American Journal of Applied Psychology

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Algorithmic Thinking and Mathematical Learning Difficulties Classification

Received: 26 September 2016    Accepted: 17 October 2016    Published: 10 November 2016
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Abstract

Learning difficulties research within the frame of dyscalculia has proceeded so far, nevertheless, they seem to fail in providing an overall conceptual map of the deficit. This paper objective is to propose a new classification in reference to dyscalculia features noticed at various ages. Although, there are several approaches on dyscalculia features, algorithmic thinking ability deficits are not taken into consideration. Authors focus on problem solving and algorithmic thinking difficulties within the frame of dyscalculia.

DOI 10.11648/j.ajap.20160505.11
Published in American Journal of Applied Psychology (Volume 5, Issue 5, September 2016)
Page(s) 22-31
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Algorithmic Thinking, Dyscalculia, Learning Memory, Reasoning, Problem Solving, Spatial Perception, Visual Perception

References
[1] R. S. Shalev and M. G. Von Aster, “Identification, classification, and prevalence of developmental dyscalculia,” Encyclopedia of Language and Literacy Development. pp. 1–9, 2008.
[2] D. C. Geary, “Dyscalculia at an Early Age: Characteristics and Potential Influence on Socio-Emotional Development,” Encyclopedia on Early Childhood Development Learning Disabilities. 2006.
[3] G. Karagiannakis, A. Baccaglini-Frank, and Y. Papadatos, “Mathematical learning difficulties subtypes classification,” Front. Hum. Neurosci., vol. 8, p. 57, Jan. 2014.
[4] J. Munro, “Information processing and mathematics learning difficulties,” Aust. J. Learn. Disabil., vol. 8, no. 4, pp. 19–24, Dec. 2003.
[5] R. S. Shalev, O. Manor, B. Kerem, M. Ayali, N. Badichi, Y. Friedlander, and V. Gross-Tsur, “Developmental Dyscalculia Is a Familial Learning Disability,” J. Learn. Disabil., vol. 34, no. 1, pp. 59–65, Jan. 2001.
[6] D. C. Geary, C. Hamson, and M. Hoard, “Numerical and arithmetical cognition: a longitudinal study of process and concept deficits in children with learning disability.,” J. Exp. Child Psychol., vol. 77, no. 3, pp. 236–63, Nov. 2000.
[7] R. Cohn, “Developmental dyscalculia.,” Pediatr. Clin. North Am., vol. 15, no. 3, pp. 651–68, Aug. 1968.
[8] J. Munro, “Dyscalculia: A unifying concept in understanding mathematics learning disabilities,” Aust. J. Learn. Disabil., vol. 8, no. 4, pp. 25–32, Dec. 2003.
[9] L. Kosc, “Developmental Dyscalculia,” J. Learn. Disabil., vol. 7, no. 3, pp. 164–177, Mar. 1974.
[10] M. Rosselli, E. Matute, N. Pinto, and A. Ardila, “Memory Abilities in Children With Subtypes of Dyscalculia,” Dev. Neuropsychol., Jun. 2010.
[11] L. Feigenson, S. Dehaene, and E. Spelke, “Core systems of number.,” Trends Cogn. Sci., vol. 8, no. 7, pp. 307–14, Jul. 2004.
[12] J. Fenn and N. Richardson, Newly Qualified Teachers and Other Entrants Into Teaching: Essays in Leadership for Changing Times. 2009.
[13] W. J. Friedman, “Memory for the time of past events.,” Psychol. Bull., vol. 113, no. 1, pp. 44–46, 1993.
[14] L. Fradkin, “Teaching algebra and calculus to engineering freshers via Socratic Dialogue and Eulerian sequencing,” in International Conference on Engineering Education ICEE, Gliwice, Poland, 2010.
[15] D. Tall, “Students’ Difficulties in Calculus,” in Proceedings of Working Group, ICME, Québec, Canada, 1993, pp. 13–28.
[16] D. R. LaTorre, J. W. Kenelly, I. B. Reed, L. R. Carpenter, and C. R. Harris, Calculus Concepts: An Informal Approach to the Mathematics of Change. 2011.
[17] A. Arcavi, “The role of visual representations in the learning of mathematics,” Educ. Stud. Math., vol. 52, no. 3, pp. 215–241, 2006.
