6 Relationship of Achievement to Student Backgrounds and Attitudes

This chapter examines the relationships between student achievement and various background and attitudinal variables. Mathematics achievement and relationships are discussed first, followed by science. In all cases, it is important to note the difference between statistical significance and significance in educational terms. With large samples of students, it is possible to obtain statistically significant results based on very small observed differences, as little as one percentage point in this assessment. Judgments must be made as to whether or not an actual difference in achievement between clusters of students is of any practical value for educational purposes.

This section reports results involving relationships between mathematics achievement and student variables. It examines, for example, levels of achievement and sets of variables corresponding to student background, attitudes and perceptions, and classroom practices as reported by students. A discussion of each category follows.

Several student background variables are examined with relationship to corresponding levels of achievement. Among them are gender, English spoken at home, availability of a computer at home, and program.

6.1.1.1 Gender and Mathematics Achievement

There were five mathematics core items in each of Grades 4 and 10, compared with six in Grade 7. At the Grade 10 level, results are combined for Mathematics 10 and Mathematics 10A.

Boys outperformed girls on the core mathematics items at each grade level. For example, 65% of the Grade 4 boys answered either four or five out of a total of five core items correctly. This compares with 62% of the Grade 4 girls. At the Grade 7 level, a similar pattern is shown, with 35% of the boys and 33% of the girls answering either five or six items out of six correctly. Again, a similar result was also found at the Grade 10 level, where 45% of the boys and 40% of the girls answered either four or five items out of five correctly. The mean scores for girls and boys by grade and form are shown in Table 6.1.

Table 6.1 Gender Differences in Achievement for Each Form (5K)

Over all of the multiple choice items, boys consistently outscored girls by a small amount (less than three percentage points at most). In Grades 4 and 7, a difference of 0.3 in mean score represents a difference of about one percentage point. In Grade 10, the same difference represents about one and a half percentage points. There is little educational significance in differences of this magnitude.

6.1.1.2 English Spoken in the Home and Mathematics Achievement

Students were asked a question on the extent to which English was spoken in their homes. Students in homes where English was always or almost always spoken did better than their counterparts at that Grade 4 level. Two thirds (65%) of students from these homes answered either four or five of the core items correctly. In comparison, 55% of students from homes where English was sometimes spoken, and 44% from homes where it was never spoken scored at the same level.

In Grade 7, results shifted among the three groups. About a third (34%) of students from homes where English was almost always spoken answered either five or six out of the six core items correctly. This compared to 35% of the students from homes where it was sometimes spoken, and 37% of those from homes where it was never spoken. This pattern continues at the Grade 10 level. Here the proportions of students were 41%, 49%, and 49% respectively.

These results show a significant trend as students increased in grade level. In the early grades, the performance of students from non-English speaking homes is behind that of other students, then meets the level of other students, and finally surpasses the achievement level of students from primarily English speaking homes.

6.1.1.3 Program Enrolled in and Achievement on Mathematics Core Items

Students were also asked which program they were enrolled in. At the Grade 4 level they selected from the regular English program, Early Immersion, or Programme Cadre. At Grades 7 and 10, Late Immersion was added as an option. All test items were administered in English.

Students in Grade 4 enrolled in the regular English program and in Early Immersion performed at essentially the same level. Regardless of program, 30% of the students scored five out of five on the mathematics core items. Similar proportions in each of these groups scored at each of the other levels of correctness. A big difference, however was shown for students enrolled in Programme Cadre. They did not do as well as the other two groups: only 17% answered all of the core questions correctly. This result may have been due, at least in part, to the language in which the test was administered.

Grade 7 results were similar to those in Grade 4. The addition of Late Immersion as an option added another category with results similar to those for Early Immersion and the regular English Program. A closer look at the lower performance end, however, shows a slightly higher proportion of students in the regular English program than those in either in Early or in Late Immersion (8%, 6%, and 7% respectively scored only zero or one out of five). Results for Programme Cadre students, relative to the others, were similar to those in Grade 4.

At the Grade 10 level, students in Early and Late Immersion did significantly better than those in the regular English program. About half of the students in each program (Early Immersion: 53%; Late Immersion: 50%) scored either four or five out of five on the core items, compared with 42% in the regular English program, and 34% in Programme Cadre. Again, the Programme Cadre results are likely affected by the language of the test.

