Full-text resources of CEJSH and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


2019 | 55 | 100-111

Article title

Year Five Pupils’ Number Sense and Algebraic Thinking: the Mediating Role of Symbol and Pattern Sense

Content

Title variants

Languages of publication

Abstracts

EN
This study mainly focused on the relationship between number sense and algebraic thinking. Previous studies have provided evidence that number sense plays an important role in developing algebraic thinking. The role of symbol and pattern sense are yet to discover in relation to number sense and algebraic thinking. The purpose of this study was to identify the mediating effects of symbol sense and pattern sense in year five pupils’ relationship between number sense and algebraic thinking. To do so, two mathematics tests were carried out among 720 year five pupils in the district of Malacca, Malaysia. The collected data were analysed using a partial least squares-structural equation modeling approach. The data collected were analysed using SPSS 22.0 and SmartPLS 3.0. Results demonstrated that symbol sense and pattern sense are good mediators between year five pupils’ number sense and algebraic thinking. This result of the study supports the past studies related to the role of number sense, symbol and pattern sense in developing algebraic thinking. The presented study provides suggestions as intervention to increase students’ making sense ability in numbers, symbols and patterns to develop algebraic thinking.

Year

Volume

55

Pages

100-111

Physical description

Dates

published
2019

Contributors

  • University of Malaya
  • University of Malaya
author
  • University of Malaya

References

  • Alibali, M.W., Knuth, E.J., Hattikudur, S., McNeil, N.M., & Stephens, A.C. (2007). A longitudinal examination of middle school students’ understanding of the equal sign and equivalent equations. Mathematical Thinking and Learning, 9, 221–247. doi:10.1080/10986060701360902
  • Baron, R.M., & Kenny, D.A. (1986). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51(6), 1173–1182. doi:10.1037/0022–3514.51.6.1173
  • Berkman, R.M. (1998). Exploring interplanetary algebra to understand earthly mathematics. Teaching Children Mathematics, 5(2), 78–81. Retrieved from http://ezproxy.um.edu.my:2132/docview/214140437?accountid=28930
  • Blanton, M.L., & Kaput, J.J. (2003). Developing elementary teachers’: “Algebra eyes and ears”. Teaching Children Mathematics, 10(2), 70–77. Retrieved from http://www.jstor.org/stable/41198085
  • Brizuela, B., & Schliemann, A. (2004). Ten-year-old students solving linear equations. For the Learning of Mathematics, 24(2), 33–40. Retrieved from http://ase.tufts.edu/educa-tion/earlyalgebra/publications/2004/10yrLinear.pdf
  • Cai, J., & Moyer, J. (2008). Developing algebraic thinking in earlier grades: some insights from international comparative studies. In National Council of Teachers of Mathematics (pp. 169–193). Reston, VA: NCTM.
  • Carpenter, T.P., & Levi, L. (2000). Developing conceptions of algebraic reasoning in the primary grades (Report No. 002). Retrieved from Wisconsin Center for Education Research website: http://ncisla.wceruw.org/publications/reports/RR-002.PDF
  • Carpenter, T.P., Franke, M.L., & Levi, L. (2003). Thinking mathematically: Integrating arithmetic and algebra in elementary school. Portsmouth, NH: Heinemann.
  • Carpenter, T.P., Levi, L., Berman, P.W., & Pligge, M. (2005). Developing algebraic reasoning in the elementary school. In T.A. Romberg, T.P. Carpenter, & F. Dremock (Eds.), Understanding mathematics and science matters (pp. 81–98). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
  • Ferrini-Mundy, J., Lappan, G., & Phillips, E. (1997). Experiences in patterning. Teaching Children Mathematics, 282–288. Retrieved from http://math.wiki.inghamisd.org/file/view/Experiences+with+patterning.pdf
  • Herscovics, N., & Linchevski, L. (1994). A cognitive gap between arithmetic and algebra. Educational Studies in Mathematics, 27(1), 59–78. doi: 10.1007/BF01284528
  • Hsu, C.Y., Yang, D.C., & Li, F.M. (2001). The design of “The fifth and sixth grade number sense rating scale”. Chinese Journal of Science Education, 9(4), 351–374. Retrieved from http://www.fed.cuhk.edu.hk/en/cjse/200100090004/0351.htm
