A study on the relationship between students’ cognitive style and Mathematical word and procedural problem solving while controlling for students’ intelligent quotient and math anxiety
A study on the relationship between students’ cognitive style and Mathematical word and procedural problem solving while controlling for students’ intelligent quotient and math anxiety
Main Article Content
Abstract
The main purpose of the study is to investigate whether field dependency could predict students? mathematical problem solving in word and procedural mathematical problems and to explore whether this association remains significant when students? Mathematics anxiety and intelligent quotient (IQ) is controlled. So, we used data of 100 samples of guidance school girls and inferential statistical analysis (ANOVA and ANCOVA) for investigating the hypothesis of the study. Obtained results indicated that there were significant differences in students? mathematical performance in word and procedural problems by the groups of field dependency. Moreover, this difference is still significant when IQ and Mathematics anxiety as covariate variables were considered. However, the amount of omega square for ANCOVA analysis decreased when covariate variables inserted to the model. Findings of this study are suitable for researchers in field of psychology of learning Mathematics and who interested in how cognitive style affect students? performance in particular Mathematics.
References
Alamolhodaei, H. (1996). A study in higher education calculus and students’ learning styles. Ph.D. Thesis. Glasgow, UK: University of Glasgow.
Alamolhodaei, H. (2002). Students? cognitive style and mathematical problem solving. J. the Korea Society of Math. Edu. Series D: Res.in Math. Edu., 6(1), 171-182.
Alamolhodaei, H. (2009a). A Working Memory Model Applied to Mathematical word Problem Solving. Asia Pac. Educ. Rev., 10(1), 183-192.
Alamolhodaei, H. (2009b). Foundation of Mathematical Education. Tehran, Iran: Jahan Farda Publisher.
Alamolhodaei, H. & Farsad, N. (2009). A Psychological Model Applied to Mathematical Problem Solving. J. the Korea Society of Math. Edu. Series D: Res. in Math. Edu., 13(3),181-195.
Alamolhodaei, H., Hedayat, A. & Radmehr, F .(2011). Students? Field-dependency and Their Mathematical Performance based on Bloom?s Cognitive Levels. Journal of the Korean
Society of Mathematical Education Series D: Research in Mathematical Education., 15(4), 373-386.
Amani, A., Alamolhodaei, A. & Radmehr, F. (2011). A gender study on predictive factors of mathematical performance of University students. Educational Research, 2(6), 11791192.
Amani, A., Alamolhodaei, A. & Radmehr, F. (2012).The relationship between students? cognitive abilities, mathematical performance and the level of Testosterone, Thyroid-Stimulating Hormone, Prolactin and Thyroxine. The Journal of Mathematics and Computer Science, 5(1), 1-16.
Ashcraft, M. & Kirk, E. (2001). The relationships among working memory, math anxiety, and performance. J. Exper. Psychol., 130, 224-237.
Ashcraft, M. (2002). Math Anxiety: Personal, Educational, and Cognitive Consequences, Current Directions. J Psychological Sci., 11(5), 181-185.
Cassidy, S. (2004). Learning styles: An overview of theories models and measures. Educational Psychology, 24(4), 419-444.
Cho, S. & Ahn, D. (2003). Strategy acquisition and maintenance of gifted and nongifted young children. Exceptional Children, 69(4), 497-505.
Deary, I., Strand, S., Smith, P. & Fernandes, C. (2007). Intelligence and educational achievement. Intelligence, 35, 13-21.
Eagle, M., Goldberger, L. & Breitman, M. (1969). Field dependence and memory for social vs. neutral and relevant vs. irrelevant incidental stimuli. Percept. Motor Skills, 29, 903-910.
Ferguson, R. (1986). Abstraction anxiety: A factor of mathematics anxiety. Journal for Research in Mathematics Education, 17, 145-150.
Flexer, B. (1984). Predicting eighth-grade algebra achievement. Journal for Research in Mathematics Education, 15(5), 352-360.
