a Multi-Institutional Study of the Relationship between High School Mathematics Achievement and Performance in Introductory COLLEGE Statistics

Danielle N. Dupuis

University of Minnesota

dupui004@umn.edu

Amanuel Medhanie

University of Minnesota

medha001@umn.edu

Michael Harwell

University of Minnesota

harwe001@umn.edu

brandon lebeau

University of Minnesota

lebea027@umn.edu

debra monson

University of Minnesota

stra0042@umn.edu

thomas r. post

University of Minnesota

postx001@umn.edu

ABSTRACT

In this study we examined the effects of prior mathematics achievement and completion of a commercially developed, National Science Foundation-funded, or University of Chicago School Mathematics Project high school mathematics curriculum on achievement in students' first college statistics course. Specifically, we examined the relationship between students' high school mathematics achievement and high school mathematics curriculum on the difficulty level of students' first college statistics course, and on the grade earned in that course. In general, students with greater prior mathematics achievement took more difficult statistics courses and earned higher grades in those courses. The high school mathematics curriculum a student completed was unrelated to statistics grades and course-taking.

Keywords: Statistics education research; Post-secondary education; Course-taking

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Statistics Education Research Journal, 11(1), 4-20, http://www.stat.auckland.ac.nz/serj

(c) International Association for Statistical Education (IASE/ISI), May, 2012

REFERENCES

ACT, Inc. (2009). ACT test prep. Iowa City, IA: ACT, Inc.

[Online: http://www.actstudent.org/testprep/descriptions/mathdescript.html ]

Baloglu, M., & Zelhart, P. F. (2003). Statistical anxiety: A detailed review of the literature. Psychology and Education: An Interdisciplinary Journal, 40, 27-37.

Boyer, E. (1983). High school: A report on secondary education in America. New York: Harper and Row.

Brown, R. G., Dolciani, M. P., Sorgenfrey, R. H., Cole, W. L., Campbell, C., & Macdonald Piper, J. (1997). Algebra: Structure and methods book one. New York: McDougal, Litell, and Company.

Carnegie Foundation. (2009a). Undergraduate instructional program classification. Stanford, CA: The Carnegie Foundation for the Advancement of Teaching.

[Online: http://classifications.carnegiefoundation.org/descriptions/ugrad_program.php ]

Carnegie Foundation. (2009b). Undergraduate profile classification. Stanford, CA: The Carnegie Foundation for the Advancement of Teaching.

[Online: http://classifications.carnegiefoundation.org/descriptions/undergraduate_profile.php ]

Cochran, W. G. (1977). Sampling techniques (3^rd ed.). New York: John Wiley & Sons.

College Board. (2010a). 2010 statistics score distribution. New York: Author.

[Online: http://www.collegeboard.com/student/testing/ap/statistics/dist.html?stats ]

College Board. (2010b). SAT practice. New York: Author.

[Online: http://sat.collegeboard.com/practice/sat-practice-questions-math/math-concepts ]

College Board. (2010c). The SAT preparation booklet. New York: Author.

Coxford, A. F., Fey, J. T., Hirsch, C. R., Schoen, H. L., Burrill, G., Hart, E. W., ... Ritsema, B. (1998). Contemporary mathematics in context: A unified approach. Chicago, IL: Everyday Learning Corporation.

Delucchi, M. (2007). Assessing the impact of group projects on examination performance in social statistics. Teaching in Higher Education, 12(4), 447-460.

Everson, M. (2005, August). Implementing the GAISE recommendations in an online statistics course. Paper presented at the Joint Statistics Meeting, Minneapolis, MN.

Fendel, D., Resek, D., Alper, L., & Fraser, S. (1998). Interactive mathematics program: Integrated high school mathematics, (Year 1-4). Berkeley, CA: Key Curriculum Press.

Foster, A. G., Gordon, B. W., Gell, J. M., Rath, J. N., & Winters, L. J. (1995). Merrill algebra 2 with trigonometry. New York: Glencoe.

Gal, I., & Garfield, J. (Eds.) (1997). The assessment challenge in statistics education. Amsterdam: IOS Press and the International Statistical Institute.

Garfield, J., & Ben-Zvi, D. (2009). Helping students develop statistical reasoning: Implementing a statistical reasoning learning environment. Teaching Statistics, 31(3), 72-77.

Garfield, J., & Gal, I. (1999). Teaching and assessing statistical reasoning. In L. Stiff (Ed.), Developing mathematical reasoning in grades K-12 (pp. 207-219). Reston, VA: National Council Teachers of Mathematics.

Garfunkel, S., Godbold, L., & Pollak, H. (1998). Mathematics: Modeling our world. Cincinnati, OH: South-Western Educational Publishing.

