Classroom Context: The Classroom Context for Year 5 Students' Mathematics and Science Achievement in 2006

Classroom characteristics

Classroom size

TIMSS asked teachers about the size of their mathematics and science classes, as larger or smaller classes can influence how the teacher chooses to teach mathematics and science topics. At Year 5, students tend to have the same teacher for both mathematics and science. Average class size in New Zealand was 26 students in 2006/07, the same as the international average. In the majority of countries, students were in medium-sized classes (defined as those with 20 to 32 students), with notable exceptions including Singapore, Hong Kong SAR, Yemen, Chinese Taipei, Colombia and Japan, all of which had average class sizes of more than 30 students.

Class sizes in New Zealand have decreased since the first cycle of TIMSS. In 1994 the average class size was 29 students, significantly higher than 26 students in 2006/07. It is difficult to disentangle the relationship between class size and achievement. For example, in some countries smaller classes tend to be in rural areas where there are fewer resources, and larger classes in urban areas with more resources. Remedial classes may also be smaller. However, TIMSS studies repeatedly show that high performing Asian countries, such as Singapore and Hong Kong SAR, have some of the largest class sizes. For example, in Singapore, 94 percent of all students are in large classes (defined as those with more than 32 students).

Teaching mathematics

Time spent teaching mathematics

According to their teachers, New Zealand Year 5 students spent around 16 percent of total instructional time, on average, on mathematics tasks per week in 2006/07 – about the same as the average for all participating countries (see Table 8). This was a significant increase of one percentage point since the previous cycle of TIMSS in 2002/03. Over the school year, New Zealand teachers reported spending 148 hours, on average, a year on mathematics – slightly more than the international average of 144 hours and 6 hours more per year than in 2002/03.

As with class size, the relationship between the amount of instructional time and student achievement is complex. While countries with higher hours of instruction tended to be among the higher achieving, there were also high-achieving countries with relatively fewer hours of instruction than average as shown in Figure 1. For example, Chinese Taipei is one of the top performing countries in mathematics, but its teachers only spent an average of 13 percent of classroom time on mathematics, or 112 hours per year. Chinese Taipei has other aspects of its education system that ‘make up’ for the lack of hours of instruction. For example, teachers in Chinese Taipei usually assign more mathematics homework per week than New Zealand teachers (homework is discussed in more detail later in this report). Also, lower achieving students in Chinese Taipei are assigned a tutor to teach them after school.

Note: A dash (-) indicates comparable data are not available.
n/a indicates that the country did not participate in the 2002/03 study at this level.
Standard errors are presented in parentheses.
▲ indicates that the change between 2002/03 and 2006/07 was statistically significant.

Source: Adapted from Exhibits 5.1 & 5.2 Mullis, Martin and Foy, 2008.

Figure 1: Mathematics instructional time by mean mathematics achievement for selected countries

Note:  This is a graphical representation of the data in Table 8.

Time spent on mathematics content domains

TIMSS divides Year 5 mathematics content into three domains: number, geometric shapes and measures, and data display. Note that number is defined in TIMSS as including both number and algebra, and the New Zealand curriculum combines both of these topics in the number and algebra strand. Although New Zealand teachers reported spending two-thirds (66%) of their mathematics instruction time on number, more time than any other country in TIMSS (50% on average), student performance was relatively poor. Number was the only domain where New Zealand scored significantly lower than the TIMSS scale average of 500 (see Caygill, Lang, and Cowles, 2010 for a more detailed discussion on the learning of number concepts in English-speaking countries).

The amount of instructional time spent on the other two domains, geometric shapes and measures and data display was relatively small (30%), compared with both number and other TIMSS countries (40% – see Table 9). However, New Zealand students scored around the international average in geometric shapes and measures and significantly above the average in data display.

Note:  A dash (-) indicates comparable data are not available.
Standard errors are not presented here for ease of reading but can be found in Table 33 in the Appendix.
Total time may not add to 100 percent as the ‘Other’ category is not included in table.

Source: Adapted from Exhibits 5.2 & 5.3 Mullis, Martin and Foy, 2008.

