U.S. counterparts to have been introduced to new, more advanced material during the eighth grade. The more advanced material includes:

(1) geometric congruence and similarity;

(2) geometric transformations and symmetry;

(3) constructions and three-dimensional geometry;

(4) proportionality: slope, trigonometry, and interpolation;

(5) functions, relations and patterns; and

(6) sets and logic.

While the data on instructional coverage give us some clues as to when FiW and U.S. fourth-and eighth-graders are introduced to different topics, the data do not provide much insight into the level or depth of coverage. Further research in this area could potentially give a fuller understanding of the differences in implemented curriculum between the FiW and the U.S.

Textbook Use and Topic Coverage

Could the difference in achievement be influenced by variations in the way textbooks are used in the classroom or the textbooks chosen? This section looks at TIMSS questionnaire data and a special study commissioned by FiW to examine the degree to which teachers rely on their textbooks to structure their teaching time, as well as the types of topics covered in these textbooks and the relative emphasis given to each topic.

TIMSS teacher questionnaires indicate that nearly all students use a textbook in FiW and U.S. eighth-grade math classes (100 percent of FiW students and 97 percent of U.S. students). The degree to which eighth grade math teachers use these books to structure their teaching time varies considerably, however, according to teacher reports. FiW students are more likely than U.S. students to be in classes where a large percentage of the teaching time is based on material in the text. As seen in exhibit 3, 55 percent of eighth-grade students are in classes where more than three-fourths of the teaching time is based on material in the textbook. In contrast, only 36 percent of U.S. students are in classes that rely this heavily on material in the textbook.

FiW teachers also report using a considerable amount of supplementary material in addition to their main textbook. As shown in exhibit 3, 91 percent of FiW and all U.S. students have teachers who use other materials in the place of or in addition to their main textbook. In both cases, textbooks appear to be used as one resource out of many rather than the sole resource.

Exhibit 3: Teachers' Report on Use of Textbooks and Other Teaching Materials and Percent of Mathematics Teaching Time Based on Textbooks

Data from the TIMSS curriculum study done by researchers at Michigan State University catalogued the topics covered by different textbooks and the relative emphasis given to each topic. Their analysis of math textbooks used by the FiW, U.S. and TIMSS²³ countries report the following conclusions:

• "The number of topics in Consortium textbooks is similar to that in textbooks of the US composite at all populations. [grade levels]. "²⁴

• At the fourth-grade level, "the consortium's textbooks are essentially no different in their content profiles from the US as a whole and [they also have] a great deal of overlap in content with Japan."

• The major exception is "the prominent presence of decimals in the Japanese textbooks, which is not the case in U.S. or FiW textbooks."²⁵

• "At the eighth-grade level, there are notable differences in the topics emphasized in the Consortium...with the topic of 'Equations and Formulas' for example, more emphasized in the Consortium than is the case for the most commonly used textbooks in the U.S."²⁶

• "The emphasis of Consortium textbooks on 'Equations and Formulas' in Grade 8 is similar to that of TIMSS countries in which mean student achievement was significantly higher than mean student achievement in the U.S."²⁷

• "This greater focus and emphasis on algebra is further reflected by the fact that the Consortium's books for the non-algebra tracks do not have any of the standard arithmetic topics among the top 5 contained in the book. This is in marked contrast to U.S. non-algebra books."

• "The Consortium teachers clearly emphasize algebra (linear equations) and geometry (2D geometry basics) more than is common for their U.S. peers, an emphasis that appears to be aided by the fact that the textbooks themselves provide more material in these areas."²⁸

In sum, some differences in curriculum may contribute to the differences in achievement between the FiW and the U.S. At both grade levels, these differences do not seem to be driven by differences in the number of topics found in textbooks used by FiW and U.S. students, as the number of topics covered by FiW math textbooks is very similar to the number covered by other U.S. math textbooks.

However, FiW eighth-grade textbooks tend to emphasize algebra and geometry more heavily, while U.S. textbooks emphasize arithmetic. This is true even for the students in the non-algebra tracks. In addition, at the eighth-grade level, a higher percentage of FiW students than U.S. students are likely to be in classrooms where most of the teaching time is centered on material in the book.

However, there is some anecdotal information that indicates FiW teachers are more apt to customize the textbooks used, e.g. carefully selecting chapters and exercises to be completed. This might be in contrast to the typical use of textbooks and could be an important component in understanding how FiW teachers can use textbooks with a large number of topics effectively.

Summary

Differences in achievement do not appear to be driven by the number of topics covered in the classroom or in the textbooks. According to teacher reports, FiW students seem to cover just as many topics as their U.S. peers. Likewise, FiW textbooks cover the same number of topics as U.S. textbooks.

