International Electronic Journal of Mathematics Education

International Electronic Journal of Mathematics Education
Preference for Solution Methods and Mathematical Performance: A Critical Review
APA
In-text citation: (Mainali, 2021)
Reference: Mainali, B. (2021). Preference for Solution Methods and Mathematical Performance: A Critical Review. International Electronic Journal of Mathematics Education, 16(3), em0651. https://doi.org/10.29333/iejme/11089
AMA
In-text citation: (1), (2), (3), etc.
Reference: Mainali B. Preference for Solution Methods and Mathematical Performance: A Critical Review. INT ELECT J MATH ED. 2021;16(3), em0651. https://doi.org/10.29333/iejme/11089
Chicago
In-text citation: (Mainali, 2021)
Reference: Mainali, Bhesh. "Preference for Solution Methods and Mathematical Performance: A Critical Review". International Electronic Journal of Mathematics Education 2021 16 no. 3 (2021): em0651. https://doi.org/10.29333/iejme/11089
Harvard
In-text citation: (Mainali, 2021)
Reference: Mainali, B. (2021). Preference for Solution Methods and Mathematical Performance: A Critical Review. International Electronic Journal of Mathematics Education, 16(3), em0651. https://doi.org/10.29333/iejme/11089
MLA
In-text citation: (Mainali, 2021)
Reference: Mainali, Bhesh "Preference for Solution Methods and Mathematical Performance: A Critical Review". International Electronic Journal of Mathematics Education, vol. 16, no. 3, 2021, em0651. https://doi.org/10.29333/iejme/11089
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Mainali B. Preference for Solution Methods and Mathematical Performance: A Critical Review. INT ELECT J MATH ED. 2021;16(3):em0651. https://doi.org/10.29333/iejme/11089

Abstract

Preferences for solution methods have an important implication teaching and learning mathematics and students’ mathematical performances. In the domain of learning mathematics, there are two modes of processing mathematical information: verbal logical and visual-pictorial. Learners who process mathematical information using verbal logical and visual -pictorial modes are respectively called verbalizers and visualizers. Based on the verbalizer-visualizer continuum, students can be placed in a continuum with regard to their preference for solution methods and correlation between the two modes of thought. They belong to one of three categories: (a) visualizers (geometric), who have a preference for the use of visual solution methods, which involve graphic representation (i.e., figures, diagrams, and pictures); (b) verbalizers (analytic), who have a preference for the use of nonvisual solution methods, which involve algebraic, numeric, and verbal representation; and (c) harmonics (mixer), who use visual and verbal methods equally. Several research studies have been conducted to examine the relationship between preferences for solution methods and mathematical performances; however, no conclusive findings were reported. Regardless of inconclusive findings, it is important for students to develop preferences for both solution methods: visual and nonvisual. The mathematical instructional strategies need to equally incorporate preferences for both solution methods, utilizing different modes of mathematical representations, in order to enhance learning mathematics.

