International Electronic Journal of Mathematics Education

Comparing Extracted and Stipulated Definitions in Algebra 1 Textbooks and Khan Academy
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Bayda NI, Sutliff G. Comparing Extracted and Stipulated Definitions in Algebra 1 Textbooks and Khan Academy. INT ELECT J MATH ED. 2020;15(2), em0579. https://doi.org/10.29333/iejme/7601
APA 6th edition
In-text citation: (Bayda & Sutliff, 2020)
Reference: Bayda, N. I., & Sutliff, G. (2020). Comparing Extracted and Stipulated Definitions in Algebra 1 Textbooks and Khan Academy. International Electronic Journal of Mathematics Education, 15(2), em0579. https://doi.org/10.29333/iejme/7601
Chicago
In-text citation: (Bayda and Sutliff, 2020)
Reference: Bayda, Nicholas Ivan, and Grant Sutliff. "Comparing Extracted and Stipulated Definitions in Algebra 1 Textbooks and Khan Academy". International Electronic Journal of Mathematics Education 2020 15 no. 2 (2020): em0579. https://doi.org/10.29333/iejme/7601
Harvard
In-text citation: (Bayda and Sutliff, 2020)
Reference: Bayda, N. I., and Sutliff, G. (2020). Comparing Extracted and Stipulated Definitions in Algebra 1 Textbooks and Khan Academy. International Electronic Journal of Mathematics Education, 15(2), em0579. https://doi.org/10.29333/iejme/7601
MLA
In-text citation: (Bayda and Sutliff, 2020)
Reference: Bayda, Nicholas Ivan et al. "Comparing Extracted and Stipulated Definitions in Algebra 1 Textbooks and Khan Academy". International Electronic Journal of Mathematics Education, vol. 15, no. 2, 2020, em0579. https://doi.org/10.29333/iejme/7601
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Bayda NI, Sutliff G. Comparing Extracted and Stipulated Definitions in Algebra 1 Textbooks and Khan Academy. INT ELECT J MATH ED. 2020;15(2):em0579. https://doi.org/10.29333/iejme/7601

Abstract

Previous research has established the importance of definitions in mathematics and have distinguished the difference between extracted and stipulated definitions. Much remains unknown, however, about the role definitions serve in developing students’ disciplinary literacy. In this study, we analyze how definitions from four US Algebra 1 textbooks and Khan Academy define vocabulary in the context of quadratics. Results show that Khan Academy tends to use extracted definitions, where textbooks tend to use stipulated definitions. Implications from this study are that there is a need to teach students both stipulated and extracted definitions.

