Four questionnaires directed at teachers of mathematics were developed, one each for teachers of Grade 4, Grade 7, Mathematics 10, and Mathematics 10A. The Grade 4 and Grade 7 mathematics questions were contained in the same questionnaire as the questions for science teachers (see Chapter 10) since most teachers at those levels teach both mathematics and science to their classes. Each questionnaire contained sets of questions about the following areas: subject implementation and classroom practices, perceptions of subject topics in school, and student evaluation. A number of background information questions were also included. Overall descriptions of the questionnaires are provided in Chapter 2.

The first part of the teacher questionnaires asked teachers a variety of questions about themselves and their backgrounds. The responses provided by teachers of mathematics at the Grade 4, 7, and 10 levels are presented next.

9.1.1.1 Age, Gender, and Teaching Experience of Mathematics Teachers

Table 9.1 shows the gender, age, and teaching experience of Grades 4, 7, and 10 teachers of mathematics in British Columbia (two questions are not reported because of ambiguity in the wording: whether the teacher was full-time or part-time, and the type of contract). Data for 1995 and 1990 are reported in the table; a discussion follows. It should be noted that data are reported to the nearest whole number percent; the totals within categories will therefore often not equal 100% because of rounding.

In 1990, 64% of the teachers teaching mathematics in Grade 4 were female; 36% were male. According to the 1995 assessment, the ratio has changed significantly; only one teacher in four (26%) is male. A similar shift has taken place in Grade 7: the gender balance is now 54% male (down from 66% in 1990) to 46% female (up from 34% in 1990). It is not immediately apparent why these changes have occurred.

It is not news that the teaching population in British Columbia is ageing. That is well documented elsewhere. Of interest in the present assessment, however, is the information that only 22% and 18% of Grade 4 and 7 teachers respectively are in the 50 and over group, compared to more than 30% for both Math 10 and 10A. Clearly, there will be proportionately a much greater need for replacement mathematics teachers at the Grade 10 level as members of this over-50 group begin to retire.

Responses to the question on teaching experience showed a smaller proportion of teachers in their first year of teaching at the elementary level than at secondary. For example, 3% of elementary respondents were in their first year of teaching, compared to 7% for Math 10A and 5% for Math 10. Further, 62% of elementary teachers had more than 10 years' experience compared to 66% and 69% for Math 10A and 10 respectively.

These results show higher proportions of teachers of secondary mathematics in both younger and older groups, compared to those at the elementary level. Correspondingly, a larger proportion of elementary teachers are in the middle group.

Table 9.1 Age, Gender, and Teaching Experience of Mathematics Teachers (10K)

9.1.1.2 Educational Background of Mathematics Teachers

Several questions on the questionnaires pertained to teachers' educational backgrounds. Table 9.2 reports the educational background of British Columbia mathematics teachers; a discussion of the information summarized in the table follows.

Teachers of Grades 4 and 7 have fewer degrees than those in Grade 10. Nine percent in Grade 4 and six percent in Grade 7 report having no degree, compared to fewer than one-half of one percent of the teachers in Grade 10. Grade-level differences were also evident for teachers who reported having a master's degree. They were as follows: Grade 4: 10%; Grade 7: 21%; Math 10A: 26%; and Math 10: 25%.

Teachers were asked how many post-secondary courses they had completed in mathematics content and methods. Percentages of teachers with no post-secondary mathematics content courses were as follows: Grade 4: 19%; Grade 7: 21%; Math 10A: 11%; and Math 10: 2%. Results for mathematics methods courses were quite different among the teacher groups: 15% of Grade 4 and 24% of Grade 7 teachers had taken no mathematics methods courses, compared to 36% of the Math 10A and 19% of the Math 10 teachers.

Table 9.2 Educational Background of Mathematics Teachers (10K)

While secondary teachers have taken considerably more post-secondary mathematics content courses than elementary teachers, there are a number of significant differences when it comes to methods courses. Compared to the other teacher groups, a larger percentage of Math 10A teachers have had no methods courses. On the other hand, a higher proportion of Math 10A teachers have taken three or more methods courses in mathematics than have teachers at either of the two elementary grades. Teachers of Math 10A therefore have a wide range of preparation for teaching the subject; there are well-trained mathematics teachers, and there are others with little or no training in mathematics.

9.1.1.3 Mathematics Teachers' Instructional Preferences

Teachers were asked to indicate the subjects and grade levels they preferred to teach. Their preferences are reported in Table 9.3 and discussed below.

