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Pre-service Teacher Procedural and Conceptual Knowledge of Fractions

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Research Advances in the Mathematical Education of Pre-service Elementary Teachers

Part of the book series: ICME-13 Monographs ((ICME13Mo))

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.

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References

  • Ball, D. L. (1988). Unlearning to Teach Mathematics. For the Learning of Mathematics, 8(1), 40–48.

    Google Scholar 

  • Ball, D. L. (1990). The Mathematical Understandings That Prospective Teachers Bring to Teacher Education. The Elementary School Journal, 90(4), 449–466.

    Google Scholar 

  • Ball, D. L., Hill, H. C., & Bass, H. (2005). Knowing mathematics for teaching: Who knows mathematics well enough to teach third grade, and how can we decide. American Educator, 29(1), 14–17, 20–22, 43–46. Retrieved from http://hdl.handle.net/2027.42/65072.

  • Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education 59(5), 389–407.

    Google Scholar 

  • Barmby, P., Harries, T., Higgins, S., & Suggate, J. (2009). The array representation and primary children’s understanding and reasoning in multiplication. Educational Studies in Mathematics 70, 217–241. doi:10.1007/s10649-008-9145-1.

  • Behr, M., Harel, G., Post, T., & Lesh, R. (1993). Rational Numbers: Toward a Semantic Analysis—Emphasis on the Operator Construct. In T. Carpenter, E. Fennema & T. Romberg (Eds.), Rational Numbers: An Integration of Research (pp. 13–47). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Charalambous, C. Y., & Pitta-Pantazi, D. (2007). Drawing on a theoretical model to study students’ understandings of fractions. Educational Studies in Mathematics, 64(3), 293–316.

    Google Scholar 

  • Chinnappan, M., & Forrester, P. (2014). Generating procedural and conceptual knowledge of fractions by pre-service teachers. Mathematics Education Research Journal, 26, 871–896. doi:10.1007/s13394-014-0131-x.

  • Depaepe, F., Torbeyns, J., Vermeersch, N., Janssens, D., Janssen, R., Verschaffel, L., & Van Dooren, W. (2015). Teachers’ content and pedagogical content knowledge on rational numbers: A comparison of prospective elementary and lower secondary school teachers. Teaching and Teacher Education, 47, 82–92.

    Google Scholar 

  • Eisenhart, M., Borko, H., Underhill, R., Brown, C., Jones, D., & Agard, P. (1993). Conceptual Knowledge Falls through the Cracks: Complexities of Learning to Teach Mathematics for Understanding. Journal for Research in Mathematics Education, 24(1), 8–40.

    Google Scholar 

  • Hallett, D., Nunes, T., & Bryant, P. (2010). Individual differences in conceptual and procedural knowledge when learning fractions. Journal of Educational Psychology, 102(2), 395–406.

    Google Scholar 

  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406.

    Google Scholar 

  • Kieren, T. E. (1976). On the mathematical, cognitive and instructional foundations of rational numbers. In R. A. Lesh (Ed). Number and Measurement: Papers from a research workshop (pp. 101–144). Columbus, OH: ERIC/SMEAC.

    Google Scholar 

  • Lin, C.-Y., Becker, J., Byun, M.-R., & Ko, Y.-Y. (2013). Enhancing pre-service teachers’ fraction knowledge through open approach instruction. Journal of Mathematical Behavior, 32, 309–330.

    Google Scholar 

  • Ma, L. (1999). Knowing and Teaching Elementary School Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States (Mahwah, Nj: Lawrence Erlbaum).

    Google Scholar 

  • Moseley, B. (2005). Students’ Early Mathematical Representation Knowledge: The Effects of Emphasizing Single or Multiple Perspectives of the Rational Number Domain in Problem Solving. Educational Studies in Mathematics, 60(1), 37–69.

    Google Scholar 

  • National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, D.C.: U.S. Department of Education.

    Google Scholar 

  • Newton, K. J. (2008). An extensive analysis of preservice elementary teachers’ knowledge of fractions. American Educational Research Journal, 45(4), 1080–1110.

    Google Scholar 

  • Rittle-Johnson, B., Siegler, R. S., and Alibali, M. W. (2001). Developing Conceptual Understanding and Procedural Skull in Mathematics: An Iterative Process. Journal of Educational Psychology, 93(2), 346–362.

    Google Scholar 

  • Shulman, L. S. (1986). Those who understand: Knowledge Growth in Teaching. Educational Researcher, 15(2), 4–14.

    Google Scholar 

  • Stoddart, T., Connell, M., Stofflett, R., & Peck, D. (1993). Reconstructing elementary teacher candidates’ understanding of mathematics and science content. Teaching and Teacher Education, 9(3), 229–241.

    Google Scholar 

  • Van Steenbrugge, H., Valcke, M., & Desoete, A. (2010). Mathematics learning difficulties: Teachers’ professional knowledge and the use of commercially available learning packages. Educational Studies, 36(1), 59–71.

    Google Scholar 

  • Van Steenbrugge, H., Valcke, M., & Desoete, A. (2014). Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge? Curriculum Studies, 46(1), 138–161.

    Google Scholar 

  • Vula, E., Kingji-Kastrati, J., & Podvorica, F. (2015). A comparative analysis of mathematics textbooks from Kosovo and Albania based on the topic of fractions. In K. Krainer & N. Vondrová (Eds). Proceedings of the Ninth Congress of the European Society for Research in Mathematics Education, CERME 9 (pp. 1759–1765). Czech Republic: Prague.

    Google Scholar 

  • Wilson, S. M. (2010). Knowledge for teaching mathematics in a primary school: Perspectives of pre-service teachers. (Master thesis). University of Canterbury. Retrieved from http://hdl.handle.net/10092/5187.

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Author information

Authors and Affiliations

  1. University of Pristina, Pristina, Kosovo

    Eda Vula & Jeta Kingji-Kastrati

Authors
  1. Eda Vula
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  2. Jeta Kingji-Kastrati
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Corresponding author

Correspondence to Eda Vula .

Editor information

Editors and Affiliations

  1. Department of Education, University of Oxford, Oxford, United Kingdom

    Gabriel J. Stylianides

  2. Graduate School of Education, Utsunomiya University, Utsunomiya, Tochigi, Japan

    Keiko Hino

Appendix

Appendix

Fraction Knowledge Tasks

  1. 1.

    Which of the following correspond of \( \frac{2}{3} \)?

  2. 2.

    What part of each circle is coloured?

  3. 3.

    This is the a whole.

    What fraction represents this piece?

  4. 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.

  5. 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?

  6. 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?

    1. (a)

      \( \frac{5}{20} \) is bigger than \( \frac{1}{4} \)

    2. (b)

      \( \frac{1}{4} \) is bigger than \( \frac{5}{20} \)

    3. (c)

      \( \frac{5}{20} \) and \( \frac{1}{4} \) are equal

  7. 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?

  8. 8.

    \( \frac{1}{3} \) of which number is the number 5?

  9. 9.

    How many halves (\( \frac{1}{2 } \)) are there in six wholes? Illustrate your reasoning with a figure.

  10. 10.

    What number should go at the point marked by X?

  11. 11.

    Represent, with X, the fractions : \( \frac{1}{2} \) and \( \frac{5}{4} \) on a number line below.

  12. 12.

    Place number 1 on the number line each of the number lines below.

Calculate:

  1. 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

  1. 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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  • DOI: https://doi.org/10.1007/978-3-319-68342-3_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68341-6

  • Online ISBN: 978-3-319-68342-3

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