6.1.1.4 Other Background Variables and Mathematics Achievement

Students in Grade 10 were asked several additional questions in the background section of the survey forms. These were questions about part-time jobs, plans following high school graduation, and proposed enrolment in mathematics courses at the senior secondary level.

An examination of the performance levels of student with and without part-time jobs showed that students without part-time jobs did slightly better than those with. Nearly half (45%) of the students without part-time jobs scored either four or five out of five on the core items, compared with 37% of those who held both weekday and weekend jobs. Students who worked only on weekends (40%) and those who worked only on weekdays (41%) did slightly better than those holding jobs at both times during the week.

Students were asked two questions related to their perceptions of how well they did in mathematics and how much they liked the subject.

6.1.2.1 Student Perceptions of How Well They Do and Their Achievement

Students' perceptions of how well they do in mathematics correspond closely to their actual levels of achievement. At each grade level, proportions of correct responses to the core items consistently increased or decreased depending on how well students thought they did in mathematics. Those who thought they did well, did so; those who had a low opinion of their proficiency in mathematics generally did poorly.

6.1.2.2 How Much Students Like Mathematics and Their Achievement

In response to a question on how much they liked mathematics, students selected one of the following options: like a lot, like, dislike, and dislike a lot. As may have been expected, students who said they liked mathematics outperformed those who said they did not. At Grade 4, 90% of those who chose like a lot answered either four or five of the core items correctly, compared with only 50% of those who chose dislike a lot. At Grade 7, results were 46% and 18% respectively for those answering either five or six out of the six core items correctly. Differences at the Grade 10 level were even more pronounced, with respective percentages of 65% and 19%.

6.1.2.3 Mathematics Achievement and Classroom Practices

Students at each grade level were asked how often certain classroom activities occurred in math lessons. Among the options were the following:

• the teacher shows us how to do math problems
• we copy notes from the board
• we have a quiz or a test
• we work from worksheets or textbooks on our own
• we work on math projects
• we use calculators
• we use computers
• we work together in small groups
• we use things from everyday life in solving math problems
• we can begin our homework in class
• the teacher gives us homework
• the teacher checks homework
• we check each other's homework
• we discuss our completed homework

The frequency with which these activities were reported to have occurred in classrooms at each of the grade levels is reported in Chapter 3. It is intended at this point, however, to examine the frequency of these activities when compared to student achievement. In this way, profiles of these activities will be developed for those students who were successful and those who were not.

6.1.2.4 Most and Least Frequent Activities in Classrooms of Successful Students

The most frequent and least frequent activities identified by students who answered all of the core items correctly by grade are shown in Table 6.2.

Table 6.2 Classroom Activities Most and Least Frequently Occurring in Classrooms of Students Answering All Core Items Correctly (8K)

Activities classified as most frequent were those in which 70% or more students who answered all mathematics core items correctly reported occurrence in their classrooms as either quite often or almost always. Activities reported as least frequent were reported to have occurred frequently by fewer than 30% of the students. Both sets of activities are listed in order of frequency: decreasing in the most frequent category and increasing in the least frequent category.

Across the three grade levels, students who were most successful came from classrooms in which the following activities occurred frequently: they worked from worksheets or textbooks on their own; the teacher showed students how to do math problems; and the teacher gave homework. In contrast, the least frequent activities across grade levels for these students were: using a computer; working on math projects; checking each other's homework; and working in pairs or small groups.

Differences across grade levels were in the use of calculators and discussion of completed homework. Almost all (93%) of the successful students at the Grade 10 level came from classrooms in which calculators were used frequently, compared with 29% in Grade 7 and 61% in Grade 4. Discussion of completed homework occurred frequently in 70% of the cases at Grade 10, compared with 57% in Grade 7 and 37% in Grade 4.

6.1.2.5 Comparing Frequencies of Activities in Classrooms of Both Successful and Unsuccessful Students

Next, the frequencies of occurrence of all activities in classrooms of both successful and unsuccessful students are examined and compared. For purposes of this analysis, successful students are viewed as those who answered all of the core mathematics items correctly, and unsuccessful students are those who answered no more than one correctly.