However, FiW eighth graders are more likely than their U.S. peers to use textbooks that emphasize algebra and geometry. In addition, FiW students may be introduced to more advanced topics earlier than their U.S. peers.

Additional analysis is necessary to determine whether more advanced concepts are actually covered or just presented in a simplistic way.

Nevertheless, according to teacher reports, FiW students receive more reinforcement of topics introduced in earlier grades and cover more new material.

This pattern is found in both the fourth-and eighth-grades, and as might be expected, is more pronounced in the eighth grade.

The next section explores whether there are notable differences between the instructional strategies used by FiW and U.S. teachers that may also contribute to the differences in achievement.

Classroom Instructional Practices

There is a rich research base regarding what happens in most classrooms in the U.S. While much of the literature documents established patterns of teacher-student interactions, some studies have examined the relationship between classroom instructional practices and student achievement. The indicators selected for analysis in this section are based on that literature and some of the unique practices in FiW districts.

As discussed in the following three sections, data from the TIMSS teacher and student surveys suggest that some of the explanation for the differences in achievement may be due to differences between the methods that FiW and U.S. teachers use to present material to their students.

In particular, data on teachers' reports on class activities and classroom organization, as well as students' reports on the same, indicate that notable differences may exist between the FiW and the U.S. in the context for learning in student classrooms.

Teachers' Reports on Class Activities

Differences in classroom activities, that is, the actual tasks that teachers require their students to do in class, may account for some of the variations in achievement.

For example, some teachers may ask their students to tackle more challenging tasks or complex math problems that require students to apply their skills to different problems. Other teachers may challenge students to explain the reasoning behind new concepts more frequently.

Some students may spend more time using computers to apply new math concepts to solve exercises or problems. Other students may spend their time completing less challenging tasks, like completing drills or practicing basic computational skills.

This section explores whether differences exist between the types of activities used frequently in the FiW and U.S. math classes.

Data on the types of activities that teachers report they ask their students to do in class indicate that important differences may exist between the classroom activities in FiW and U.S. classes. However, the data also show many similarities. Both the differences and similarities are discussed below.

According to teachers, FiW math students in both the fourth and eighth grades are asked to perform reasoning tasks more frequently and complete drills less frequently than U.S. students.

As shown in exhibit 4, FiW students are more likely than U.S. students to have math teachers who ask them to explain the reasoning behind an idea during "every lesson." Thirty percent of FiW fourth-grade students have math teachers who ask them to explain their reasoning during "every lesson," 21 percent of U.S. fourth graders fall into this category.

At the eighth-grade level, the difference is more pronounced: 48 percent of FiW students have teachers who ask their students to explain the reasoning behind an idea during "every lesson," while roughly half as many (23 percent) of U.S. students have teachers that do.

FiW students are also more likely than U.S. students to be asked by their teachers to write equations during "most lessons" or "every lesson." In eighth grade, three fourths of FiW students have math teachers who ask their students to write equations during "most lessons" or "every lesson."

The percentage of U.S. students being asked to express relationships in equations in "most lessons" or "every class" is far lower-only 38 percent of eighth-graders.

While the difference between FiW and U.S. eighth-grade students may be a function of the higher percent of FiW students taking algebra classes, the difference is notable.

In the fourth grade, FiW and U.S. students are asked to use equations to express relationships less frequently, however FiW students are more likely than their U.S. counterparts to be asked to write equations (94 percent of FiW students, 83 percent of U.S. students).

Most fourth-and eighth-grade students, in both the FiW and the U.S., are only asked to undertake more complex or challenging activities-such as representing and analyzing relationships using tables, charts, or graphs or working on problems for which there is no immediate solution-during "some lessons."

Roughly 80 percent of FiW and U.S. fourth-grade math students and 70 percent of FiW and U.S. eighth grade students spend time during "some lessons" representing and analyzing relationships using tables, charts, or graphs.

In both the fourth and eighth grades, teachers reported roughly 65 percent of FiW and U.S. students are asked by their teachers to work on problems for which there is no immediate solution during "some lessons."

According to teacher reports, FiW students also practice computational skills in class less frequently than their U.S. counterparts. Teachers report that 58 percent of FiW fourth graders practice their computation skills during "most lessons" or "every lesson" compared to 70 percent of their U.S. counterparts.

In the eighth grade, students in both FiW schools and schools across the U.S. are less likely to practice computational skills frequently. However, the difference between the FiW and the U.S. eighth graders is even more striking: 25 percent of FiW math students practice computational skills during "most lessons" or "every lesson," compared to 59 percent of U.S. students.

