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 2 of 2)

Teacher Engagement

Teacher engagement and involvement in the instructional process as well as in general school activities may also have an impact on student achievement. Although it can be difficult to measure teacher engagement directly, a number of factors can give us insight into the overall level of engagement and commitment.

For example, the amount of time and effort that math teachers put into preparing and planning for their classes, both during the regular school day and outside of regular classroom hours, may provide a good indication of teacher engagement.

Similarly, the amount of influence that teachers have over basic school budget allocation and curriculum decisions provide another useful measure.

Teacher familiarity with key curriculum and assessment documents may offer an indication of the level of knowledge of significant reform efforts.

Data from the TIMSS teacher surveys suggest that teachers in the FiW may be more engaged in school activities than U.S. teachers. Accordingly, this section presents data on four measures of teacher engagement:

• Teacher involvement in school-related activities outside the school day;

• frequency of teacher meetings;

• teacher influence over key school decisions; and

• teacher familiarity with key curriculum and assessment documents.

Together, these measures provide some insight into the relative levels of teacher engagement in the FiW and the U.S.

Teacher Involvement in School-related Activities Outside the School Day

Many teachers spend time outside the school day involved in school-related activities. The types of activities that they undertake are varied and range from preparing for class activities (e.g., planning lessons and grading homework) to helping, teaching, or working with individual students (e.g., tutoring students, meeting with parents, or consulting with other educational personnel on the progress of a particular student).

Teachers may also spend time outside the school day attending to administrative or other record-keeping tasks (e.g., attending staff meetings, updating class grade books). Teacher involvement in any of these activities are used as a proxy for the level of teacher engagement.

FiW and U.S. teachers spend similar amounts of their own time outside the formal school day working on nearly all types of school-related activities, with FiW fourth- and eighth-grade math teachers more likely than U.S. teachers to spend their own time on a few key activities.

Exhibit 7 contains data on teachers' reports of hours spent per week on activities outside the formal school day. Larger percentages of FiW students than U.S. students-at both the fourth-and eighth-grade levels-have teachers who report spending more than three hours per week planning lessons by themselves.

In the fourth grade, 67 percent of FiW students have teachers who spend more than three hours a week preparing lessons outside the formal school day, compared to 46 percent in the U.S., according to teacher's reports.

In the eighth grade, 48 percent of FiW students have teachers who spend over three hours per week preparing for classes outside of the formal school day, as compared to 34 percent of U.S. students.

In the eighth grade, larger percentages of FiW students than U.S. students have teachers who devote more than three hours per week to preparing or grading student tests or exams outside the classroom.

Seventy-two percent of FiW students have teachers who spend over three hours a week of their own time preparing or grading student tests or exams, compared to 47 percent of U.S. students. This difference is not found in the fourth grade.

Differences also exist between FiW and U.S. eighth-grade students with regard to how much time their teachers spend meeting with students outside the classroom. On average, eighth-grade FiW teachers spend more time meeting with their students on their own time than U.S. teachers (3.2 hours/week in FiW versus 2.0 hours/week in U.S.). Teachers of 72 percent of FiW eighth-grade students report that they spend over three hours a week meeting with their students, as compared to teachers of 29 percent of U.S. students.

To summarize, TIMSS teacher questionnaire data indicate that FiW and U.S. fourth-and eighth-grade math students have teachers who spend similar amounts of time outside the classroom on many school-related activities.

Differences exist in the amount of time spent on a number of activities, however.

According to the data, FiW fourth-and eighth-graders are more likely than U.S. students to have teachers who spend their spare time preparing lessons.

In addition, eighth-grade FiW students are more likely to have teachers who spend more of their spare time preparing or grading tests and meeting with students outside of their class, perhaps suggesting higher levels of teacher engagement among FiW teachers than among U.S. teachers.

SOURCE: NCREL analysis of IEA's Third International Mathematics and Science Study (TIMSS) data, 1994-95; FiW Teacher Questionnaire results, NCREL; table 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; table 5.6 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.

