Abstract
Through the lenses of statistical investigations and cognitive demands, we examined bivariate data tasks offered in US high school mathematics textbook series—a popular representative of three curriculum types: traditional, integrated, and hybrid. We developed a framework grounded in literature of association topics for the inclusion and exclusion of tasks. Using the Guidelines for Assessment and Instruction of Statistics Education (GAISE) framework, textbook tasks were coded for four investigation components (formulate questions, collect data, analyze data, and interpret results) and levels of statistical sophistication, as well as levels of cognitive demand as suggested by the Mathematical Complexity framework. Across the three series 582 statistical association tasks, all components of statistical investigation were evident with different levels of treatment: (a) all questions for statistical investigations were provided by textbook authors; (b) tasks rarely afforded student opportunities to collect data; and (c) nearly all of the tasks required students to analyze data and most required them to interpret results. Tasks in the integrated series were more numerous (n = 246) and required higher levels of mathematical complexity and statistical sophistication than tasks in the traditional and hybrid series. The vast majority of tasks were coded at the GAISE Level B for analyze data and interpret results and moderate level for mathematical complexity. Further analyses show the concordance between the developmental levels for statistical sophistication and mathematical complexity. Suggestions for curriculum development, content analysis, and future research are provided.
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Arnold, P. (2008, July). What about the P in the PPDAC cycle? An initial look at posing questions for statistical investigation. Paper presented at 11th International Congress of Mathematics Education, Monterrey, Mexico. Retrieved from http://tsg.icme11.org/tsg/show/15.
Bakker, A., & Derry, J. (2011). Lessons from inferentialism for statistics education. Mathematical Thinking and Learning, 13(1–2), 5–26.
Batanero, C., Burrill, G., & Reading, C. (2011). Preface. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics-challenges for teaching and teacher education (pp. ix–xvi). New York, NY: Springer.
Bowen, G. A. (2009). Document analysis as a qualitative research method. Qualitative Research Journal, 9(2), 27–40.
Brown, L. (2001). Making the most of your textbook. In L. Haggarty (Ed.), Aspects of teaching secondary mathematics (pp. 228–247). London, United Kingdom: Routledge-Falmer.
Brown, S. A., Breunlin, R. J., Wiltjer, M. H., Degner, K. M., Eddins, S. K., Edwards, M. T., et al. (2008). The University of Chicago School Mathematics Project: Algebra—Teacher’s edition (3rd ed.). Chicago, IL: McGrawHill - Wright Group.
Burrill, G., & Biehler, R. (2011). Fundamental statistical ideas in the school curriculum and in training teachers. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics-challenges for teaching and teacher education (pp. 57–69). New York, NY: Springer.
Charalambous, C. Y., Delaney, S., Hsu, H.-Y., & Mesa, V. (2010). A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. Mathematical Thinking and Learning, 12(2), 117–151. https://doi.org/10.1080/10986060903460070.
Common Core State Standards Initiative. (2010). Common core state standards for mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.
Connor, D. (2002). CensusAtSchool 2000: Creation to collation to classroom. In B. Phillips (Ed.), Proceedings of sixth international conference on teaching of statistics. Cape Town, South Africa: International Statistical Institute and International Association for Statistical Education. Retrieved from www.stat.auckland.ac.nz/~iase/publications.
Crocker, J. (1981). Judgment of covariation by social perceivers. Psychological Bulletin, 90(2), 272–292. https://doi.org/10.1037/0033-2909.90.2.272.
Cuoco, A., Goldenberg, E. P., & Mark, J. (2010). Organizing a curriculum around mathematical habits of mind. Mathematics Teacher, 103(9), 682–688.
delMas, R. C. (2004). A comparison of mathematical and statistical reasoning. In B.-Z. Dani & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 79–95). Dordrecht, The Netherlands: Springer.
Dossey, J. A., Halvorsen, K., & McCrone, S. (2012). Mathematics education in the United States 2012: A capsule summary fact book. Reston, VA: National Council of Teachers of Mathematics.
England Department of Education (2014). The national curriculum in England: Key stages 3 and 4 framework document. Retrieved from https://www.gov.uk/government/publications.
Fan, L. (2013). Textbook research as scientific research: Towards a common ground on issues and methods of research on mathematics textbooks. ZDM, 45(5), 765–777. https://doi.org/10.1007/s11858-013-0530-6.
Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007). Guidelines and assessment for instruction in statistics education (GAISE) report: A pre-K-12 curriculum framework. Alexandria, VA: American Statistical Association.
Gattuso, L., & Ottaviani, M. G. (2011). Complementing mathematical thinking and statistical thinking in school mathematics. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics-challenges for teaching and teacher education (pp. 121–132). New York, NY: Springer.
Goodman, L. A., & Kruskal, W. H. (1954). Measures of association for cross classifications. Journal of the American Statistical Association, 49(268), 732–764. https://doi.org/10.2307/2281536.
Hall, J. (2011). Engaging teachers and students with real data: Benefits and challenges. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics—challenges for teaching and teacher education (pp. 335–346). New York, NY: Springer.
Heaton, R. M., & Mickelson, W. T. (2002). The learning and teaching of statistical investigation in teaching and teacher education. Journal of Mathematics Teacher Education, 5(1), 35–59.