Table 9.3 Mathematics Teachers' Instructional Preferences (10K)

Teachers of Grade 4 most prefer to teach language arts (81%), mathematics (76%), and social studies (66%). Specialty subjects such as music (14%), French (12%), and physical education (34%) were the least popular teaching assignments. At the Grade 7 level, the favorite teaching assignment was mathematics (78%), followed by language arts (67%), and social studies (65%). Teachers of Math 10 and Math 10A were mostly mathematics specialists; it is not surprising that 98% of the Math 10 and 84% of the Math 10A teachers identified mathematics as their most preferred subject to teach.

Most (83%) of the Grade 4 teachers preferred to teach at the intermediate (4--7) level, 29% identified primary (K--3) as a preferred area, and 5% indicated a preference for secondary. Since teachers could indicate more than one level of preference, results total more than 100%. Seventeen percent of the Grade 4 teachers, however, indicated a preference for teaching at a level other than their current level.

Teachers of Math 10A were evenly divided in preference between junior secondary and senior secondary. Most (72%) of the Math 10 teachers would prefer to be teaching in senior secondary grades.

Teachers responded to several questions relating to their mathematics teaching loads, their involvement in professional development activities, and the time they spent outside of school on educational activities.

9.1.2.1 Teaching Load and Instructional Organization in Mathematics

Table 9.4 provides some comparative data regarding teaching loads and length of class periods, and an indication of the number of times that classes meet in a given week for Grades 4, 7, and 10. Discussion of the results presented in the table follows.

Table 9.4 Teaching Load and Instructional Organization in Mathematics (8K)

9.1.2.1.1 Teaching Load in Mathematics at the Secondary Level

Teachers of Math 10 tend to specialize more in the teaching of mathematics as a subject than those of Math 10A. For example, only 4% of Math 10 teachers spend twenty percent or less of their time teaching the subject, compared to 15% of Math 10A teachers. Further, 63% of Math 10 teachers spend more than 80% of their time teaching mathematics, compared to 41% of Math 10A teachers.

9.1.2.1.2 Length of Mathematics Classes

Mathematics classes are shorter in length at the elementary level than at secondary. For example, more than 90% of teachers of Grades 4 and 7 reported that classes were 60 or fewer minutes in length. Of these, approximately half were between 31 and 45 minutes, with the balance between 46 and 60 minutes. Most classes at the secondary level ranged between 46 and 75 minutes in length, 80% for Math 10A and 84% for Math 10.

9.1.2.2 Time Spent on Educational Activities Outside of School

Teachers were asked to estimate the number of hours per week they normally spend on educational activities outside the school day. They responded on a five-point scale ranging from none to more than 4 hours. Results rounded to the nearest whole number percent, are shown in Table 9.5.

Table 9.5 Mathematics Teachers' Time Spent per Week on Activities Outside the Formal School Day (13K)

Teachers reported spending the most time outside of school hours on planning lessons, reviewing other student work, administrative tasks, and preparing and grading examinations and tests. They reported spending the least time in meeting parents, professional development, and meeting students.

Teachers at the secondary level spend considerably more out of class hours preparing and grading examinations, and meeting students than do teachers at the elementary level. For example, 62% of Math 10 teachers and 51% of Math 10A teachers spend three or more hours preparing and grading student tests or exams, compared to 20% at Grade 4 and 26% at Grade 7. Thirty-seven percent of Math 10 and 20% of Math 10A teachers spend three or more hours with students each week outside of regular class time. This compares to 8% and 16% of Grade 4 and Grade 7 teachers respectively.

Elementary teachers spend more time reading and grading student work, and on administrative tasks than their counterparts at secondary. For example, almost twice the proportion of elementary as secondary teachers (63% and 64% compared to 37% and 35%) spend three or more hours reading and grading other student work. This is not surprising, given that elementary teachers teach most if not all subjects, and most secondary teachers specialize in one or two.

9.1.2.3 In-Service and Professional Involvements of Mathematics Teachers

9.1.2.3.1 Mathematics Teacher's Professional Organizations

Another question asked teachers which professional organizations they belonged to. The results are shown in Table 9.6. Fifty-three percent of Math 10 teachers belonged to the BC Association of Mathematics Teachers, compared to 33%, 4%, and 3% of teachers of Math 10A, Grade 7, and Grade 4 respectively. Similar results, although of smaller magnitudes, were found on membership in the National Council of Teachers of Mathematics.

Table 9.6 Mathematics Teachers' Professional Organizations (5K)

This evidence supports an earlier finding on preparation and training in mathematics, which found that teachers of Math 10A have a wide range of both preparation and professional involvement in mathematics education. This outcome is likely due to the fact that, because of time-tabling and staffing issues, both trained mathematics teachers and those with no mathematics training at all teach this course.

