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International Electronic Journal of Mathematics Education

International Electronic Journal of Mathematics Education
Science and Engineering Students’ Difficulties With Fractions At Entry-Level To University
Johanna Coetzee, Kuttickattu J. Mammen
  • Article Type: Research Article
  • International Electronic Journal of Mathematics Education, 2017 - Volume 12 Issue 3, pp. 281-310
  • Published Online: 18 Jun 2017
  • Article Views: 2442 | Article Download: 2273
  • Open Access Full Text (PDF)
APA
In-text citation: (Coetzee & Mammen, 2017)
Reference: Coetzee, J., & Mammen, K. J. (2017). Science and Engineering Students’ Difficulties With Fractions At Entry-Level To University. International Electronic Journal of Mathematics Education, 12(3), 281-310.
AMA
In-text citation: (1), (2), (3), etc.
Reference: Coetzee J, Mammen KJ. Science and Engineering Students’ Difficulties With Fractions At Entry-Level To University. INT ELECT J MATH ED. 2017;12(3), 281-310.
Chicago
In-text citation: (Coetzee and Mammen, 2017)
Reference: Coetzee, Johanna, and Kuttickattu J. Mammen. "Science and Engineering Students’ Difficulties With Fractions At Entry-Level To University". International Electronic Journal of Mathematics Education 2017 12 no. 3 (2017): 281-310.
Harvard
In-text citation: (Coetzee and Mammen, 2017)
Reference: Coetzee, J., and Mammen, K. J. (2017). Science and Engineering Students’ Difficulties With Fractions At Entry-Level To University. International Electronic Journal of Mathematics Education, 12(3), pp. 281-310.
MLA
In-text citation: (Coetzee and Mammen, 2017)
Reference: Coetzee, Johanna et al. "Science and Engineering Students’ Difficulties With Fractions At Entry-Level To University". International Electronic Journal of Mathematics Education, vol. 12, no. 3, 2017, pp. 281-310.
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Coetzee J, Mammen KJ. Science and Engineering Students’ Difficulties With Fractions At Entry-Level To University. INT ELECT J MATH ED. 2017;12(3):281-310.

Abstract

This study was carried out at a South African university. The aim of the study was to test entry-level students’ fractions skills in order to facilitate teaching at appropriate levels. The sample consisted of 94 first-year entry level students (54 mainstream and 40 extended stream) who were enrolled for national diplomas in science and engineering, out of a population of 120 students. The instrument had 20 items, including three multiple choice questions (MCQs). The data were analyzed using Microsoft Excel 2013. The main finding was that entry-level students enrolled for engineering and science diplomas performed poorly in a test of numeracy skills. The average score (47.8%) was regarded as a cause for concern, especially considering that the test was pitched at Grade 8 level. The study also found that students struggled to apply proportional reasoning when dealing with word problems. Mathematics teachers and lecturers need to be aware of students’ difficulties and ought to attempt to assist them to overcome such challenges. It is hoped that this paper will be useful to mathematics curriculum implementers at school level, subject advisors at the district level, pre-service teacher educators at Teachers’ colleges and universities, and university lecturers teaching mathematics at first year level.