6.1.2.5.1 Grade 4 Results

Grade 4 results show that the following activities occur more frequently in classrooms of successful students than in those of students who were not successful: the teacher shows students how to do math problems; students work from worksheets or textbooks on their own; teachers assign homework; and students can begin homework in class. It should be noted, however, that although these activities occur more frequently in classrooms of successful students, they still occur often in most other classrooms. Another observation relates to beginning homework in class. Since the more successful students are likely quicker in completing class assignments, they may have more time than the others do to begin homework assignments during remaining class time.

A further examination of results at the Grade 4 level identifies some interesting comparisons among less frequent activities. For example, students who were successful spent less time working on projects, using calculators and computers, working in small groups, and checking each other's homework than did students who were less successful.

6.1.2.5.2 Grade 7 Results

Compared to less successful students, students who were successful at the Grade 7 level came from classrooms in which teachers more frequently show students how to do math problems, give quizzes and tests, have students work from worksheets and textbooks, and discuss homework. On the other hand, the following activities occur more frequently in classrooms of students who were less successful: copying notes from the board, working on math projects, using computers, and working in small groups.

6.1.2.5.3 Grade 10 Results

At the Grade 10 level, students who were more successful than the others likely had teachers who spent more time showing their students how to do math problems, having students copy notes, having them work from worksheets and textbooks, using calculators, assigning homework, and discussing homework.

Similar to results at the other levels, working on math projects, working in small groups, and checking each other's homework occurred more frequently in the classrooms of less successful students than in those of students who did better.

6.1.2.5.4 Findings Across Grade Levels

These results do not determine causal relationships. However, they do identify profiles of success based on frequencies of occurrence. Across grade levels, students who were more successful than others came from classrooms in which greater focus was given to showing students how to do math problems, administering tests and quizzes, and assigning homework and discussing results. Correspondingly, there was less time spent overall on math projects, working in small groups, copying notes from the board, and checking each other's homework.

These results do not prove that the latter activities are ineffective learning strategies. Rather, they suggest that the frequency of occurrence and the time allocated to these various activities should be balanced according to the findings. Given the results, it is therefore recommended

Recommendation 6.1

That teachers at all levels continue to use a variety of learning strategies and activities in their classrooms, with a focus on showing students how to do math problems, administering quizzes and tests, assigning homework, and discussing results of homework assignments in class.

Students' scores on free-response items were cross tabulated with their responses to the background question on gender. This allowed for comparisons to be made between the achievement of boys and girls, on respective sets of items at each grade level.

Since not all forms contained the same number of items, results were grouped into three levels of achievement: high, medium, and low. Results categorized as high included the top one third of scores overall; those classified as medium consisted of scores in the middle third; and those classified as low consisted of those in the bottom third. Given these categories, the percentage of boys and girls within each was then calculated. Results are shown in Table 6.3.

Table 6.3 Achievement Level By Gender (5K)

6.1.3.1 Grade 4 Mathematics Results

Results for Grade 4 show similar levels of achievement for both genders, with slightly higher scores by girls. For example, 35% of girls scored in the top category, compared with 34% of boys. A further inspection of results examined proportions of students by gender at each extreme, the very top and the very bottom. Those at the very top answered 90% or more of the items correctly; those at the bottom gave correct answers to less than 10%. At the top, performance was again similar between boys and girls. Proportions at this level were 11% and 11% of boys and girls respectively. At the bottom extreme, however, there was a notable difference between boys and girls. For example, 5% of boys and 8% of girls were in this category.

Girls did slightly better than boys overall. However, boys did somewhat better at each of the extremes.

6.1.3.2 Grade 7 Mathematics Results

At the Grade 7 level, boys did considerably better than girls. The proportion of boys in the high achievement category was 30%, compared with 23% of girls. Correspondingly, proportions of girls in the medium and low levels were higher than boys. These results were also similar at the extremes. For example, 10% of boys and 7% of girls scored higher than 90% correct.

6.1.3.3 Grade 10 Mathematics Results

Girls did better overall than boys at the Grade 10 level. Although proportions of each gender were similar in the high category (30% and 29% of girls and boys respectively), a significantly higher proportion of boys scored in the low category; 38% of boys, compared with 30% of girls, performed at this level.

