Abstract
Elementary students in Ontario are bombarded with various mathematical classroom instructional methodologies, in order to assist them in improving their mathematical cognition. Children’s first formal years of schooling can determine a student’s awareness regarding their mathematical achievement, their math anxiety, and motivational stance regarding mathematics (Gunderson et al. 2018). While formal schooling is the most prominent way to disperse mathematical knowledge, children do discuss and embody math and its properties outside of the classroom environment. Mathematical knowledge can be acquired outside of formal school instruction and become a positive influence on mathematical performance throughout one’s lifetime (Brownell 1941). Ideas such as financial literacy, probability, and patterning are easy topics in which young students can encounter within their everyday lives. Nonetheless, students in Ontario are still experiencing difficulties when applying their understanding of mathematics to given problems within standardized testing. While the author of this chapter is aware of the problematic nature of standardized testing, it is important to note these results as a basis for the argument for the rest of this chapter. Ontario’s Education Quality and Accountability Office (EQAO 2016/2017) released their annual results of standardized testing on mathematical skills. The 2017–2018 results showed that fewer than half of the province’s grade 6 pupils—49%—met the provincial standard in math in the 2017–18 academic year. According to the EQAO standardized test in the 2016–17 academic year, only 49% of grade 3 girls in Ontario agreed with the statement they are good at math compared to 62% of boys. The difference widened in grade 6, where 46% of girls said that they were good at math compared to 61% of boys. While these statistics are problematic for Ontario educational partners, they only demonstrate the surface of the problem. Students are doing poorly not only on their results of testing, but also on their self-confidence, and specifically math anxiety within females is also distressful. This chapter examines methodologies to go beyond twenty-first-century skills, and how future mathematical instructional methods must become more rigorous in order to change and make an impact on Ontario student’s mathematical cognition. This chapter explores possible instructional methodologies in which educators should explore in order to find best practices for their students to build upon.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Arryo, I., Woolf, B., Burelson, W., Muldner, K., Rai, D., and Tai, M. (2014). A multimedia adaptive tutoring system for mathematics that addresses cognition, metacognition and affect. International Journal of Artificial Intelligence Education 24: 87–426.
Balfanz, B. (1990). Elementary school quality, the mathematics curriculum and the role of local knowledge. International Review of Education 36 (1): 43–56.
Baroody, A. J. and Dowker, A. (2003). The development of arithmetic concepts and skills: Constructing adaptive expertise. Mahwah, NJ: Erlbaum.
Bell, S. (2010) Project-based learning for the 21st century: Skills for the Future. The Clearing House 83: 39–43
Boaler, J. (1999). Mathematics for the moment, or the millennium? Education Week 17(29): 30–34.
Bredekamp, S. (2004). Standards for preschool and kindergarten mathematics education. In: H. Clements and J. Sarama (eds.), Engaging young children in mathematics: Standards for early childhood mathematics education, (pp. 77–87). Mahwah, NJ: Lawrence Erlbaum Associates.
Brenner, M. (1985). The practice of arithmetic in Liberian schools. Anthropology and Education Quarterly 16: 177–186.
Brownell, W. A. (1941). Arithmetic in grades I and II. Durham, NC: Duke University Press.
Bull, R., Espy, K. A., and Wiebe, S. A. (2008). Short-term memory, working memory, and executive functions in preschoolers: Longitudinal predictors of mathematical achievement at age 7 years. Developmental Neuropsychology 33: 205–228.
Carraher, T. N., Carraher, D. W., and Schliemann, A. D. (1987). Written and oral mathematics. Journal for Research in Mathematics Education 18: 83
Cohen, J., Casa, T., Miller, H., and Firmender, J. (2015). Characteristics of second graders’ mathematical writing. School Science and Mathematics 115 (7): 344–55.
Costa, S. (2015). Exploring student “Math Talk” in 21st Century Classrooms. In: M. Bockarova, M. Danesi, D. Martinovic, D., and R. Núñes (eds.), Mind in mathematics: Essays on mathematical cognition and mathematical method, (pp. 176–182). Münich: Lincom Europa.
Costa, S. (2016). Math discourse in a Grade 2 Knowledge Building classroom. Master’s thesis, University of Toronto.
Furner, J., and Berman, B. (2012). Review of research: Math anxiety: Overcoming a major obstacle to the improvement of student math performance. Childhood Education 79 (3): 170–174.