[18] L. J. Rips, A. Bloomfield, and J. Asmuth, “From numerical concepts to concepts of number,” Behav. brain Funct., vol. 31, pp. 623–67, 2008.
[19] T. J. Simon, “Reconceptualizing the Origins of Number Knowledge: A ‘Non-Numerical’ Account,” Cogn. Dev., vol. 12, no. Ablex Publishing, pp. 349–371, 1997.
[20] M. Piazza, “Neurocognitive start-up tools for symbolic number representations.,” Trends Cogn. Sci., vol. 14, no. 12, pp. 542–51, Dec. 2010.
[21] S. F. Lourenco, J. W. Bonny, E. P. Fernandez, and S. Rao, “Nonsymbolic number and cumulative area representations contribute shared and unique variance to symbolic math competence,” Proc. Natl. Acad. Sci., vol. 109, no. 46, pp. 18737–18742, Oct. 2012.
[22] M. Piazza, A. Mechelli, B. Butterworth, and C. Price, “Are Subitizing and Counting Implemented as Separate or Functionally Overlapping Processes?,” NeuroImage, Elsevier Sci., vol. 15, pp. 435–446, 2002.
[23] H. Zimiles, “The Development of Conservation and Differentiation of Number,” in Monographs of the Society for Research in Child Development Vol. 31, No. 6, 1966, pp. 1–46.
[24] B. J. Forrest, “The utility of math difficulties, internalized psychopathology, and visual-spatial deficits to identify children with the nonverbal learning disability syndrome: evidence for a visualspatial disability.,” Child Neuropsychol., vol. 10, no. 2, pp. 129–46, Jun. 2004.
[25] C. Mussolin, S. Mejias, and M.-P. Noël, “Symbolic and nonsymbolic number comparison in children with and without dyscalculia.,” Cognition, vol. 115, no. 1, pp. 10–25, Apr. 2010.
[26] K. Skagerlund and U. Träff, “Development of magnitude processing in children with developmental dyscalculia: space, time, and number.,” Front. Psychol., vol. 5, p. 675, Jan. 2014.
[27] R. K. Vukovic and N. K. Lesaux, “The relationship between linguistic skills and arithmetic knowledge,” Learn. Individ. Differ., vol. 23, pp. 87–91, 2013.
[28] K. Menninger, Number Words and Number Symbols: A Cultural History of Numbers. 2013.
[29] W. Adams, “Problems of Pictorial Perception,” Leonardo, MIT Press, vol. 10, no. 2, pp. 107–112, 1977.
[30] D. Elkind, “The Development of Quantitative Thinking: A Systematic Replication of Piaget’s Studies,” J. Genet. Psychol., vol. 98, no. 1, pp. 37–46, Mar. 1961.
[31] J. G. Greeno, “Number Sense as Situated Knowing in a Conceptual Domain on JSTOR,” J. Res. Math. Educ., vol. 22, no. 3, pp. 170–218, 1991.
[32] S. Dehaene, The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition. 2011.
[33] P. Aunio and P. Räsänen, “Core numerical skills for learning mathematics in children aged five to eight years – a working model for educators,” Eur. Early Child. Educ. Res. J., pp. 1–21, Jan. 2015.
[34] K. C. Fuson, Children’s counting and concepts of number. Springer series in cognitive development. 1988.
[35] R. S. Siegler and J. E. Opfer, “The Development of Numerical Estimation: Evidence for Multiple Representations of Numerical Quantity,” Psychol. Sci., vol. 14, no. 3, pp. 237–250, May 2003.
[36] S. Gifford, “Number in Early Childhood,” Early Child Dev. Care, vol. 109, no. 1, pp. 95–119, Jan. 1995.
[37] A. W. Young and J. McPherson, “Ways of Making number judgments and children’s understanding of quantity relations,” Br. J. Educ. Psychol., vol. 46, no. 3, pp. 328–332, Nov. 1976.
[38] J. Hiebert, Conceptual and Procedural Knowledge: The Case of Mathematics. 2013.
[39] D. Szűcs, A. Devine, F. Soltesz, A. Nobes, and F. Gabriel, “Cognitive components of a mathematical processing network in 9-year-old children,” Dev. Sci., vol. 17, no. 4, pp. 506–524, Jul. 2014.
[40] T. Gebuis and B. Reynvoet, “Generating nonsymbolic number stimuli.,” Behav. Res. Methods, vol. 43, no. 4, pp. 981–6, Dec. 2011.
[41] K. C. Fuson, “Issues in Place-Value and Multidigit Addition and Subtraction Learning and Teaching on JSTOR,” J. Res. Math. Educ., vol. 12, no. 4, pp. 273–280, 1990.
