How Do We Learn Mathematics? A Framework for a Theoretical and Practical Model

Sinan Olkun

Vol. 14 No. 3 (2022) Special Issue: Typical and Atypical Mathematics Learning: What do We Learn from Recent Studies?

How Do We Learn Mathematics? A Framework for a Theoretical and Practical Model

Sinan Olkun

Published March 16, 2022 | Pages: 295-302 | Views: 512

Download PDF

SHARE

Abstract

The purpose of this paper is to propose an effective learning environment for the initial stages of mathematical learning. Basic numerical skills and the objects and actions that trigger those skills are conceptualized as a mathematics-learning environment. We discuss numerical learning mechanism and the basic skills and environments we use to learn numbers briefly within the human cognition system. The three subsystems of number, i.e., exact number system, approximate number system and access to symbol system, are explained with reference to basic number competencies. They are discussed within the framework of "number sense” by drawing evidences from the neuroscience and mathematics education literature. Finally, how to manipulate the components of these subsystems for an effective learning of number is exemplified in a proposed model of mathematical learning environment.

Listen -

References

Antell, S. E., & Keating, D. P. (1983). Perception of numerical invariance in neonates. Child Dev, 54(3), 695-701.
Balakrishnan, J. D., & Ashby, F. G. (1992). Subitizing: magical numbers or mere superstition? Psychol Res, 54(2), 80-90. doi:10.1007/BF00937136
Benoit, L., Lehalle, H., & Jouen, F. (2004). Do young children acquire number words through subitizing or counting? Cognitive Development, 19(3), 291-307. doi:10.1016/j.cogdev.2004.03.005
Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Dev Psychol, 42(1), 189-201. doi:10.1037/0012-1649.41.6.189
Butterworth, B., & Laurillard, D. (2010). Low numeracy and dyscalculia: identification and intervention. Zdm, 42(6), 527-539. doi:10.1007/s11858-010-0267-4
Clements, D. H., Sarama, J., & MacDonald, B. L. (2019). Subitizing: The Neglected Quantifier. In Constructing Number (pp. 13-45).
Cohen Kadosh, R., Dowker, A., Heine, A., Kaufmann, L., & Kucian, K. (2013). Interventions for improving numerical abilities: Present and future. Trends in Neuroscience and Education, 2(2), 85-93. doi:10.1016/j.tine.2013.04.001
Dehaene, S. (1992). Varieties of numerical abilities. Cognition, 44(1-2), 1-42. doi:10.1016/0010-0277(92)90049-n
Dehaene, S. (2009). Origins of mathematical intuitions: the case of arithmetic. Ann N Y Acad Sci, 1156, 232-259. doi:10.1111/j.1749-6632.2009.04469.x
Dehaene, S., Molko, N., Cohen, L., & Wilson, A. J. (2004). Arithmetic and the brain. Curr Opin Neurobiol, 14(2), 218-224. doi:10.1016/j.conb.2004.03.008
Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cogn Neuropsychol, 20(3), 487-506. doi:10.1080/02643290244000239
Desoete, A., Ceulemans, A., Roeyers, H., & Huylebroeck, A. (2009). Subitizing or counting as possible screening variables for learning disabilities in mathematics education or learning? Educational Research Review, 4(1), 55-66. doi:10.1016/j.edurev.2008.11.003
Groffman, S. (2009). Subitizing: Vision Therapy for Math Deficits. Optom Vis Dev, 40(4), 229-238.
Hyde, D. C., Khanum, S., & Spelke, E. S. (2014). Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children. Cognition, 131(1), 92-107. doi:10.1016/j.cognition.2013.12.007
Kinzler, K. D., & Spelke, E. S. (2007). Core systems in human cognition. In From Action to Cognition (pp. 257-264).
Krajcsi, A., Szabo, E., & Morocz, I. A. (2013). Subitizing is sensitive to the arrangement of objects. Exp Psychol, 60(4), 227-234. doi:10.1027/1618-3169/a000191
Kucian, K., Grond, U., Rotzer, S., Henzi, B., Schonmann, C., Plangger, F., . . . von Aster, M. (2011). Mental number line training in children with developmental dyscalculia. Neuroimage, 57(3), 782-795. doi:10.1016/j.neuroimage.2011.01.070
Lipton, J. S., & Spelke, E. S. (2003). Origins of number sense. Large-number discrimination in human infants. Psychol Sci, 14(5), 396-401. doi:10.1111/1467-9280.01453
Mandler, G., & Shebo, B. J. (1982). Subitizing: an analysis of its component processes. J Exp Psychol Gen, 111(1), 1-22. doi:10.1037//0096-3445.111.1.1
Mazzocco, M. M., Feigenson, L., & Halberda, J. (2011). Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child Dev, 82(4), 1224-1237. doi:10.1111/j.1467-8624.2011.01608.x
Olkun, S., Altun, A., & Göçer-Şahin, S. (2015). Beyond Subitizing: Symbolic Manipulations of Numbers. International Journal of Learning, Teaching and Educational Research, 10(1), 93-103.
Olkun, S., Altun, A., Göçer Şahin, S., & Akkurt Denizli, Z. (2015). Deficits in Basic Number Competencies May Cause Low Numeracy in Primary School Children. Egitim ve Bilim, 40(177). doi:10.15390/eb.2015.3287
Olkun, S., Karslı-Çalamak, E., Sözen-Özdoğan, S., Solmaz, G., & Haşlaman, T. (2018). Subitizing and beyond: Perception of set cardinality from different spatial representations. Paper presented at the 4. Cyprus International Congress of Educational Research, Kyrenia, TRNC.
Olkun, S., & Özdem, Ş. (2015). The Effect of Conceptual Subitizing Training on Calculation Performance. Baskent University Journal of Education, 2(1), 1-9.
Ozdem, S., & Olkun, S. (2019). Improving mathematics achievement via conceptual subitizing skill training. International Journal of Mathematical Education in Science and Technology, 1-15. doi:10.1080/0020739x.2019.1694710
Piazza, M., Mechelli, A., Butterworth, B., & Price, C. J. (2002). Are subitizing and counting implemented as separate or functionally overlapping processes? Neuroimage, 15(2), 435-446. doi:10.1006/nimg.2001.0980
Sankey, M. D., Birch, D., & Gardiner, M. W. (2011). The impact of multiple representations of content using multimedia on. International Journal of Education and Development using Information and Communication Technology (IJEDICT), 7(3), 18-35.
Schleifer, P., & Landerl, K. (2011). Subitizing and counting in typical and atypical development. Dev Sci, 14(2), 280-291. doi:10.1111/j.1467-7687.2010.00976.x
Schmithorst, V. J., & Brown, R. D. (2004). Empirical validation of the triple-code model of numerical processing for complex math operations using functional MRI and group Independent Component Analysis of the mental addition and subtraction of fractions. Neuroimage, 22(3), 1414-1420. doi:10.1016/j.neuroimage.2004.03.021
Spelke, E. S. (2017). Core Knowledge, Language, and Number. Language Learning and Development, 13(2), 147-170. doi:10.1080/15475441.2016.1263572
Spelke, E. S., & Kinzler, K. D. (2007). Core knowledge. Dev Sci, 10(1), 89-96. doi:10.1111/j.1467-7687.2007.00569.x
Vogel, S. E., Goffin, C., & Ansari, D. (2015). Developmental specialization of the left parietal cortex for the semantic representation of Arabic numerals: an fMR-adaptation study. Dev Cogn Neurosci, 12, 61-73. doi:10.1016/j.dcn.2014.12.001
Wakeley, A., Rivera, S., & Langer, J. (2000). Can young infants add and subtract. Child Development, 71(6), 1525–1534.
Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358(6389), 749-750. doi:10.1038/358749a0