The differences between how often FiW and U.S. students are asked to practice computational skills could be a function of higher expectations of mastery in earlier grades without the need for teaching and re-teaching the same topics year after year.

Classroom computer usage is another area where notable differences exist between FiW and the U.S. Neither FiW nor U.S. students use computers routinely to solve exercises or problems. However, in both the fourth- and eighth-grades, FiW teachers report that over half of the students use computers during "some lessons," while only a little over one-third of U.S. fourth-graders, and less than a quarter (21 percent) of U.S. eighth-graders, use computers.

While these data point out interesting contrasts, the differences in computer use may be a function of the availability of technology. A further look needs to be taken at how computers are actually used in FiW classrooms, as compared to the U.S.

Finally, one additional key point that can be made after reviewing exhibit 4 is the pattern, or lack of pattern, that emerges in FiW and U.S. classrooms.

It is interesting to note that the most predominant activities in FiW fourth grade classrooms-explaining the reasoning behind an idea, practicing computational skills, and writing equations-are consistent with the U.S. patterns.

At the eighth-grade level, however, there is a striking difference between FiW and U.S. reports in the areas of writing equations and practicing computational skills.

Taken together, these data suggest that FiW and U.S. teachers ask their students to do similar things in their math classes. However, there are a number of noteworthy differences.

In general, FiW students are challenged to perform reasoning tasks more frequently and complete drills less often than their U.S. peers. As noted above, the differences are particularly evident at the eighth-grade level, where FiW students are more frequently required to write equations, rather than practice their computational skills.

One could reasonably conclude that students in FiW eighth-grade classrooms are experiencing very different content and instruction from students in U.S. classrooms.

Exhibit 4: Teachers' Report on How Frequently Students Are Asked to Complete Specific Tasks

SOURCE: NCREL analysis of IEA's Third International Mathematics and Science Study (TIMSS) data 1994-95; FiW Teacher Questionnaire results, NCREL; tables 5.10 and 5.17 in Mullis, I.V.S., et al, (1997). Mathematics Achievement in the Primary School Years: IEA's Third International Mathematics and Science Study. Chestnut Hill, MA: Center for the Study of Testing, Evaluation, and Educational Policy, Boston College; tables 5.10 and 5.17 in Beaton, A.E., et al. (1996). Mathematics Achievement in the Middle Years: IEA's Third International Mathematics and Science Study. Chestnut Hill, MA: Center of Testing, Evaluation, and Educational Policy, Boston College.

NOTE: Totals may not add to 100 due to rounding.

Teachers' Reports on Classroom Organization

The different methods that math teachers employ to organize their classrooms and the different pedagogical approaches they use may have an impact on the achievement of their students.

In particular, the amount of time teachers spend standing up in front of their class introducing new material, explaining new concepts, and answering student questions, as opposed to having students work through exercises on their own, may play an important role in explaining the differences in achievement between FiW and U.S. students.

Similarly, whether students work together as a class or break off into small groups may affect student achievement. Furthermore, the choice of organizational or pedagogical approach that may have the strongest impact on the achievement of younger students may be different than the most effective choice for older students.

Accordingly, this section examines TIMSS teacher data on classroom organization for any differences in patterns between the FiW and the U.S. for both fourth— and eighth— graders.

Teachers' reports on classroom organization show some differences between the FiW and the U.S., and some similarities between FiW and countries with high math achievement.

As shown in exhibit 5, FiW fourth grade math teachers reported that FiW students are less likely than their counterparts in both the U.S. and high performing countries to be taught by teachers that rely either heavily or predominantly on any one classroom organizational approach.

In fact, the method that is the most heavily relied upon for teaching FiW fourth-grade math students — students working together as a class with their math teacher leading the whole class — is used during "most or every lesson" for less than half of fourth-grade FiW students.

FiW fourth graders are considerably less likely than both U.S. students and their counterparts in Japan, Korea, and Singapore to spend "most or every lesson" working individually with assistance from their math teacher, according to teacher reports.

This is the one area where there are notable differences between FiW and the U.S.: twenty-four percent of FiW students are asked to take this approach, compared to 55 percent of U.S. students, according to their teachers.

In the eighth grade, classroom organizational patterns are different from those in the fourth grade. FiW teachers reported that three quarters of their students work together as a class with the math teacher teaching the whole class during "most or every lesson."

The strong emphasis on whole class instruction was also reported in other countries with high achievement. According to teacher reports, over 60 percent of eighth grade math students in Singapore, Korea, and Japan spend "most or every lesson" working together with the math teacher teaching the whole class.