References

  • Arcavi, A. (2003). The role of representation in the learning of mathematics. Educational Studies in Mathematics, 52, 215-241. https://doi.org/10.1023/A:1024312321077
  • Battista, M. T. (1990). Spatial visualization and gender difference in high school geometry. Journal for Research in Mathematics Education, 21, 47-60. https://doi.org/10.2307/749456
  • Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). National Council of Teachers of Mathematics.
  • Clements, K. (2014). Fifty years of thinking about visualization and visualizing mathematics education: A historical overview. In M. N. Fried & T. Dryfus (Eds), Mathematics and mathematics education: searching for common ground, advances in mathematics education (pp. 177-191). Springer Science + Media Dordrecht. https://doi.org/10.1007/978-94-007-7473-5_11
  • Galindo, E. M. (1994). Visualization in the calculus class: Relationship between cognitive style, gender, and use of technology (Unpublished doctoral dissertation). The Ohio State University, Ohio.
  • Gegatsis, A., & Shaikalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem solving. Education Psychology, 24, 645-657. https://doi.org/10.1080/0144341042000262953
  • Goldin, G. A. (1987). Cognitive representational systems for mathematical problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning mathematics (pp. 19-26). Lawrence Erlbaum.
  • Goldin, G. A. (2001). Systems of representation and the development of mathematical concepts. In A. A Cuoco & F. R. Curcio (Eds.), The role of representation in school mathematics (pp. 1-23). National Council of Teachers of Mathematics.
  • Gorgorio, N. (1998). Exploring the functionality of visual and non-visual strategies in solving rotation problems. Educational Studies in Mathematics, 35, 207-231. https://doi.org/10.1023/A:1003132603649
  • Haciomeroglu, E. S., & Chicken, E. (2011). Investigating relations between ability, preference, and calculus performance. In L. R. Wiest & T. Lamberg (Eds.), Proceedings of the 33rd annual meeting of the North American Chapter of the International Group of Psychology of Mathematics Education. University of Nevada.
  • Haciomeroglu, E. S., Aspinwall, L., & Presmeg, N. C. (2009). Visual and analytical thinking in calculus. Mathematics Teacher, 103, 140-145. https://doi.org/10.5951/MT.103.2.0140
  • Haciomeroglu, E. S., Aspinwall, L., & Presmeg, N. C. (2010). Contrasting cases of calculus students’ understanding of derivative graphs. Mathematical Thinking and Learning, 12, 152-176. https://doi.org/10.1080/10986060903480300
  • Haciomeroglu, E. S., Chicken, E., & Dixon, J. K. (2013). Relationships between gender, cognitive ability, preference, and calculus performance. Mathematical Thinking and Learning, 15(3), 175-189. https://doi.org/10.1080/10986065.2013.794255
  • Hegarty, M., & Kozhevnikov, M. (1999). Types of visual-spatial representation and mathematical problem solving. Journal of Educational Psychology, 91, 684-689. https://doi.org/10.1037/0022-0663.91.4.684
  • Hitt, F. (1998). Difficulties in articulation of different representation linked to the concept of function. The Journal of Mathematical Behavior, 17, 123-134. https://doi.org/10.1016/S0732-3123(99)80064-9
  • Janvier, C. (1987a). Translation process in mathematics education. In C. Janvier (Ed.), Problems of representation in the teaching and learning mathematics (pp. 27-32). Lawrence Erlbaum.
  • Janvier, C. (1987b). Representation and understanding: The notion of function as an example. In C. Janvier (Ed.), Problems of representation in the teaching and learning mathematics (pp. 67-71). Lawrence Erlbaum.
  • Janvier, C. (1987c). Conceptions and representations: The circle as an example. In C. Janvier (Ed.), Problems of representation in the teaching and learning mathematics (pp.147-158). Lawrence Erlbaum.
  • Kaput, J. (1987). Representation system and mathematics. In C. Janvier (Ed.), Problems of representation in the teaching and learning mathematics (pp. 19-26). Lawrence Erlbaum.
  • Kolloffel, B. (2012). Exploring the relation between visualizer-verbalizer cognitive styles and performance with visual or verbal learning material. Computers & Education, 58, 697-706. https://doi.org/10.1016/j.compedu.2011.09.016
  • Kozhevnikov, M., Hegarty, M., & Mayer, R. (2002). Revising the visualizer-verbalizer dimensions: Evidence for two types of visualizers. Cognition and Instruction, 20, 47-77. https://doi.org/10.1207/S1532690XCI2001_3
  • Kozhevnikov, M., Kosslyn, S. M., & Shepard, J. (2005). Spatial versus object visualizers: A new characterization of visual cognitive style. Memory and Cognition, 33, 710-726. https://doi.org/10.3758/BF03195337
  • Krutetskii, V. A. (1963). Some characteristics of thinking of pupils with little capacity for mathematics. In B. Simon & J. Simon (Eds.), Educational psychology in the USSR (pp. 214-233). Stanford University Press.
  • Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren. University Of Chicago Press.
  • Lean, G., & Clements, M. A. (1981). Spatial ability, visual imagery, and mathematical performance. Educational Studies in Mathematics, 12, 267-299. https://doi.org/10.1007/BF00311060
  • Lesh, R., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representation in the teaching and learning mathematics (pp. 33-40). Lawrence Erlbaum.
  • Ling, G. W., & Ghazali, M. (2007). Solution strategies, modes of representation, and justifications of primary five pupils in solving pre-algebra problems: An experience of using task-based interview and verbal protocol analysis. Journal of Science and Mathematics Education in Southeast Asia, 30, 45-66.
  • Lohman, D. E. (1996). Spatial ability and g. In I. Dennis & P. Tapsfield (Eds.), Human abilities their nature and measurement (pp 97-116). Lawrence Erlbaum.
  • Lohman, D. E., & Larkin, J. (2009). Consistencies in sex difference on the cognitive abilities test scores across counties, grades, test forms, and cohorts. British Journal of Educational psychology, 79, 389-407. https://doi.org/10.1348/000709908X354609
  • Lowrie T., & Kay, R. (2001). Relationship between visual and nonvisual solution methods and difficulty in elementary mathematics. The Journal of Educational Research, 94, 248-255. https://doi.org/10.1080/00220670109598758
  • Ma, L. (1999). Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum Associates, Inc. https://doi.org/10.4324/9781410602589
  • Mainali, B. (2014). Investigating the relationships between preferences for solution methods, gender and high school students’ geometry performance (Doctoral Dissertation). University of Central Florida, USA.
  • Mainali, B. (2019). Investigating the relationships between preferences, gender, task difficulty, and high school students’ geometry performance. International Journal of Research in Education and Science (IJRES), 5(1), 224-236.
  • Moses, B. E. (1977). The nature of spatial ability and its relationship to mathematical problem solving (Unpublished doctoral dissertation). Ohio State University, Ohio.
  • National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. Author.
  • Pitta-Pantazi, D., & Christou, C. (2009). Cognitive styles, dynamic geometry, measurement performance. Educational Studies in Mathematics, 70, 5-26. https://doi.org/10.1007/s10649-008-9139-z
  • Presmeg, N. C. (1985). The role of visually mediated process in high school mathematics: A classroom investigation (Unpublished doctoral dissertation). University of Cambridge, United Kingdom.
  • Presmeg, N. C. (1986a). Visualization and mathematical giftedness. Educational Studies in Mathematics, 17, 297-311. https://doi.org/10.1007/BF00305075
  • Riding, R. J., & Rayner, S. (1998). Cognitive styles and learning strategies. Understanding style difference in learning and behavior. D Fulton.
  • Roubicek, F. (2006). Variety of representational environments in early geometry. Proceedings of the 30th Conference of International group for the Psychology of Mathematics Education, Czech Republic, 1, 321.
  • Sevimli, E., & Delice, A. (2011). The investigation of the relationship between calculus students’ cognitive process types and representation preferences in definite integral problems. In C. Smith (Ed.). Proceedings of the British Society for Research into Learning Mathematics, 3(13), November. https://doi.org/10.1080/14794802.2012.734988
  • Stenberg, R. J., & Grigorenko, E. L. (1997). Are cognitive styles still in style? The American psychologist, 52, 700-712. https://doi.org/10.1037/0003-066X.52.7.700
  • Suwarsono, S. (1982). Visual imagery in the mathematical thinking in seventh grade students (Unpublished doctoral dissertation). Monash University, Australia.
  • Vergnaud, G. (1987). Conclusions. In C. Janvier (Ed.), Problems of representation in the teaching and learning mathematics (pp. 227-4232). Lawrence Erlbaum.
  • Vergnaud, G. (1998). A comprehensive theory of representation for mathematics education. Journal of Mathematical Behavior, 17, 167-181. https://doi.org/10.1016/S0364-0213(99)80057-3
  • Webb, N. L. (1979). Processes, conceptual knowledge, and mathematical problem-solving ability. Journal for Research in Mathematics Education, 10, 83-93. https://doi.org/10.2307/748820
  • Zazkis, R., & Liljedhal, P. (2004). Understanding the primes: The role of representation. Journal for Research in Mathematics Education, 35, 164-168. https://doi.org/10.2307/30034911
  • Zazkis, R., Dubinsky, R. Z., & Dautermann, J. (1996). Coordinating visual and analytic strategies: A study of students’ understanding of the group D. Journal for Research in Mathematics Education, 27, 435-457. https://doi.org/10.2307/749876

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