Measuring student knowledge and skills

Mathematical “big ideas”
As indicated earlier, the purposes of the OECD/PISA mathematics assessment are rather different
from those of earlier comparative studies of mathematics, in particular IEA/TIMSS. Some of the most per-
tinent differences are described below.
Figure 5.
Example item using simple “mathematisation”
A class has 28 students. The ratio of girls to boys is 4:3. How many girls are in the class?
Source: TIMSS Mathematics Achievement in the Middle Years, 
p. 98.
Figure 5.
Example item using simple “mathematisation”
A class has 28 students. The ratio of girls to boys is 4:3. How many girls are in the class?
Source: TIMSS Mathematics Achievement in the Middle Years, 
p. 98.
In a certain country, the national defence budget is $30 million for 1980. The total budget for
that year is $500 million. The following year the defence budget is $35 million, while the total
budget is $605 million. Inflation during the period covered by the two budgets amounted to
10 per cent.
a)
You are invited to give a lecture for a pacifist society. You intend to explain that the defence
budget decreased over this period. Explain how you would do this.
b)
You are invited to lecture to a military academy. You intend to explain that the defence
budget increased over this period. Explain how you would do this.
Source: 
de Lange (1987); see also MSEB (1991). Used with permission.
Figure 6.
Example item using more complex “mathematisation”
In a certain country, the national defence budget is $30 million for 1980. The total budget for
that year is $500 million. The following year the defence budget is $35 million, while the total
budget is $605 million. Inflation during the period covered by the two budgets amounted to
10 per cent.
a)
You are invited to give a lecture for a pacifist society. You intend to explain that the defence
budget decreased over this period. Explain how you would do this.
b)
You are invited to lecture to a military academy. You intend to explain that the defence
budget increased over this period. Explain how you would do this.
Source: 
de Lange (1987); see also MSEB (1991). Used with permission.
Figure 6.