Abstract
This chapter assessed pre-service teacher knowledge of fraction interpretations and their ability to demonstrate procedural and conceptual knowledge of adding and subtracting fractions. The sample included 58 pre-service teachers in Kosovo. The twenty tasks given in the study’s test were related to fraction concepts, fraction addition and fraction subtraction. It was found that the pre-service teachers had limited knowledge regarding different fraction interpretations. It was also found that they had limited knowledge on showing the explanation of the procedures of adding and subtracting fractions. This chapter discusses the findings taking into considerations the context in which the study was conducted and provides suggestion for future research.
Keywords
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Appendix
Appendix
Fraction Knowledge Tasks
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1.
Which of the following correspond of \( \frac{2}{3} \)?
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2.
What part of each circle is coloured?
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3.
This is the a whole.
What fraction represents this piece?
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4.
How can you best define the fraction that represents number of coloured circles in the set below? Give at least two fractions which represent the figure below and explain how you determined your answer.
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5.
Based on the figure below, who gets more pizza, the boys or girls? How can boys and girls share the pizza equally? Express in fractions how many slices of pizzas did take each of them?
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6.
Two boys have the same amount of money. One decides to save \( \frac{1}{4} \) of his money and the other boy saves \( \frac{5}{20} \) portion of his money. What do you think is the correct way to represent a comparison of the amount saved by the boys?
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(a)
\( \frac{5}{20} \) is bigger than \( \frac{1}{4} \)
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(b)
\( \frac{1}{4} \) is bigger than \( \frac{5}{20} \)
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(c)
\( \frac{5}{20} \) and \( \frac{1}{4} \) are equal
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(a)
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7.
The diagram below shows the vehicle which works under a rule: “the 2/3 of the input quantity gives the output quantity”. How much will be the output quantity if input quantity is 12?
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8.
\( \frac{1}{3} \) of which number is the number 5?
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9.
How many halves (\( \frac{1}{2 } \)) are there in six wholes? Illustrate your reasoning with a figure.
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10.
What number should go at the point marked by X?
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11.
Represent, with X, the fractions : \( \frac{1}{2} \) and \( \frac{5}{4} \) on a number line below.
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12.
Place number 1 on the number line each of the number lines below.
Calculate:
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13.
\( \frac{1}{3} + \frac{1}{2} = \) 14. \( 7\frac{5}{8} + 4\frac{1}{2} = \) 15. \( \frac{5}{6} - \frac{1}{3} = \) 16. \( 3\frac{2}{3} - 1\frac{1}{2} = \)
Perform the following operations and justify solutions using any form of fraction presentation
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17.
\( \frac{1}{4} + \frac{2}{3} = \) 18. \( 2\frac{1}{3} + \frac{1}{9} = \) 19. \( \frac{ 3}{5} - \frac{1}{2} = \) 20. \( 3\frac{1}{4} - \frac{2}{3} = \)
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Vula, E., Kingji-Kastrati, J. (2018). Pre-service Teacher Procedural and Conceptual Knowledge of Fractions. In: Stylianides, G., Hino, K. (eds) Research Advances in the Mathematical Education of Pre-service Elementary Teachers. ICME-13 Monographs. Springer, Cham. https://doi.org/10.1007/978-3-319-68342-3_8
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