The Error Pattern of Students with Mathematics Learning Disabilities in the Inclusive School on Fractions Learning

Trisno Ikhwanudin, Sufyani Prabawanto, Wahyudin .

Abstract


This study examines the error pattern of students with mathematics learning disabilities when they learn fractions. This research uses a qualitative approach. The respondents are 23 students of the 7th graders in the inclusive school. The data are collected through student tests, class observations, and teacher interviews. The grounded theory with the constant comparison is conducted to the data analysis. There are four similar error patterns: (1) a lack of understanding of fraction representation; (2) a lack of understanding of fraction comparisons; (3) a mistake in applying the common denominator approach to the fraction addition operation; (4) a mistake in applying the procedure of fraction multiplication operation. The results of this study can be used by the teachers as a guideline when teaching fractions to students in inclusive schools.

https://doi.org/10.26803/ijlter.18.3.5


Keywords


Fraction Learning, Inclusive Education, Pattern Error Analysis, Mathematics Learning Disabilities

Full Text:

PDF

References


Bailey, D.H., Hoard, M.K., Nugent, L., Geary, D.C. (2012). Competence with fractions predicts gains in mathematics achievement. Journal of Experimental Child Psychology, 113(3), 447-455. doi:10.1016/j.jecp.2012.06.004

Brousseau, G. (2002). Theory of didactical situations in mathematics. Dordrecht: Kluwer Academic Publishers.

Butterworth, B., & Reigosa-Crespo, V. (2007). Information processing deficits in dyscalculia. In D.B. Berch & M. M. M. Mazzocco (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 65–81). Baltimore, MD: Paul H. Brookes.

Castellon, L. B., Burr, L. G., & Kitchen, R. S. (2011). English language learners’ conceptual understanding of fractions: An interactive interview approach as a means to learn with understanding. In K. Téllez, J. N. Moschkovich, & M. Civil (Eds.), Latinos/As and mathematics education: Research on learning and teaching in classrooms and communities (pp. 259–282). Charlotte, NC: Information Age Publishing.

Clarke, C., Fisher, W., Marks, R., Ross, S., Zbiek, R.S. (2010). Developing essential understanding of rational numbers for teaching mathematics in grades 3-5. Reston, VA: NCTM.

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.

Gall, M.D., Gall, J.P., & Borg, W.R. (2010). Applying educational research. Boston, MA: Allyn and Bacon Inc.

Geary, D.C. (2004). Mathematics and Learning Disabilities. Journal of Learning Disabilities, 37(1), 4-15. doi:10.1177/00222194040370010201

Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, M. C. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88(2), 121–151. doi:10.1016/j.jecp.2004.03.002

Hecht, S. A., & Vagi, K. J. (2010). Sources of group and individual differences in emerging fraction skills. Journal of Educational Psychology, 102(4), 843–859. doi:10.1037/a0019824

Hunt, J.H., Welch-Ptak, J.J., Silva, J.,M. (2016). Initial understandings of fraction concepts evidenced by students with mathematical learning disabilities and difficulties: a framework. Learning Disability Quarterly, 1(13), 1-13.

doi:10.1177/0731948716653101

Lewis, K.E. (2014). Difference not deficit: reconceptualizing mathematics learning disabilities. Journal for Research in Mathematics Education, 3(45), 351-396. doi: 10.5951/jresematheduc.45.3.0351

Lewis, K.E. (2016a). Understanding mathematical learning disabilities as developmental difference: a fine-grained analysis of one student’s partitioning strategies for fractions. Journal for the Study of Education and Development, 1(21), 812-857.

doi:10.1080/02103702.2016.1215085

Lewis, K.E. (2016b). Beyond error patterns: a sociocultural view of fraction comparison errors in students with mathematical learning disabilities. Learning Disability Quarterly, 1(14), 1-14. doi:10.1177/0731948716658063

Lewis, K.E. and Fisher, M.B. (2016). Taking Stock of 40 Years of Research on Mathematical Learning Disability: Methodological Issues and Future Directions. Journal for Research in Mathematics Education, 4(47), 338-371.

doi:10.5951/jresematheduc.47.4.0338

Mazzocco, M. M. M., & Devlin, K. T. (2008). Parts and “holesâ€: Gaps in rational number sense among children with vs. without mathematical learning disabilities. Developmental Science, 11(5), 681–691. doi: 10.1111/j.1467-7687.2008.00717.x

Mazzocco, M. M. M., Devlin, K. T., & McKenney, S. J. (2008). Is it a fact? Timed arithmetic performance of children with mathematical learning disabilities (MLD) varies as a function of how MLD is defined. Developmental Neuropsychology, 33(3), 318–344. doi:10.1080/87565640801982403

Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011). Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child Development, 82(4), 1224–1237.

a. doi: 10.1111/j.1467-8624.2011.01608.x

Mazzocco, M,M.M., Myers, G.F., Lewis, K.E., Hanich, L.B., Murphy, M.M. (2013). Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) versus low mathematics achievement. Journal of Experimental Child Psychology, 115(2), 371-387. doi: 10.1016/j.jecp.2013.01.005

McKenna, J.M., Shin, M., & Ciullo, S. (2015). Evaluating Reading and Mathematics Instruction for Students with Learning Disabilities: A Synthesis of Observation Research. Learning Disability Quarterly, 38(4), 195–207. doi:10.1177/0731948714564576

NCTM. (2000). Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.

Newton, K.J., Willard, C., Teufel, C. (2014). An examination of the ways that students with learning disabilities solve fraction computation problems. The Elementary School Journal, 115(1), 1-21. doi:10.1086/676949

Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., . . . Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33–41.

doi:10.1016/j.cognition.2010.03.012

Schifter, D. (2005). Engaging students’ mathematical ideas: Implications for professional development design. Journal for Research in Mathematics Education Monograph, 13. Reston, VA: National Council of Teachers of Mathematics.

Shin, M.&Bryant, D.P. (2016). Improving the Fraction Word Problem Solving of Students with Mathematics Learning Disabilities: Interactive Computer Application. Remedial and Special Education, 38(2), 76-86. doi:10.1177/0741932516669052

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, 37, 5-13.

doi:10.1016/j.learninstruc.2014.03.002

Zembat, I.O. (2015). An Alternative Route to Teaching Fraction Division: Abstraction of Common Denominator Algorithm. International Electronic Journal of Elementary Education, 7(3), 399-422.

Retrieved from https://www.iejee.com/index.php/IEJEE/article/view/88

Zevenbergen, R., Dole, S., & Wright, R. J. (2004). Teaching mathematics in primary schools. New South Wales: Allen & Unwin.


Refbacks

  • There are currently no refbacks.


e-ISSN: 1694-2116

p-ISSN: 1694-2493