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Chinese and Singaporean sixth-grade students’ strategies for solving problems about speed

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Abstract

This study examined 361 Chinese and 345 Singaporean sixth-grade students’ performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies of these groups of students. The strategy analysis indicates that the Chinese sample used algebraic strategies more frequently and more successfully than the Singaporean sample, although the Chinese sample used a limited variety of strategies. The Singaporean sample’s use of model-drawing produced a performance advantage on one problem by converting multiplication/division of fractions into multiplication/division of whole numbers. Several suggestions regarding teaching and learning of mathematical problem solving, algebra, and problems about speed and its related concepts of ratio and proportion are made.

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Notes

  1. We use the terms heuristic and strategy interchangeably in this study to denote the methods or problem solving procedures that direct the search for a solution.

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Acknowledgments

This work was sponsored by a Multi-Year Research Grant from the University of Macau. Any opinions expressed herein are those of the author and do not necessarily represent the views of the university.

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Authors and Affiliations

  1. University of Macau, Macao, China

    Chunlian Jiang

  2. University of Delaware, 523 Ewing Hall, Newark, DE, 19716, USA

    Stephen Hwang & Jinfa Cai

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  1. Chunlian Jiang
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  2. Stephen Hwang
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Correspondence to Chunlian Jiang.

Appendix

Appendix

1.1 Test problems

  1. 1.

    A man drove at 72 km/h for 2 h, then the distance he travelled was ________km.

  2. 2.

    It takes a motorist __________ hours to travel 136 km at a speed of 68 km/h.

  3. 3.

    Judy cycled 45 km in 3 h, then her speed was __________km/h.

  4. 4.

    A man went to visit his friend who lived 27 km away. After walking at a speed of 6 km/h for \( 1\frac{1}{2} \) hours, he finished the remaining journey at a jogging speed of 12 km/h and got to his friend’s house at the appointed time. Find his average speed for the whole journey.

  5. 5.

    Mike made a journey from City P to City Q. In the first hour, he covered \( \frac{1}{3} \) of it. In the second hour, he covered \( \frac{1}{5} \) of the whole journey. Finally, he took 2 h to finish the remaining journey at a speed of 42 km/h. Calculate his average speed for the whole journey.

  6. 6.

    Town A and Town B are 20 km apart. Mike left Town A at 8.00 am and cycled at 16 km/h towards Town B. 10 min after Mike started, Bill cycled from Town B towards Town A at 15 km/h.

  7. (a)

    At 8.30 am, how far was Mike away from Town A and how far was Bill away from Town B?

  8. (b)

    Did they meet up at 8.30 am? If not, how far were they apart from each other at 8.30 am?

  9. 7.

    Mike made a journey from City P to City Q. In the first half an hour, he covered \( \frac{1}{7} \) of it. In the second half an hour, he covered \( \frac{1}{3} \) of the remaining journey. Finally, he took another half an hour to finish the journey at a speed of 72 km/h. Calculate his average speed for the whole journey.

  10. 8.

    Yesterday afternoon, Mike drove to the kindergarten to take back his son. It was raining on the way to the kindergarten, so he had to drive at a slow speed of 39 km/h, and it took him \( 1\frac{1}{3} \) hours to get there. He returned soon at a faster speed along the same way. When he came back home, his wife told him that his average speed for the round trip is 52 km/h (Ignoring time spent in the kindergarten). Find his speed on the way back.

  11. 9.

    On Sunday, Judy went to see her grandma who lives 150 km away. After cycling at an average speed of 15 km/h for a few hours, she got tired and took a lift from a passing truck. The truck’s average travelling speed is 75 km/h. When she got to her grandma's house, she checked the time and knew that the trip took her 6 h. Find the time she cycled.

  12. 10.

    Two places R and S are 300 km apart. Mike left R and drove at 84 km/h towards S. At the same time, Bill left S at 60 km/h and drove towards R. How long did they take to meet?

  13. 11.

    Two motorists, Jack and John, are having a race in the athletic track. John starts first. Half an hour later, Jack begins to chase after him. John’s driving speed is 84 km/h, and Jack’s driving speed is 90 km/h. How long does Jack take to catch up with John?

  14. 12.

    On Sunday, the students of one class went out for a picnic. At first they travelled in the crowded city 40 min at a speed of 27 km/h. Then they covered \( \frac{1}{5} \) of the remaining journey at a speed of 54 km/h. Finally, they travelled \( \frac{2}{3} \) of the whole journey in one hour on the expressway. Calculate the average speed for the whole journey.

  15. 13.

    Sunday morning, Rebecca and her parents went out to enjoy the natural scenery. On the way to the destination, they travelled at a slow speed of 40 km/h. On the way back, they drove at a faster speed of 120 km/h. When they came back home, they found that they had been out for 2 h. Find the average speed for this round trip (ignore time at the destination).

  16. 14.

    On the first day of this new term, Teacher Lee went to the bookshop to take back the ordered textbooks. On the way to the bookshop, his speed was as slow as 24 km/h because of the heavy traffic. On the way back, the traffic was light so that he took only one hour. If the average speed for the round trip was 36 km/h, find the speed on the way back (ignore time spent in the bookshop).

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Jiang, C., Hwang, S. & Cai, J. Chinese and Singaporean sixth-grade students’ strategies for solving problems about speed. Educ Stud Math 87, 27–50 (2014). https://doi.org/10.1007/s10649-014-9559-x

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