6.1.3.4 Summary

Results across grade levels showed a consistent pattern at the two extremes. In most cases, boys did better at the upper extreme and worse at the lower extreme. Overall performance, however, favored boys in Grade 7 and girls in Grade 10, with almost identical results between genders in Grade 4.

Students who wrote free-response test booklets also responded to the question about how frequently English was spoken in the home (see Table 6.4).

Table 6.4 Frequency of English Spoken at Home by Achievement Level (percent) (5K)

Students chose from the options always or almost always, sometimes, and never. Since few students selected never as their option (i.e., only 13 in Grade 4, 10 in Grade 7, and 20 in Grade 10), further analysis corresponding to this option is not reported. Results for the other two options were cross-tabulated with achievement scores and are reported in Table 6.4.

6.1.4.1 Grade 4 Mathematics Results

Students in Grade 4 who spoke English at home either always or almost always did better than those who spoke it only sometimes. For example, 34% of students in the former group scored in the high category, compared to 31% of those in the latter. Differences are even more apparent when proportions in the low achievement category are compared. For example, 33% of students from homes where English was spoken most often achieved at the low level, compared to 43% of the others. When the extremes were compared, there was little difference in performance between the groups at the upper level, but a lower proportion of students who usually spoke English at home scored at the bottom extreme.

6.1.4.2 Grade 7 Mathematics Results

Grade 7 results were similar to those for Grade 4, where students who usually spoke English at home did better than the others. This was evident through the proportions who scored in the high group, 40% of frequent English speakers, compared with 33% of those who spoke it only sometimes. However, differences appeared in results for the extremes. For example, a higher proportion of students who only spoke English sometimes answered 90% or more of the questions correctly. At the bottom extreme this result was reversed.

6.1.4.3 Grade 10 Mathematics Results

A very significant shift in achievement levels between the two groups was apparent in Grade 10. At this level, students who only spoke English at home sometimes did better than those who spoke it all or most of the time. Nearly half (47%) of the infrequent English speakers scored in the high category, compared with 33% of the frequent speakers. This pattern was similar at the lower level, where higher proportions of students were from English-speaking homes. Similar results were found for performance at the extremes; 34% of those who spoke English at home sometimes answered more than 88% of the questions correctly, compared to only 22% of frequent English speakers.

6.1.4.4 Summary

These results show an interesting trend, where achievement patterns between frequent and infrequent English speakers reverse as students proceed from lower to higher grade levels. At Grades 4 and 7, for example, students from homes where English is spoken frequently did better than the other group. However, this pattern is completely reversed by Grade 10. Examination of the extremes shows the reversal starting to build in Grade 7, where a greater proportion of students at the upper extreme were from the group who only spoke English at home sometimes. Performance levels on multiple-choice items showed a similar trend.

These results could be affected by a number of factors. For example, it is likely that improvement in the command of English by students for whom English is a second language enables them to improve their achievement in mathematics as they proceed through the system. Another factor may have been the influx of foreign students at the secondary level who come to British Columbia to complete high school. These students tend to be higher achievers than their counterparts.

.2 Achievement in Science and Related Student Variables 6.2.1 Gender Differences in Achievement

Analysis of variance procedures were applied to the achievement results to determine if there were any significant differences between male and female students. Table 6.5 shows the results of the analysis for each form for each grade. The mean correct scores were based on all of the multiple choice achievement questions in each form (35 in Grade 4, 36 in Grade 7, and 20 in Grade 10).

Table 6.5 Gender Differences in Science Achievement by Form and Grade (5K)

In each of the multiple choice forms where a difference was found to be statistically significant, males outscored females by a mean of two percentage points or less. In the open-ended forms where significant difference was found, males outscored females by about one percentage point. Although these differences are statistically significant, the mean difference is so small as to have no practical implications. For educational purposes, the achievement for both genders was essentially the same.

This section reports the results of analyses examining the relationship between various science oriented activities outside the classroom and student achievement.

6.2.2.1 Out-of-School Science-Oriented Activities

Student achievement was related to various science-oriented activities in which students can be involved outside of the classroom. Students responded yes, several times, yes, once or twice, or no, never to questions about how often they visited science museums, outdoor nature centres, planetariums, and aquariums; their participation in science fairs; their watching of science programs on television; and how often they created and conducted experiments on their own.