Gaultney, J.F., Bjorklund, D.F. & Goldstein, D. (1996).To be young, gifted and strategic:
Advantages for memory performance. Journal of Experimental Child Psychology, 61, 43-66.
Helmke, A. (1992). Selbstvertrauen und schulische Leistung [Selfconfidence and school achievement]. Göttingen: Hogrefe.
Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21(1), 33-46.
Klauer, K.J., Willmes, K. & Phye, G.D. (2002). Inducing inductive reasoning: Does it transfer to fluid intelligence? Contemporary Educational Psychology, 27, 1-25.
Jausovec, N. (1991). Flexible strategy use: A characteristic of gifted problem solving. Creativity Research Journal, 4, 349-366.
Jensen, A. (1980). Bias in mental testing London: Methuen In Italy, north–south differences in IQ predict differences in income, education, infant mortality, stature, and literacy. Intelligence, 38, 93-100.
Johnstone, A. & Al-Naeme, F. (1991). Room for scientific thought. Int. J. Sci. Edu, 13(2), 187192.
Johnstone, A., Hogg, W. & Ziane, M. (1993). A working memory model applied to physical problem solving. International Journal of Science Education, 15(6), 663-672.
Johnstone, A. & Al-Naeme, F. (1995). Filling a curriculum gap in chemistry. Inter. J. Sci. Edu., 17(2), 219-232.
Karimi, B. & Venkatesan, S. (2009). Mathematics Anxiety, Mathematics Performance and Academic Hardiness in High School Students. Int. J. Edu. Sci., 1(1), 33-37.
Kramarski, B., Weisse, I. & Kololshi-Minsker, I. (2010). How can self-regulated learning support the problem solving of third-grade students with mathematics anxiety? ZDM, 42, 179193. DOI 10.1007/s11858-009-0202-8.
Kyttala, M. & Lehto, J. (2008). Some factors underlying mathematical performance: The role of visuospatial working memory and non-verbal intelligence. European Journal of Psychology of Education, 23(1), 77-94.
Margaret, M., Gullick, L. & Sprute, E. (2011) Individual differences in working memory, nonverbal IQ, and mathematics achievement and brain mechanisms associated with symbolic and no symbolic number processing. Learning and Individual Differences, 21, 644-654.
Mousavi, S., Radmehr, F. & Alamolhodaei, H. (2012). The role of mathematical homework and
prior knowledge on the relationship between students? mathematical performance, cognitive style and working memory capacity. Electronic Journal of Research in Educational Psychology, 10(3), 1223-1248.
Muir-Broaddus, J. (1995). Gifted underachievers: Insights from the characteristics of strategic functioning associated with giftedness and achievement. Learning and Individual Differences, 7, 189-206.
Nicolaou, A.A. & Xistouri, X. (2011). Field dependence/independence cognitive style and problem posing: an investigation with sixth grade students, Educational Psychology: An International Journal of Experimental Educational Psychology, 31(5), 611-627.
Norwood, K. (1994). The effect of instructional approach on mathematics anxiety and achievement. School Science and Mathematics, 94(5), 248-254.
Oltman, P., Raskin, E. & Witkin, H. (1971). A manual for the embedded figures test. Palo Alto, CA: Consulting Psychologists Press, Inc.
Oltman, P., Goodenough, D., Witkin, H., Freedman, N. & Friedman, F. (1975). Psychological differentiation as a factor in conflict resolution. J.Pers. Soc. Psychol., 32, 730-736.
Pezeshki, P., Alamolhodaei, H. & Radmehr, F. (2011). A predictive model for mathematical performance of blind and seeing students. Educ. Res., 2(2), 864-873.
Pressley, M. & Hilden, K. (2006). Cognitive strategies. In D. Kuhn, R.S. Siegler, W. Damon & R.
Lerner (Eds.), Handbook of child psychology (pp. 511-566). NY: John Wiley & Sons, Inc.
