Findings from the TIMSS 2019 Problem Solving and Inquiry Tasks

Ina V.S. Mullis, Michael O. Martin, Bethany Fishbein, Pierre Foy, and Sebastian Moncaleano

Chapter 3: Mathematics Grade 8


Screen 4 – Constructing the Walls

This item of the Building task involved understanding measurements and reasoning with geometric shapes. Students were presented with a 14 m × 14 m board marked with a grid of 1 m × 1 m squares. They were asked to use the drawing tool to indicate where they would cut out the piece for the back wall of the shed and the two pieces for the side walls. The three pieces fit on the board with extra room leftover, and there was not a requirement to use the smallest amount of the board.

To help them relate the three-dimensional representation of the shed to the two-dimensional board, students could use the tabs to view the dimensions of the back of the shed as well as the dimensions of one side and the front of the shed. For full credit (2 points), students needed to fit all three wall pieces—back and two sides—onto the board. The back wall was 4 m × 3 long (for the shed’s three sections) by 4 m high. Calculating the dimensions of the sidewalls did require realizing that a side wall was comprised of a 4 m × 4 m square and the right angle triangle holding up the roof which had been the focus of the previous screen (requiring application of the Pythagorean Theorem), and of course, that there were two side walls.

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Maximum Score Points: 2
Content Domain: Geometry
Topic Area: Geometric Shapes and Measurement
Cognitive Domain: Reasoning


Exhibit 28 shows the percentages of responses awarded full credit (2 points) for correctly measuring and including all three walls. Having already demonstrated some understanding of the dimensions of the right angle triangle that formed the top of each side (in their responses to Screen 3), the students in Singapore, Chinese Taipei, and Hong Kong SAR once again had the highest percentages of full credit responses with 53, 45, and 42 percent fully correct, respectively. However, only 26 percent of the students on average across the eTIMSS countries received full credit (2 points), with another 11 percent of the students on average receiving partial credit (1 point) for fitting the back wall rectangle on the board. There was very little difference in achievement between girls and boys.

Students rarely are presented with a “blank canvas” and asked to proceed on their own. Much more research could be done trying to determine whether the students planned or not, and if so, was there any evidence of a forward-looking strategy. For example, students were awarded partial credit for fitting the back wall onto the board. However, putting that wall in the middle of the board would not be a good strategy for leaving room for the side walls and obtaining two points.

As an example of the potential for using the TIMSS 2019 PSI data for research, the TIMSS & PIRLS International Study Center used the responses from this graphical constructed-response item to explore the possibilities of using automated scoring in future TIMSS assessment cycles (see Appendix C). Artificial neural networks (ANNs) were trained according to the TIMSS scoring guide and example responses to classify the students’ responses. The ANNs scoring was at least as reliable as the human scoring, suggesting that in the future TIMSS might be able to replace the second human scorer in reliability scoring with ANNs scoring.