Hirsch, C. R., Fey, J. T., Hart, E. W., Schoen, H. L., Watkins, A. E., Ritsema, B. E., et al. (2008). Core-Plus mathematics: Contemporary mathematics in context, course 1 (2nd ed.). New York, NY: McGraw Hill Glencoe.
Hong, D. S., & Choi, K. M. (2014). A comparison of Korean and American secondary school textbooks: The case of quadratic equations. Educational Studies in Mathematics, 85(2), 241–263.
House, P. A. (2003). Integrated mathematics: An introduction. In S. A. McGraw (Ed.), Integrated mathematics: Choices and challenges (pp. 3–11). Reston, VA: National Council of Teachers of Mathematics.
Jones, D. L., & Tarr, J. E. (2007). An examination of the levels of cognitive demand required by probability tasks in middle grades mathematics textbooks. Statistics Education Research Journal, 6(2), 4–27.
Larson, R., Boswell, L., Kanold, T. D., & Stiff, L. (2012). Hotl McDougal Larson algebra 1—teacher’s edition. Orlando, FL: Holt McDougal - Houghton Mifflin Harcourt.
MacGillivray, H., & Pereira-Mendoza, L. (2011). Teaching statistical thinking through investigative projects. In C. Batanero, G. Burrill, & C. Reading (Eds.), Teaching statistics in school mathematics-challenges for teaching and teacher education (pp. 109–120). New York, NY: Springer.
Mattis, K. V. (2015). Flipped classroom versus traditional textbook instruction: Assessing accuracy and mental effort at different levels of mathematical complexity. Technology, Knowledge and Learning, 20(2), 231–248.
McConnell, J. W., Brown, S. A., Karafiol, P. J., Brouwer, S., Ives, M., Lassak, M., et al. (2010). The University of Chicago School Mathematics Project: Functions, statistics, and trigonometry—teacher’s edition (3rd ed.). Chicago, IL: McGrawHill - Wright Group.
McGraw Hill Education (2015). Mcgraw Hill Education mathematics programs. Retrieved March 1, 2015, from https://www.mheonline.com/discipline/narrow/2/16/169/.
Moore, D. S. (1990). Uncertainty. In L. Steen (Ed.), On the shoulders of giants: A new approach to numeracy (pp. 95–137). Washington, DC: National Academy of Sciences.
Moritz, J. B. (2004). Reasoning about covariation. In D. Ben-Zvi & J. Garfield (Eds.), The challenge of developing statistical literacy, reasoning and thinking (pp. 227–256). Dordrecht, The Netherlands: Springer.
National Assessment Governing Board. (2013). Mathematics framework for the 2013 National Assessment of educational progress. Washington, DC: The National Academies Press.
Paas, F., & van Merrienboër, J. J. (1994). Variability of worked examples and transfer of geometrical problem-solving skills: A cognitive load approach. Journal of Educational Psychology, 86, 122–133.
Remillard, J. T., & Bryans, M. B. (2004). Teachers’ orientations toward mathematics curriculum materials: Implications for teacher learning. Journal for Research in Mathematics Education, 35(2), 352–388.
Schmidt, W., McKnight, C., Valverde, G., Houang, R., & Wiley, D. (2007). Many visions, many aims: A cross-national investigation of curricular intentions in school mathematics. Norwell, MA: Kluwer.
Shaughnessy, J. M. (2007). Research on statistics learning and reasoning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 957–1009). Charlotte, NC: Information Age Publishing.
Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50–80.
Stein, M. K., Remillard, J., & Smith, M. S. (2007). How curriculum influences student learning. In F. K. J. Lester (Ed.), Second handbook of research on mathematics teaching and learning (Vol. 1, pp. 319–369). Charlotte, NC: Information Age Publishing.
Sweller, J. (1994). Cognitive load theory, learning difficulty, and instructional design. Learning and Instruction, 4, 295–312.
Tran, D. (2013). Learning trajectories related to bivariate data in contemporary high school mathematics textbook series in the United States (Doctoral dissertation). University of Missouri, Columbia. Retrieved from https://mospace.umsystem.edu/xmlui/handle/10355/44043.
Tran, D. (2016). Statistical Association: Alignment of current U.S. high school textbooks with the Common Core State Standards for Mathematics. School Science and Mathematics , 116(5), 286–296.
Usiskin, Z. (2003). The integration of the school mathematics curriculum in the United States: History and meaning. In S. A. McGraw (Ed.), Integrated mathematics: Choices and challenges (pp. 13–31). Reston, VA: NCTM.
Valverde, G. A., Bianchi, L. J., Wolfe, R. G., Schmidt, W. H., & Houang, R. T. (2002). According to the book: Using TIMSS to investigate the translation of policy into practice through the world of textbooks. Boston, MA: Kluwer Academic Publishers.
Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–248. https://doi.org/10.2307/1403699.
Zieffler, A., & Garfield, J. (2009). Modeling the growth of students’ covariational reasoning during an introductory statistics course. Statistics Education Research Journal, 8(1), 7–31.
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Tran, D., Tarr, J.E. Examination of Bivariate Data Tasks in US High School Textbooks Through the Statistical Investigation and Cognitive Demands Frameworks. Int J of Sci and Math Educ 16, 1581–1603 (2018). https://doi.org/10.1007/s10763-017-9851-1
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DOI: https://doi.org/10.1007/s10763-017-9851-1