Price, L. (2004). Individual differences in learning: cognitive control, cognitive style and learning style. Educational Psychology, 24(5), 681-698.
Riding, R. & Al-Sanabani, S. (1998). The effect of cognitive style, age, gender and structure on the recall of prose passages. International Journal of Education Research, 29, 173-183.
Richardson, F. & Suinn, R. (1972). The mathematics anxiety rating scale. J. Couns. Psychol., 19, 551-554.
Rollock, D. (1992). Field-dependence/independence and learning condition: an exploratory study of styles vs. ability. Perceptual and Motor Skills, 74, 807-818.
Sachin, J. & Martin, D. (2009). Mathematics anxiety as a function of multidimensional selfregulation and self-efficacy Contemporary Educational Psychology Contemporary. Educational Psychology, 34, 240-249.
Saracho, O. (1998). Editor?s introduction cognitive style research and its relationship to various disciplines. International Journal of Educational Research, 29, 169-172.
Saracho, O. (2003). Matching teachers? and students? cognitive styles. Early Child Development and Care, 173(2-3), 161-173.
Scardamalia, M. (1977). Information processing capacity and the problem of horizontal decalage: A demonstration using combinatorial reasoning tasks. Child Development, 48(1), 28-37.
Schleifer, M. & Douglas, M. (1973). Moral judgments, behavior and cognitive style in young children. J. Behav. Sci., 5, 133-144.
Shaywitz, B., Fletcher, J., Holahan, J. & Shaywitz, S. (1992). Discrepancy compared to low achievement definitions of reading disability: Results from the Connecticut Longitudinal Study. Journal of Learning Disabilities, 25, 639-648.
Sherman, B. & Wither, D. (2003). Mathematics anxiety and mathematics achievement. Mathematics Education Research Journal, 15, 138-150.
Shinn, M., Ysseldyke, J., Deno, S. & Tindal, G. (1986). A comparison of differences between students labeled learning disabled and low achieving on measures of classroom performance. Journal of Learning Disabilities, 19, 545-552.
Shore, B. (2000). Metacognition and flexibility: Qualitative differences in how gifted children think. In R.C. Friedman & B.M. Shore (Eds.), Talents unfolding: Cognition and development (pp. 167-187). American Psychological Association.
Singh, A. & Broota, A. (1992). Socio-personal variables and examination anxiety. Journal of the Indian Academy of Applied Psychology, 18, 73-78.
Sirvastava, P. (1997). Cognitive style in educational perspective. New Delhi, India: Anmol Publications Pvt. Ltd.
Sousa-Poza, J., Rohrberg, R. & Shulman, E. (1973). Field dependence and self-disclosure. Percept. Motor Skills., 36, 735-738.
Spinath, B., Spinath, F., Harlaar, N. & Plomin, R. (2006). Predicting school achievement from general cognitive ability, self-perceived ability, and intrinsic value. Intelligence, 34(4), 363-374.
Steiner, H. (2006). A microgenetic analysis of strategic variability in gifted and average-ability children. The Gifted Child Quarterly, 50(1), 62-74.
Suinn, R. (1970). The mathematics anxiety rating scale. Department of Psychology, Colorado State University, Fort Collins, CO.
Talbi, M. (1990). An information processing approach to the investigation of mathematical problem solving at secondary and university levels. Ph.D. Thesis. Glasgow, UK: University of Glasgow.
Tinajero, C. & Paramo, M. (1997). Field-dependence/independence and academic achievement: a re-examination of their relationship. British Journal of Educational Psychology, 67, 199212.
Tobias, S. (1993). Overcoming Math Anxiety. New York: W.W. Norton & Company.
Watkins, M., Lei, P. & Canivez, G. (2007). Psychometric ntelligence and achievement: A crosslagged panel analysis. Intelligence, 35, 59-68.
Winne, P. & Nesbit, J. (2010). The psychology of academic achievement. Annual Review of Psychology, 61, 653-678.