References

  • Alkhateeb, M. (2018). Multiple Representations in 8th Grade Mathematics Textbook and the Extent to which Teachers Implement Them. International Electronic Journal of Mathematics Education, 14(1), 137-145. https://doi.org/10.12973/iejme/3982
  • Bruun, F., Diaz, J. M., & Dykes, V. J. (2015). The language of mathematics. Teaching Children Mathematics, 21(9), 530-536. https://doi.org/10.5951/teacchilmath.21.9.0530
  • Buehl, D. (2017). Developing readers in the academic disciplines. Stenhouse Publishers.
  • Charles, R. I. (2013). Algebra 1: Common Core (New ed.). Boston, MA: Pearson Education.
  • Common Core State Standards Initiative. (2010). Standards for Mathematical PracticeRetrieved from http://www.corestandards.org/Math/Practice/
  • Dietiker, L., Baldinger, E., & Kassarjian, M. (2013). Core Connections: Algebra (13th ed.). Sacramento, CA: CPM Educational Program.
  • Dreher, A., & Kuntze, S. (2015). Teachers’ professional knowledge and noticing: The case of multiple representations in the mathematics classroom. Educational Studies in Mathematics, 88(1), 89-114. https://doi.org/10.1007/s10649-014-9577-8
  • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational studies in mathematics, 61(1-2), 103-131. https://doi.org/10.1007/s10649-006-0400-z
  • Edwards, B. S., & Ward, M. B. (2004). Surprises from mathematics education research: Student (mis) use of mathematical definitions. The American Mathematical Monthly, 111(5), 411-424. https://doi.org/10.2307/4145268
  • Edwards, B., & Ward, M. (2001). The role of mathematical definitions in mathematics and in undergraduate mathematics courses. In M. Carlson & C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics (pp. 221–230). Washington, DC: Mathematical Association of America.
  • Eraslan, A. (2008). The notion of reducing abstraction in quadratic functions. International Journal of Mathematical Education in Science and Technology, 39(8), 1051-1060. https://doi.org/10.1080/00207390802136594
  • Fang, Z., & Schleppegrell, M. J. (2010). Disciplinary literacies across content areas: Supporting secondary reading through functional language analysis. Journal of Adolescent and Adult Literacy, 53(7), 587-597. https://doi.org/10.1598/JAAL.53.7.6
  • High School: Functions » Interpreting Functions. (n.d.). Retrieved from http://www.corestandards.org/Math/Content/HSF/IF/
  • Hillman, A. M. (2014). A literature review on disciplinary literacy. Journal of Adolescent & Adult Literacy, 57(5), 397-406. https://doi.org/10.1002/jaal.256
  • Hoon, T. S., Singh, P., & Halim, U. K. A. (2018). Understanding of Function and Quadratic Function among Secondary School Students in Selangor. Asian Journal of University Education, 14(1), 77-88.
  • Kaiser, G., & Willander, T. (2005). Development of mathematical literacy: Results of an empirical study. Teaching mathematics and its applications, 24(2-3), 48-60. https://doi.org/10.1093/teamat/hri016
  • Khan Academy. (2017). 2017 Annual Report. Retrieved from https://khanacademyannualreport.org/
  • [Khan Academy]. (2017a, April 3). Solving equations with zero product property [Video File]. Retrieved from https://www.youtube.com/watch?v=-lWVpoPaPBc&t=11s
  • [Khan Academy]. (2017b, April 3). Visual introduction to parabolas [Video File]. Retrieved from https://www.youtube.com/watch?v=BGz3pkoGPag
  • Kotsopoulos, D. (2007). Unraveling student challenges with quadratics: A cognitive approach. Australian Mathematics Teacher, 63(2), 19-24.
  • Landau, S. (2001). Dictionaries: The art and craft of lexicography (2nd ed.). Cambridge: Cambridge University Press.
  • Larson, R., & Boswell, L. (2015). Algebra 1: A Common Core Curriculum (Student ed.). Erie, Pennsylvania: Big Ideas Learning.
  • Mosvold, R., & Fauskanger, J. (2013). Teachers’ beliefs about mathematical knowledge for teaching definitions. International Electronic Journal of Mathematics Education, 8(2-3), 43-61.
  • NCTM (National Council of Teachers of Mathematics) (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM.
  • Ohio Department of Education. (2018). Ohio’s Learning Standards Mathematics Algebra 1. Retrieved from http://education.ohio.gov/getattachment/Topics/Learning-in-Ohio/Mathematics/Ohio-s-Learning-Standards-in-Mathematics/ALGEBRA-1-Standards.pdf.aspx?lang=en-US
  • Robinson, R. (1962). Definitions. London: Oxford University Press.
  • Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading and Writing Quarterly, 23(2), 139-159. https://doi.org/10.1080/10573560601158461
  • Shanahan, T., & Shanahan, C. (2008). Teaching disciplinary literacy to adolescents: Rethinking content area literacy. Harvard Educational Review, 78(1), 40-59. https://doi.org/10.17763/haer.78.1.v62444321p602101
  • Son, J. W., & Diletti, J. (2017). What Can We Learn from Textbook Analysis?. In What Matters? Research Trends in International Comparative Studies in Mathematics Education (pp. 3-32). Springer, Cham. https://doi.org/10.1007/978-3-319-51187-0_1
  • SpringBoard Algebra I. (2014). New York: CollegeBoard.
  • Thompson, C. (2011). How Khan Academy is changing the rules of education. Wired Magazine, 126, 1-5.
  • Vinner, S. (1991). The Role of Definitions in the Teaching and Learning of Mathematics (vol. 11). Netherlands: Advanced Mathematical Thinking.
  • Zaslavsky, O. (1997). Conceptual obstacles in the learning of quadratic functions. Focus on Learning Problems in Mathematics, 19(1), 20-44.

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.