Keywords

quantity

Affiliations

Sinan Olkun

Final International University

Downloads

Download data is not yet available.

How to Cite

Olkun, S. (2022). How Do We Learn Mathematics? A Framework for a Theoretical and Practical Model. International Electronic Journal of Elementary Education, 14(3), 295–302. Retrieved from https://iejee.com/index.php/IEJEE/article/view/1706

Author Biography

Sinan Olkun

Qualifications

I completed my undergraduate education in the field of Mechanical Education at Marmara University, Technical Education Faculty in 1985. I received my master's degree in the Department of Educational Sciences at Middle East Technical University in 1995 and my doctoral degree in 1999, in Curriculum and Instruction with an emphasis on Mathematics Education and Elementary Education from Arizona State University, USA.

From 1999 to 2004, I worked as an assistant professor at Abant Izzet Baysal University in Mathematics and Science Education Department. I transferred to Ankara University Faculty of Educational Sciences in 2004. I served as the head of the elementary education department and the head of the primary education department at the same faculty. At the same time, I was the coordinator of the primary education undergraduate, mathematics education master's and mathematics education doctoral programs. From 2014 to 2018, I worked as a full professor, head of department and dean of the Faculty of Education at TED University. I then worked as the dean of the Faculty of Educational Sciences at Final International University.

As a professor in the field of mathematics education in elementary education, I teach undergraduate, graduate and doctoral courses and conduct research. I have also specialized on mathematics learning difficulties, number sense and development, development of mathematical thinking in children, development of geometric thinking, developing basic mathematical skills with games. I have designed two board games to improve children’s number sense.

Teaching philosophy

I have a learner-centered mindset. I believe in learning rather than teaching for individuals’ intellectual development. This is also valid for learning mathematics. The role of teachers include designing learning environments for effective learning of mathematics, and encouraging and motivating students to learn. The learning environment should be designed in accordance with multiple representations of mathematical knowledge to address multiple senses of the learners, who might have different learning styles.