Green, J. J., Stone, C. C., Zegeye, A., & Charles, T. A. (2009). How much math do students need to succeed in business and economics statistics? An ordered probit analysis. Journal of Statistics Education, 17(3).

[Online: http://www.amstat.org/publications/jse/v17n3/green.html ]

Harwell, M. R., Post, T. R., Cutler, A., Maeda, Y., Anderson, E., Norman, K. W., & Medhanie, A. (2009). The preparation of students from National Science Foundation-funded and commercially developed high school mathematics curricula for their first university mathematics course. American Educational Research Journal, 46(1), 203-233.

Harwell, M. R., LeBeau, B., Post, T. R., Dupuis, D., & Medhanie, A. (2011). A multi-site study of the relationship between high school mathematics curricula and developmental mathematics course-taking and achievement in college (Unpublished manuscript).

Johnson, M., & Kuennen, E. (2006). Basic math skills and performance in an introductory statistics course. Journal of Statistics Education, 14(2).

[Online: http://ww.amstat.org/publications/jse/v14n2/johnson.html ]

Lutzer, D. J., Rodi, S. B., Kirkman, E. E., & Maxwell, J. W. (2007). Statistical abstract of undergraduate programs in the mathematical sciences in the United States: Fall 2005 CBMS survey. Providence, RI: American Mathematical Society.

Mathematical Sciences Education Board. (2004). On evaluating curricular effectiveness: Judging the quality of K-12 mathematics evaluations. Washington, DC: National

Academy Press.

Mulhern, G., & Wylie, J. (2005). Mathematical prerequisites for learning statistics in psychology: Assessing core skills of numeracy and mathematical reasoning among undergraduates. Psychology Learning and Teaching, 5(2), 119-132.

National Center for Education Statistics (2002). Schools and staffing survey (SASS), public school questionnaire, charter school questionnaire, and private school questionnaire, 1999-2000. Washington, DC: Author.

[Online: http://nces.ed.gov/pubsearch/pubsinfo.asp?pubid=2002313 ]

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.

National Research Council. (2004). On evaluating curricular effectiveness: Judging the quality of K-12 mathematics evaluations. Committee for a Review of the Evaluation Data on the Effectiveness of NSF-Supported and Commercially Generated Mathematics Curriculum Materials, Mathematical Sciences Education Board, Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: National Academies Press.

Perkins, D. V., & Saris, R. N. (2001). A "jigsaw classroom" technique for undergraduate statistics courses. Teaching of Psychology, 28(2), 111-113.

Post, T. R., Medhanie, A., Harwell, M. R., Norman, K., Dupuis, D., Muchlinkski, T., ... Monson, D. (2010). The impact of prior mathematics achievement on the relationship between high school mathematics curricula and post-secondary mathematics performance, course-taking, and persistence. Journal of Research in Mathematics Education, 41(3), 274-308.

The R Project for Statistical Computing (Version 2.12.2) [Computer software].

[Online: http://www.r-project.org/foundation/main.html ]

Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (2^nd ed.). Newbury Park, CA: Sage.

Raudenbush, S. W., Spybrook, J., Congdon, R., Liu, X., & Martinez, A. (2009). Optimal Design Software for Multi-level and Longitudinal Research (Version 2.0) [Computer software].

[Online: http://www.wtgrantfoundation.org ]

Schoen, H. L., & Hirsch, C. R. (2003). The Core-Plus mathematics project: Perspectives and student achievement. In S. L. Senk & D. R. Thompson (Eds.), Standards-based school mathematics curricula: What are they? What do students learn? (pp. 311-343). Mahwah, NJ: Lawrence Erlbaum Associates.

Schram, C. M. (1996). A meta-analysis of gender differences in applied statistics achievement. Journal of Educational and Behavioral Statistics, 21(1), 55-70.

Shadish, W. R., Cook, T. D., & Campbell, D. T. (2002). Experimental & quasi-experimental designs for generalized causal inference (2^nd ed). New York: Houghton Mifflin.

Sidak, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions. Journal of the American Statistical Association, 62, 626-633.

Spybrook, J., Raudenbush, S. W., Congdon, R., & Martinez, A. (2009). Optimal Design for Longitudinal and Multilevel Research: Documentation for the Optimal Design Software (Version 2.0) [Computer software].

Usiskin, Z. (1986). The UCSMP: Translating grades 7-12 mathematics recommendations into reality. Educational Leadership, 44(4), 30-35.

Zieffler, A., Garfield, J., delMas, R., & Reading, C. (2008). A framework to support research on inferential reasoning. Statistics Education Research Journal, 7(2), 40-58.

[Online: http://www.stat.auckland.ac.nz/~iase/serj/SERJ7%282%29_Zieffler.pdf ]

danielle n. dupuis

56 East River Road

Minneapolis, MN 55455