9.1.2.4 Number of Mathematics In-Service Sessions Attended

Teachers were asked how many mathematics in-service sessions they had attended over the past four years. Results are shown in Table 9.7.

Table 9.7 Teachers Attendance at Mathematics In-Service Sessions Over Past Four Years (5K)

Table 9.7 shows that teachers of Grades 4 and 7 attended fewer mathematics in-service sessions during the past four years than teachers at the secondary level. For example, 23% of Grade 4 and 22% of Grade 7 teachers had attended three or more mathematics in-service sessions during that period, compared to 37% of Math 10A teachers and 54% of Math 10 teachers. At the secondary level, however, additional differences were apparent between the two groups. Math 10 teachers were much more involved in mathematics in-service than teachers of Math 10A. Almost a third (31%) of Math 10A teachers had not attended any in-service activities during the past four years, compared to 12% of Math 10 teachers.

Among the questions on mathematics implementation and classroom practices were several regarding teaching strategies, use of technology, and the role of homework.

9.1.3.1 Mathematics Teachers' Teaching Strategies

About three-quarters of the teachers at each grade reported that their approach to teaching mathematics had changed during the past four years. The percentages reporting changes were 76% for each of Grades 4 and 7, 75% for Math 10A, and 74% for Math 10.

Teachers were asked to identify, from a list of teaching strategies, those which reflected their approach to teaching mathematics. A summary of results, rounded to the nearest whole number percent, is shown in Table 9.8.

The most popular strategies at Grade 4 were the use of concrete materials and problem-solving processes. The least popular were the use of computers and calculators. In Grade 7, problem-solving processes and cooperative learning were the two most popular; using computers and an activities-based approach were least popular. The most popular strategies in Math 10 and Math 10A were using calculators and problem-solving processes. Computers and an activities-based approach were used least often.

Respondents were also asked how frequently they showed students what to do on the blackboard or overhead, how often students used objects like blocks or counters, and how frequently students worked individually on problems from textbooks or other exercises. Teachers at all levels used the blackboard or overhead frequently (most or every lesson): Grade 4: 82%; Grade 7: 88%; Math 10A: 88%; and Math 10: 94%. Ninety-two percent of Grade 4 teachers and 66% of Grade 7 teachers use objects like blocks and counters at least some of the time. Only 38% of Math 10A and 37% of Math 10 teachers reported the same level of use.

Table 9.8 Teachers' Approaches to Teaching Mathematics (5K)

Students worked frequently from textbooks or exercise sheets at all levels. More than 95% of all teachers reported that this occurred in at least some lessons.

9.1.3.2 Practices in Mathematics Classrooms

Teachers of Grade 7 mathematics, Mathematics 10, and Mathematics 10A were asked a series of three questions related to various practices in their classrooms. The first involved the frequency with which they assigned student activities, the second dealt with the extent to which students worked individually and in groups, and the third focussed on how incorrect oral responses were dealt with.

9.1.3.2.1 FREQUENCY OF VARIOUS ACTIVITIES

In answering questions about the frequency with which they assign various activities to students, teachers responded to a four-point scale, ranging from never to every lesson. Results are shown in Table 9.9.

Table 9.9 Teachers' Assignment of Student Activities in Mathematics (8K)

The activities occurring most frequently (most or all lessons) across courses were: explaining the reasoning behind ideas; practising computation skills; and writing equations to represent relationships. For example, more than 61% of the teachers indicated that they frequently have students explain the reasoning behind the mathematical idea. The use of computers to solve exercises or problems was the least common activity, with only 2%, 1%, and 3% of the teachers of Grade 7, Math 10, and Math 10A respectively, reporting frequent use of this activity in their classrooms.

Comparisons of the frequencies of classroom activities among teachers of different levels show greater focus on some activities than others. For example, practising computational skills was reported to occur more frequently in Grade 7 (66% of respondents) than in Math 10 (41% of respondents). On the other hand, students in Math 10 wrote equations to represent relationships more frequently than those in Math 7, as indicated by 49% and 34% of respondents respectively.

9.1.3.2.2 Working Individually and in Groups

Teachers were asked how often students worked on their own, how often they worked as a class, and how often they worked in pairs or small groups. In each case, they were asked how frequently these activities occurred both with and without teacher assistance. A four-point frequency scale was used, with the following options: never or almost never, some lessons, most lessons, and every lesson. Results are shown in Table 9.10.