Statistically significant (p<.05) relationships were found for all of the above questions, although the difference in achievement is only a few percentage points. Students who answered yes, regardless of frequency (sometimes or often), scored higher on the assessment than students who answered no to these items. These results would seem to support the value of having students participate in science fairs and of taking them on field trips to places such as nature centres and aquariums. They may also indicate that parents who expose their children to these types of informal science activities are having a positive influence on their children in terms of science achievement. Teachers may wish to consider the benefits of encouraging parents to engage in these types of activities as well as including these types of activities in their science programs.

6.2.2.2 Classroom Activities

Students were also asked about classroom activities, and responded on a five-point scale: always, quite often, sometimes, rarely, or never. The classroom activities are shown in Table 6.6.

Table 6.6 Questions Asked of Grade 7 Science Students Regarding Science Classroom Activities (5K)

In general, students who answered quite often, sometimes, or rarely to the questions shown in Table 6.6 scored higher (usually by about three or four percentage points) than those who answered always or never. As in previous science assessments, this would seem to indicate that student exposure to a variety of teaching activities is associated with higher achievement than is exposure to predominately the same teaching strategy. Much of the literature about differing learning styles and effective schools has indicated that variety is a key ingredient in effective student learning. The results of this assessment tend to reinforce that concept. It is therefore recommended, as it was in the 1986 and 1991 assessments,

Recommendation 6.2

That intermediate teachers enlarge and improve their repertoire of strategies and methods for teaching science.

Teachers cannot, of course, implement this recommendation by themselves. Appropriate support from the ministry, from school districts, and from universities is needed in the form of adequate funding and the provision of suitable professional development, pre-service programs, and graduate course offerings.

6.2.3.1 Out-of-School Science-Oriented Activities

Grade 10 students were asked the same questions as Grade 7 students regarding out of school activities. In Grade 10, the frequency of participation in science-oriented activities has increased somewhat from what students reported in 1991. However, the level of student achievement does not seem to have changed in any significant way. It must be remembered that caution is needed when attempting to interpret these results and infer cause-and-effect relationships from correlations. For example, although students who visit a planetarium or an aquarium tend to perform better on the assessment than students who do not, it cannot be assumed that performance in science will improve simply by taking students on such field trips. There are likely other contributing factors. Students who have a greater interest in and aptitude for science, and who perform well in science may be more likely to take opportunities in and out of school to visit science facilities in the community. It is tempting to infer cause and effect from the fact that students who have participated in any of the above science-oriented activities score higher than their counterparts who have not, but more in-depth study is needed before any cause-and-effect conclusion is warranted.

6.2.3.2 Classroom Activities

The Grade 10 students completed the same questions about their classroom activities as the Grade 7 students. In general, as reported earlier, it would seem that a variety of classroom or instructional practices serves to maximize student achievement. In most cases, performance is lower when a particular practice is reported with a frequency of always or never. In the case of always, excessive use of any one particular practice (such as field trips, library work or testing) takes time away from other worthwhile forms of instruction. On the other hand, non-exposure to these strategies creates a deficit in learning experiences.

Higher student achievement is noted in most areas where students have had at least some experience. The highest student performance is associated with students presumably augmenting their learning by reading a textbook. Students who read the notes handed out by the teacher also seem to perform better. Recommendations for improvement in overall achievement can be derived from identification of maximum level of performance and the response with the highest frequency. For example, maximum achievement is evidenced by students who say that they use computers quite often. It would follow then, that students should be given greater opportunities to use computers as a regular part of their science instruction.

The surprising result associated with field trips might suggest that the relationship of the activity to the units of instruction plays an important role in achievement. Simply going on a field trip is not enough. Students must have the opportunity to incorporate the experience into the current unit of instruction and to make connections between the field trip and the content being taught. Providing student notes either on the board (or overhead) or through handouts seems to be associated with higher student performance. Evidently, most students at Grade 10 require a formalized set of study notes. This follows with the result that student readings from the textbook are also important. What is not clear from the evidence is whether or not any one of these approaches is more beneficial than any other. All are probably important components of a science program designed to maximize student achievement.

