© 2001 International Association for the Evaluation of Educational Achievement (IEA)
What Preparation Do Teachers Have for Teaching Mathematics?
This section presents information about background characteristics of mathematics teachers, including age and gender, major area of study, and certification. Teachers confidence in teaching various mathematics topics is also discussed.
As shown by the international average at the bottom of Exhibit 6.1, the majority of the eighth-grade students internationally were taught mathematics by teachers in their 30s and 40s. If there were a steady replenishing of the teaching force, one might expect approximately equivalent percentages of students taught by teachers in their 20s, 30s, 40s, and 50s. Very few countries, however, had a comparatively younger teaching force. Internationally on average, only 16 percent of students were taught by teachers younger than age 30. Although 21 percent of students internationally were taught by teachers age 50 or older, the teaching force was relatively older in a number of countries.
Most Benchmarking participants did not differ substantially from the international profile. However, the Academy School District and the Jersey City Public Schools had no students with teachers in their 20s and had larger percentages of students with teachers in their 40s and 50s than internationally. Similarly, the Chicago Public Schools, the Miami-Dade County Public Schools, the Project SMART Consortium, and the Southwest Pennsylvania Math and Science Collaborative had more than 65 percent of their students taught by teachers 40 years or older compared with 54 percent internationally. On the other hand, the teachers in the Fremont/Lincoln/Westside Public Schools were younger than the international average 67 percent of the students had teachers under age 40 compared with 46 percent internationally.
Internationally on average, 60 percent of eighth-grade students were taught mathematics by females and 40 percent by males, and similar percentages were found in a number of countries. None of the TIMSS 1999 Benchmarking states differed from the international profile of having more students taught by female mathematics teachers than males. In South Carolina, in particular, 85 percent of the students were taught mathematics by female teachers. Among the Benchmarking districts and consortia, the First in the World Consortium, the Fremont/Lincoln/Westside Public Schools, Guilford County, and Montgomery County had more than three-fourths of their students taught by female mathematics teachers. In comparison, the Michigan Invitational Group, the Naperville School District, and the Southwest Pennsylvania Math and Science Collaborative had more male than female teachers.
Exhibit 6.2 presents teachers reports about their major areas of study during their post-secondary teacher preparation programs. Teachers undergraduate and graduate studies give some indication of their preparation to teach mathematics. Also, research shows that higher achievement in mathematics is associated with teachers having a bachelors and/or masters degree in mathematics.(1) According to their teachers, however, U.S. eighth-grade students were less likely than those in other countries to be taught mathematics by teachers with a major area of study in mathematics.
On average internationally, 71 percent of students were taught by teachers who had mathematics as a major area of study. (Note that teachers can have dual majors, or different majors at the undergraduate and graduate level.) This compares with 41 percent for the United States, a figure not too different from that for many Benchmarking participants, although there was a range of 16 percent in Jersey City to 73 percent in First in the World and Naperville. Suffice it to say that in the United States and most Benchmarking entities, a smaller percentage of students than the international average was taught by mathematics teachers with a major in mathematics. Canada and Italy were the only nations that reported lower percentages than the United States.
Internationally on average, 31 percent of the students were taught by teachers with mathematics education as a major area of study. In comparison, more than half of the students were taught by teachers with this major in the states of Illinois, Michigan, and Pennsylvania, as well as in the districts and consortia of Chicago, First in the World, the Fremont/Lincoln/Westside Public Schools, Guilford County, Project SMART, Rochester, and the Southwest Pennsylvania Math and Science Collaborative.
Internationally on average, 32 percent of the students were taught by teachers with education as a major area of study. Significantly more students in the United States (54 percent) had mathematics teachers with an education major than did students internationally. In general across the Benchmarking participants, about twice as many teachers reported an education major as did internationally. It is clear that teachers in the United States have less in field mathematics preparation than their counterparts around the world.
To gauge teachers confidence in their ability to teach mathematics topics, TIMSS constructed an index of teachers confidence in their preparation to teach mathematics (CPTM), presented in Exhibit 6.3. Teachers were asked how well prepared they felt to teach each of 12 mathematics topics (e.g., properties of geometric figures, solving linear equations and inequalities). There were three possible responses: very well prepared was assigned a value of three, somewhat prepared two, and not well prepared one. Students were assigned to the high level of the index if their teachers reported feeling very well prepared, on average, across the 12 topics (2.75 or higher). The medium level indicates that teachers reported being somewhat to well prepared (averages from 2.25 to 2.75), and the low level that they felt only somewhat prepared or less (averages less than 2.25).
The results show that average mathematics achievement is related to how well prepared teachers felt they were to teach mathematics, with higher achievement related to higher levels of teachers confidence. On average internationally, teachers reported relatively high degrees of confidence, with 63 percent of students taught by teachers who believed they were very well prepared. Interestingly, for the United States as a whole and most Benchmarking entities, more students were taught mathematics by teachers confident about their preparation than in almost all the comparison countries. Interpreting these results should take several factors into account. For example, cultural issues may dictate that teachers in the high-scoring Asian countries are more reserved about reporting their strengths and abilities. Also, when the mathematics curriculum is more challenging, teachers may feel less confident in their academic and pedagogical preparation. Nevertheless, it appears that in relation to both high- and low-performing countries around the world, teachers in many Benchmarking entities and in the United States overall may be overconfident about their preparation to teach eighth-grade mathematics.