Table 9.10 Teachers' Assignment of Individual and Group Activities (10K)

Across courses, organizing students to work individually with assistance from the teacher was reported as the most frequent activity; working in pairs or small groups without assistance from the teacher occurred least often. Individual work, both with and without assistance from the teacher, occurred more often in Math 10A classes than in either Grade 7 or Math 10.

9.1.3.2.3 Handling Incorrect Student Oral Responses

Teachers were asked how they dealt with incorrect oral responses from students. In these cases, they were asked how frequently they reacted in the following ways: corrected the error in front of the class, asked another leading question, called on other students likely to give the correct response, and called on other students to get various responses. A summary of results is shown in Table 9.11.

Table 9.11 Teachers' Management of Students' Incorrect Oral Responses (5K)

Results show that in the majority of cases, when a student gives an incorrect response, teachers either ask another question to help arrive at a correct response or else call on other students to generate a variety of responses for use in discussing the correct answer. For example, more than 71% reported frequent use of the former technique, and more than 61% reported the latter. These results show that teachers in each course used similar methods to deal with incorrect oral responses.

It was clear that teachers do not frequently correct a student in front of the class or call on another student who is likely to give the correct answer. Through using the two most frequent techniques, teachers are able to utilize an incorrect response to create a learning situation for the student as well as for the rest of the class.

9.1.3.3 Use of Technology

Several questions dealt with enjoyment of, access to, and use of calculators and computers. Among them were questions asking how much teachers enjoyed using calculators and computers in math class and at home, what level of access students had to these technologies, and what activities students used calculators for.

The question dealing with enjoyment asked whether or not teachers used calculators and computers in class or at home, and, if so, how much they enjoyed their use. A summary of results is shown in Table 9.12.

Computers are not used in mathematics classes by the majority of teachers: between 58% and 65% of teachers across grade and subject levels reported that they did not use computers. Of those who did use computers in mathematics classes, the vast majority said that they liked to use them. Although at most 42% said they used computers in math class, 80% or more reported using computers at home.

Table 9.12 Teachers' Use and Enjoyment of Calculators and Computers (8K)

Calculators are used in mathematics classes extensively at the secondary level. For example, more than 97% of Grade 10 teachers reported their use. The level of use at Grade 7 was also relatively high with 92% saying they are used, compared to 78% at Grade 4.

Most students have access to calculators during mathematics lessons, especially at the secondary level. However, access to computers is far more limited. In more than 70% of cases, teachers reported that students had no access to computers during mathematics lessons.

Teachers were asked how often students use calculators for various activities. The most popular uses at Grade 4 were for checking answers, solving complex problems, and exploring number concepts. All uses occurred more frequently at Grade 7, with the most popular being solving complex problems and exploring number concepts. Calculators were used far more extensively at Grade 10 for all activities than at either Grade 4 or 7. In addition to frequent use in all of the activities already mentioned, calculators were also used for tests and exams, and for routine computation.

9.1.3.4 Role of Homework

Several questions at Grades 7 and 10 dealt with homework. Teachers were asked how often homework was assigned, how much student time was required for assignments, what kinds of tasks were assigned, and how results were dealt with.

The question which dealt with how often homework was assigned asked teachers if they never or almost never assigned it; or if they did, was it with some lessons, most lessons, or every lesson. Teachers of Math 10 assigned homework most often, Grade 7 teachers were next, followed by Math 10A. Almost all (91%) of Math 10 teachers assigned homework most lessons or every lesson, compared with 80% for Grade 7 and 68% for Math 10A. Two percent of Math 10 and Grade 7 teachers claimed they never assigned homework, compared with 9% of those teaching Math 10A.

The most frequent length of a homework assignment was 15 to 30 minutes, assigned by 73% of Grade 7, 57% of Math 10A, and 53% of Math 10 teachers. On the other hand, the longest assignments were given by teachers of Math 10. Forty-three percent of them gave assignments longer than 30 minutes, compared with 24% for Math 10A and 16% for Grade 7.

Teachers of Grade 7, Math 10, and Math 10A responded to two questions related to the type of, and the follow-up to, homework assignments. They were asked how frequently various types of tasks were assigned and what they did with written results from students. Responses were on a four-point scale, with an additional option if they didn't assign homework. Options were as follows: never, rarely, sometimes, always, and I don't assign homework. Results are reported in Table 9.13 and Table 9.14.