Analysis of variance procedures were also used to test the relationship of responses on certain background items to specific cognitive and affective domains. Overall achievement scores were compared to the Environmental Issues scale and the Science in Society scale.

6.2.4.1 Grade 10 Student Background and Environmental Issues

The total mean scores for the Environmental Issues scale were analysed on the basis of the total number of Environmental Issues items (see Chapter 3) and were related to student responses to the questions about classroom and out of class activities (see Table 6.6 for questions).

Visiting a science museum such as Science World or an outdoor education centre such as the North Vancouver Outdoor School was found to be associated with higher student achievement scores, but it appears that visiting such facilities is associated with less rather than more positive environmental attitudes. This is a rather confusing finding.

There was no educationally significant change to be noted in environmental attitude no matter what science-oriented activity was undertaken.

6.2.4.2 Grade 10 Student Background and Science in Society issues

The total mean scores for the Science in Society scale were related to student responses on science classroom activity items.

Whether or not students go on field trips does not seem to be associated with student attitudes toward science in society issues. For the rest of the science-related activities, even an occasional experience seems to be associated with more desirable student perceptions of, and attitudes toward, societal issues related to science and technology. For example, making several visits to the aquarium is associated with an increase of five percentage points (from 67% to 72%) in attitude total score. Using a computer as opposed to never having access to one, providing opportunities for students to design and conduct their own experiments, providing set notes, and allowing students a chance to read about science in textbooks or to research in the library are all associated with higher attitude scores with respect to science and society.

Increased involvement in these science-oriented activities is not necessarily associated with higher overall scores in achievement. Frequency of field trips is a case in point. The highest achievement scores are obtained by students who rarely go on field trips. There may be several factors influencing this relationship. First, field trips are sometimes taken out of context with the lesson at hand. That is, they may be unconnected and unrelated to the topic being studied at the moment, or be simply isolated visits or excursions away from school. It is important that students be guided to relate some of what is learned in the classroom to what is happening on the field trip. Similarly, the connections back to the classroom should also be addressed. Second, the costs in terms of funding, time, and effort probably combine to make field studies and field trips an increasingly unlikely part of the school program.

Judging from the results, it appears that more positive attitudes about science in society are associated with increased frequency of particular classroom or instructional practices, although performance in the cognitive domains (knowledge and processes) does not show the same relationship. The same finding existed with respect to the Careers in Science and School Science scales on the 1991 science assessment.

The data for each of the three target grades for each of the Likert-type instruments were analysed to see if there were any differences in the responses given by females and males.

In the case of the School Science scale, the analyses indicated that there were no practical differences between females and males on the mean total score at any of the three target grade levels. It would appear that, in general, females and males have the same attitude toward the study of school science and that, as previously mentioned, it is generally positive.

The results of the analyses of the responses of Grades 7 and 10 students to the Science in Society scale indicated that the mean total score of males is also basically the same as the mean total score of females, and that their perceptions of the value of science and technology to society are equivalent.

When the results for the Grades 7 and 10 students who completed the Careers in Science scale were analysed, there was again no practical difference found between the mean total score of males and that of females.

The results of the Specific Issues instrument showed that, although both males and females generally hold positive environmental attitudes, females are more strongly positive than are males; these differences tend to become larger as students get older (see Figure 6.1). This finding is congruent with the results reported in the 1991 science assessment; however, the gap between genders in this area seems to have decreased. At the Grade 10 level, the difference now amounts to about one percentage point in terms of scores on the Environmental Issues scale (see Table 6.7). Females took a more negative position than males on the statements "Scientists should do more research about creating life in the laboratory" and "Scientists should conduct experiments on live animals if they think people will be helped." Females were more strongly in favour in response to the statement "People should be more critical of companies' claims that their medical drugs are safe."

Figure 6.1 (5K)

Table 6.7 Comparison of Grade 10 Males and Females For Goal A (Attitudes) for Each Attitude Scale (5K)

In general, outcomes pertaining to Goal A (Attitudes), as measured in this assessment, seem to be at least very satisfactory. Students have a positive attitude toward science, recognize the importance of science to our society, are improving in their attitudes toward a career in science, and express generally "friendly" environmental attitudes.