By contrast, less than half of eighth-grade math students in the U.S. spend "most or every lesson" receiving instruction in large groups. U.S. teachers also report that half of eighth-graders spend "most or every lesson" working individually with assistance from teachers.

This is a much higher percentage than in the FiW Consortium, where only 35 percent are in classes where this technique is used as frequently.

To summarize, TIMSS teacher data suggest the existence of important differences between FiW and U.S. and similarities between the FiW and high math achievement countries in the context for teaching math.

According to these data, fourth-grade FiW students are more likely than both their U.S. and international peers to be taught by multiple methods of instruction.

FiW eighth-graders, however, spend more time receiving whole class instruction–in this case, the pattern is similar to their international peers but differs considerably from that found in the U.S.

Again, one might conclude that the FiW students are being exposed to more new content in the eighth grade than U.S. students and that higher expectations are imposed on them to learn more complex mathematics.

SOURCE: FiW Teacher Questionnaire results, NCREL; figure 5.5 in Mullis, I.V.S., et al. (1997). Mathematics Achievement in the Primary School Years: IEA's Third International Mathematics and Science Study. Chestnut Hill, MA: Center for the Study of Testing, Evaluation, and Educational Policy, Boston College; figure 5.3 in Beaton, A.E., et al. (1996). Mathematics Achievement in the Middle Years: IEA's Third International Mathematics and Science Study. Chestnut Hill, MA: Center of Testing, Evaluation, and Educational Policy, Boston College.

* Fourth/eighth grad in most countries

Students' Reports on Classroom Organization and Class Activities

TIMSS also collected data from students on what happens in the classroom. As in the teacher questionnaires, the student questionnaires asked students to report on how frequently different classroom organization methods were used and how often varying class activities were undertaken

This section looks at FiW and U.S. student reports on what happens in their math classrooms in order to get a fuller understanding of the varying classroom organizational and activity patterns commonly used, as well as some insight into the differences between teachers' and students' reports.

FiW and U.S. students' reports on classroom organization and class activities provide an interesting picture of the similarities between what goes on in FiW and U.S. math classes. Exhibit 6 presents data on students' reports on the frequency of math class activities. As shown in the exhibit, fourth-and eighth- grade students in FiW and U.S. schools report similar patterns for the four most frequently emphasized activities in their math classes.

These activities are:

(1) teacher demonstrations of how to do math problems;

(2) distribution of homework;

(3) teacher checking of homework (fourth grade)/class discussions of completed homework (eighth grade); and

(4) students working from worksheets or textbooks on their own.

The majority of students in both the FiW and the U.S. report that they perform these activities during "most lessons."

Although important similarities emerge, students also reported differences between the FiW and U.S., and between the fourth and eighth grades.

The relative importance placed on two common activities, copying notes from the board and taking quizzes or tests, illustrates some of these differences. In the fourth grade, 32 percent of U.S. students reported that they copy notes from the board during "most lessons" compared to 22 percent of FiW students.

In the eighth grade, this technique is relied upon more frequently than in fourth-grade classrooms, in both FiW and U.S. math classes. Interestingly, unlike in the fourth grade, eighth-grade FiW math students are more likely than their U.S. counterparts to report that they copy notes from the board during "most lessons" (47 percent of FiW students versus 42 percent of U.S. students).

As for taking quizzes or tests, differences also exist between the FiW and the U.S. in both the fourth and eighth grades. In the fourth grade, U.S. students are more likely than FiW students to report that they are tested during "most lessons" (48 percent of U.S. students compared to 32 percent of FiW students).

In the eighth grade, however, FiW students reported that they are more likely to be tested during "most lessons" than their U.S. counterparts (46 percent of FiW students compared to 39 percent of U.S. students).

FiW fourth-grade math students reported that they used calculators more frequently than their U.S. counterparts, however, most FiW students (75 percent) reported that calculators were only used during "some lessons." For the U.S., 46 percent of students reported that calculators are used during "some lessons," while almost four out of ten U.S. students (39 percent) reported that they are never used.

Calculator usage was reported more frequently in the eighth grade than in the fourth grade by both FiW and U.S. students, although the gap between FiW and the U.S. remains. Sixty-nine percent of eighth-grade FiW students reported that calculators were used during "most lessons," while only 38 percent of U.S. students reported that calculators were used "most lessons." This could either be a resource issue, (i.e. availability of calculators), or a function of the content and topic coverage in math classrooms.

Other differences between the FiW and the U.S. exist in how homework is assigned and used. In both the fourth and eighth grades, FiW students are more likely than U.S. students to report that they have homework assigned regularly.