Coverage of mathematics topics

Teachers provided information on mathematics topics taught to Year 5 students prior to or during the year of the TIMSS assessment. For each of 35 topics, teachers were asked if the topics were: mostly taught before this year, mostly taught this year, or not yet taught or just introduced. On average, 73 percent of New Zealand students had been taught all 35 topics listed in the questionnaire, compared to 66 percent across all countries. Data display topics were covered during or before the testing year by 82 percent of students, followed by number (72%) and geometric shapes and measures (64%). Across the three content domains, there were no clear relationships between percentage of topics taught and student achievement. For example, Japanese students achieve well above the international average in mathematics despite having covered just over half of the topics listed, and although New Zealand students had covered around three-quarters of the number topics by the time of testing, their performance was significantly below the international average.

Mathematics topics covered by fewer than half of all New Zealand students were:

• Adding and subtracting with decimals (40%);
  
• Describing relationships between adjacent terms in a sequence (47%);
  
• Comparing angles by size and drawing angles (e.g. a right angle, angles larger or smaller than a right angle) (32%); and
  
• Using informal co-ordinate systems to locate points in a plane (47%).

For a complete list of topics and coverage please refer to Table 34 in the Appendix.

Mathematics homework

Students often do extra mathematics in out-of-school time, although Year 5 students are not routinely assigned homework in all countries. In fact, only ten countries³ had specific policies about Year 5 mathematics homework in 2006/07. The relationship between homework and student achievement is not straightforward. For example, homework may be a remedial task for students who are weak at mathematics, and higher-ability students may be quicker at completing homework. Results varied by country but New Zealand students who reported doing more homework tended to do less well in mathematics.

TIMSS constructed an index from student responses to questions about the frequency of mathematics homework assigned per week and the amount of time spent on it. ⁴ More than half of all New Zealand students reported doing little mathematics homework (at the low level of the index), compared with around one in five students internationally. Australia, Sweden, England, Scotland and the Netherlands had more than half of their students at the low level, whilst Kazakhstan, Singapore and the Russian Federation had at least one third of their students at the high level of the index.

Teachers were asked about the mathematics homework they assigned to their classes. Most New Zealand teachers (84%) placed a low emphasis on homework.⁵ Only one-third of all TIMSS students, on average internationally, had teachers who placed a low emphasis on homework.

There was no clear relationship between teachers’ emphasis on homework and mathematics achievement, possibly because of the complexity of untangling the effect of ability of students and the purpose of assigning the homework. This does not imply that homework should be omitted from New Zealand classrooms or indeed classrooms worldwide. Rather research on the impact of homework needs to focus on the purpose of homework and what is learnt from the homework as well as the amount of homework.

Mathematics teaching activities

Within any given mathematics lesson, a variety of activities may take place in order to ensure children learn the desired content or skill. Teachers were asked to estimate the proportion of time spent in a typical week of mathematics lessons on each of eight activities:

• reviewing homework;
  
• listening to lecture-style presentations;
  
• working on problems with teacher guidance;
  
• working on problems on their own without teacher guidance;
  
• listening to the teacher re-teaching and clarifying content or procedures;
  
• taking tests or quizzes;
  
• participating in classroom management tasks not related to the lesson’s content or purpose (e.g., interruptions and keeping order); and
  
• other student activities.

The most common activities, on average, for New Zealand Year 5 students were working on problems either with or without teacher guidance; around 60 percent of time was spent on these two activities combined (see Table 10). Students spent most of the remaining time listening to the teacher presenting material or clarifying and re-teaching content and procedures. A similar pattern was observed across many of the countries in TIMSS, although listening to the teacher give lecture-style presentations was much more common in Hong Kong SAR and Chinese Taipei.

Note:  Standard errors are not presented here for ease of reading but can be found in Table 35 in the Appendix.
Proportions in each row should add to 100%; inconsistencies are due to rounding.

Source: Adapted from Exhibit 7.9 Mullis, Martin and Foy, 2008.

This question was first asked in TIMSS 2002/03. There has been little change in the proportions of time Year 5 students spent on each of the activities during mathematics lessons since 2002/03.

Learning activities in mathematics lessons

The previous section examined the mix of different teaching activities during a week of lessons from the teachers’ perspective. This section examines mathematics lessons from a slightly different perspective, looking at the frequency of learning activities that take place within mathematics lessons from both the teacher and student perspective. The questions examine content specific activities, such as working on fractions and decimals, as well as cognitive activities, such as memorising how to solve problems. The response categories for this question were: almost every lesson, about half the lessons, some lessons and never. Table 10 lists all the activities teachers and students were asked about with responses for almost every lesson and about half the lessons combined.