Wise, B., Ring, J. & Olson, R. (1999). Training phonological awareness with and without explicit attention to articulation. Journal of Experimental Child Psychology, 72, 271-304.
Witkin, H., Moore, C., Goodenough, D. & Cox, P. (1977). Field-dependent and field-independent cognitive stylesand their educational implications. Review of Educational Research, 47(1), 1-64.
Witkin, H. & Goodenough, D. (1977). Field dependence and interpersonal behavior. Psychol. Bull., 4, 661-689.
Witkin, H. & Goodenough, D. (1981). Cognitive Styles: Essence and Origins. International Universities Press Madison, CT.
Alamolhodaei, H. (2002). Students? cognitive style and mathematical problem solving. J. the Korea Society of Math. Edu. Series D: Res.in Math. Edu., 6(1), 171-182.
Alamolhodaei, H. (2009a). A Working Memory Model Applied to Mathematical word Problem Solving. Asia Pac. Educ. Rev., 10(1), 183-192.
Alamolhodaei, H. (2009b). Foundation of Mathematical Education. Tehran, Iran: Jahan Farda Publisher.
Alamolhodaei, H. & Farsad, N. (2009). A Psychological Model Applied to Mathematical Problem Solving. J. the Korea Society of Math. Edu. Series D: Res. in Math. Edu., 13(3),181-195.
Alamolhodaei, H., Hedayat, A. & Radmehr, F .(2011). Students? Field-dependency and Their Mathematical Performance based on Bloom?s Cognitive Levels. Journal of the Korean
Society of Mathematical Education Series D: Research in Mathematical Education., 15(4), 373-386.
Amani, A., Alamolhodaei, A. & Radmehr, F. (2011). A gender study on predictive factors of mathematical performance of University students. Educational Research, 2(6), 11791192.
Amani, A., Alamolhodaei, A. & Radmehr, F. (2012).The relationship between students? cognitive abilities, mathematical performance and the level of Testosterone, Thyroid-Stimulating Hormone, Prolactin and Thyroxine. The Journal of Mathematics and Computer Science, 5(1), 1-16.
Ashcraft, M. & Kirk, E. (2001). The relationships among working memory, math anxiety, and performance. J. Exper. Psychol., 130, 224-237.
Ashcraft, M. (2002). Math Anxiety: Personal, Educational, and Cognitive Consequences, Current Directions. J Psychological Sci., 11(5), 181-185.
Cassidy, S. (2004). Learning styles: An overview of theories models and measures. Educational Psychology, 24(4), 419-444.
Cho, S. & Ahn, D. (2003). Strategy acquisition and maintenance of gifted and nongifted young children. Exceptional Children, 69(4), 497-505.
Deary, I., Strand, S., Smith, P. & Fernandes, C. (2007). Intelligence and educational achievement. Intelligence, 35, 13-21.
Eagle, M., Goldberger, L. & Breitman, M. (1969). Field dependence and memory for social vs. neutral and relevant vs. irrelevant incidental stimuli. Percept. Motor Skills, 29, 903-910.
Ferguson, R. (1986). Abstraction anxiety: A factor of mathematics anxiety. Journal for Research in Mathematics Education, 17, 145-150.
Flexer, B. (1984). Predicting eighth-grade algebra achievement. Journal for Research in Mathematics Education, 15(5), 352-360.
Gaultney, J.F., Bjorklund, D.F. & Goldstein, D. (1996).To be young, gifted and strategic:
Advantages for memory performance. Journal of Experimental Child Psychology, 61, 43-66.
Helmke, A. (1992). Selbstvertrauen und schulische Leistung [Selfconfidence and school achievement]. Göttingen: Hogrefe.
Hembree, R. (1990). The nature, effects, and relief of mathematics anxiety. Journal for Research in Mathematics Education, 21(1), 33-46.
Klauer, K.J., Willmes, K. & Phye, G.D. (2002). Inducing inductive reasoning: Does it transfer to fluid intelligence? Contemporary Educational Psychology, 27, 1-25.