[42] T. Koponen, K. Aunola, T. Ahonen, and J.-E. Nurmi, “Cognitive predictors of single-digit and procedural calculation skills and their covariation with reading skill.,” J. Exp. Child Psychol., vol. 97, no. 3, pp. 220–41, Jul. 2007.
[43] M. G. von Aster and R. S. Shalev, “Number development and developmental dyscalculia.,” Dev. Med. Child Neurol., vol. 49, no. 11, pp. 868–73, Nov. 2007.
[44] R. H. Logie, Visuo-spatial Working Memory. 2014.
[45] S. Ashkenazi, N. Mark-Zigdon, and A. Henik, “Do subitizing deficits in developmental dyscalculia involve pattern recognition weakness?,” Dev. Sci., vol. 16, no. 1, pp. 35–46, Jan. 2013.
[46] L. W. Barsalou, “Perceptions of perceptual symbols,” Behav. Brain Sci., vol. 22, no. 4, pp. 637–660, Aug. 1999.
[47] D. Harel, “On visual formalisms,” Commun. ACM, vol. 31, no. 5, pp. 514–530, May 1988.
[48] D. Sasanguie, S. M. Göbel, K. Moll, K. Smets, and B. Reynvoet, “Approximate number sense, symbolic number processing, or number-space mappings: what underlies mathematics achievement?,” J. Exp. Child Psychol., vol. 114, no. 3, pp. 418–31, Mar. 2013.
[49] S. Dehaene, E. Dupoux, and J. Mehler, “Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison.,” J. Exp. Psychol. Hum. Percept. Perform., vol. 16, no. 3, pp. 626–641, 1990.
[50] C. Sackur-Grisvard and F. Léonard, “Intermediate Cognitive Organizations in the Process of Learning a Mathematical Concept: The Order of Positive Decimal Numbers,” Cogn. Instr., vol. 2, no. 2, Dec. 2009.
[51] M. D. de Hevia, G. Vallar, and L. Girelli, “Visualizing numbers in the mind’s eye: the role of visuo-spatial processes in numerical abilities.,” Neurosci. Biobehav. Rev., vol. 32, no. 8, pp. 1361–72, Oct. 2008.
[52] A. Plerou, “Dealing with Dyscalculia over time,” in International Conference on Information Communication Technologies in Education, 2014.
[53] G. R. Wankhade, “Dyscalculia: From Detection to Diagnosis,” SSRN Electron. J., Apr. 2010.
[54] J. E. Richmond, “School Aged Children: Visual perception and Reversal Recognition of Letters and Numbers Separately and in Contex,” 2010.
[55] A. U. Frank, “Qualitative spatial reasoning: cardinal directions as an example,” Int. J. Geogr. Inf. Syst., vol. 10, no. 3, pp. 269–290, Apr. 1996.
[56] G. Santi and A. Baccaglini-Frank, “Forms of generalization in students experiencing mathematical learning difficulties,” PNA, vol. 9, no. 3, pp. 217–243, Mar. 2015.
[57] M. L. Crowley, “The Van Hiele Model of the Development of Geometric Thought,” in Learning and Teaching Geometry, Yearbook of the National Council of Teachers of Mathematics, 1987, pp. 1–16.
[58] D. H. Clements, “Geometric and Spatial Thinking in Young Children.,” Nov. 1997.
[59] A. Gutiérrez and A. Jaime, “On the Assessment of the Van Hiele Levels of Reasoning,” Focus Learn. Probl. Math., vol. 20, pp. 27–46, 1998.
[60] S. Olkun, “Geometric Explorations with Dynamic Geometry Applications based on van Hiele levels,” International Journal for Mathematics Teaching and Learning, vol. 1, no. 2. 05-Dec-2009.
[61] M. T. Battista, “Spatial Visualization and Gender Differences in High School,” J. Res. Math. Educ., vol. 21, no. 1, pp. 47–60, 1990.
[62] M. A. Yazdani, “The Gagne – van Hieles Connection: A Comparative Analysis of Two Theoretical Learning Frameworks,” J. Math. Sci. Math. Educ. Vol. 3, No. 1 58, vol. 3, no. 1, pp. 58–63, 1998.
[63] E. Smith and M. de Villiers, “A comparative study of two Van Hiele testing instruments,” in Conference for the Psychology of Mathematics Education (PME- 13), Paris, 1989.
[64] R. Cohen Kadosh, J. Lammertyn, and V. Izard, “Are numbers special? An overview of chronometric, neuroimaging, developmental and comparative studies of magnitude representation.,” Prog. Neurobiol., vol. 84, no. 2, pp. 132–47, Feb. 2008.
[65] G. Hannell, Dyscalculia: Action Plans for Successful Learning in Mathematics. 2013.