Greenfield, P. and Lave, J. (1982). Cognitive aspects of informal education. In: H. Stevenson (ed.), Child development in cross-cultural perspective. San Francisco: Freeman Press.
Gunderson, E., Park, D., Maloney, E., Beilock, S., and Levine, S. (2018). Reciprocal relations among motivational frameworks, math anxiety, and math achievement in early elementary school. Journal of Cognition and Development 19 (1): 21–46.
Haylock, D. (1997). Recognizing mathematical creativity in schoolchildren. Zentralblatt fuer Didaktik der Mathematik 29(3): 68–74.
Henning, J. E., Mckeny, T., Foley, D., and Balong, M. (2012). Mathematics discussions by design: Creating opportunities for purposeful participation. Journal of Mathematics Teacher Education 15 (6): 453–478.
Human Resources and Skills Development Canada, Council of Ministers of Education, Canada and Statistics Canada (2004). Measuring Up: Canadian results of the OECD PISA Study: The performance of Canada’s youth in mathematics, reading, science and problem solving, 2003, Vol. 2, Catalogue number 81–590-XIE2004001.
Greeno, J. G., Collins, A. M. and Resnick, L. B (1996). Cognition and learning. In: D. C. Berliner and R. C. Calfee (eds.), Handbook of educational psychology, pp. 15–46. New York: Macmillan.
Murata, A. (2015). Interactions between teaching and learning mathematics in elementary classrooms. In: D. Scott and E. Hargreaves (eds.), The Sage handbook of learning, (pp. 233–242). London: Sage.
Novita, R. and Putra, M., (2016). Using task like PISA’s problem to support student’s creativity in mathematics. Journal of Mathematics Education 7 (1): 31–42.
Ontario. (2016/2017). EQAO: Education Quality and Accountability Office. Toronto: The Office.
Ritchhart, R. (2015). Creating cultures of thinking: The 8 forces we must master to truly transform our schools. Hoboken: Wiley.
Rittle-Johnson, B., Siegler, R. S., and Alibali, M. W. (2001). Developing conceptual understanding and procedural skill in mathematics: An iterative process. Journal of Educational Psychology 93: 346–362.
Scardamalia, M. (2002). Collective cognitive responsibility for the advancement of knowledge. In: B. Smith, and C. Bereiter (eds.), Liberal education in a knowledge society, (pp. 67–98). [Berkeley, CA.]: Distributed by Publishers Group West.
Scardamalia, M., and Bereiter, C. (2014). Knowledge building and knowledge creation: Theory, pedagogy, and technology. In: K. Sawyer (ed.), The Cambridge handbook of the learning sciences, pp. 397–417. New York: Cambridge University Press.
Sidney, P., and Alibali, M. (2015). Making connections in math: Activating a prior knowledge analogue matters for learning. Journal of Cognition and Learning 16(1): 160–185.
Stockero, S. L. and Van Zoest, L. R. (2013). Characterizing pivotal teaching moments in beginning mathematics teachers’ practice. Journal of Mathematics Teacher Education 16: 125–147.
Van Zoest, L. R., Stockero, S. L., Leatham, K. R., Peterson, B. E., Atanga, N. A., and Ochieng, M. A. (2017). Attributes of instances of student mathematical thinking that are worth building on in whole-class discussion. Mathematical Thinking and Learning 19: 33–54.
Wagner, T., and Dintersmith, T. (2015). Most likely to succeed: Preparing Our kids for the innovation era. New York: Scribner.
World Economic forum (2016). 10 skills you need to thrive tomorrow—and the universities that will help you get them. Directors of Research and Evaluation, US Department of State. https://www.weforum.org/agenda/2016/08/10-skills-you-need-to-thrive-tomorrow-and-the-universities-that-will-help-you-get-them/
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Costa, M.S.A. (2019). Knowledge Building, Mathematics, and Creative Thinking: An Overview on Ontario Elementary Mathematical Teaching Beyond Twenty-First-Century Skills. In: Danesi, M. (eds) Interdisciplinary Perspectives on Math Cognition. Mathematics in Mind. Springer, Cham. https://doi.org/10.1007/978-3-030-22537-7_15
Download citation
DOI: https://doi.org/10.1007/978-3-030-22537-7_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-22536-0
Online ISBN: 978-3-030-22537-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)