Keywords

mathematics education numeracy fractions ratios proportions

References

  • Akyuz, G. (2015). Determining the Numeracy and Algebra Errors of Students in a Two-year Vocational School. Community Collge Journal of Research and Practice, 39(3), 252-264.
  • Bailey, D.H, Zhou. X.,  Zhang, Y., Cui,  J.,  Fuchs,  L.S.,  Jordan, N. C., Gersten, R. & Siegler,  R. S. (2015). Development of fraction concepts and procedures in U.S and Chinese children. J Exp Child Psychol, 129, 68-83.
  • Ball, D.L. (1990). The mathematical understandings that prospective teachers bring to teacher education. THe Elementary School Journal, 90, 449-466.
  • Barwell, R. (2004). What is Numeracy? For the Learning of Mathematics, 24(1), 20-22.
  • Blais, K. & Bath, J. (1992). Drug calculation errors of baccalaureate nursing students. Nurse Educator, 17(1), 12-15.
  • Bone, A. A., Carr, J. A,  Daniele, V.A., Fisher, R., Fones, N .B., Innes, J. I., Maher,  H. P., Osborn, H.G. & Rockwell, D.L. (1984). Promoting a clear path to technical education. Washington DC: Model Secondary School for the Deaf.
  • Booth, J.L. & Newton, K.J. (2012). Fractions: Could they really be the gatekeeper’s doorman? Contemporary Educational Psychology, 37(4), 247-253.
  • Booth, J.L., Newton, K.J. & Twiss-Garrity, L.K. (2014). The impact of fraction magnitude knowledge on algebra performance and learning. Journal of Experimental Child Psychology, 118, 110-118.
  • Bowie, L. (2014). Report on mathematics courses for intermediate phase student teachers at five universities. Johannesburg: JET Education Services. Retrieved  24 March 2016  from http://www.jet.org.za/publications/initial-teacher-education-research-project/copy_of_bowie-report-on-maths-courses-offered-at-5-case-study-institutions-18-feb.pdf.
  • Bowie, L. & Frith, V. (2006). Concerns about the South African Mathematical Literacy curriculum arising from experience of material development. Pythagoras, 64, 29-36.
  • Brousseau, G., Brousseau, N. & Warfield, V. (2004). Rationals and decimals as required in the school curriculum. Part 1: Rationals as measurements. Journal of Mathematical Behavior, 23, 1-20.
  • Cai, J. (1995). A Cognitive Analysis of U. S. and Chinese Students' Mathematical Performance on Tasks Involving Computation, Simple Problem Solving, and Complex Problem Solving (Vol. monograph series 7). Reston, VA: National Council of Teachers of Mathematics.
  • Campbell, A. (2009). Remediation of First-year  mathematics students algebra difficulties. (MSc), University of KwaZulu-Natal, KwaZulu-Natal, South Africa. Retrieved  30 April 2014  from  http://researchspace.ukzn.ac.za/xmlui/bitstream/handle/10413/761/Campbell_A_2009.pdf?sequence=1
  • Case, J. (2006). Issues facing engineering education in South Africa. Paper presented at the Engineering Education for Sustainable Development: Proceedings of the 3rd African Regional Conference, 26-27 September 2006, University of Pretoria, Pretoria, South Africa, 26-27 September 2006.
  • Cetin, H & Ertekin, E. (2011). The relationship between eighth grade primary school students' proportional reasoning skills and success in solving equations. International Journal of Instruction, 4(1), 47-62.
  • Clarke, D. (2006). Fractions as division: The forgotten notion. Australian Primary Mathematics Classroom, 11(3), 4-10.
  • Coetzee, J. & Mammen, K. J. (2016). Challenges Faced by Entry-level University Students in Word Problems Involving Fractions Terminology. International Journal of Education Sciences (IJES)., 15(3), 461-473.
  • DoBE, (2011a). National Curriculum Statement (NCS): Curriculum and Assessment Policy Statement (CAPS)  Further Education and Training Phase MATHEMATICS  GR 7-9. Pretoria: Department of Basic Education. Retrieved  30 April 2014  from http://www.education.gov.za.
  • DoBE, (2011b). National Curriculum Statement (NCS): Curriculum and Assessment Policy Statement (CAPS)  Further Education and Training Phase MATHEMATICS Grades 10-12. Pretoria, South Africa: Department of Basic Education. Retrieved  30 April 2014  from http://www.education.gov.za.