Jausovec, N. (1991). Flexible strategy use: A characteristic of gifted problem solving. Creativity Research Journal, 4, 349-366.
Jensen, A. (1980). Bias in mental testing London: Methuen In Italy, north–south differences in IQ predict differences in income, education, infant mortality, stature, and literacy. Intelligence, 38, 93-100.
Johnstone, A. & Al-Naeme, F. (1991). Room for scientific thought. Int. J. Sci. Edu, 13(2), 187192.
Johnstone, A., Hogg, W. & Ziane, M. (1993). A working memory model applied to physical problem solving. International Journal of Science Education, 15(6), 663-672.
Johnstone, A. & Al-Naeme, F. (1995). Filling a curriculum gap in chemistry. Inter. J. Sci. Edu., 17(2), 219-232.
Karimi, B. & Venkatesan, S. (2009). Mathematics Anxiety, Mathematics Performance and Academic Hardiness in High School Students. Int. J. Edu. Sci., 1(1), 33-37.
Kramarski, B., Weisse, I. & Kololshi-Minsker, I. (2010). How can self-regulated learning support the problem solving of third-grade students with mathematics anxiety? ZDM, 42, 179193. DOI 10.1007/s11858-009-0202-8.
Kyttala, M. & Lehto, J. (2008). Some factors underlying mathematical performance: The role of visuospatial working memory and non-verbal intelligence. European Journal of Psychology of Education, 23(1), 77-94.
Margaret, M., Gullick, L. & Sprute, E. (2011) Individual differences in working memory, nonverbal IQ, and mathematics achievement and brain mechanisms associated with symbolic and no symbolic number processing. Learning and Individual Differences, 21, 644-654.
Mousavi, S., Radmehr, F. & Alamolhodaei, H. (2012). The role of mathematical homework and
prior knowledge on the relationship between students? mathematical performance, cognitive style and working memory capacity. Electronic Journal of Research in Educational Psychology, 10(3), 1223-1248.
Muir-Broaddus, J. (1995). Gifted underachievers: Insights from the characteristics of strategic functioning associated with giftedness and achievement. Learning and Individual Differences, 7, 189-206.
Nicolaou, A.A. & Xistouri, X. (2011). Field dependence/independence cognitive style and problem posing: an investigation with sixth grade students, Educational Psychology: An International Journal of Experimental Educational Psychology, 31(5), 611-627.
Norwood, K. (1994). The effect of instructional approach on mathematics anxiety and achievement. School Science and Mathematics, 94(5), 248-254.
Oltman, P., Raskin, E. & Witkin, H. (1971). A manual for the embedded figures test. Palo Alto, CA: Consulting Psychologists Press, Inc.
Oltman, P., Goodenough, D., Witkin, H., Freedman, N. & Friedman, F. (1975). Psychological differentiation as a factor in conflict resolution. J.Pers. Soc. Psychol., 32, 730-736.
Pezeshki, P., Alamolhodaei, H. & Radmehr, F. (2011). A predictive model for mathematical performance of blind and seeing students. Educ. Res., 2(2), 864-873.
Pressley, M. & Hilden, K. (2006). Cognitive strategies. In D. Kuhn, R.S. Siegler, W. Damon & R.
Lerner (Eds.), Handbook of child psychology (pp. 511-566). NY: John Wiley & Sons, Inc.
Price, L. (2004). Individual differences in learning: cognitive control, cognitive style and learning style. Educational Psychology, 24(5), 681-698.
Riding, R. & Al-Sanabani, S. (1998). The effect of cognitive style, age, gender and structure on the recall of prose passages. International Journal of Education Research, 29, 173-183.
Richardson, F. & Suinn, R. (1972). The mathematics anxiety rating scale. J. Couns. Psychol., 19, 551-554.
Rollock, D. (1992). Field-dependence/independence and learning condition: an exploratory study of styles vs. ability. Perceptual and Motor Skills, 74, 807-818.