9.1.3.4.1 Kinds of Homework Tasks

The most popular homework assignments were those involving problem/question sets in the textbook, and the use of worksheets or a workbook. The former activity was sometimes or always assigned by 94%, 96%, and 93% of teachers of Grade 7, Math 10, and Math 10A respectively. Teachers of Math 10 used worksheets or workbooks more than the others. For this type of homework, 82% of the Math 10 teachers reported sometimes or always assigning them, compared with 60% of Grade 7 and 76% of Math 10A teachers.

Keeping a journal and preparing oral reports were the least used types of homework assignments. Fewer than 12% of teachers claimed they assigned either of these kinds of tasks on a sometimes or always basis.

9.1.3.4.2 Follow-up to Homework Assignments

Table 9.14 summarizes teachers' responses to questions about how often they used procedures such as record-keeping, correction of answers, class discussion, and assignment of marks in following up on homework assignments.

The most common follow-up activities for a homework assignment were to record whether or not it was completed, and to give feedback on the assignment to the whole class. More than 90% of teachers at each level reported the use of these activities. The least common follow-up activity was to collect, correct, and keep the assignments. This practice was reported as sometimes or always by only 52% of Grade 7, 26% of Math 10, and 41% of Math 10A teachers. These percentages, however, increased significantly if the practice included return of the corrected assignments to students. In this case the percentages increased to 80%, 73%, and 83% for teachers of Grade 7, Math 10, and Math 10A respectively.

Table 9.13 Teachers' Assignment of Types of Homework Tasks (13K)

Table 9.14 Teachers Follow-up to Written Homework Assignments (13K)

9.1.4 Teachers' Perceptions of Mathematics Topics and Activities

Teachers were asked to rate the importance of, difficulty of teaching, and enjoyment of teaching the major topics and activities in each course. Each topic or activity was rated on a five-point scale ranging from not at all important to very important, from very difficult to very easy, and from dislike a lot to like a lot for each of the importance, difficulty, and enjoyment scales respectively. Results are shown in a separate table for each course.

9.1.4.1 Teachers of Grade 4

Table 9.15 reports how Grade 4 mathematics teachers rated 12 major topics and activities. Discussion of the results follows.

Table 9.15 Grade 4 Teachers' Perceptions of Topics and Major Activities (25K)

9.1.4.1.1 Importance Ratings

The three most important topics, in order of rating, were operations with whole numbers, place value, and problem solving (see Table 9.15). Each of these was rated as important or very important by more than 96% of the teachers. The lowest ratings were for using calculators, geometry, and using objects. These received ratings of 69%, 82%, and 82% respectively. With the exception of using calculators, all topics and activities received combined important and very important ratings of over 80%.

Student rankings for these topics and activities were similar to their teachers'. For example, they rated the most important topic to be operations with whole numbers and the second least important as using calculators. Although the magnitudes of ratings were less than their teachers', students held similar perceptions of importance.

9.1.4.1.2 Difficulty Ratings

Teachers reported the three easiest topics to teach as using graphs, geometry, and operations with whole numbers (see Table 9.15). Each of these was considered easy or very easy to teach by more than 71% of teachers. Teachers said the most difficult topics to teach were problem solving, place value, and estimation. Only 32%, 40%, and 42% rated these respective topics as easy to teach.

These results differed somewhat from those of students, who rated them in terms of how easy they were to learn. For example, students found the easiest topics or activities to learn were using calculators, checking answers, and using objects. Similar to their teachers, they found problem solving to be the most difficult.

9.1.4.1.3 Enjoyment Ratings

Teachers enjoyed teaching operations with whole numbers the most, with 96% reporting that they liked to teach this topic. Other topics receiving enjoyment ratings of over 80% were using graphs, 88%; fractions, 85%; and geometry, 84%. Teachers least enjoyed teaching using calculators, checking answers, and estimation, all of which received combined like and like a lot ratings of less than 70%. The topics most actively disliked by teachers (disliked or disliked a lot) were checking answers (12%), estimation (11%), and place value (11%).

9.1.4.2 Teachers of Grade 7

Teachers of Grade 7 mathematics rated topics and activities in the same way as those in Grade 4. The topics and activities, however, corresponded to those of major importance at this level. As a result, some topics were different and some were the same. Results are shown in Table 9.16.

9.1.4.2.1 Importance Ratings

More than 90% of the teachers rated eight of the 12 topics/activities as important or very important. Those with the highest combined ratings were decimals (97%), percents (97%), and problem solving (97%). The topics with the lowest combined ratings were fractions (75%) and integers (75%).

In contrast, students ranked fractions as the most important topic. They agreed with most of teachers' other ratings, however, with decimals and percents among the highest ratings and integers among the lowest.

