Building
Screen 6 – Water Tank
Screen 6 shifted the narrative of the scenario from the building to its water tank. Students were given the formula for determining the volume V of a cylinder and asked to use π = 3.14. However, this may have influenced the 13 percent of the students on average that omitted the items on this screen.
Item 6A
In item 6A, students were asked to calculate the volume of a water tank with a radius of 0.5 m and a height of 3 m. The topic was classified as geometry in the context of this PSI, but the algebra content area also includes: Find the value of a formula given values of the variables.
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Maximum Score Points: 1
Content Domain: Geometry
Topic Area: Geometric Shapes and Measurement
Cognitive Domain: Applying
Results 6A
Exhibit 32 presents the percentages of students in each country providing the correct answer. About three-fourths of the Singaporean students provided the correct answer, leading the other eTIMSS countries by a substantial margin. The next highest percentages of correct responses represented only about half the students: Hong Kong SAR (52%), Russian Federation (48%), and Chinese Taipei (47%). The average percent correct for the participating countries was 33 percent (mostly due to the 3 countries just mentioned), because 13 countries had achievement of 33 percent correct or lower. Across countries, girls had higher average performance than boys.
Item 6B
Item 6B asked students to increase the radius by multiplying it by 2. This essentially removed the radius from the calculation (0.5 × 2 = 1, 12 = 1), leaving 3.14 × 3.
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Maximum Score Points: 1
Content Domain: Geometry
Topic Area: Geometric Shapes and Measurement
Cognitive Domain: Reasoning
Results 6B
As shown in Exhibit 33, 5B results closely mirrored those for 5A. Singapore had the highest achievement at 77 percent correct, followed by about half the students in Chinese Taipei (50%), Hong Kong SAR (48%), and Korea (46%). The average across eTIMSS countries was 32 percent correct. On average, there was little or no performance difference between girls and boys.
Calculator Use for 6A and 6B
Exhibits 34 and 35 provide data about calculator use on 6A and 6B, respectively. On the whole, TIMSS mathematics items are developed to be calculator neutral, such that there is not an advantage or disadvantage to having a calculator. Students were not permitted to bring their own calculators, but the eighth grade students were provided a TIMSS on-screen calculator as part of the eTIMSS user interface. The calculator has the four basic functions, a square root key, and the negative sign. On average more students providing correct answers used the calculator than did not (29% vs. 3% on 6A and 26% vs. 5% on 6B). However, the percentages of students that used calculators to obtain correct answers was similar to the percentages of students that used calculators to obtain incorrect answers (28% for 6A and 24% for 6B). It appears that if the students did know the correct procedure to solve the problems in 6A and 6B, the calculator was a useful tool. However, if the students did not know the procedures for solving the problems, the calculator did not help.
Item 6C
Perhaps because the problem did not ask for any specific calculations, item 6C about how increasing the radius would impact the volume of the rain barrel left most of the students perplexed. Based on the formula and supported by the pattern of results in 6A and 6B, students could reason that the volume will increase. Students who explained why the volume would more than double received full credit (2 points).
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Maximum Score Points: 2
Content Domain: Geometry
Topic Area: Geometric Shapes and Measurement
Cognitive Domain: Reasoning
Results 6C
Exhibit 36 presents the results. Only 4 countries managed to achieve at least double-digit success in answering the question for full credit—Singapore and Chinese Taipei (both 13%), Korea (11%), and Hong Kong SAR (10%). The cross-country average was 4 percent. However, another 3 percent on average received partial credit (1 point) for working out an example comparing two cylinders, with one cylinder having 1.5 times the radius of the other. On average across countries, boys slightly outperformed girls (4% vs. 3%).