[66] M. Cappelletti, E. D. Freeman, and B. L. Butterworth, “Time processing in dyscalculia.,” Front. Psychol., vol. 2, p. 364, Jan. 2011.
[67] S. Sainsbury, “Strategies for learning to tell the time on analog clocks,” Aust. J. Learn. Disabil., vol. 4, no. 4, pp. 30–35, Dec. 1999.
[68] D. F. Benson and W. F. Weir, “Acalculia: Acquired Anarithmetia,” Cortex, vol. 8, no. 4, pp. 465–472, Dec. 1972.
[69] A. Ardila and M. Rosselli, “Acalculia and Dyscalculia,” Neuropsychol. Rev., vol. 12, no. 4, pp. 179–231, 2002.
[70] A. Ardila and M. Rosselli, “Spatial Acalculia,” Int. J. Neurosci., vol. 78, no. 3–4, pp. 177–184, Jul. 2009.
[71] A. Avizienis, “Arithmetic Algorithms for Error-Coded Operands,” IEEE Trans. Comput., vol. C-22, no. 6, pp. 567–572, Jun. 1973.
[72] S. Ashkenazi, N. Mark-Zigdon, and A. Henik, “Numerical distance effect in developmental dyscalculia,” Cogn. Dev., vol. 24, no. 4, pp. 387–400, Jan. 2009.
[73] S. Chinn, The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties. 2014.
[74] P. Räsänen and T. Ahonen, “Arithmetic disabilities with and without reading difficulties: A comparison of arithmetic errors,” Dev. Neuropsychol., vol. 11, no. 3, pp. 275–295, Nov. 2009.
[75] J. M. Engelhardt, “Analysis of Children’s Computational Errors: A Qualitative Approach,” Br. J. Educ. Psychol., vol. 47, no. 2, pp. 149–154, Jun. 1977.
[76] A. Fain, “The Effects of Using Direct Instruction and the Equal Additions Algorithm to Promote Subtraction with Regrouping skills of Students with Emotional and Behavioral Disorders with Mathematics Difficulties,” 2013.
[77] B. Butterworth, L. Cipolotti, and E. K. Warrington, “Short-term memory impairment and arithmetical ability.,” Q. J. Exp. Psychol. A., vol. 49, no. 1, pp. 251–62, Feb. 1996.
[78] D. P. Bryant, P. Hartman, and S. A. Kim, “Using Explicit and Strategic Instruction to Teach Division Skills to Students With Learning Disabilities,” Exceptionality, vol. 11, no. 3, pp. 151–164, Sep. 2003.
[79] L. Mundia, “The Assessment of Math Learning Difficulties in a Primary Grade-4 Child with High Support Needs: Mixed Methods Approach,” Int. Electron. J. Elem. Educ., vol. 4, no. 2, pp. 347–366, 2012.
[80] D. H. Jonassen, “Toward a design theory of problem solving,” Educ. Technol. Res. Dev., vol. 48, no. 4, pp. 63–85, Dec. 2000.
[81] A. Plerou and P. Vlamos, “Algorithmic Problem Solving Using Interactive Virtual Environment: A Case Study,” Engineering Applications of Neural Networks, 2013.
[82] G. Futschek, “Algorithmic Thinking: The Key for Understanding Computer Scienc,” in Informatics Education – The Bridge between Using and Understanding Computers Lecture Notes in Computer Science, vol. 4226, R. T. Mittermeir, Ed. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006, pp. 159–168.
[83] M. G. Voskoglou and S. Buckley, “Problem Solving and Computational Thinking in a Learning Environment,” p. 19, Dec. 2012.
[84] A. Schoenfeld, “Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics,” in Handbook of research on mathematics teaching and learning, 1992, pp. 334–370.
[85] J. Munro, “The role of working memory in mathematics learning and numeracy,” in Memory and Learning: What Works?, 2010.
[86] T. P. Alloway, “Working memory, reading, and mathematical skills in children with developmental coordination disorder.,” J. Exp. Child Psychol., vol. 96, no. 1, pp. 20–36, Jan. 2007.
[87] S. G. Vandenberg and A. R. Kuse, “Mental rotations, a group test of three-dimensional spatial visualization.,” Percept. Mot. Skills, vol. 47, no. 2, pp. 599–604, Oct. 1978.
[88] D. Knuth, “Algorithmic Thinking and Mathematical Thinking,” The American Mathematical Monthly, vol. 92, no. 3, pp. 170–181, 1985.
[89] R. Bird, The Dyscalculia Toolkit: Supporting Learning Difficulties in Maths. 2013.
Author Information
  • Bioinformatics and Human Electrophysiology Laboratory, Department of Informatics, Ionian University, Corfu, Greece