Sachin, J. & Martin, D. (2009). Mathematics anxiety as a function of multidimensional selfregulation and self-efficacy Contemporary Educational Psychology Contemporary. Educational Psychology, 34, 240-249.
Saracho, O. (1998). Editor?s introduction cognitive style research and its relationship to various disciplines. International Journal of Educational Research, 29, 169-172.
Saracho, O. (2003). Matching teachers? and students? cognitive styles. Early Child Development and Care, 173(2-3), 161-173.
Scardamalia, M. (1977). Information processing capacity and the problem of horizontal decalage: A demonstration using combinatorial reasoning tasks. Child Development, 48(1), 28-37.
Schleifer, M. & Douglas, M. (1973). Moral judgments, behavior and cognitive style in young children. J. Behav. Sci., 5, 133-144.
Shaywitz, B., Fletcher, J., Holahan, J. & Shaywitz, S. (1992). Discrepancy compared to low achievement definitions of reading disability: Results from the Connecticut Longitudinal Study. Journal of Learning Disabilities, 25, 639-648.
Sherman, B. & Wither, D. (2003). Mathematics anxiety and mathematics achievement. Mathematics Education Research Journal, 15, 138-150.
Shinn, M., Ysseldyke, J., Deno, S. & Tindal, G. (1986). A comparison of differences between students labeled learning disabled and low achieving on measures of classroom performance. Journal of Learning Disabilities, 19, 545-552.
Shore, B. (2000). Metacognition and flexibility: Qualitative differences in how gifted children think. In R.C. Friedman & B.M. Shore (Eds.), Talents unfolding: Cognition and development (pp. 167-187). American Psychological Association.
Singh, A. & Broota, A. (1992). Socio-personal variables and examination anxiety. Journal of the Indian Academy of Applied Psychology, 18, 73-78.
Sirvastava, P. (1997). Cognitive style in educational perspective. New Delhi, India: Anmol Publications Pvt. Ltd.
Sousa-Poza, J., Rohrberg, R. & Shulman, E. (1973). Field dependence and self-disclosure. Percept. Motor Skills., 36, 735-738.
Spinath, B., Spinath, F., Harlaar, N. & Plomin, R. (2006). Predicting school achievement from general cognitive ability, self-perceived ability, and intrinsic value. Intelligence, 34(4), 363-374.
Steiner, H. (2006). A microgenetic analysis of strategic variability in gifted and average-ability children. The Gifted Child Quarterly, 50(1), 62-74.
Suinn, R. (1970). The mathematics anxiety rating scale. Department of Psychology, Colorado State University, Fort Collins, CO.
Talbi, M. (1990). An information processing approach to the investigation of mathematical problem solving at secondary and university levels. Ph.D. Thesis. Glasgow, UK: University of Glasgow.
Tinajero, C. & Paramo, M. (1997). Field-dependence/independence and academic achievement: a re-examination of their relationship. British Journal of Educational Psychology, 67, 199212.
Tobias, S. (1993). Overcoming Math Anxiety. New York: W.W. Norton & Company.
Watkins, M., Lei, P. & Canivez, G. (2007). Psychometric ntelligence and achievement: A crosslagged panel analysis. Intelligence, 35, 59-68.
Winne, P. & Nesbit, J. (2010). The psychology of academic achievement. Annual Review of Psychology, 61, 653-678.
Wise, B., Ring, J. & Olson, R. (1999). Training phonological awareness with and without explicit attention to articulation. Journal of Experimental Child Psychology, 72, 271-304.
Witkin, H., Moore, C., Goodenough, D. & Cox, P. (1977). Field-dependent and field-independent cognitive stylesand their educational implications. Review of Educational Research, 47(1), 1-64.
Witkin, H. & Goodenough, D. (1977). Field dependence and interpersonal behavior. Psychol. Bull., 4, 661-689.
Witkin, H. & Goodenough, D. (1981). Cognitive Styles: Essence and Origins. International Universities Press Madison, CT.