Eighty-four percent of New Zealand Year 5 students were in classes where teachers reported students practised adding, subtracting, multiplying, and dividing without using a calculator during at least half of lessons. This is consistent with the finding that students spend two-thirds of their time on number topics, including algebraic content. Writing equations for word problems (37% at least half of lessons) and working on fractions and decimals (21% at least half of lessons) are the next most common content areas. Although number activities were also the most common activities from the point of view of students, students were much more likely to report measuring things, making charts, graphs, and tables, and learning about shapes than their teachers.

In terms of cognitive activities, the questions asked of students and teachers had only two common activities: explaining answers and memorising (although the wording was slightly different). According to teachers, the cognitive emphasis in their lessons was on getting students to explain answers and to relate mathematics lessons to their daily lives, rather than memorising formulas and procedures. Students, however, perceived that they did rather a lot of memorising and a little less of explaining their answers.

Note:  Standard errors are presented in parentheses.
For most statements in the student questionnaire there are similar statements in the teacher questionnaire – where there is no comparable statement this is indicated.

Getting students to explain their answers and practise adding, subtracting, multiplying, and dividing without using a calculator were also the two most common activities reported by teachers across most of the English-speaking and high-performing countries. An interesting exception was Chinese Taipei and Japan where writing equations for word problems was a very common activity reported by teachers.

None of these statements showed a clear link with achievement. A possible explanation for this is that it is not necessarily the doing of activities that is important as much as how they are done and what is learnt during the activity. For example, if students are able to explain an underlying mathematical concept and understand how it applies to a range of increasingly complex problems they are demonstrating more learning than if they are only explaining very simple problems or explaining in a simple way.

Trends in mathematics activities

For most of the activities there has been little change since 2002, according to their teachers, in the frequency of students doing each of the activities, with the exception of how often teachers ask students to explain their answers. Students were more likely to be in classes where students are asked to give explanations almost every lesson in 2006 (up from 51% in 2002 to 71% in 2006). This change may be attributable to the professional development work of the Numeracy Development Projects which emphasise thinking and understanding.

Mathematics curriculum levels

New Zealand teachers were asked at which level of the Mathematics in the New Zealand Curriculum (MiNZC)⁶ most of their TIMSS students were currently working for each of the strands: number, algebra, measurement, geometry, and statistics.⁷ Teachers’ responses were assigned to each individual student in the class for analysis purposes. The majority of Year 5 students were working at Level 3 of the curriculum, but there were still a significant number of students in classes working at Level 2, particularly in the algebra and measurement strands.

Students whose classes are working at higher levels of the curriculum have higher achievement on average across the TIMSS content domains. However, we are not suggesting there is a causal link between higher achievement and working at the higher level. It is interesting to look at these results in an international context and observe that if only those students working at Level 3 of the curriculum were included in the TIMSS testing, New Zealand’s overall mathematics score would still have been below that of the high-performing countries, Singapore, Chinese Taipei, Hong Kong SAR, and Japan. For example, the mean score for Singaporean students on the number domain was 611 scale score points, while New Zealand students whose classes were working mostly at Level 3 had a mean score of 501 scale score points. For more information on this topic see Caygill and Kirkham (2008).

Teaching Science 

Time spent teaching science

The teaching of science is more varied across countries than the teaching of mathematics. Internationally, around three-quarters of all students (78%) learnt science as a separate curriculum area or subject, but this average masks a wide variation across individual countries. For example, in Kazakhstan science was a stand-alone subject for all students but in Norway all of the TIMSS science lessons were integrated with other subjects. Science was a separate subject for fewer than half (42%) of New Zealand Year 5 students in 2006, which was relatively low by comparison to the international average. At this level of the curriculum, science is often taught as part of a specific topic or focus area.

All of the countries that took part in TIMSS 2006/07 spent less time on science instruction when compared to mathematics. On average, New Zealand Year 5 students spent only 5 percent of class instructional time on science, which was 3 percentage points less than the international average of 8 percent (see Table 12). The average number of science instructional hours per week at Year 5 decreased significantly (by 2 percentage points) between 2002/03 and 2006/07. Over a year, the amount of time spent on science was 45 hours in 2006/07, a drop of 21 hours from 2002/03.

As mentioned earlier, the relationship between the amount of instructional time and student achievement is complex. While countries with higher hours of instruction tended to be among the higher achieving, there were also high-achieving countries with relatively fewer hours of instruction than average as shown in Figure 2. For example, the Russian Federation is one of the top performing countries in science, but its teachers only spent an average of 6 percent of classroom time on science, or 40 hours per year.