Table 9.16 Grade 7 Teachers' Perceptions of Topics and Major Activities (25K)

9.1.4.2.2 Difficulty Ratings

Teachers considered using calculators and data and graphs to be the easiest topics to teach, with 76% and 72% rating them as easy or very easy. Problem solving, estimation, and equations were rated as the most difficult. For example, only 26% considered problem solving to be easy or very easy to teach.

These results differ somewhat from those of students, who rated the same topics and activities in terms of how easy or difficult they were to learn. For example, students agreed that using calculators was the easiest, but considered data and graphs to be the one of the most difficult topics to learn.

9.1.4.2.3 Enjoyment Ratings

The majority of teachers enjoyed teaching most topics, with the exception of basic facts. All but this topic received combined like and like a lot ratings of over 65%. In contrast, only 47% reported they liked or liked a lot teaching basic facts. The most popular topics and activities were learning geometry and percents, with combined like and like a lot ratings of 88% and 88% respectively. Other topics with ratings greater than 80% were data and graphs; decimals; equations; and perimeter, area, and volume.

Students enjoyed learning to use calculators the most, and integers and basic facts the least. All of their other combined like and like a lot ratings were more conservative than their teachers', ranging from 48% to 58%.

9.1.4.3 Teachers of Math 10 and Math 10A

Teachers of Math 10 and Math 10A rated the same topics and activities for importance, difficulty, and enjoyment. Although the courses are different, major topics are similar. The differences between the courses relate to purpose and application. Math 10 topics focus more on academic applications and on preparation for further study, whereas Math 10A topics focus on applications in the workplace or in the consumer marketplace. Results for each course are reported in Table 9.17 and Table 9.18.

Table 9.17 Mathematics 10 Teachers' Perceptions of Topics and Major Activities (25K)

Table 9.18 Mathematics 10A Teachers' Perceptions of Topics and Major Activities (25K)

9.1.4.3.1 Importance Ratings

The most important topics (based on combined important and very important ratings) identified by teachers of Math 10 were problem solving (98%) and equations and expressions (95%). Others with combined ratings higher than 80%, in order, were trigonometry; fractions, decimals, and percent; geometry; exponents; perimeter, area, and volume; estimating answers; and estimation. Those with the lowest combined ratings were using computers; data analysis; and basic facts. These topics received ratings of 58%, 61%, and 66% respectively.

Math 10A teachers rated problem solving (combined important and very important ratings of 97%); perimeter, area, and volume (97%); and decimals, fractions, and percent (96%) as the most important topics. Those with the lowest ratings were trigonometry (54%), computers (55%), and exponents (65%).

Teachers of both courses ranked problem solving very high, whereas Math 10 teachers rated equations and expressions, trigonometry, and exponents more highly than teachers of Math 10A. Those teaching Math 10A, on the other hand, rated fractions, decimals, and percent; and perimeter, area, and volume more highly than their Math 10 counterparts. These differences reflect content differences between the courses.

9.1.4.3.2 Difficulty Ratings

Math 10 teachers reported that the easiest topics to teach were: perimeter, area, and volume; trigonometry; and exponents. These topics received combined easy and very easy ratings of 81%, 73%, and 63% respectively. Computers, problem solving, and basic facts were rated the most difficult, with easy and very easy ratings ranging from a low 15% to 38%.

The order of ratings of Math 10A teachers was similar to that of Math 10 teachers, but the proportions of teachers who found topics easy to teach were considerably lower than for teachers of Math 10. For example, the easiest topic to teach was reported by teachers of Math 10A to be perimeter, area, and volume. The proportion of these teachers who judged this topic as easy or very easy was 70%, compared with 81% of those teaching Math 10. No other topics received a combined easy and very easy rating greater than 50% from Math 10A teachers. The next easiest topics were exponents (50%) and data analysis (49%).

Teachers of both courses found the teaching of computers and problem solving to be very difficult. Fewer than 17% of them found these topics to be easy or very easy to teach. Given the importance of these topics, it is therefore recommended

Recommendation 9.1

That the Ministry of Education and school districts provide teachers of Math 10 and Math 10A in-service and training in the teaching of problem solving, and in the integrated use of computers for the teaching of mathematics.

9.1.4.3.3 Enjoyment Ratings

Teachers of Math 10 most liked teaching equations and expressions, and trigonometry. Math 10A teachers liked to teach perimeter, area, and volume; and equations and expressions more than the other topics.