.3 Differences in Achievement According to Timetable Pattern

There has been a considerable shift in timetable patterns in secondary schools over the past few years, but there has been little opportunity to examine the relationship of timetable pattern to student outcome measures. The 1995 assessment provided an excellent opportunity to examine this relationship with respect to two key academic areas.

6.3.1.1 Timetables and Student Achievement

One of the background items included in Part A of the Grade 10 forms was directed at the particular timetable pattern students used for science and mathematics. Students were asked whether they were on a 10-month, semester, or quarter system. If they were on a semester or quarter system, they were also asked in which semester or quarter they took science or mathematics.

Analyses of variance techniques were used to examine the effects of timetable pattern on student achievement. The results are reported in the next two sections.

6.3.1.1.1 Timetables and Student Achievement in Mathematics

In the analysis examining the relationship of timetable organization to mathematics achievement, the independent variable in the analysis was timetable pattern, and the dependent variables were the scores on the mathematics core items, scores on the mathematics literacy items, scores on the other items, and total scores. There were therefore four contrasts for each form and 16 contrasts overall for the four forms. Fourteen of the contrasts were statistically significant, and all 16 showed basically the same trend in student achievement. Table 6.8 displays the results of those analyses.

Table 6.8 shows that, in every case, students in 10-month programs outscored students on semester timetables, who, in turn, outscored students taking mathematics in a quarter system.

At the level of the individual items, rather than total score, the same pattern again emerges extremely clearly for Mathematics 10 students. The results for Mathematics 10A are less certain, given the relatively small number of students and the possible large impact of measurement and sampling error. However, the pattern is still there. Out of the 80 items presented on all the forms, Mathematics 10 students in 10-month programs scored highest on 74 of them, second on five of them, and last on only one of the items. Semester students scored highest on three items, were second on 68 items, and scored lowest on nine items. The quarter students scored highest on three, second on seven, and last on 70 of the items. The pattern is very clear.

Of students taking Mathematics 10A, those in 10-month programs scored highest on 46 items, second on 28, and lowest on six. Semester students scored highest on 18 items, second on 37, and lowest on 25 items. Students on the quarter system scored highest on 16 items, second on 15 items and lowest on 49 items. The pattern, while not as clear as for Mathematics 10 students, is still quite apparent, although there may be some confounding due to low numbers of students.

Further analyses showed that, within the semester system, students who took mathematics in the first semester consistently outscored those in the second semester. However, it must be remembered that these survey instruments were administered in May, and students in the second semester had not yet completed their mathematics course. This creates an "opportunity to learn" problem for those students. Among the quarter-system students, those in the various quarters were not consistent in their ranking. This is almost certainly a problem of the small numbers of Mathematics 10A students in the quarter system. On Form U, there were only 33, 32, 28, and 31 students taking Mathematics 10A in the first, second, third and fourth quarters respectively. There are therefore large sampling and measurement errors associated with their scores.

Table 6.8 Grade 10 Student Mean Mathematics Scores by Timetable Pattern (8K)

It appears that the hypothesized benefits of semester and quarter systems, in terms of student achievement, are not being realized in mathematics in British Columbia. In fact, it appears that students on semester and quarter systems may actually be disadvantaged in the area of mathematics achievement as measured by this assessment. There may be other benefits to these alternative timetable systems, but they have not been displayed in this assessment. This problem of lower scores in semester schools was reported in the 1986 science assessment, and results were also published in the Journal of Research in Science Teaching (Bateson, 1990). It seems that what has been known about difficulties in science associated with various timetable patterns applies to the area of mathematics as well.

6.3.1.1.2 Timetables and Student Achievement in Science

As in the mathematics analysis above, the independent variable was timetable pattern and the dependent variables were the scores on the science core items, scores on the science literacy items, scores on the other items, and total scores. There were therefore four contrasts for each form and 16 contrasts overall for the four forms. Fourteen of the contrasts were statistically significant, and all 16 showed basically the same trend in student achievement. Table 6.9 displays the results of those analyses.

Table 6.9 shows that, in every case, students in 10-month programs outscored students on semester timetables, who, in turn, outscored students taking science in a quarter system.

For results at the goal level rather than at the item level, see Table 6.10.