Note:  A dash (-) indicates comparable data are not available.
n/a indicates that the country did not participate in the 2002/03 study at this level.
Standard errors are presented in parentheses.
▲ and ▼ indicate that the change between 2002/03 and 2006/07 was statistically significant.

Source: Adapted from Exhibit 5.2 and 5.3 Martin, Mullis and Foy, 2008.

     Figure 2: Science instructional time by mean science achievement for selected countries

Note: This is a graphical representation of the data in Table 12.

Time spent on science content domains

TIMSS divides Year 5 science content into three domains: life science, physical science and Earth science. New Zealand students spent more time on life science topics during the school year (43%) than the two other domains (26% on physical science and 28% on Earth science). Relatively less time was spent on physical science, an area in which our students performed least well. On the whole, countries performing best in physical science spent more time on this domain relative to the other two, although this was not the case across all countries (see Table 13 for details). The high-achieving countries of Singapore and Chinese Taipei spent over 40 percent of class time on physical science but their students also did very well in the other two content domains.

Note:  Standard errors are not presented here for ease of reading but can be found in Table 36 in the Appendix.
Total time may not add to 100 percent as the ‘Other’ category is not included in table.

Source: Adapted from Exhibits 5.3 & 5.4 Martin, Mullis and Foy, 2008.

Coverage of science topics

Teachers provided information on science topics taught to Year 5 students during or before the year of the TIMSS assessment. For each of the 35 topics, teachers were asked if the topics were: mostly taught before this year, mostly taught this year, or not yet taught or just introduced. On average, just over half of New Zealand students (53%) had been taught all 35 topics listed in the questionnaire, compared to 61 percent across all countries. New Zealand students were most likely to have covered life science topics during or prior to the testing year (65%), followed by Earth science (52%). Only 43 percent of students had covered all the physical science topics on average. As in mathematics, there were no clear relationships between percentage of topics taught and student achievement.  For example, only one in three Japanese students (36%) had been taught all of the science topics on average but Japan’s science achievement score was significantly above the international average.

Science topics covered by only one-third of New Zealand students or less were:

• Plant and animal reproduction (passing on of general characteristics) (33%);
  
• Properties and uses of metals (23%);
  
• Heat flow and temperature (33%);
  
• Magnets (north and south poles, magnetic attraction and repulsion) (33%);
  
• Rocks, minerals, sand and soil (31%);
  
• Air (composition, proof of its existence, uses, and importance for supporting life (31%); and
  
• Fossils of animals and plants (31%).

For a complete list of topics and coverage, please refer to Table 37 in the Appendix.

Science homework

Students may also do science homework after school, although Year 5 students were not assigned homework on a regular basis in most of the TIMSS countries. Only nine countries⁸ had specific policies about science homework at the Year 5 level.

TIMSS constructed an index from student responses to questions about the frequency of science homework assigned per week and the amount of time spent on it. ⁹ Three-quarters of all New Zealand students reported doing little science homework (at the low level of the index), compared with just over half of all students (57%) internationally. Other countries at the low level of the index included Australia, Sweden, Japan, England, Scotland and the Netherlands, whilst Colombia and Yemen were the only two countries with 20 percent or more of their students at the high level. Average science achievement was highest among students doing less homework and lowest among students doing the most homework. There may be a number of possible reasons for this, including a need for less able students to ‘catch up’ with work or to spend more time on their homework tasks.

Teachers were asked about their emphasis on science homework.¹⁰ Almost all New Zealand students (95%) had teachers who placed low emphasis on homework, as did 65 percent of students internationally. There was some variation across participating countries but Italy, Singapore, Kazakhstan and Colombia were the only countries with more than one-fifth of their students whose teachers placed a relatively high emphasis on homework. On average, students doing more science homework had lower achievement scores, which may relate to teachers assigning homework as a remedial exercise for weaker students (Martin, Mullis and Foy, 2008).

Learning activities in science lessons

Teachers and students were asked about the frequency of learning activities in science lessons. However the response categories differed between the student and teacher questionnaire. The frequency options for teachers were: every or almost every lesson, about half the lessons, some lessons, and never. In contrast, the frequency options for students were: at least once a week, once or twice a month, a few times a year and never. However, given that teachers reported the amount of time spent on science over a year was 45 hours on average, about half the lessons is likely to be similar to once or twice a month. The questions examine activities such as doingexperiments or investigations and relating what they are learning in science to their daily lives. Table 14 lists all the activities teachers and students were asked about.

