Key factors for successful solving of mathematical word problems in fifth-grade learners
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Submission date: 2014-02-28
Final revision date: 2014-03-25
Acceptance date: 2014-03-25
Online publication date: 2014-05-16
Publication date: 2014-05-15
Health Psychology Report 2014;2(1):27–38
Difficulties in solving mathematical word problems (MWP) are one of the most common reasons for weak mathematics performance, and poor mathematical literacy has important implications for an individual’s further education, employment opportunities, mental health and quality of life in today’s modern technological society.
The purpose of the study was to examine whether Slovenian good and poor MWP solvers differ in arithmetic knowledge and skills, non-verbal reasoning, pupils’ self-evaluations of MWP abilities, teachers’ assessment of their mathematical knowledge and what strategies fifth- grade learners use in solving MWP.
The larger sample included 233 pupils from 14 fifth-grade classes (mean age 10 years 3 months) and 14 teachers. On the basis of the teachers’ opinions and the results of MWP solving two sub-samples of 24 students were formed, good and poor MWP solvers. Several tests were used to determine MWP solving ability, automation of arithmetic facts and procedures as well as Raven’s SPM. Questionnaires for pupils were used to assess pupils’ estimations of MWP tasks’ difficulty, their own ability to solve them and the strategies used. To assess pupils’ knowledge a questionnaire for teachers was used.
Slovenian 5th graders in the larger sample generally used very few empirically proven effective cognitive and metacognitive strategies to solve MWP. Pupils with lower achievement in solving MWP, compared to pupils with higher achievement demonstrated significantly less automated arithmetic facts and procedures of the algorithm, less flexible use of arithmetic skills, as well as qualitatively different MWP solving, which is also related to their lower non-verbal reasoning. Teachers’ assessments and pupils’ self-assessments matched the achieved test results.
The results exposed important key factors for successful solving of mathematical word problems with significant implications for learning, teaching and professional training. Improving mathematics literacy in the Slovenian school system requires greater consideration for strategy teaching and motivational factors.
Adler, B. (2001). What is dyscalculia? An e-book from the Kognitive Centrum Sweden. Retrieved: June 12, 2006, from www.dyscalculiainfo.org.
Clark, C.A.C., Pritchard, V.E. & Woodward, L.J. (2010). Preschool executive functioning abilities predict early mathematics achievement. Development Psychology, 46, 1176-1191.
Dawson, P. (2010). Lazy or not? Educational Leadership, 68, 35-38.
Dermitzaki, I., Leonardari, A. & Goudas, M. (2009). Relations between young students’ strategic behaviours, domain-specific self concept, and performance in a problem-solving situation. Learning and Instruction, 19, 144-157.
Desoete, A., Roeyers, H. & De Clercq, A. (2004). Children with mathematics learning disabilities in Belgium. Journal of Learning Disabilities, 37, 50-61.
Desoete, A. & Roeyers, H. (2005). Cognitive building blocks in mathematical problem solving in grade 3. British Journal of Educational Psychology, 75, 119-138.
De Corte, E., Greer, B. & Verschaffel, L. (1996). Mathematics teaching and learning. In: D. Berliner & R. Calfee (eds.). Handbook of educational psychology. New York: Macmillan.
Efklides, A., Kourkoulou, A., Mitsiou, F. & Ziliaskopoulou, D. (2006). Effort regulation, effort perceptions, mood, and metacognitive experiences: What determines the estimate of effort expenditure? Metacognition and Learning, 1, 33-49.
Flavell, J. (1987). Speculations about the nature and development of metacognition. In: F.E. Weinert & R.H. Kluwe (eds.). Metacognition, motivation and understanding (pp. 21-29). Hillsdale, NJ: Lawrence Erlbaum.
Flere, S., Klanjšek, R., Musil, B., Tavčar Krajnc, M. & Kirbiš, A. (2009). Kdo je uspešen v slovenski šoli? Znanstveno poročilo [Who is successful in the Slovene school? Scientific report]. Ljubljana: Pedagoški inštitut.
Fleischner, J.E., Nuzum, M.B. & Marzola, E.S. (1987). Devising an instructional program to teach arithmetic problem-solving skills to students with learning disabilities. Journal of Learning Disabilities, 20, 214-217.
Fletcher, J.M., Lyon, G.R., Fuchs, L.S. & Barnes, M.A. (2007). Learning disabilities: From identification to intervention. New York: The Guilford Press.
Fuchs, L.S., Fuchs, D., Compton, D.L., Powell, S.R., Seethaler, P.M., Capizzi, A.M., Schatschneider, C. & Fletcher, J.M. (2006). The cognitive correlates of third-grade skill in arithmetic, algorithmic computation and arithmetic word problems. Journal of Educational Psychology, 98, 29-43.
Fuchs, L.S., Powell, S.R., Seethaler, P.M., Cirino, P.T., Fletcher, J.M., Fuchs, D., Hamlett, C.L. & Zumeta, R.O. (2009). Remediating number combination and word problem deficits among students with mathematics difficulties: A randomized control trial. Journal of Educational Psychology, 101, 561-576.
Gagnon, J. & Maccini, P. (2008). S.T.A.R. Strategy for Problem Solving. Retrieved: March 8, 2010, from http://www.k8accesscenter.org..... MathSIforMiddleschoolStudentswithLD.pdf.
Geary, D.C. (1994). Children’s Mathematical Development. Research and Practical Applications. Washington: American Psychological Association.
Geary, D.C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4-15.
Hoffman, B. & Spatariu, A. (2008). The influence of self-efficacy and metacognitive prompting on math problem-solving efficiency. Contemporary Educational Psychology, 33, 875-893.