Frequency of Teacher Meetings

Another indicator of teacher engagement is how actively teachers seek feedback on ways to improve instruction. Teacher meetings to plan and discuss curriculum and instructional approaches allow teachers to get feedback from their colleagues on the best methods to present different types of topics, or the relative ease or difficulty that other classes are having covering similar material.

Teacher meetings not only allow teachers to learn about more effective strategies for teaching their respective subjects, but also permit teachers to keep abreast of changes in major national, state, and local curricular standards and assessments. Further, they may provide important opportunities for teachers to share resources and ideas for instructing and motivating their students.

As shown in exhibit 8, FiW students are more likely than U.S. students to have teachers who report meeting frequently with other teachers in their subject area to discuss and plan curriculum or teaching approaches.

In the fourth grade, 26 percent of FiW students have teachers who meet with their colleagues daily to discuss curriculum. In contrast, 10 percent of U.S. students have teachers who meet with their colleagues this frequently.

This gap between FiW and U.S. is even more pronounced for weekly teacher encounters. Eighty-one percent of FiW fourth-grade students have teachers who meet with other teachers at least once a week, compared to 59 percent in the U.S. (These percentages are calculated by combining the following categories: "almost every day" + "two or three times a week" + "once a week").

In both FiW and U.S. schools, eighth-grade math teachers meet with their colleagues less frequently than fourth-grade math teachers. However, notable differences exist between FiW and the U.S.

Approximately half (51 percent) of FiW eighth-grade students have teachers who report that they meet with other teachers to plan at least once a week, compared to about one-third of U.S. students (34 percent). (Again this is calculated by combining the categories noted above).

At the other end of the spectrum, a notable gap also exists between the FiW and the U.S. One-third of U.S. eighth-grade students have teachers who meet with their colleagues two or fewer occasions (never, once, or twice) over the course of a full school year. Three percent of FiW students fall into this category.

As with the TIMSS data on the amount of out-of-school time that teachers devote to their work, data on the frequency teacher meetings also suggest that FiW fourth-and eighth-grade math teachers may be more engaged than their U.S. counterparts in planning curriculum and seeking feedback from their colleagues.

Disparities between the number of students whose teachers participate in weekly planning sessions are most noteworthy, and exist at both the fourth-and eighth-grade levels.

Exhibit 8: Teachers' Report on the Frequency of Meetings with Other Teachers in Their Subject Area to Discuss and Plan Curriculum or Teaching Approaches

SOURCE: NCREL analysis of TIMSS data; FiW Teacher Questionnaire results, NCREL
NOTE: Totals may not add to 100 due to rounding.

Teacher Influence Over Key School Decisions

The level of teacher involvement in school budget and curricular decisions can also provide yet another indication of the level of teacher engagement. Although the degree to which states and districts allow their teachers to be involved in these discussions varies considerably, actively engaged teachers may exert a lot of influence over these decisions, while teachers who are less engaged in improving curriculum, instruction, or the overall school environment may not.

This section looks at data on the influence that eighth-grade math teachers in the FiW and the U.S. have over basic school decisions. (Data are not available for fourth graders).

As shown in exhibit 9, eighth-grade math students in the FiW Consortium were more likely than U.S. students to have math teachers who report they have a lot of influence over key school decisions.

Nearly half (47 percent) of FiW eighth-grade students had teachers who reported having "a lot" of influence over the subject matter to be taught.

Ninety-two percent of FiW eighth-grade math students had teachers who reported that they had at least "some" (if not "a lot") of influence over the subject matter to be taught.

By contrast, U.S. students tended to have teachers who reported that they had less control. Thirty-eight percent of U.S. students had teachers who reported that they had "a lot" of control over the subject matter, and 73 percent had teachers who felt they had at least "some" control. Seventy-four percent of FiW eighth-grade math students had math teachers who claimed they have "some" or "a lot" of control over which textbooks are used, compared to only 63 percent of U.S. eighth-graders.

This difference may reflect the fact that, in some schools, these choices are made at the state or district level.

FiW eighth-grade students were also more likely than U.S. students to have math teachers who reported that they have "a lot" of control over what supplies are purchased (47 percent of FiW teachers compared to only 23 percent of U.S. teachers).