  • DoBE, (2011c). National Curriculum Statement (NCS): Curriculum and Assessment Policy Statement (CAPS)  Intermediate Phase MATHEMATICS GR 4-6. Pretoria: Department of Basic Education. Retrieved  30 April 2014  from http://www.education.gov.za.
  • DoBE, (2012). National Senior Certificate 2012: National diagnostic report on learners’ performance. Pretoria, South Africa: Department of Basic Education. Retrieved  15 October 2015  from http://www.education.gov.za.
  • Dorko, A & Speer, N. (2014). Calculus Students' Understanding of Units. Paper presented at the 17th Annual Conference on Research in Undergraduate Mathematics Education, February 26 - March 2, 2014, Denver, Colorado.
  • Duffin,  J. (2003). Numeracy in Higher Education. In J. K. Peter Kahn (Ed.), Effective Learning and Teaching in Mathematics and Its Applications: Routledge, London.
  • Fonseca, K & Petersen, N. (2015). Online supplementary mathematics tuition in a first-year childhood teacher education programme. South African Journal of Childhood Education, 5(3), 9 pages.
  • Gabaldon, T.A. (2015). Strength in Numbers: Teaching Numeracy in the Context of Business Associations. St. Louis University Law Journal, 59, 701-709.
  • Graffeo, M., Polonio, L. & Bonini, N. (2015). Individual differences in competent consumer choice: the role of cognitive reflection and numeracy skills. Frontiers in Psychology, 6.
  • Gravetter, F.J. & Wallnau, L.B. (2009). Statistics for the Behavioral Sciences (8th ed.). Belmont, CA: Wadsworth.
  • Houston, J., Tenza, S.P.,  Hough, S., Singh, R. & Booyse, C. (2015). The rationale for teaching Quantitative Literacy in 21st century South Africa: A case for the renaming of Mathematical Literacy. The Independent Journal of Teaching and Learning, 10. Retrieved  6 April 2016  from http://hdl.handle.net/11622/53
  • Johnson, A.W. & Johnson, R. (2002). Cooperative Learning Methods: A meta-analysis. Journal of Research in Education, 12(1), 5-14.
  • Jukes, L & Gilchrist, M. (2006). Concerns about numeracy skills of nursing students. Education in Practice, 6(4), 192-198.
  • Kremmer, M., Brimble, M., Freudenberg, B. & Cameron, C. (2010). Numeracy of First Year Commerce Students: Preliminary Analysis of an Intervention. The International Journal of Learning, 17(1), 1-13.
  • Lamon, S.L. (2001). Presenting and Representing: From Fractions to Rational Numbers. In A. Cuoco & F. Curcio (Eds.), The Roles Of Representations in School Mathematics-2001 Yearbook (pp. 146-165). Reston: NCTM.
  • Lesh, R., Post, T. & Behr,  M. (1988). Proportional Reasoning. In J. Hiebert & M. Behr (Eds.), Number Concepts and Operations in the Middle Grades (pp. 93-118). Reston, VA: Lawrence Erlbaum & National Council of Teachers of Mathematics.
  • Lin, C.Y., Becker, J., Byun, M-R., Yang, D.C. & Huang, T.W. (2013). Preservice Teachers’ Conceptual and Procedural Knowledge of Fraction Operations: A Comparative Study of the United States and Taiwan. School Science and Mathematics, 113(1), 41-51.
  • Livy, S. & Herbert, S. (2013). Second-Year Pre-Service Teachers’ Responses to Proportional Reasoning Test Items. Australian Journal of Teacher Education, 38(11), 17-32.
  • Long, C.,  Dunne, T. & De Kock, H. (2014). Mathematics, curriculum and assessment: The role of taxonomies in the quest for coherence. Pythagoras 35, 35(2), 14.
  • Lortie-Forgues,  H., Tian, J. & Siegler, R.S. (2015). Why Is Learning Fraction and Decimal Arithmetic So Difficult. Developmental Review, 38, 201-221.
  • Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' knowledge of fundamental mathematics in China and the United States. Mahwah, NJ: Erlbaum.
  • Naureen, D. & Vicki, N.T. (2012). The role of numeracy skills in graduate employability. Education and Training, 54(5), 419-434.
  • NMAP, (2008). Foundations for Success: The final report of the National Mathematics Advisory Panel. Washington, DC: National Mathematics Advisory Panel. Retrieved  27 February 2016  from http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf.