The lowest ratings reported by both Math 10 and Math 10A teachers were for teaching basic facts and computers. These topics were liked or liked a lot by no more than 36% in each group. Teachers from both groups most actively disliked teaching basic facts: about a quarter of the teachers in each group indicated that they disliked or disliked a lot the teaching of basic facts. Both groups were much more neutral about computers: they did not particularly like this area, but they did not express a strong dislike, either; just over six percent in each group indicated a dislike.

Each questionnaire included a series of questions dealing with student evaluation. Teachers were asked whether their approach to student evaluation had changed, which evaluation strategies they used, what uses they made of assessment data, how they weighted results, and what factors helped to explain why some students are not making satisfactory progress. A discussion of results follows.

9.1.5.1 Approach to Student Evaluation

The majority of teachers indicated that their approach to student evaluation had changed during the past four years. The proportions of teachers indicating that change had taken place were 65% at Grade 4, 64% at Grade 7, 62% for Math 10A, and 58% for Math 10.

9.1.5.2 Use of Evaluation Strategies

The question dealing with the use of evaluation strategies asked teachers to select from a list the strategies that reflected their approach to student evaluation in mathematics. Results are summarized in Table 9.19.

Table 9.19 Teachers' Steategies for Student Evaluation (8K)

The most popular student evaluation strategies across levels were evaluating problem-solving strategies as well as answers, and use of quizzes and tests. At the Grade 4 level, 82% of teachers reported the use of informal observations. This percentage decreases in the higher grades, with 64% of Grade 7, 46% of Math 10A, and 37% of Math 10 teachers indicating the use of informal observations.

Most teachers indicated that changes in their evaluation practices did not include fewer quizzes and tests, particularly at the Grade 10 level. Fewer than 10% of teachers at that level reported less frequent use, compared to 26% and 16% of teachers of Grades 4 and 7 respectively.

Student self-assessment is used more frequently in Grade 4 than at higher levels. Compared to Math 10 teachers, more than twice the proportion of Grade 4 teachers reported using this strategy.

9.1.5.3 Uses of Assessment Data and Weighting of Results

Results for questions related to uses of assessment information and weights given to different types of assessment information are discussed next. Summaries are shown in Table 9.20 and Table 9.21.

The most extensive uses of assessment information were for feedback to the student and for determining grades or marks. More than 90% of the teachers across levels reported they used assessment information for these purposes either quite a lot or a great deal. The least frequent use was for assigning students to programs or tracks. Approximately half the teachers reported frequent use of this application, and the balance reported that they used it either little or not at all.

Although most teachers used assessment information a lot for reporting to parents, teachers at the Grade 4 and 7 levels used it more than teachers at Grade 10. Nearly nine out of 10 teachers of Grades 4 (89%) and 7 (88%) used assessment information for this purpose quite a lot or a lot, compared to 82% and 76% of teachers of Math 10 and Math 10A respectively.

Table 9.20 Teachers' Use of Assessment Information (8K)

Two other major differences between teachers of elementary and secondary levels were apparent in the extent to which assessment information was used: elementary teachers made greater use of assessment information in diagnosing learning problems of students and in planning for future lessons. Given the importance of these uses it is recommended

Recommendation 9.2

That teachers of secondary mathematics make greater use of assessment information for diagnosing student learning problems and for course planning.

To facilitate achievement of this objective, it is also recommended

Recommendation 9.3

That school districts and the Ministry of Education provide teachers with in-service opportunities and resource packages related to using assessment information for diagnosing student learning problems and for course planning.

9.1.5.3.1 Weights Given to Different Types of Assessment Information

Weights given to different types of information collected for assessment purposes are discussed next. Teachers were asked how much weight they gave to each source of information listed in Table 9.21.

Teachers of Grade 4 reported that they assigned the most weight to information based on observations of students, responses of students in class, and how well students did on projects or practical/lab assignments. The least weights were assigned to standardized tests produced outside of school and to teacher-made multiple-choice, true-false, or matching tests.

Grade 7 teachers, similar to those in Grade 4, assigned their greatest weights to information based on observations of students and responses of students in class. The proportions who assign a lot of weight to these sources, however, are more than 20 percentage points lower than at Grade 4. The third highest weight for Grade 7 was for performance on homework assignments. Sources of information assigned the least weights were standardized tests produced outside of school and teacher-made multiple-choice, true-false, or matching tests, the same as for Grade 4.

Teachers of Math 10 and Math 10A assigned less weight to most categories than did elementary teachers. The greatest weights were for teacher-made short-answer or essay tests and for performance on homework assignments; the lowest weights were for standardized tests and teacher-made multiple-choice tests.