  • Jacobs, V.R., Franke, M.L., Carpenter, T.P., Levi, L., & Battey, D. (2007). Professional development focused on children’s algebraic reasoning in elementary school. Journal for Research in Mathematics Education, 38(3), 258–288. Retrieved from http://homepages.math.uic.edu/~martinez/PD-EarlyAlgebra.pdf
  • Kaput, J.J. (2008). What is algebra? What is algebraic reasoning? In J.J. Kaput, D.W. Carraher, & M.L. Blanton (Eds.), Algebra in the early grades (pp. 5–17). New York, NY: Taylor and Francis Group.
  • Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 8(1), 139–151. Retrieved from http://link.springer.com/
  • Knuth, E.J., Alibali, M.W., McNeil, N.M., Weinberg, A., & Stephens, A.C. (2011). Middle school students’ understanding of core algebraic concepts: Equivalence & variable. In J. Cai, & E. Knuth, Early Algebraization (pp. 259–276). [Adobe Digital Editions]. doi:10.1007/978–3-642–17735–4_15
  • Lannin, J.K. (2005). Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning, 7(3), 231–258. doi:10.1207/s15327833mtl0703_3
  • Lannin, J.K., Barker, D.D., & Townsend, B.E. (2006). Recursive and explicit rules: How can we build student algebraic understanding? Journal of Mathematical Behavior, 25, 299–317. doi:10.1016/j.jmathb.2006.11.004
  • MacGregor, M., & Stacey, K. (1997). Students’ understanding of algebraic notation: 11–15. Educational Studies in Mathematics, 33(1), 1–19. doi:10.1023/A:1002970913563
  • Mason, J. (1996). Expressing generality and roots of algebra. In N. Bednarz, C. Kieran, & L. Lee (Eds.), Approaches to Algebra: Perspectives for Research and Teaching (pp. 65–86). Dordrecht: Kluwer Academic Publishers.
  • McNeil, N.M. (2008). Limitations to teaching children 2 + 2 = 4: Typical arithmetic problems can hinder learning of mathematical equivalence. Child Development, 79(5), 1524–1537. doi:10.1111/j.1467–8624.2008.01203.x
  • Molina, M., & Ambrose, R. (2008). From an operational to a relational conception of the equal sign. Thirds graders’ developing algebraic thinking. Focus on Learning Problems in Mathematics, 30(1), 61–80. Retrieved from http://digibug.ugr.es/bit¬stream/10481/4721/1/Molina%20y%20Ambrose%20%20FOCUS%20to%20divulge.pdf
  • National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
  • Ralston, N.C. (2013). The development and validation of a diagnostic assessment of algebraic thinking skills for students in the elementary grades (Doctoral dissertation). Available from ProQuest Dissertations and Theses database. (UMI No. 3588844)
  • Rittle-Johnson, B., & Alibali, M.W. (1999). Conceptual and procedural understanding: Does one lead to the other? Journal of Educational Psychology, 91(1), 175–189. doi:10.1037/0022–0663.91.1.175
  • Rittle-Johnson, B., Matthews, P.G., Taylor, R.S., & McEldoon, K.L. (2011). Assessing knowledge of mathematical equivalence: A construct-modeling approach. Journal of Educational Psychology, 103(1), 85–104. doi:10.1037/a0021334
  • Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 20(2), 147–164. Retrieved from http://www.jstor.org/stable/3482495
  • Stephens, A. (2005, September). Developing students’ understandings of variable. Mathematics Teaching in the Middle School, 11(2), 96–100. Retrieved from http://labweb.education.wisc.edu/~knuth/taar/papers_rep_pub/MTMS_variable.pdf
  • Strother, S.A. (2011). Algebra knowledge in early elementary school supporting later mathematics ability (Doctoral dissertation). Available from ProQuest Dissertations and Theses database. (UMI No. 3502276)
  • Warren, E.A., Cooper, T.J., & Lamb, J.T. (2006). Investigating functional thinking in the elementary classroom: Foundations of early algebraic reasoning. Journal of Mathematical Behavior, 25, 208–223. doi: 10.1016/j.jmathb.2006.09.006
  • Yang, D.C., Hsu, C.J., & Huang, M.C. (2004). A study of teaching and learning number sense for sixth grade students in Taiwan. International Journal of Science and Mathematics Education, 2(3), 407–430. doi: 10.1007/s10763–004–6486–9

Document Type

Publication order reference

Identifiers

Biblioteka Nauki
1967800

YADDA identifier

bwmeta1.element.ojs-doi-10_15804_tner_2019_55_1_08
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.