According to teachers, the most common activities in science lessons were getting students to give explanations about something they are studying (57% of students were in classes where this was reported to happen in at least half the lessons) and having students relate what they are learning in science to their daily lives (52%). Fewer teachers reported that they asked students to memorise facts and principles (5%) or watch the teacher do a science experiment (5%). In contrast, the most common activities reported by students were memorising science facts (60%) and reading books about science (59%).

Getting students to give explanations about something they are studying and having students relate what they are learning in science to their daily lives were also the two most common activities reported by teachers across most of the English-speaking and high-performing countries. One exception was Chinese Taipei where doing experiments or investigations was the most common activity reported by teachers.

None of these statements showed a clear link with achievement. A likely explanation for this is that it is not necessarily the doing of activities that is important as much as how they are done and what is learnt during the activity. For example, if a class reads a book about a science topic that confirms and elaborates on work already done in class, it is likely to be a more valuable learning activity than if the book is read in isolation.

Note:  Standard errors are presented in parentheses.
For most statements in the student questionnaire there are similar statements in the teacher questionnaire – where there is no comparable statement this is indicated.

Trends in science activities

As mentioned earlier in this report, the average number of instructional hours per week spent on Year 5 science in New Zealand decreased between 2002 and 2006. Teachers also reported a drop in the proportion of students doing each of the individual activities listed in the questionnaire. The class activity with the greatest decrease was observe natural phenomena such as the weather or a plant growing and describe what they see. In 2002, according to their teachers, 44 percent of students were expected to observe and describe natural phenomena in about half the lessons or more often; by 2006, the proportion of students had reduced to 14 percent. Similarly, less experimentation was reported in 2006 compared with 2002. In 2002, according to their teachers, 69 percent of students were asked to work together in small groups on experiments or investigations in at least half the lessons, compared with 46 percent in 2006.

Science curriculum levels

New Zealand teachers were asked at which level of the Science in the New Zealand Curriculum (SciNZC)¹¹ levels most of their TIMSS students were currently working for each of the strands: living world, material world, physical world, planet Earth and beyond. Teachers’ responses were assigned to each individual student in the class for analysis purposes. The majority of Year 5 students were working at Level 3 of the curriculum, but there was still a significant number of students in classes working at Level 2.

Students whose classes were working at higher levels of the curriculum have higher achievement on average across the associated TIMSS content domains. Note that no attempt is being made here to infer a causal link – that is, we are not saying the higher mean achievement is because they are working at the higher level.

It is interesting to look at these results in an international context and observe that if only those students whose classes were mostly working at Level 3 of the curriculum were included in the TIMSS testing, New Zealand’s overall science score would still have been below that of the high-performing countries, Singapore, Chinese Taipei, Hong Kong SAR, and Japan. For example, the mean score for Singaporean students on the life science domain was 582 scale score points, while New Zealand students whose classes were mostly working at Level 3 had a mean score of 526 scale score points. For more information on this topic see Caygill (2008).

Footnotes

3. Algeria, Georgia, Morocco, Germany, Ukraine, Yemen, Austria, Qatar, Lithuania, Slovak Republic
4. High level indicates homework assigned at least 3 or 4 times a week and students spend more than 30 minutes on homework. Low level indicates homework assigned no more than twice a week and no more than 30 minutes spent on each assignment. Medium level includes all other possible combinations of responses.
5. An index was created from the teachers responses. High level indicates more than 30 minutes spent on homework assigned about half the lessons or more. Low level indicates no homework assigned or assignment of less than 30 minutes of homework about half of the lessons or less. Medium level includes all other possible combinations of responses.
6. This was the curriculum in place at the time of testing.
7. The Mathematical Processes strand of the MiNZC relates more to the TIMSS cognitive domains and so is not included in this discussion.
8. Algeria, Georgia, Iran, Morocco, Yemen, Ukraine, Qatar, Slovak Republic, Lithuania
9. High level indicates homework assigned at least 3 or 4 times a week and students spend more than 30 minutes on homework. Low level indicates homework assigned no more than twice a week and no more than 30 minutes spent on each assignment. Medium level includes all other possible combinations of responses.
10. An index was created from the teachers responses. High level indicates more than 30 minutes spent on homework assigned about half the lessons or more. Low level indicates no homework assigned or assignment of less than 30 minutes of homework about half of the lessons or less. Medium level includes all other possible combinations of responses.
11. This was the curriculum in place at the time of testing.