Table 6.9 Grade 10 Student Mean Science Scores by Timetable Pattern (8K)

Table 6.10 shows exactly the same pattern as that evident in Table 6.9, with the 10-month students scoring highest, then the students on semester, and last the students on the quarter system. The only minor break in that pattern is on Form U for Goal C (Scientific Knowledge), where the quarter students had a mean of 6.11 out of 12 items and the semester students had a mean of 6.10.

Table 6.10 Grade 10 Student Mean Science Goal Scores by Timetable Pattern (8K)

At the individual item level, the same pattern emerges. Out of the 80 items presented on all the forms, students in 10-month programs scored highest on 59 of them, second on 16 of them, and last on only five of the items. Semester students scored highest on 14 items, were second on 57 items, and scored lowest on nine. The quarter students scored highest on seven, second on seven, and last on 66 of the items. The pattern is very clear.

Further analyses showed that, within the semester system, students who took science in the first semester consistently outscored those in the second semester. However, it must be remembered that these survey instruments were administered in May, and students in the second semester had not yet completed their science course. This creates an "opportunity to learn" problem for those students. Among the quarter-system students, those taking science in the third quarter consistently outscored all other quarter-system students (but never outscored either the semester or 10-month students). Possibly, they had just finished their course and the material was still relatively fresh in their minds.

Students who took science in the second quarter were consistently the bottom scorers, lower even than the fourth-quarter students for whom opportunity to learn was a definite disadvantage. In some cases, the differences between the second-quarter students and the 10-month students were very large indeed. For example, on Form T, the second-quarter students had a mean of 10.37 out of 20 on the total score; the 10-month students had a mean of 12.37. This is a significant difference. Perhaps the break at the end of December or loss of class time due to special seasonal events has an effect on these second-quarter students.

It appears that the hypothesized benefits of semester and quarter systems, in terms of student achievement, are not being realized, at least in science in British Columbia. In fact, it appears that students on semester and quarter systems may actually be disadvantaged in the area of science achievement as measured by this assessment. There may be other benefits to these alternative timetable systems, but they have not been displayed in this assessment. This problem of lower scores in semester schools was also reported in the 1986 science assessment, and results were also published in the Journal of Research in Science Teaching (Bateson, 1990).

Since a large number of schools are adopting alternative timetable patterns, and many schools and districts are contemplating changes, the ministry should take rapid steps to investigate further the effects of various timetable systems on the achievement of students in order to enable informed choices by administrative decision-makers. It is recommended

Recommendation 6.3

That the Ministry of Education investigate further the effects of various timetable systems on the achievement of students in order to enable informed choices by administrative decision-makers.

One thing that could be done quite rapidly is to confirm that such difficulties exist by reanalysing past assessment data where the questions that were asked of the students and the method of administration allows for such analyses to be validly performed.

As a final note, it is useful to examine the possible impact of the date of administration of the assessment. As noted earlier, a possible opportunity-to-learn problem existed for semester- and quarter-system students in that they likely had more of their science and mathematics courses left to cover than students in 10-month systems.

The assessment was administered in either the third or fourth week of May 1995 (the earliest date was May 23). The 1994-95 school year in British Columbia began September 6, 1994 and ended June 30, 1995. This does not mean, of course, that instruction continued until June 30. Grade 12 students write compulsory provincial examinations in academic subjects; these examinations began on June 19, and most, if not all, secondary schools had June 16 as the last day of attendance for all students. Assuming that instruction continued until June 16, there would have been a maximum of 18 instructional days. In a "regular" 10-month 5 x 8 timetable, that would provide about 12 hours of instructional time per course. In a semester system, the amount of time would be 18--22 hours; and a quarter system would have had 36--45 hours. The opportunity-to-learn factor, then, is a maximum of 6--10 hours for semester students and 24--33 hours for quarter-system students. For quarter-system students particularly, this is a significant amount of time; perhaps a quarter of the course.

It might be argued, then, that the significant amount of time (and therefore course content) remaining for students not on 10-month systems explains the differences in achievement shown in Table 6.8 to Table 6.10. Unfortunately, students who took mathematics or science in the third quarter, and who therefore had completed those courses, did not show any advantage in scores compared to either the semester or 10 month students who had yet to complete their courses. Further, the fourth-quarter students were consistently at the bottom on items testing material that would have been covered in the early and middle parts of the course.