In the fourth grade, approximately three-fourths of FiW students, versus two-thirds of U.S. students, report that their math teacher gives them homework during "most lessons." They are also more likely than their U.S. counterparts to be able to start their homework in class during "most lessons" or "some lessons" (83 percent of FiW fourth-graders versus 69 percent of U.S. fourth-graders) and to discuss their completed homework in class during "most lessons" or "some lessons" (87 percent of FiW fourth-graders versus 72 percent of U.S. fourth-graders).

In the eighth grade, differences persist in how homework is handled in class. Exhibit 6 also shows a higher percentage of FiW eighth-grade math students reported that homework is assigned during "most lessons" (86 percent of FiW eighth-grade students versus 72 percent of U.S. eighth graders).

Classroom time spent on homework-related activities follows a slightly different pattern in eighth grade than in fourth grade. In the eighth grade, FiW students are much more likely than U.S. students to report that they discuss their completed homework in class during "most lessons" (72 percent of FiW eighth-graders versus 54 percent of U.S. eighth-graders).

In both FiW and U.S. math classes, eighth- grade math students reported that they are less likely to spend time in class working on homework than in the fourth grade. But, unlike in the fourth grade, FiW eighth-grade students are less likely than their U.S. counterparts to report that they can start their homework in class during "most lessons" (32 percent of FiW eighth-graders versus 50 percent of U.S. eighth-graders).

As discussed earlier in this section, it appears as if most FiW fourth-and eighth-grade students have the same types of experiences in their math classes as their fellow U.S. students.

According to student accounts, the most frequently emphasized activities in the FiW and the U.S., in both fourth- and eighth-grades, are:

(1) teacher demonstrations;

(2) homework distribution, checking or discussion of homework; and

(3) independent work on worksheets or on material in the textbook.

The three areas in eighth grade where students report differences between the U.S. and the FiW are:

(1) calculator use;

(2) beginning homework in class; and

(3) discussing completed homework.

These reports support the findings reported in the two preceding sections, and suggest that important differences between what FiW and U.S. students do in class may exist.

SOURCE: NCREL analysis of TIMSS data; FiW Student Questionnaire results.

NOTE: Totals may not add 100 due to rounding.

*The fourth grade and eighth grade student questionnaires contained a set of slightly different possible responses to this question. To make comparisons across grades, some categories from the grade 8 survey were combined. These new categories, along with the remaining responses were then matched to similar items on the grade 4 survey. Accordingly, "Some Lessons" in the sum of responses to "Pretty Often" and "Once in a While" on the Grade 8 survey. Also, "Most Lessons" is "Almost Always" on the grade 8 survey.

Summary

In summary, data on instructional practices indicate that there are differences between FiW and U.S. fourth- and eighth-grade math classes. According to students, the most common activities in both the FiW and the U.S. show similarities, with students reporting that the four most frequently used activities were:

(1) teacher demonstrations of how to do math problems;

(2) teacher assigning of homework;

(3) teacher checking of homework (grade 4)/class discussions of homework (grade 8); and

(4) students working from worksheets or textbooks on their own.

Teacher and student reports indicate that FiW and U.S. math teachers rely on different methods when demonstrating how to do math problems.

In the fourth grade, FiW teachers rely on a variety of approaches for teaching, so that no one method dominates. Perhaps reflecting the different way in which younger students learn and process material, some instructional time is spent in large groups, some in small groups, and some individually.

In the eighth grade, however, FiW teachers report that the most frequently used method involves the math teacher instructing the whole class. This approach is used far more frequently than in U.S.-eighth grade math classes.

In addition, in the FiW, both fourth-and eighth-grade students are more likely than U.S. students to be asked to explain the reasoning behind an idea, or write an equation to represent a relationship.

According to teacher reports, FiW students receive instruction in large and small groups more frequently than their U.S. counterparts, with the form of instruction varying according to the grade level. In all cases, FiW math teachers are more likely than U.S. math teachers to challenge their students to demonstrate their mastery of more difficult ideas or concepts.

The data also indicate that differences exist in how homework is assigned and used. FiW students are more likely than U.S. students to have homework assigned every day and to discuss their completed homework in class.

This pattern of homework assignment and use may mean that FiW students spend more time outside of class reinforcing new concepts. Classroom discussions of homework may clarify common difficulties and serve to solve outstanding problems.

In the fourth-grade, FiW math students are also more likely to spend class time starting their homework in class. Until the content of the homework is analyzed, however, it is difficult to determine whether this time enhances instruction by allowing teachers to work more directly with their students on a regular basis.

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[ Do Home Factors Explain the High Achievement of the FiW Consortium? ]

[ What is th Context for Teaching Math in the FiW Consortium? ]

This page last modified on November 23, 1999. (dtm)