ANALYSIS OF LEARNING DIFFICULTIES WITH FRACTIONS IN THREE AFRICAN COUNTRIES: FOCUSING ON THE SCOPE, SEQUENCE AND MODELS OF FRACTIONS
DOI:
https://doi.org/10.47604/ajep.1267Keywords:
Fraction curriculum, Concept of fraction, Models for fraction, Mathematics in African countriesAbstract
Purpose: This study aims to compare and analyze learning content with regard to fractions, the order in which that content is taught in primary school mathematics curricula, and how it is presented in textbooks in three eastern and southern African countries, Zambia, Ethiopia, and Mozambique as well as to clarify the characteristics of the instruction concerning fraction in each of these countries.
Methodology: Firstly, we refer to the curriculum to extract information about the learning contents and their order in each grade. Secondly, concerning the meaning of fractions, we refer to the textbooks since we cannot clearly judge from the description in the curriculum. Thirdly, we focus on the common points and differences among the three countries and analyze the causes of difficulty in learning fractions.
Findings: There is a significant discrepancy between the grades in learning fractions among the three countries. In addition, the learning order differs to a certain degree. A common feature of the three countries regarding the order is the multiplication and division of fractions. For all three countries, while the addition and subtraction of fractions and types of fractions are handled separately by different grades, the multiplication and division are all taught in one grade. Further, how the meaning of fractions is taught is common to all three countries. In all the countries, the part-whole concept of fractions is mainly employed, and the fraction as measurement concept is not taught at all. Unfortunately, since children learn without considering fractions as measurements, their understanding of fractions will be limited.
Unique contribution to theory, practice, and policy: Regarding fraction, basic research on the teaching content and their order in African countries have not been conducted extensively. While improving the quality of education is a common goal globally, it is paramount to analyze the difficulty in learning fractions from the perspectives of the intended curriculum and textbook. The result will be the implication for revising the curriculum and suggestions for teaching fractions.
Downloads
References
Atweth, B., & Clarkson, P. (2001). Internationalization and globalization of mathematics education: Toward an agenda for research/action. In B. Atweh, H. Forgasz, & B. Nebres (Eds.), Sociocultural research in mathematics education (pp.77-94). Mahwah, NJ: Lawrence Erlbaum.
Cramer, K., & Henry, A. (2002). Using Manipulative Models to Build Number Sense for Addition of Fractions. In B. Litwiller & G. Bright (Eds.), Making Sense of Fractions, Ratios, and Proportions: 2002 Yearbook (pp. 41-48). Reston, VA: National Council of Teachers of Mathematics.
Cramer, K.A., Post, T.R. & Del Mass, R.C.(2002). Initial fraction learning by fourth- and fifth-grade students: A comparison of the effects of using commercial curricula with the effects of using the rational number project curriculum. Journal for Research in Mathematics Education 33(2), 111–144. Retrieved from https://www.jstor.org/stable/749646
Cramer, K., Wyberg, T., & Leavitt, S. (2008). The Role of Representations in Fraction Addition and Subtraction. Mathematics Teaching in the Middle School, 13(8), 490–496.
Cramer, K. & Whitney, S. (2010). Learning rational number concepts and skills in elementary school classrooms. In D. V. Lambdin & F. K. Lester Jr. (Eds.), Teaching and learning mathematics: Translating research for elementary school teachers. (pp.15-22). Reston, VA: The National Council of Teachers of Mathematics.
Cramer, K., Monson, D., Whitney, S., Leavitt, S., & Wyberg, T. (2010). Dividing fractions and problem solving. Mathematics Teaching in the Middle School, 15(6), 338-346.
Curriculum Development Centre. (2013). Mathematics Syllabus (Grades 1-7). Ministry of Education, Science, Vocational Training and Early Education, Zambia.
English, L., & Halford, G. (1995). Mathematics education. Models and processes. New Jersey: Erlbaum.
Hecht, S. A., Close, L., & Santisi, M. (2003). Sources of individual differences in fraction skills. Journal of Experimental Child Psychology, 86(4), 277–302. https://doi.org/10.1016/j.jecp.2003.08.003
Johanning, D. I. (2008). Learning to use fractions: Examining middle school students’ emerging fraction literacy. Journal for Research in Mathematics Education, 39, 281–310.
Kieren, T. E. (1980). The rational number construct-Its elements and mechanisms. In T. E. Kieren (Ed.). Recent Research on Number Learning (pp.125-149). Columbus, OH: ERIC/SMEAR.
Lo, J., J. & Luo, F. (2012). Prospective Elementary Teachers’ Knowledge of Fraction Division. Journal of Math Teacher Education, 5, 481-500.
Martinie, S. L. (2007). Middle school rational number knowledge (Doctoral dissertation). Kansas State University. Retrieved from https://core.ac.uk/download/pdf/5164377.pdf
Ministério da Educação. (2015). Programas do Ensino Primário Língua Portuguesa, Matemática e Educação Física. Mozambique, Ministério da Educação.
Ministry of Education. (2009). Mathematics syllabus grades 1 to 7. Addis Ababa Ethiopia: The Federal Democratic Republic of Ethiopia, Ministry of Education.
Neagoy, M. (2017). Unpacking fractions: classroom-tested strategies to build students mathematical understanding. Alexandria, VA, USA: ASCD.
NMAP. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.
Petit, M., Laird, R., & Marsden, E. (2010). A Focus on Fractions: Bringing Research to the Classroom. New York: Routledge-Taylor Francis Group.
Siebert, D., & Gaskin, N. (2006). Creating, naming and justifying fractions. Teaching Children Mathematics, 12, 394-400.
Siegler, R. S., Thompson, C. A., & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(4), 273-296. https://doi.org/10.1016/j.cogpsych.2011.03.001
Steffe, L. P., & Olive, J. (2010). Children’s fractional knowledge. New York, NY: Springer.
Usiskin Z (2007). The arithmetic operations as mathematical models. In Blum W, Galbraith PL & Henn H, Niss, M. (Eds.), Modelling and Applications in Mathematics Education: The 14th ICMI Study. New York.
Vale,C. & Davies, A. (2007). Dean’s great discovery: Multiplication, division and fractions. Australian Primary Mathematics Classroom. 12(3), 18–22.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Satoshi Kusaka
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution (CC-BY) 4.0 License that allows others to share the work with an acknowledgment of the work’s authorship and initial publication in this journal.
