Investigating Student Use of Electronic Support Tools and Mathematical Reasoning

Abstract

Mathematical reasoning involves comprehending mathematical information and concepts in a logical way and forming conclusions and generalizations based on this comprehension. Computer-based learning has been incorporated into classrooms across the country, and specific aspects of technology need to be studied to determine how programs are influencing student reasoning and learning. This article explores how one aspect of computer-based learning, electronic support tools (ESTs), influences students’ mathematical reasoning over the course of an online supplemental mathematics program, the Math Learning Companion (MLC). Students in Grades 3, 4, and 5 (N = 31) from two private schools participated in MLC, and their reasoning was assessed before and after participating in the program. EST use was measured by using frequency counts for each tool. Results describe students’ tool use and reflect an overall change in their reasoning over the course of the intervention, indicating that students use ESTs as needed to individualize the learning program. Students specifically used ESTs as needed to improve their mathematical reasoning, their correctness of response, and their mathematical explanations of their answers over the course of the intervention.

Keywords

• Mathematical reasoning, Computer-based instruction, Electronic support tools, Mathematics education

Kaynakça

1. Aleven, V., McLaren, B.M., Roll, I., & Koedinger, K.R. (2006). Toward meta-cognitive tutoring: A model of help seeking with a Cognitive Tutor. International Journal of Artificial Intelligence in Education, 16, 101-128.
2. Anderson-Inman, L. & Horney, M. (1996). Computer-based concept mapping: Enhancing literacy tools for visual thinking. Journal of Adolescent & Adult Literacy, 40, 302-306.
3. Bernbaum Wilmont, D. (2012). Math reasoning inventory. (Technical Report) Sausalito, CA: Math Solutions, Scholastic.
4. Burns, M. (2012). Math reasoning inventory. Retrieved July 22, 2013 from www.mathreasoninginventory.com
5. Crawford, L., & Freeman, B. (2011). The Math Learning Companion: Initial research into two curriculum components. Presentation at Society for Research on Educational Effectiveness. Washington D.C., September 8-10, 2011.
6. Crawford, L., Higgins, K., & Freeman. B. (2012). Exploring the use of computer based electronic support tools by students with learning disabilities. Learning Disabilities: A Multidisciplinary Journal, 18(3), 135-144.
7. Crawford, L., Higgins, K., D’Angelo, J. & Hall, L. (2016). Use of active electronic support tools in mathematics. Manuscript under review.
8. D’Angelo, J., Higgins, K., & Crawford, L. (2016). Technology, affective characteristics and mathematics: A review of the literature from 1985-2013. Manuscript under review.

9. Digital Directions International (2005). HELPMath. Retrieved July 2, 2014 from http://www.helpprogram.net
10. Digital Directions International (2013). Math Learning Companion. Retrieved July 2, 2014 from www.mathlearningcompanion.net
11. Englert, C., Manalo, M., & Zhao, Y. (2004). I can do it better: The effects of technology enabled scaffolding on young writers’ composition. Journal of Special Education Technology, 19(1), 5- 22.
12. Francisco, J. M., & Maher, C. A. (2010). Teachers attending to students’ mathematical reasoning: Lessons from an after-school research program. Journal of Mathematics Teacher Education, 14(1), 49-66.
13. Hanushek, E.A., Peterson, P.E., & Woessman, L. (2012). Achievement growth: International and U.S. state trends in student performance. Program on Education Policy & Governance report No: 12-03. Cambridge, MA: Harvard Kennedy School.
14. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
15. Kramarski, B., & Zeichner, O. (2001). Using technology to enhance mathematical reasoning: Effects of feedback and self-regulation learning. Educational Media International, 38(2/3), 77-82.
16. Mevarech, Z.R. & Kramarski, B. (1997). IMPROVE: A multidimensional method for teaching mathematics in heterogeneous classrooms, American Educational Research Journal, 34, 365-394.
17. Miller, R.G. (1981). Simultaneous statistical inference. 2nd ed. (pp. 6-8), New York NY: Springer- Verlag.
18. National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.No Child Left Behind [NCLB] Act of 2001, Pub. L. No. 107- 110, 115, Stat. 1425 (2002).
19. National Council of Teachers of Mathematics. (2009). Guiding principles for mathematics curriculum and assessment. Retrieved on August 11, 2014 from http://www.nctm.org/standards/content.aspx?id=23273
20. National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors.
21. Organisation for Economic Co-operation and Development. (2013a). Lessons from PISA 2012 for the United States, Strong Performers and Successful Reformers in Education. Retrieved on September 9, 2014 from http://dx.doi.org/10.1787/9789264207585-en
22. Organisation for Economic Co-operation and Development. (2013). PISA 2012 Results: What Makes Schools Successful? Resources, Policies and Practices (Volume IV). Retrieved on September 10, 2014 from http://dx.doi.org/10.1787/9789264201156-en
23. O’Donnell, A.M. (2006). Introduction: Learning with technology. In A.M. O’Donnell, C.E. Hmelo- Silver, & G. Erkens (Eds.) Collaborative learning, reasoning, and technology (pp. 1-14), Mahwah, NJ: Lawrence Erlbaum Associates.
24. Reasoning [Def. 1]. (2014) Merriam Webster Online. Retrieved July 7, 2014, from http://www.merriam-webster.com/dictionary/reasoning
25. Renkl, A. (2002). Worked-out examples: Instructional explanations support learning by self- explanations. Learning and Instruction, 12, 529-556.
26. Rosenstein, J.G., Caldwell, J.H., & Crown, W.D. (1996). New Jersey Mathematics Curriculum Framework: A collaborative effort of the New Jersey Mathematics Coalition and the New Jersey Department of Education. New Brunswick, NJ: The New Jersey Mathematics Coalition, Rutgers, The State University of New Jersey.
27. Tran, Z. (2005). Help with English Language Proficiency “HELP” program evaluation of sheltered instruction multimedia lessons [White paper]. Retrieved from www.helpprogram.net
28. U.S. Department of Education, Office of Educational Technology. (2010). Transforming American Education: Learning Powered by Technology, Washington, D.C.: U.S. Department of Education.
29. Yian-Shu, C., Haw-Ching, Y., Shian-Shyong, T., & Che-Ching, Y. (2014). Implementation of a model- tracing-based learning diagnosis system to promote elementary students' learning in mathematics. Journal of Educational Technology & Society, 17(2), 347-357.
30. Correspondence: Kristina N. Higgins, Assistant Professor, Department of Curriculum and
31. Instruction, College of Education, Tarleton State University, Fort Worth, Texas, United States