Mathematics: Trends in Year 5 mathematics achievement 1994 to 2006

Student attitudes

Students were asked how much they agree with eight statements about learning mathematics (listed in Table 18 – positive and negative statements were interwoven in the questionnaire but are reordered here for easier reading). They were given four response options: "agree a lot, agree a little, disagree a little, disagree a lot".

Students were generally positive about mathematics with 79 percent agreeing that they enjoy learning mathematics and 68 percent disagreeing that mathematics was boring. A reasonably high proportion of the students agreed that they would like to do more mathematics in school (64%), but just under half the students agreed that mathematics was harder for them than for many of their classmates.

Table 18: Proportion of students who responded positively to statements about learning mathematics

Note:
The values for agree combine student responses to ‘agree a lot’ and ‘agree a little’. Similarly the values for disagree combine little and a lot.
Standard errors are presented in parentheses.

Generally, students with positive attitudes towards mathematics had higher achievement than students with negative attitudes. In order to examine the relationship with achievement the international researchers combined the data in two indices: the index of students’ positive affect toward mathematics and the index of students’ self-confidence in learning mathematics.

Index of students’ positive affect toward mathematics

The three statements: I enjoy learning mathematics; mathematics is boring; and I like mathematics; were combined to form the index of students’ positive affect toward mathematics (PATM).¹ Two-thirds of the students were at the high level of this index; that is, on average, they were positive about mathematics. Seventeen percent of students were at the low level of the index; that is, on average, they were negative about mathematics. There are now proportionally fewer students at the high level on the index and more at the medium and low levels than there were in 1994. As shown in Figure 19 students who were more positive about mathematics (at the high level of the PATM index) had higher mean mathematics achievement than those that were more negative. There was no difference between those at the medium and low levels of the index.

Figure 19: Proportion and mean mathematics achievement of students at each level of the positive affect toward mathematics (PATM) index

Note:
The bars on the graph represent the proportions of Year 5 students while the points represent mean scores. Lines extending from the points represent the 95% confidence interval, i.e. the range within which we are 95 percent confident that the true population value lies.
Standard errors are presented in parentheses.

In relation to other countries, relatively low proportions of New Zealand students were at the high level of the PATM index. That is, few students reported positive attitudes towards mathematics in comparison to their international counterparts. However, this proportion was the same as the United States and Australia (66% each); England and Scotland had lower proportions of students who responded positively to these statements (62% and 59% respectively at the high level of the PATM index).

Index of students’ self-confidence in learning mathematics

The four statements: I usually do well in mathematics; mathematics is harder for me than for many of my classmates; I am just not good at mathematics; and I learn things quickly in mathematics; were combined to form the index of students’ self-confidence in learning mathematics (SCM).² Just over half (52%) of the students were at the high level of this index; that is, on average, they were positive about their own abilities in mathematics. Eleven percent of students were at the low level of the index; that is, on average, they were negative about their abilities in mathematics.

The proportions of the students at all levels of the index have changed significantly since 2002. More students are now positive about their abilities to learn mathematics (13 percentage point increase), but also more students are negative about their abilities to learn mathematics (7 percentage point increase). Fewer students are, therefore, at the medium level of the index.

As shown in Figure 20, students who were more positive about their abilities to learn mathematics (at the high level of the SCM index) had higher mean mathematics achievement than those that were more negative. Those students with the lowest self-confidence had the lowest mathematics achievement on average. Note that the difference in mean mathematics score between students that were high and those that were low on the SCM index (89 scale score points) is greater than those in the respective groups on the PATM index (15 scale score points). Thus the self-confidence of students had a stronger relationship with mathematics achievement than having a positive attitude towards mathematics.

Figure 20: Proportion and mean mathematics achievement of students at each level of the students’ self-confidence in learning mathematics (SCM) index

Note:
The bars on the graph represent the proportions of Year 5 students while the points represent mean scores. Lines extending from the points represent the 95% confidence interval, i.e. the range within which we are 95 percent confident that the true population value lies.
Standard errors are presented in parentheses.

In relation to other countries, quite low proportions of New Zealand students were at the high level of the SCM index. However this proportion was similar to that for the Russian Federation (54%). In comparison, England, Australia, Scotland and the United States had a larger proportion of students who responded positively to these statements about their abilities in mathematics (64%, 64%, 67% and 67% respectively at the high level of the SCM index). High-performing countries including Singapore, Hong Kong and Japan had lower proportions at the low level of the SCM index (46%, 46% and 45% respectively).

Attitudes to mathematics by gender

Boys and girls demonstrated some similar attitudes to mathematics. Around two-thirds of girls and boys were very positive about mathematics and were at the high level of the PATM index (65% and 66% respectively). However, boys were more confident in their mathematics ability than girls, with a significantly higher proportion of boys at the high level of the SCS index (54% compared with 49% for girls).

Attitudes to mathematics by ethnicity

Some differences were evident among the ethnic groupings when attitudes to mathematics were considered. More Asian students (79%) reported positive attitudes to mathematics and were at the high level of the PATM index. The Other grouping had a similar proportion to Asian students with 78 percent. Significantly fewer Pakeha/European students (61%) reported positive attitudes to mathematics than any of the other ethnic groups (Pasifika 76%, and Maori 68%).

Similar to the PATM index, more Asian students were confident in their own mathematics abilities (65%) and were at the high level of the index. In contrast, fewer Pasifika (43%) and Maori (46%) students expressed high self-confidence compared to their Asian, Pakeha/European (53%), and Other (55%) counterparts.

Footnotes

1. An average was computed across a 4-point scale with 1 agree a lot, 2 agree a little, 3 disagree a little, 4 agree a lot. The statement ‘mathematics is boring’ was reversed so that students disagreeing a lot were given a value of 1.
2. An average was computed across a 4-point scale with 1 agree a lot, 2 agree a little, 3 disagree a little, 4 agree a lot. The statements ‘mathematics is harder for me than for many of my classmates’ and ‘I am just not good at mathematics’ was reversed so that students disagreeing a lot were given a value of 1.