  • Bioinformatics and Human Electrophysiology Laboratory, Department of Informatics, Ionian University, Corfu, Greece

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    Antonia Plerou, Panayiotis Vlamos. (2016). Algorithmic Thinking and Mathematical Learning Difficulties Classification. American Journal of Applied Psychology, 5(5), 22-31. https://doi.org/10.11648/j.ajap.20160505.11

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    Antonia Plerou; Panayiotis Vlamos. Algorithmic Thinking and Mathematical Learning Difficulties Classification. Am. J. Appl. Psychol. 2016, 5(5), 22-31. doi: 10.11648/j.ajap.20160505.11

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    Antonia Plerou, Panayiotis Vlamos. Algorithmic Thinking and Mathematical Learning Difficulties Classification. Am J Appl Psychol. 2016;5(5):22-31. doi: 10.11648/j.ajap.20160505.11

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  • @article{10.11648/j.ajap.20160505.11,
      author = {Antonia Plerou and Panayiotis Vlamos},
      title = {Algorithmic Thinking and Mathematical Learning Difficulties Classification},
      journal = {American Journal of Applied Psychology},
      volume = {5},
      number = {5},
      pages = {22-31},
      doi = {10.11648/j.ajap.20160505.11},
      url = {https://doi.org/10.11648/j.ajap.20160505.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajap.20160505.11},
      abstract = {Learning difficulties research within the frame of dyscalculia has proceeded so far, nevertheless, they seem to fail in providing an overall conceptual map of the deficit. This paper objective is to propose a new classification in reference to dyscalculia features noticed at various ages. Although, there are several approaches on dyscalculia features, algorithmic thinking ability deficits are not taken into consideration. Authors focus on problem solving and algorithmic thinking difficulties within the frame of dyscalculia.},
     year = {2016}
    }
    

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