The greatest differences between weights assigned by elementary and secondary teachers were for observations of students in class and for responses of students in class. The percentages of teachers who assigned a lot of weight to these were 84% and 79% at Grade 4; 60% and 55% at Grade 7; 22% and 21% at Math 10; and 31% and 25% at Math 10A respectively. A major reason for these differences is likely the extent to which most teachers at the elementary level have an opportunity to know and observe a single classroom of students compared to the several different classes taught by secondary teachers working with a rotating timetable.

Given that the provincial curriculum stresses active learning, and that direction from the Ministry of Education is for the use of criterion-referenced assessment, it is increasingly important that teachers make extensive use observational techniques in their assessment of students. Therefore, it is recommended

Recommendation 9.4

That the Ministry of Education and school districts provide teachers with training opportunities in the use of observational techniques for the assessment of students and that these techniques be used more extensively in classrooms, particularly those of Grade 7, Math 10, and Math 10A.

Table 9.21 Teachers' Assignment of Weights to Types of Assessment (10K)

Table 9.22 Teachers' Ratings of Factors Affecting Student Success in Mathematics (10K)

9.1.5.4 Teachers' Opinions of Factors Affecting Student Success in Mathematics

Teachers were given a list of factors that could explain why some students do not make satisfactory progress in mathematics and were asked to indicate on a three-point scale how important each factor was in students' failure to succeed. Table 9.22 provides an indication of teachers' reasons for students' lack of success in mathematics.

The factor having the greatest impact on lack of student success identified by mathematics teachers was student indifference or lack of motivation. This factor was considered to be of major importance by 72%, 81%, 93%, and 91% of teachers of Grade 4, Grade 7, Math 10, and Math 10A, respectively. The second greatest factor was student absenteeism (particularly in Grade 10), followed by lack of ability and misbehavior.

Of the factors listed, those considered by mathematics teachers to have the least impact on student failure were insufficiency of the teacher in dealing with student difficulties, insufficient school time for math, and limited resources and materials.

9.1.5.5 Similarities and Differences Among Grades 4, 7, and 10 Teachers

Within this section, a different method of reporting some of the scales is used. Traditionally, when a set of items that use the same response scale is presented (such as when teachers were asked to respond on a scale of frequently, occasionally, seldom, or never regarding how often they use different instructional approaches) the results are reported in a series of tables (see previous sections). However, the completeness and detail of this method of reporting make it very difficult to "see the picture"; the tables are difficult to understand, even for people who are very familiar with numbers and tables. The following approach presents a more visual method which has been developed to present the data in one "picture."

For each item, or set of items, using a common scale, a weighted mean was calculated by assigning consecutive numeric values, beginning with "1," to each of the ordered response categories. While the response categories never form an interval scale, and the weighted mean therefore has no meaning in and of itself, such a procedure does allow for the ranking of the various items and allows a perception of the relative "closeness" or "farness" of the item responses from one another. By plotting these means on a number line, one can then visualize this relative ranking of the items. By placing identical number lines for each of the grades one above the other, one can also visualize the relative changes or differences from one grade to the next on the set of items. In addition, each of the whole number points on the number line represents the response category from which it was derived. These points can then be labeled for additional interpretability. The true "distance" from frequently to occasionally may be much larger or smaller than the "distance" from occasionally to seldom, and the same is true for the differences among all the various response category. The number lines used in this report, however, treat the distances as being equal intervals. Therefore, the number lines, while they present a true ranking of the items and true ranking differences among the grades, may not present a true picture of the relative spacing that may exist between the response categories. However, they do enable one to readily "picture" the collated data.

Figure 9.1 shows the relative amounts of time each week that mathematics teachers spend outside the formal school day on various school-related tasks. Teachers spend the majority of their out of classroom time preparing, reading, and grading student work; planning lessons; and doing administrative tasks. There are three notable differences among the grade levels on this set of responses. First, as the grades advance, teachers spend relatively more time preparing or grading student tests or exams. However, second, there is a corresponding drop in the amount of time spent reading and grading other student work as the grades progress. The third notable difference is the higher the grade, the more time spent by teachers meeting with students outside of classroom time. This seems to be particularly true for teachers of Math 10A students.

Figure 9.1 (8K)

Figure 9.2 shows the relative assignment of weights by teachers to different sources of assessment information. At the higher grades, teachers of mathematics place relatively less emphasis on practical and in-class work of students than teachers in Grades 4 and 7. Observations of students and responses of students in class go from being the two highest weighted assessment information sources in the elementary grades to having little weight at Grade 10.

Figure 9.2 (5K)