Mathematics Remedial Intervention for Indigenous Pupils with Learning Difficulties: Does It Work?

CHENG YONG POON (Universiti Teknologi Malaysia, cypoon2@live.utm.my), KEE JIAR YEO (Universiti Teknologi Malaysia, kiyeo@utm.my), NOOR AZLAN AHMAD ZANZALI (Universiti Teknologi Malaysia, azanzali@utm.my)

Abstract


A systematic and explicit instruction using the concrete-representation-abstract sequence is commonly used for diagnostic and remedial approaches. However, this instructional approach might prevent pupils with learning difficulties to think and reason during mathematics learning. In this study, the authors integrated behaviorist and constructivist approach to help indigenous pupils learn addition and subtraction of whole number using manipulative and drawings. The usual practice in mathematics remediation and effect of an alternative instructional approach were investigated. Using a case study design, a teacher and six indigenous pupils were involved. Data was collected using observation, pupils’ work, and interview. Analysis process involved transcribing, segmenting, coding, creating themes, and inter-relating themes. Results indicated that explicit instruction and drill-and-practice were commonly used in the mathematics remediation classroom. Pupils were weak in conceptual understanding and also arithmetic skills. However, participation in mathematical processes and extensive use of physical, pictorial, and symbolic representations of mathematical ideas had helped the participating pupils gained firm conceptual understanding of addition and subtraction, and thus improved their arithmetic skills. Some pupils responded positively towards constructivist approach of instruction but others still needed explicit and individual instruction from their teacher.

Keywords: Conceptual understanding, concrete materials, drawings, integrated approach, procedural knowledge


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References


Baroody, A. J. 1987. The development of counting strategies for single-digit addition. Journal for Research in Mathematics Education 18(2): 141-157.

Borich, G. 2011. Effective Teaching Methods: Research-based Practice. 7th edition. Boston, MA: Pearson Education, Inc.

Bryant, D. P., Bryant, B. R., Gersten, R., Scammacca, N. & Chavez, M. M. 2008. Mathematics intervention for firstand second-grade students with mathematics difficulties: The effects of tier 2 intervention delivered as booster lessons. Remedial and Special Education 29(1): 20-32.

Byrnes, J. 2008. Cognitive Development and Learning in Instructional Contexts. 3rd edition. Boston, MA: Pearson Education, Inc.

Carpenter, T. & Moser, J. 1982. The development of addition and subtraction problem-solving skills. In Addition and Subtraction: A Cognitive Perspective, edited by T. Carpenter, J. Moser, & T. Romberg. Hillsdale, NJ: Lawrence Erlbaum Associates.

Cawley, J. F., & Parmar, R. S. 1992. Arithmetic programming for students with disabilities: An alternative. Remedial and Special Education 13(3): 6-18.

Creswell, J. W. 2008. Educational Research: Planning, Conducting, and Evaluating Quantitative and Qualitative Research. 3rd edition. New Jersey: Pearson Education, Inc.

Das, J. P. & Janzen, C. 2004. Learning math: Basic concepts, math difficulties, and suggestions for interventions. Developmental Disabilities Bulletin 32(2): 191-205.

Evans, D. 2007. Developing mathematical proficiency in the Australian context: Implications for students with learning difficulties. Journal of Learning Disabilities 40(5): 420-426.

Flores, M. M. 2009. Using the concrete representational abstract sequence to teach subtraction with regrouping to students at risk for failure. Remedial and Special Education OnlineFirst. Hammill Institute on Disabilities. Published on February 9, 2009 as doi:10.1177/0741932508327467.

Available online at http://rse.sagepub.com.

Fuchs, L. S. and Fuchs, D. 2001. Principles for the prevention and intervention of mathematics difficulties. Learning Disabilities Research and Practice 16: 85-95.

Gan, T. & Poon, C. 2008. To push or not to push, that’s the question: Exploring ways to help Sarawakian pupils learn mathematics. Paper presented at International Conference of Indigenous Pedagogies in Diverse Cultural Contexts: Issues, Challenges and Opportunities, 10-12 November, Miri, Malaysia.

Groen, G. J. & Parkman, J. M. 1972. A chronometric analysis of simple addition. Psychological Review 79: 329-343.

Gurganus, S. P. 2007. Math Instruction for Students with Learning Problems. 1st edition. Boston: Pearson Education, Inc.

Lambe, J. 2003. Indigenous education, mainstream education, and native studies: Some considerations when incorporating indigenous pedagogy into native studies. American Indian Quarterly 27(1 & 2): 308-324.

Lang, H. R. & Evans, D. N. 2006. Models, Strategies, and Methods for Effective Teaching. Boston, MA: Pearson Education, Inc.

Ketterlin-Geller, L. R., Chard, D. J., & Fien, H. 2008. Making connections in mathematics: Conceptual mathematics intervention for low-performing students. Remedial and

Special Education 29(1): 33-45.

Ma, L. 1999. Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.

Mayer, R. E. & Wittrock, M. C. 2006. Problem solving. In Handbook of Educational Psychology (2nd edition), edited by P. A. Alexander, & P. H. Winne. Mahwah, NJ: Erlbaum.

McKay, M. R. 2005. Indigenous pedagogy: Can this concept be successfully implemented within the current curriculum? Available on-line at http://uregina.ca/~mckaymm/ip.html.

McNally, M. D. 2004. Indigenous pedagogy in the classroom: A service learning model for discussion. American Indian Quarterly 28(3 & 4): 604-617.

Mercer, C. D. & Miller, S. P. 1992. Teaching students with learning problems in math to acquire, understand, and apply basic math facts. Remedial and Special Education 13(3): 19-35.

Merriam, S. B. 1998. Qualitative Research and Case Study Applications in Education : Revised and Expanded from Case Study Research in Education. California: Jossey – Bass Publishers.

Micallef, S. & Prior, M. 2004. Arithmetic Learning Difficulties in Children. Educational Psychology 24(2): 175-200.

Moscardini, L. 2009. Tools or crutches? Apparatus as a sensemaking aid in mathematics teaching with children with

moderate learning difficulties. Support for Learning 24(1): 35-41.

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

O’Donnell, A. M., Reeve, J. & Smith, J. K. 2007. Educational Psychology: Reflection for Action. Hoboken, NJ: John Wiley & Sons, Inc.

Resnick, L. B. 1989. Developing mathematical knowledge. American Psychologist 44: 162-169.

Reys, R. E., Lindquist, M. M., Lambdin, D.V. & Smith, N. L. 2007. Helping Pupils Learn Mathematics. 8th edition. New Jersey: John Wiley & Sons, Inc.

Rittle-Johnson, B., Siegler, R. & Alibali, M. 2001. Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology 93: 346-362.

Slavin, R. E. 2009. Educational Psychology: Theory and Practice. 9th edition. Upper Saddle River, NJ: Pearson Education, Inc.

Thompson, F. 1991. Two-digit addition and subtraction: What works? Arithmetic Teacher 38(5): 10-13.

Thompson, P. W. 1994. Research into practice: Concrete materials and teaching for mathematical understanding. Arithmetic Teacher 41(9): 556-558.

Tournaki, N. 2003. The differential effects of teaching addition through strategy instruction versus drill and practice to students with and without learning disabilities. Journal of Learning Disabilities 36(5): 449-458.

Van de Walle, J. A. 2001. Elementery and Middle School Mathematics: Teaching Developmentally. 4th edition. New York, NY: Addison Wesley Longman, Inc.


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