Exhibit R3.1 in the reference section provides the detail for the 12 topics comprising the confidence in preparation index. On average across countries, the topics having the most students (from 79 to 82 percent) taught by teachers who felt very well prepared were fractions, decimals, and percentages; ratios and proportions; perimeter, area, and volume; evaluate and perform operations on algebraic expressions; and solving linear equations and inequalities. Teachers reported being least well prepared to teach simple probabilities understanding and calculations; just more than half the students internationally (55 percent on average) were taught by teachers who felt very well prepared to teach this topic.
For the Benchmarking jurisdictions, almost all students had teachers confident in their preparation to teach the two number topics that were included in the TIMSS questionnaire: fractions, decimals, and percentages; and ratios and proportions. Similarly, in algebra 90 percent or more of students in most Benchmarking entities were taught by teachers who reported being very well prepared to teach the three algebra topics: algebraic representation; evaluate and perform operations on algebraic expressions; and solving linear equations and inequalities. Similar results were obtained for the topics representation and interpretation of data in graphs, charts, and tables; and simple probabilities understanding and calculations, even though teachers in Idaho, Massachusetts, and North Carolina were less confident about this latter topic. Teachers also appeared confident in their preparation to teach measurement units, instruments, and accuracy,except in North Carolina, the Fremont/Lincoln/Westside Public Schools, Guilford County, and Rochester, where less than 80 percent of the students were taught by teachers who felt very well prepared to teach this topic. The pattern of less confidence in teaching this measurement topic was found internationally and for the United States.
Teachers in the Benchmarking entities expressed the least confidence in their preparation to teach geometry. Less than 80 percent of the students in Idaho, Oregon, the Delaware Science Coalition, and the Fremont/Lincoln/Westside Public Schools had teachers confident about their preparation in any of the three geometry topics. Across nearly all the participating states as well as in a number of the districts and consortia, teachers expressed less than full confidence in their preparation to teach geometric figures symmetry, motions and transformations, congruence and similarity. Interestingly, this pattern was also noted internationally and for the United States, even though these topics are included in the curriculum and taught to substantial percentages of eighth-grade students in the U.S. and abroad. Beyond those already mentioned, Benchmarking entities where less than 80 percent of students had teachers confident about their preparation to teach coordinate geometry were Illinois, Indiana, Missouri, the Jersey City Public Schools, and the Miami-Dade County Public Schools.
Exhibit R3.2 shows principals opinions about the degree to which shortages of qualified mathematics teachers affect the capacity to provide instruction. On average internationally, principals reported that such shortages affect the quality of instruction some or a lot for one-third of the students. This compares with 16 percent in the United States. Benchmarking entities where principals reported that such shortages affect the capacity to provide instruction for more than one-fourth of the students were Maryland, South Carolina, Texas, Chicago, Guilford County, Jersey City, Montgomery County, and Rochester.
Teachers beliefs about mathematics learning and instruction are to some degree related to their preparation. Exhibits R3.3 and R3.4 in the reference section show the percentages of eighth-grade students whose mathematics teachers reported certain beliefs about mathematics, the way mathematics should be taught, and the importance of various cognitive skills in achieving success in the discipline. In general, more students in the Benchmarking entities than internationally were taught by teachers agreeing that mathematics is primarily a formal way of representing the real world. Conversely, more students internationally than in the Benchmarking entities had teachers who agreed that some students have a natural talent for mathematics, and that an effective teaching approach is to give students having difficulty more practice by themselves during class. There was nearly complete agreement by teachers throughout the Benchmarking jurisdictions and around the world that more than one representation should be used in teaching a mathematics topic. Views varied substantially, for both the countries and the Benchmarking entities, regarding the importance of being able to remember formulas and procedures. Less than one-quarter of the students in the Delaware Science Coalition (similar to Chinese Taipei and Korea) were taught by teachers who believed remembering formulas and procedures was very important for students success in mathematics. In contrast, more than half the students in Idaho, South Carolina, Guilford County, Jersey City, and Rochester (similar to the Russian Federation) had teachers who believed this to be the case.
How teachers spend their time in school is determined mainly by school and district policies and practices, but the perspectives they gain during their teacher preparation can also have an effect. Across countries, students mathematics teachers spent only about 60 percent of their formally scheduled school time teaching mathematics (see Exhibit R3.5 in the reference section). Additionally, about 10 percent was spent teaching subjects other than mathematics, about 10 percent on curriculum planning, and about 20 percent on various administrative and other duties. The results for the United States as a whole and for most of the Benchmarking entities were very similar to the international profile.
TIMSS 1999 is a project of the International
Boston College, Lynch School of Education