How Students Communicate Mathematical Ideas: An Examination of Multimodal Writing Using Digital Technologies

Abstract

This article reports the findings of a study designed to examine the influence of multimodal writing on the communication of mathematical ideas. Elementary school students (ages 8-13) were required to write mathematics notes using two digital writing technologies, a personal digital notepad and a social mathematics blog, in the context of a formal intervention. Fortytwo students participated, across three schools. The study showed that when students wrote notes that could be assessed for correctness, their answers were predominately right, indicating that mathematical sense-making was taking place. It also showed that the digital notepad and blog were used differently and that the type of technology influences the writing content. Moreover, students’ mathematical writing were understandable by their peers and students collaboratively explored solutions. Younger students were more likely to draw pictures to represent their ideas than older students. These findings show that writing can help students acquire mathematical understanding, and suggest that multimodal writing may help them surmount difficulties often associated with learning math. Although this research demonstrated that writing can help teachers gain an awareness of their students’ mathematical understanding, it also revealed that writing environments need to be monitored and students require close guidance to bring about systematic improvement.

Keywords

• mathematics education,instructional technology,elemantary education,digital writing tools,blogging

Kaynakça

1. Ash, R. (n.d.). Remarks on expository writing in math. Retrieved on 28 September 2016 from http://www.math.uiuc.edu/~r-ash/Remarks.pdf.
2. Ashlock, B. (2006). Error patterns in computation: Using error patterns to improve instruction. Upper Saddle River, NJ: Prentice Hall.
3. Bagley, T. & Gallenberger, C. (1992). Assessing students’ dispositions: Using journal to improve students’ performance. Mathematics Teacher, 85, 660-663.
4. Ball, D. (1994, November). Developing mathematics reform: What don’t we know about teacher learning-but would make good working hypothesis? Paper presented at the Conference on Teacher Enhancement K-6, Arlington, VA.
5. Baxter, J., Woodward, J., and Olson, D. (2005). Writing in mathematics: An alternative form of communication for academically low-achieving students. Learning Disabilities Research & Practice, 20(2), 119–135.
6. Bicer, A., Capraro, R., & Capraro, M. (2013). Integrating writing into mathematics classrooms to increase students' problem solving skills. International Online Journal of Educational Sciences, 5(2), 361-369.
7. Bruner, J. S. (1968). Toward a theory of instruction. New York: W.W. Norton.
8. Burns, M. (2004). Writing in math. Educational Leadership, 62(2), 30-33.

