An Examination of Fourth-Grade Elementary School Students’ Number Sense in Context-Based and Non-Context-Based Problems

Abstract

Research on number sense presents contradictory arguments and results regarding the effects of context-based tasks and activities on students’ number sense. The aim of this study was to examine fourth-grade elementary school students’ number sense as they solve context-based (CB) and non-context-based (NCB) items. A survey design was employed and data collected using CB and NCB tests for this purpose. The results showed that students were more successful on NCB test compared to the CB test. Students performed best on the problems related to the “using a reference point” component of number sense, while they performed worst on the “understanding of the number size” component. The majority of students used rule-based strategies (RBSs) for both CB and NCB tests. Interviews with students who solved CB items using RBSs showed that students were able to recognize and use number sense-based strategies (NSBSs) to some degree when they were asked for alternative solution methods. The variability found in students’ recognition and use of number sense seem to depend on such factors as the lack of number sense, preference to RBS, task structure (e.g. involving visual representations and easy numbers), and task requirements (e.g. asking for estimation or comparison vs. exact answer, requiring additional adjustments on reference points).

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Correspondence to Derya Can.

Additional information

This paper is based on the PhD Thesis written by Derya Can under the supervision of Assoc. Prof. Dr. İ. Elif Yetkin Özdemir.

Appendix 1. Number sense test for context-based problems

Appendix 1. Number sense test for context-based problems

  1. 1.

    A factory bought 98 boxes, each of which contained 50 buttons. Which of the following is closest to the number of buttons bought by the factory?

  1. A.

    500

  2. B.

    5000

  3. C.

    50,000

  1. 2.

    Ekin wanted to check 372 − 38 = 334 using a calculator. However, she typed in 372 − 18 instead of 372 − 38. Which of the following statements best describes the result she obtained with the calculator?

    1. A.

      2 less than 334.

    2. B.

      2 more than 334.

    3. C.

      20 less than 334.

    4. D.

      20 more than 334.

  1. 3.

    Quarter of a chocolate bar

figurea

The visual representation above shows one-quarter of a chocolate bar. Draw the amount of chocolate eaten by Sevil, who ate 2 \( \frac{1}{4} \) chocolate bars.

  1. 4.

    Mert saved 150 TL to buy a bicycle costing 325 liras. Later, its price was cut in half during a sale. Does Mert have enough money to purchase the bike now?

A. Yes.

B. No.

  1. 5.

    Theater Hall A contains 9 rows, and in each row there are 18 chairs. Hall B of the theatre has 10 rows, and in each row there are again 18 chairs. Hall C of the theatre has 9 rows, and in each row there are 17 chairs. Rank the halls from the largest to smallest based on their capacity.

  1. 6.

    Ahmet and Nilay were each given 32 liras. Ahmet saved \( \frac{1}{2} \) of his money and Nilay saved \( \frac{5}{8} \) of her money. Which of the following statements is true?

A. Nilay saved more than Ahmet.

B. Ahmet saved more than Nilay.

C. Ahmet and Nilay saved the same amount.

  1. 7.
    figureb

    The height of the tree given in the visual representation is 490 cm. The height of a boy is one-fifth that of the tree. Which of the following statements is true of the boy’s height?

  1. A.

    It is 100 cm.

  2. B.

    It is higher than 100 cm.

  3. C.

    It is shorter than 100 cm.

  1. 8.

    A supermarket sells 18 packs of water, in each of which there are 12 water bottles, so it sells 216 bottles?? of water per day in total. How many bottles of water would the supermarket sell if it sold 9 packs of water with 24 bottles per day?

  2. 9.

    A bookstore joined a book fair and its four-day sales are given as follows:

Day 1: 91 liras, Day 2: 93 liras, Day 3: 97 liras, Day 4: 99 liras.

The bookstore needs to pay 380 liras to rent the bookstand. Are its sales enough to pay for the bookstand?

  1. 10.
    figurec

The expenditures of Veli at the supermarket are given above. How much did he pay for these products?

Appendix 2. Number sense test for non-context-based problems

  1. 1.

    Which of the following is closest to 50 × 98?

  1. A.

    500

  2. B.

    5000

  3. C.

    50,000

  1. 2.

    If 372 − 38 = 334, which of the following is true of 372 − 18?

  1. A.

    2 less than 334.

  2. B.

    2 more than 334.

  3. C.

    20 less than 334.

  4. D.

    20 more than 334.

  1. 3.
    figured

In the visual representation above, the shaded part shows one-quarter of the whole. Draw a visual representation representing the fraction of 2 \( \frac{1}{4} \).

  1. 4.

    Which of the following statements is true for the result of 325 ÷ 2?

  1. A.

    It is 150.

  2. B.

    It is bigger than 150.

  3. C.

    It is smaller than 150.

  1. 5.

    Rank the results of the operations 18 × 9, 18 × 10, and 17 × 9 from largest to smallest.

  1. 6.

    Make a comparison between \( \frac{1}{2} \) of 32 and \( \frac{5}{8} \) of 32.

    1. A.

      \( \frac{1}{2} \) of 32 is smaller than \( \frac{5}{8} \) of 32.

    2. B.

      \( \frac{1}{2} \) of 32 is larger than \( \frac{5}{8} \) of 32.

    3. C.

      \( \frac{1}{2} \) of 32 is equal to \( \frac{5}{8} \) of 32.

  2. 7.

    Which of the following statements is true of 490 ÷ 5?

  1. A.

    It is 100.

  2. B.

    It is larger than 100.

  3. C.

    It is smaller than 100.

  1. 8.

    If 12 × 18 = 216, what is 24 × 9?

  1. 9.

    Which of the following statements is true of 91 + 93 + 97 + 99?

  1. A.

    It is larger than 380.

  2. B.

    It equals to 380.

  3. C.

    It is smaller than 380.

  1. 10.

    What is 39 + 23 + 52 + 48 + 61 + 77?

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Can, D., Yetkin Özdemir, İ.E. An Examination of Fourth-Grade Elementary School Students’ Number Sense in Context-Based and Non-Context-Based Problems. Int J of Sci and Math Educ 18, 1333–1354 (2020). https://doi.org/10.1007/s10763-019-10022-3

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Keywords

  • Context-based and non-context-based problems
  • Elementary school mathematics
  • Fourth-grade students
  • Number sense
  • Number sense-based strategies
  • Rule-based strategies