However, FiW eighth-grade students are more likely than U.S. students to have math teachers who felt they had no control over the amount of money to be spent on supplies (46 percent in FiW compared to 35 percent in the U.S.).

Since not all schools or districts allow teachers to have a say in budgetary matters, it is not clear that these data indicate higher levels of teacher involvement in the FiW than in the U.S. However, they do indicate that FiW teachers have a greater influence on these decisions than their U.S. counterparts.

In summary, data indicate that eighth-grade FiW students are more likely to be taught by teachers who have control over some curricular and budget decisions.

Again, these findings reinforce the data reported earlier in the section that FiW teachers may be more engaged than their U.S. counterparts (to the extent that these data capture not only teacher influence, but also teacher engagement)

Exhibit 9: Teachers' Report on Their Influence over School Decisions

SOURCE: NCREL analysis of TIMSS data; FiW Student Questionnaire results.
NOTE: Totals may not add 100 due to rounding.

Exhibit 10: Teachers' Report on Their Familiarity with Key Curriculum Documents

SOURCE: NCREL analysis of IEA's Third International Mathematics and Science Study (TIMSS) data; 1994-95; FiW Teacher Questionnaire results, NCREL.
NOTE: Totals may not add 100 due to rounding.
*Eighth grade in most countries

Teacher Familiarity with Key Curriculum and Assessment Documents

As scientists, mathematicians, and researchers make advances in math and science, school textbooks and other classroom materials must be periodically updated to reflect new knowledge and ways of thinking. Standards, curriculum guidelines, and student assessment instruments also undergo regular revisions and updates so that they can accurately reflect current and emerging research and best practices.

Thus, key local, state, and national standards, curriculum, and assessment documents typically reflect the most current math and science knowledge. Teacher familiarity with, and knowledge of, these documents may provide another indication of how engaged teachers are in keeping abreast of the latest advances in math and science curriculum and assessment.

This section looks at FiW teacher familiarity with major curriculum and assessment documents. Comparative FiW and U.S. data, and those from other nations are only presented at the eighth-grade level because of limited data availability. It should also be noted that there are some definitional issues with the international comparisons, therefore these data should be interpreted with caution.

As illustrated in exhibit 10, FiW eighth-grade students have teachers who show varying degrees of familiarity with key curriculum documents. Most show the greatest familiarity with national standards. Sixty-nine percent of FiW students have teachers who are "very familiar" and 31 percent have teachers who are "fairly familiar" with the National Council of Teachers of Mathematics (NCTM) standards. In contrast, 38 percent of U.S. students have teachers who are "very familiar" and 48 percent who are "fairly familiar" with the NCTM standards.

In high math achievement countries, the pattern varies across countries. In Singapore, teachers of most students were "very familiar" with equivalent documents, while in Japan and Korea, students were more likely to have teachers who report that they are "fairly familiar" but not "very familiar."

The comparison to U.S. teachers' familiarity may indicate that FiW teachers have a greater involvement with professional associations, place more emphasis on professional knowledge, or have more opportunities to pursue outside interests.

The responses of the high performing Asian teachers are much less clear. While teachers in Singapore indicate a similar familiarity with their national curriculum, those in Japan and Korea do not. Some believe the data from Japan and Korea reflect an understated familiarity, as opposed to a lack of knowledge.

FiW teachers are less familiar with state curriculum guides than national guidelines. Math teachers of less than half of FiW eighth-grade students are "very familiar" or "fairly familiar" with state curriculum guides. U.S. math teachers are more familiar with these curriculum guides. Sixty-three percent of U.S. students have teachers who report they are "very familiar" or "fairly familiar" with these guides.

This lack of familiarity could also be a function of when, and if, states had completed development of their state standards.²⁹

As for familiarity with exam specifications for mathematics, math teachers of most FiW fourth and eighth grade students report that they are "not familiar" with the U.S. equivalent of national exam specifications-the National Assessment of Educational Progress (NAEP). This is probably because Illinois does not participate in the NAEP.

In the U.S., 16 percent of students have teachers who are "very familiar" with NAEP, and 24 percent have teachers who are "fairly familiar" with NAEP.