9. Burns, M. (1995). Writing in math class: A resource for grades 2-8. Sausalito, CA: Math Solutions.
10. Chegg, Incorporated. (2016). Chegg. Retrieved on 1 October 2016 from http://www.chegg.com/
11. Cummins, J. (1979). Cognitive/academic language proficiency, linguistic interdependence, the optimum age question and some other matters. Working Papers onBilingualism, 19, 121- 129. Retrieved on 1 October 2016 fromhttp://www.iteachilearn.com/cummins/ bicscalp.html
12. Devlin, K. (2012). Introduction to mathematical thinking. Palo Alto, CA: Keith Devlin.
13. Dewey, J. (1997). Experience and education. New York: Simon and Schuster.
14. Digital Directions International (2005). HELP Math. Retrieved on 1 October 2016 from http://www.helpprogram.net/home.htm
15. Dill, K., Freeman, B., Frazier, S., & Benito, J. (2015, Dec.). Mars Game: Creating and evaluating an engaging educational game. Interservice/Industry Training, Simulation, and Education Conference (I/ITSEC) 2015. Location 2015 Paper No. 15105. 311
16. Emig, J. (1977). Writing as a mode of learning. College Composition and Communication, 28, 122- 28.
17. Flower, L., Schriver, K., Carey, L., Haas, C. & Hayes, J. (1992). Planning in writing: The cognition of a constructive process. Technical Report 34, Center for the Study of Writing, Carnegie Mellon University, Berkeley, CA &, Pittsburg, BA.
18. Freeman, B. (2013, February 15). Fluent in math. Ed Tech Digest. Retrieved on 1 October 2016 from http://edtechdigest.wordpress.com/2013/02/15/fluent-in-math/
19. Freeman, B. (2012). Using digital technologies to redress inequities for English Language Learners in the English speaking mathematics classroom. Computers & Education, 59(1), 50-62. doi: 10.1016/j.compedu.2011.11.003
20. Gadanidis, G., Hughes, J., & Cordy, M. (2011). Mathematics for gifted students in an arts-and technology-rich setting. Journal for the Education of the Gifted, 34(3), 397-433.
21. Gibson, S.A. (2008, December). An effective framework for primary-grade guided writing instruction. The Reading Teacher, 62(4), 324–334.
22. Gould, P (2013). Teaching mathematical reasoning: The challenge of the new syllabus. Retrieved on 1 October 2016 from https://eis.uow.edu.au/content/groups/public/@web/@inf/ @math/documents/doc/uow152422.pdf
23. Gould, P (2008, August). Communicating mathematical reasoning: More than just talking. Paper presented at APEC-KHON KAEN International Symposium, KhonKaen, Thailand.
24. Haas, C. (2013). Writing technology: Studies on the materiality of literacy. New York, NY: Routledge.
25. Havelock, E. A. (1986). The muse learns to write. New Haven, CT: Yale University Press.
26. Hayes, J. R. (1996). A new framework for understanding cognition and affect in writing. In C. M. Levy & S. Ransdell (Eds.), The science of writing: Theories, methods, individual differences, and applications (pp. 1-27). Mahwah, NJ: Erlbaum.
27. Hayes, J. R. (1996). A new framework for understanding cognition and affect in writing. In C. Hsu, W. (2013). Examining the types of mathematical tasks used to explore the mathematics instruction by elementary school teachers. Creative Education, 4(6), 396-404.
28. Huscroft-D’Angelo, J., Higgins, K., & Crawford, L. (2016). Technology, affective characteristics and mathematics: A review of the literature from 1985-2013. Manuscript submitted for publication.
29. Huscroft-D’Angelo, J., Higgins, K., & Crawford, L. (2015). Communicating mathematical ideas in a digital writing environment: The impacts on mathematical reasoning for students with and without learning disabilities. Social Welfare, 4(2), 68-84.
30. Kenney, J. M., Hancewicz, E., Heuer, L., Metsisto, D., & Tutttle, C. L. (2005). Literacy strategies for improving mathematics instruction. Alexandria, VA: ASCD.
31. Krashen, S. D. (1987). Principles and practice in second language acquisition. Upper Saddle River, NJ: Prentice-Hall International. 312
32. Lee, K. (2010). A guide to writing mathematics. Retrieved on 1 October 2016 from http://web.cs. ucdavis.edu/~amenta/w10/writingman.pdf.
33. Li, Q. & Ma, X. (2010). A meta-analysis of the effects of computer technology on school students’ mathematics learning. Educational Psychology Review, 22, 215-243. doi 10.1007/s10648- 010-9125-8
34. Math Learning Companion (2016). Retrieved on 1 October 2016 from http://ansersinstitute.tcu. edu/project/math-learning-companion/
35. Mathematics eText Resaerch Center. (2012). Center for Advanced Technology in Education. University of Oregon. Retrieved on 1 October 2016 from http://metrc.uoregon.edu/
36. Meel, D. (1999). Email dialogue journals in a college calculus classroom: A look at the implementation and benefits. Journal of Computers in Mathematics and Science Teaching, 18(4), 387-413.
37. Ong, W.J. (1982). Orality and literacy: The technologizing of the word. Routledge. New York: New York.
38. Oregon Department of Education (2012). Overview of Claims and Evidence for CCSS Mathematics Assessment. Retrieved on 4 November 2014 from http://www.ode.state.or.us/search/page/ ?id=3618
39. Powell, A.B., & Lopez, J.A. (1989). Writing as a vehicle to learn mathematics: A case study. In P. Connolly & T. Vilardi (Eds.), Writing to learn mathematics and science (pp. 157-177). New York: Teachers College Press.
40. Pugalee, D. (2004). A comparison of verbal and written descriptions of students’ problem-solving processes. Educational Studies in Mathematics, 55, 27-47.
41. Purcell, K., Buchanan, J., & Friedrich, L. (2013, July). The impact of digital tools on student writing and how writing is taught in schools. Retrieved on 1 October 2016 from http://www.nwp. org/afnews/PIP_NWP_Writing_and_Tech.pdf
42. Robertson, K. & Ford, K. (2009). Retrieved on 1 October 2016 from http://www.colorincolorado. org/article/language-acquisition-overview
43. Scardamalia, M., & Bereiter, C. (1994). Computer support for knowledge-building communities. The journal of the learning sciences, 3(3), 265-283.
44. Schleppegrell, M. J. (2010). Language in mathematics teaching and learning: A research review. In J. Moschkovich (Ed.), Language and mathematics education: Multiple perspectives and directions for research (pp. 73-112). Charlotte, NC: Information Age.
45. Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading and Writing Quarterly, 23, 139-159.
46. Slavin, R. & Lake, C. (2008). Effective programs in elementary mathematics: A best-evidence synthesis. Review of Educational Research, 78, 427-515.
47. Slavin, R. E., Lake, C., & Groff, C. (2009). Effective programs in middle and high school mathematics: A best-evidence synthesis. Review of Educational Research, 79(2), 839-911. 313
48. Sylvan Learning (2016). Sylvan Learning. Retrieved on 1 October 2016 from http://www. sylvanlearning.com/
49. Tran, Z. (2005). Help with English Language Proficiency “HELP” program evaluation of sheltered instruction multimedia lessons [White paper]. Retrieved on 1 October 2016 from http://www.helpprogram.net/home.htm
50. Tutor.com, Incorporated (2016). Retrieved on 1 October 2016 from http://www.tutor.com/
51. Urquhart, V. (2009). Using writing in mathematics to deepen student learning. Denver, CO: Midcontinent Research for Education and Learning. Retrieved on 1 October 2016 from http://www.mcrel.org/products-and-services/products/product-listing/01_99/product- 19#sthash.qy8kOKiw.dpuf
52. US National Council of Teachers of Mathematics (2014). Principles to actions: Ensuring mathematics success for all. Reston, VA: The National Council of Teachers of Mathematics, Inc.
53. US National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Authors.
54. US National Institute for Literacy (2007). What content-area teachers should know about adolescent literacy. Washington DC: Author.
55. Vygotsky, L. (1981). The instrumental method in psychology. In J. V. Wertsch (Ed.), The concept of activity in Soviet psychology (pp. 134-143). Armonk, NY: M. E. Sharpe.
56. Vygotsky, L. (1986). Thought and language (Revised edition). Cambridge, MA: MIT Press. Wiliam, D. (2011). Embedded formative assessment. Bloomington, IN: Solution Tree.
57. Zemelman, S., Daniels, H., & Hyde, A. (2012). Best practice: Today's standards for teaching and learning in America's schools. Portsmouth, NH: Heinemann.