Building
Screen 5 – Painting the Walls
Item 5A
After having constructed the walls, students’ next task involved painting the walls. Item 5A asked students to calculate the area of one side of the wall. Interestingly, this was the third question in a row that included some understanding of the top triangle of the side wall. Recognizing that the triangle top of the wall was a right angle triangle was integral to solving Screen 3’s question about the width of the roof, with Singapore and Chinese Taipei having the top performance. Next, as part of Screen 4, students needed to determine the dimensions of the side walls (each a top triangle and bottom rectangle) to cut them out of the board, again with Singapore followed by Chinese Taipei and Hong Kong SAR as the top performers. Next, in 5A students were asked to determine the area of one side wall (top triangle plus bottom rectangle).
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Maximum Score Points: 1
Content Domain: Geometry
Topic Area: Geometric Shapes and Measurement
Cognitive Domain: Applying
Results 5A
Exhibit 29 presents the percentages of students determining the area of one side wall. Facilitated by their understanding of the Pythagorean Theorem, the eighth grade students in Hong Kong SAR and Chinese Taipei (68% correct) as well as Singapore (66%) and Korea (63%) had the highest performance. After a relatively large gap, Sweden had the next highest percent correct (46%). On average across the eTIMSS countries, 32 percent of the students provided a correct response to the question about the area of one side wall. In considering whether understanding that the triangle was a right angle triangle was the key to success, it is interesting that 15 percent of the students on average treated the top triangle section as if it were another rectangle (making it twice the correct area). There was little or no difference in average achievement between girls and boys.
Item 5B
Item 5B required students to calculate the total area that needed to be painted.
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Maximum Score Points: 1
Content Domain: Geometry
Topic Area: Geometric Shapes and Measurement
Cognitive Domain: Reasoning
Results 5B
As shown in Exhibit 30, Singapore (48%), Chinese Taipei (43%), and Hong Kong SAR (41%) as well as Korea (40%) had the highest performance. The average percent correct across all countries was considerably lower—20 percent. Interestingly, 7 percent of the students on average used the incorrect area for the side walls, yet still correctly calculated the total area, underscoring the complexities inherent in trying to recover from dependence among items. There were no differences in achievement between girls and boys.
Item 5C
Fortunately, the painting scenario was reset in 5C by introducing the need to buy some extra paint. Because 10 percent of the students omitted this item, some of them may not have wanted to address this complication.
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Maximum Score Points: 1
Content Domain: Algebra
Topic Area: Expressions, Operations, and Equations
Cognitive Domain: Reasoning
Results 5C
Exhibit 31 provides the percentages of students providing a correct response. In Chinese Taipei and Singapore, 60–62 percent of the students provided the correct response. Across the participating countries, 33 percent of students answered correctly on average. Further analysis revealed that 6 percent on average performed accurate calculations, but did not read the question thoroughly and used an incorrect area. Once again boys and girls performed similarly.