  • OECD, (2013). OECD Skills Outlook 2013: First Results from the Survey of Adult Skills. Paris: OECD Publishing. Retrieved  4 April 2016  from www.oecd.org/skills/.
  • Pienaar, E. (2014). Learning About And Understanding Fractions And Their Role In The High School Curriculum. (Master of Education), University of Stellenbosch, Stellenbosch. Retrieved  15 October 2015  from  https://www.google.co.za/#q=Learning+About+And+Understanding+Fractions+And+Their+Role+In+The+High+School+Curriculum
  • Pinker, S. (1998). How the mind works. London: Penguin Books
  • Reyna, V.F., Nelson, W.L., Han, P.K. & Dieckmann, N.F. (2009). How Numeracy Influences Risk Comprehension and Medical Decision Making. Psychological bulletin, 135(6), 943-973.
  • Rivera-Batiz, F.L. (1992). Quantitative Literacy and the Likelihood of Employment among Young Adults in the United States. The Journal of Human Resources, 27(2), 313-328.
  • Rizvi, N.F. & Lawson, M.J. (2007). Prospective teachers’ knowledge: Concept of division International Education Journal, 8(2), 377-392.
  • Roohr, K.C., Graf, E.A. & Liu, O.L. (2014). Assessing Quantitative Literacy in Higher Education: An Overview of Existing Research and Assessments With Recommendations for Next-Generation Assessment. ETS Research Report Series, 2014(2), 1-26.
  • Schneider, M. & Siegler, R.S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance, 36(5), 1227-1238.
  • Schollar, E. (2008). Towards Evidence-based Educational Development in South Africa: Eric Schollar and Associates c.c. Retrieved  21 March 2016  from https://www.ru.ac.za/media/rhodesuniversity/content/sanc/documents/Schollar%20-%202008%20-%20Final%20Report%20Short%20Version%20The%20Primary%20Mathematics%20Research%20Project%202004-2007%20-%20Towards%20eveidence-based%20educational%20de.pdf.
  • Siegler, R.S., Duncan, G.J ., Davis-Kean, P.E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M.I. & Chen, M. (2012a). Early Predictors of High School Mathematics Achievement. Psychological Science, 23(7), 691-697.
  • Siegler, R.S., Fazio, L.K., Bailey, D.H. & Zhou, X. (2012b). Fractions: the new frontier for theories of numerical development. Trends in Cognitive Sciences, 17(1), 13-19.
  • Siegler, R.S. & Lortie-Forgues H. (2015). Conceptual Knowledge of Fraction Arithmetic. Journal of Educational Psychology, 107(3), 909-918.
  • Siegler, R.S. & Thompson, CA. (2014). Numerical landmarks are useful-except when they're not. J Exp Child Psychol, 120, 39-58.
  • Siegler, R.S., Thompson, C.A. & Schneider, M. (2011). An integrated theory of whole number and fractions development. Cognitive Psychology, 62(2011), 273-296.
  • Spaull, N. & Kotze, J. (2015). Starting behind and staying behind in South Africa: The case of insurmountable learning deficits in mathematics. International Journal of Educational Development, 41, 13-24.
  • Sun, L.G. & Wang, L. (2005). Mathematics: Spring, Fifth grade. Nanjing, Jiangsu Province: Phoenix Education.
  • Titus, J. (1995). The concept of fractional number among deaf and hard of hearing students. American Annals of the Deaf, 140(3), 255-263.
  • Torbeyns, J., Schneider, M., Xin, Z, & Siegler, R.S. (2014). Bridging the Gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 1-9.
  • Torbeyns, J., Schneider, M., Xin, Z. & Siegler R.S. (2015). Bridging the gap: Fraction understanding is central to mathematics achievement in students from three different continents. Learning and Instruction, 37, 5-13.
  • Watts, T.W., Duncan, G.J., Siegler, R.S. & Davis-Kean, P.E. (2014). What's Past Is Prologue: Relations Between Early Mathematics Knowledge and High School Achievement. Educational Researcher, 43(7), 352-360.
  • Wilson, T.M. & MacGillivray, H.L. (2007). Counting on the basics: mathematical skills among tertiary entrants. International Journal of Mathematical Education in Science and Technology, 38(1), 19-41.
  • Wu, H. (2001). How to prepare students for Algebra. American Educator, 25(2), 10-17.

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