While FiW teachers report more familiarity with state exam specifications than with NAEP, they do not report particularly high levels of familiarity with state exams. In fact, teachers of at least half of the FiW eighth- grade math students report that they are "not familiar" with state exam specifications.

This pattern differs slightly for the U.S. In the U.S., more eighth grade math students have teachers who are "very familiar" or "fairly familiar" with the NAEP than with their state exams.

As was the case with state curriculum frameworks or standards, this could be more a function of state policy than teacher familiarity.

In summary, TIMSS questionnaire data on teacher familiarity with key curriculum documents and exam specifications reinforce some of the earlier findings on teacher engagement. Although data are not available at the fourth-grade level, FiW eighth-grade teachers report high levels of familiarity with the NCTM Standards, unlike U.S. teachers.

Data on state teaching guides and exam specifications show lower levels of teacher familiarity, in both the FiW and the U.S. High degrees of familiarity with national curriculum standards are also found in some high math achievement countries, but not all. It is unclear, however, whether this pattern reflects actual differences in familiarity or in understated familiarity (particularly in the case of Japan and Korea).

Summary

In summary, the TIMSS data indicate that FiW students have teachers that indicate more engagement than U.S. teachers in a broad array of school-related activities.

These activities include participating in school-related activities outside the school day, meeting with their colleagues, identifying and selecting textbooks, buying supplies, and keeping up with new curriculum and instructional developments and techniques.

Other research has posited that one result of greater teacher engagement is more stimulating, organized, and/or tailored instruction. While certainly not conclusive, these data may suggest that a key component to delivering better math instruction may be encouraging more active teacher participation in classroom planning, school decision-making, and keeping abreast of key changes in curriculum and assessments.

Teaching Environment

In addition to the key factors already discussed, the environment for teaching may also have an important impact on instruction, and in turn, student achievement. Teachers who must deal frequently with non-academic issues within the classroom may not have as much time to devote to instruction.

For example, many teachers must routinely spend class time dealing with discipline problems or disruptive students. External factors may also contribute to, or detract from, teaching environments in the FiW and the U.S.

In particular, state-, school district-, or school-based decisions and policy priorities which affect either the availability of equipment, the adequacy of physical facilities, or the student/teacher ratio may have an impact on the teaching environment.

Exhibit 11 presents data on teachers' reports on the factors that limit their ability to teach their classes. These reports show similar patterns exist between FiW and the U.S. and high performing countries (Japan, Korea and Singapore). In both the fourth-and eighth- grades, across all countries, the three most frequently cited factors limiting teachers' abilities to teach by "quite a lot" or "a great deal" were:

(1) students with different academic abilities;

(2) high student/teacher ratios; and

(3) disruptive students.

While different percentages of teachers from these countries reported that these factors placed "quite a lot" or "a great deal" of limitations on their ability to teach, in nearly all cases, students with different academic abilities were reported to be one of the most important limiting factors.

The only exception was for eighth-grade math students from Singapore, where students were more likely to be taught by teachers who report that high student/teacher ratios were the most important limitation placed on their ability to teach their class.

Across nearly all categories, FiW students were less likely than their counterparts in the U.S. and in high-achieving countries to have teachers who report that critical factors limit their ability to teach their class.

At the other extreme, students in Korea were the most likely to have teachers who reported that the various factors placed "quite a lot" or a "great deal" of limitations on them.

Fewer students had teachers who reported shortages of equipment as limiting factors. In the fourth grade, teachers of four percent of FiW math students reported that equipment shortages limited their ability to teach by "quite a lot" or "a great deal," compared to teachers of approximately 25 percent of students in the U.S., Japan, and Singapore.

As they did with all factors, Korean teachers reported that equipment shortages placed more limitations on their ability to teach, with teachers of 54 percent of students indicating that this limited their teaching ability "quite a lot" or "a great deal."

A similar pattern was found on the equipment shortages in the eighth-grade data from the FiW, U.S. and high achievement countries. The relative wealth of FiW districts probably has an impact on the differences in these results.

