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

**__________________________**

*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