Kavkler, M. (2011). Učenci z učnimi težavami pri matematiki – učinkovitejše odkrivanje in diagnostično ocenjevanje. In: L. Magajna & M. Velikonja (eds.). Učenci z učnimi težavami. Prepoznavanje in diagnostično ocenjevanje [Students with learning difficulties. Identification and diagnostic assessment] (pp. 130-146). Ljubljana: Faculty of Education.
Lerner, J. (1997). Learning disabilities: Theories, diagnosis, and teaching strategies. 7th ed. New York: Houghton Mifflin Company.
Lucangeli, D. & Cornoldi, C. (1997). Mathematics and metacognition: what is the nature of the relationship? Mathematical Cognition, 3, 121-139.
Lucangeli, D., Cornoldi, C. & Tellarini, M. (1998). Metacognition and learning disabilities in mathematics. In: T.E. Scruggs, M.A. Mastropieri (eds.). Advances in Learning and Behavioral Disabilities (pp. 219-244). Greenwich, CT: JAI Press.
Maccini, P. & Gagnon, J. (2006). Mathematics strategy instruction (SI) for middle school students with learning disabilities. Retrieved April 21, 2011, from www.k8accesscenter.org.
Magajna, L., Kavkler, M. & Ortar-Križaj, M. (2003). Adults with self-reported learning disabilities in Slovenia: findings from the international adult literacy survey on the incidence and correlates of learning disabilities in Slovenia. Dyslexia, 9, 229-251.
Montague, M. (1992). The effects of cognitive and metacognitive strategy instruction on the mathematical problem solving of middle school students with learning disabilities. Journal of Learning Disabilities, 25, 230-248.
Montague, M. (1997). Students’ perception, mathematical problem solving, and learning disabilities. Remedial and Special Education, 28, 46-53.
Montague, M. (2008). Self-regulation strategies to improve mathematical problem solving for students with learning disabilities. Learning Disability Quarterly, 31, 37-44.
Montague, M. & Dietez, S. (2009). Evaluating the evidence base for cognitive strategy instruction and mathematical problem solving. Exceptional Children, 75, 285-302.
National Examination Centre (2013). Nacionalno preverjanje znanja: Letno poročilo o izvedbi v letu 2012/2013 [National assessment of knowledge: Annual Report for the year 2012/2013].
OECD-PISA 2009 (2011). Program mednarodne primerjave dosežkov učencev – Prvi rezultati. Preverjanje in cenjevanje, 8, 61-96.
Passolunghi, M.C. (2010). Učne težave pri matematiki. Specifične učne težave v vseh obdobjih. Tretja mednarodna konferenca o specifičnih učnih težavah v Sloveniji in nacionalna konferenca Tempus-Isheds. Zbornik prispevkov [Learning difficulties in math. Specific learning difficulties in all periods. The 3rd International Conference on specific learning difficulties in Slovenia and the National Conference of the Tempus-Isheds. Book of articles] (pp. 14-21). Ljubljana: Bravo, društvo za pomoč otrokom in mladostnikom s specifičnimi učnimi težavami.
Passolunghi, M.C. & Bizzaro, M. (2011). Preparasi ai problemi aritmetici di scuola secondaria (Prepare for the arithmetic problems of secondary school). Trento: Erickson.
Passolunghi, M.C., Kavkler, M., Košak Babuder, M. & Magajna, M. (2011). Children’s Questionnaire on math word problems strategies. Trieste: Faculty of Psychology.
Pintrich, P.R. & De Groot, E. (1990). Motivational and self-regulated learning components of classroom academic performance. Journal of Educational Psychology, 82, 33-50.
Randhawa, B.S., Beamer, J.E. & Lundberg, I. (1993). Role of mathematics self-efficacy in the structural model of mathematical achievement. Journal of Educational Psychology, 85, 41-48.
Raven, J.C., Raven, M., Styles, I., Raven, J. & Court, J.H. (2005). Priročnik Standardne progresivne matrice, 3. zvezek [Manual for Standard Progressive Matrices. 3 Volume]. Ljubljana: Center za psihodiagnostična sredstva.
Sousa, D.A. (2008). Recognizing and addressing mathematics difficulties. How the brain learns mathematics (pp. 163-198). London: Corwin Press Ltd. A SAGE Publications Company.
Stein, M., Kinder, D., Silbert, J. & Carnine, D.W. (2006). Designing effective mathematics instruction. A direct instruction approach. 4th ed. New Jersey: Person Education, Inc.
Sweeney, C.M. (2010). The metacognitive functioning of middle school students with and without learning disabilities during mathematical problem solving. Open Access Dissertations. Paper 433.
Štraus, M., Šterman Ivančič, K. & Štigl, S. (2013). OECD PISA 2012: matematični, bralni in naravoslovni dosežki slovenskih učencev: program mednarodne primerjave dosežkov učencev 2012: nacionalno poročilo [OECD PISA 2012: math, reading and science achievements of Slovenian students: international comparisons of students’ 2012: National report]. Ljubljana: Pedagoški Inštitut.
Tancig, S., Magajna, L. & Kavkler, M. (1999). The development of numeracy in Slovenia. In: Abstracts: biennial meeting. Göteborg: European Association for Research on Learning and Instruction (EARLI).
Tomori, M., Stergar, E., Pinter, B., Rus Makovec, M. & Stikovič, S. (1998). Dejavniki tveganja pri slovenskih srednješolcih [Risk factors in Slovenian secondary school students]. Ljubljana: Psihiatrična klinika.
Van der Stel, M., Veenman, M.V.J., Deelen, K. & Haenen, J. (2010). Increasing role of metacognitive skills in math: a cross-sectional study from a developmental perspective. ZDM International Journal on Mathematics Education, 42, 219-229.
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