In summary, the TIMSS teacher data indicate that FiW, U.S., and high math- achieving countries report similar patterns in the factors that affect their ability to teach math. The limitation at the top of the list in the FiW, U.S. and all high-math achieving math countries except Singapore is dealing with students with a range of academic abilities. Students in Singapore were more likely to have teachers who reported high student/teacher ratios as their most important limitation. Concerns over facilities and supplies were less important limitations for all countries.

Exhibit 11: Teachers' Report on the Factors that Limit How They Teach Mathematics Class

SOURCE: Figure 5.4 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 Mullis, I.V.S., et al. ( 1998). Mathematics Achievement in Missouri and Oregon in an International Context: 1997 TIMSS Benchmarking. Chestnut Hill, MA: Center for the Study of Testing, Evaluation, and Educational Policy, Boston College; FiW Teacher Questionnaire results.
* Fourth/eighth grade in most countries.

A double dash (--) indicates data are not available. This question was not included on questionnaires for teachers of Japanese students.
An "r" indicates teachers response data available for 70-84 percent of students.

Summary

In sum, differences in the contexts for teaching and learning between the FiW and the U.S. may offer some insight into possible explanations for the gap in achievement levels between these two groups.

Accordingly, the preceding sections examined four broad areas that help define the context for teaching and learning for possible clues as to the factors that might drive these differences: curriculum, instructional practices, teacher engagement, and the teaching environment.

Differences in curriculum may contribute to the differences in achievement between the FiW and the U.S. These achievement gaps do not seem to be driven by differences in the number of topics covered by the textbooks used by the FiW and U.S. students, as the numbers of topics addressed by U.S. and FiW textbooks are similar.

FiW eighth-grade textbooks, however, tend to focus on algebra and geometry more heavily than U.S. books do, perhaps reflecting the difference in course-taking behavior.

Nor do the differences seem to be driven by a more focused coverage of topics in the classroom, since FiW students spend class time on just as many topics as their U.S. peers. However, FiW students seem to be introduced to more advanced topics earlier than U.S. students. This pattern is found in both the fourth- and eighth-grades, and, as might be expected, is even more pronounced in the eighth grade.

Data on instructional practices indicate that differences exist between FiW and U.S. fourth and eighth grade math classes. According to students, the FiW and the U.S. show similar patterns with respect to the four most frequently used activities. However, TIMSS data suggest 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; no one method dominate-some instructional time is spent in large groups, some in small groups, some working individually.

In the eighth grade, however, the most frequently used classroom organizational method-in the FiW and in high math achievement countries-involves the math teacher teaching the whole class; this approach is used far more frequently than in U.S. eighth grade math classes. These data suggest that FiW students may have math teachers who use direct teaching styles more frequently than their U.S. counterparts, with the form of instruction varying according to the grade level.

In addition, both FiW fourth and eighth grade students are more likely to be asked to do reasoning tasks than to spend time practicing computational skills.

The data also indicate important differences 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. Classroom discussions of homework may help to clarify common difficulties and serve to solve outstanding problems that their students encounter.

Together, these results suggest that FiW math teachers are more likely than U.S. math teachers to challenge their students to demonstrate their mastery of more advanced ideas or concepts.

The TIMSS data also suggest that FiW students may have teachers that are more engaged than U.S. teachers in a broad array of school-related activities. These include participating in school-related activities outside the regular work day, meeting with their colleagues, identifying and selecting textbooks, buying supplies, and keeping up with new curriculum and instructional developments and techniques.

Finally, similar patterns were found in teacher reports on the type of factors that limit their teaching abilities. Across the FiW, the U.S., and high achieving math countries, teachers reported similar patterns: student factors most limited their ability to teach, while the adequacy of class was less limiting.

FiW teachers reported that the adequacy of supplies hindered their ability to teach very little, no doubt reflecting the relatively high wealth of the districts.

While certainly not conclusive, these data suggest that key components of delivering a world-class math education may be encouraging the earlier introduction of advanced math topics into the curriculum and spending more time in the classroom concentrating on instruction.

Efforts to encourage active teacher participation in classroom planning, school decision-making, and keeping abreast of key changes in curriculum and assessments are also likely to be beneficial.

-###-

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

[ What is the FiW Consortium Doing to Improve Math and Science? ]

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