Facing Choices about Fourth-Year Mathematics in Arizona
Institute for Mathematics and Education Policy Retreat
University of Arizona, Tucson
18 October 2008
Materials for Fourth-Year Mathematics
Mathematics and Statistics for Informed Citizenship and Decision Making
Gregory D. Foley
Michael Mays
Michael Schmidt
Pamela Walker
There are existing resources that are related to the emerging vision for fourth-year mathematics
for all students. The University of Chicago School Mathematics Project’s two post-Algebra II
courses (Senk et al., 1998; Peressini et al., 1998) include statistics, modeling, and discrete
mathematics with precalculus topics; AQR will blend statistics, mathematical modeling, and
discrete mathematics into a single 1-year course aimed at quantitative literacy. Four of the NSF
91-100 high school curriculum projects developed 4th-year courses (Coxford et al., 2003; Fendel
et al., 2007; Garfunkel et al., 1998; Souhrada & Fong, 2006). In keeping with the 1989 NCTM
Standards, these courses were designed for college-intending students. Although there will be a
significant overlap in topics with these 4th-year courses, the AQR course will address a broader
intended student audience and will incorporate the recommendations of the Achieve (2007),
ASA (Franklin et al., 2007), and NCTM (2006) as well as other recent foundational work.
Many existing college textbooks, including several that were developed with NSF support
(e.g., Andersen & Swanson, 2005; COMAP, 2006; Sevilla & Somers, 2007), directly address
quantitative literacy, but each would need to be adapted to the broader and younger high school
student audience and to the 180-day high school instructional calendar.
Course Goals
Any 4th-year course should be designed to—
 use previous mathematics in the service of new ideas;1
 develop the student’s quantitative literacy for effective citizenship and workplace readiness;
 develop the student’s ability to solve mathematical and statistical problems, to communicate
their methods and results using precise language supported by the appropriate use of tables,
graphs, and other representations, and to use technology in their investigations and reports;
 prepare the student for postsecondary course work; and
 for high school juniors who completed Algebra I or Integrated Mathematics I in the 8th
grade, student readiness for AP Computer Sciences, AP Statistics, or Precalculus in their
senior year of high school.2
What materials need to be developed?
1
AQR will reinforce, build on, solidify, apply, and extend the student’s working knowledge of Algebra I,
Geometry, and Algebra II, or Integrated High School Mathematics I, II, and III.
2
Some students may elect to co-enroll in AQR and AP Computer Sciences, AP Statistics, or Precalculus.
1
Materials for fourth year mathematics
Page 2
We make some general observations about materials, which can then be refined and informed
based on further discussions from the Focus group. Any particular implementation must strike a
balance between the specialization into the different 4th years courses and a generalization of
meeting the 4th yr standards. Regardless of what course sequencing is decided, the materials must
meet the goals of the proposed fourth year course.
Rather than writing all materials from scratch, it makes more sense to adapt existing materials.
In particular, NSF funded projects have been written with year 4 mathematics courses building
on an integrated treatment of the first three years. Subsets of these materials cast on a framework
of an Algebra 1, Algebra 2, Geometry set of prerequisites would be make appropriate texts for
several of the models being considered. Other products that might be of use could be adapted
from CTE course and products.
How do we coordinate these and make the products available?
A national effort to provide a paradigm course has the best chance to avoid fragmentation of the
approach state by state. Achieve can be the synthesizer of those goals and can coordinate or
identify the core material list (state and national level) application of selected materials.
Material development should not wait on Achieve being embraced by all 51 states.
Annotated Bibliography of Existing Resources
Andersen, J., & Swanson, T. (2005). Understanding our quantitative world. Washington, DC:
Mathematical Association of America. [NSF-supported college textbook]
Barnett, S. (1998). Discrete mathematics: Numbers and beyond. Harlow, England, UK: Addison Wesley
Longman. [British text that blends discrete mathematics with elementary number theory]
Blocksma, M. (2002). Necessary numbers: An everyday guide to sizes, measures, and more. San Diego,
CA: Portable Press. [source for enrichment related to quantitative literacy]
Consortium for Foundation Mathematics. (2008). Mathematical models with applications [Texas
edition]. Boston: Pearson Addison-Wesley. [text for Texas’s course in Mathematical Modeling with
Applications]
Consortium for Mathematics and Its Applications (COMAP). (2003). For all practical purposes:
Mathematical literacy in today’s world (6th ed.). New York: W. H. Freeman. [encyclopedic college
textbook]
Coxford, A. F., Fey, J. T., Hirsch, C. R., Schoen, H. L., Burrill, G., Hart, E. W., et al. (2003).
Contemporary mathematics in context: A unified approach, Course 4 [Core-Plus Mathematics
Project] (2nd ed.). New York: Glencoe/MacGraw-Hill. [NSF-supported 4th-year high school
textbook]
Crisler, N., Fisher, P., & Froelich, G. (2000). Discrete mathematics through applications (2nd ed.).
New York: W. H. Freeman. [Standards-based high school textbook]
Fendel, D., Resek, D., Alper L., & Fraser, S. (2007). Interactive mathematics program: Integrated high
school mathematics, Year 4 (2nd ed.). Emeryville, CA: Key Curriculum Press. [NSF-supported 4thyear high school textbook]
Materials for fourth year mathematics
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Franklin, C., Kader, G., Mewborn, D., Moreno, J., Peck, R., Perry, M., & Scheaffer, R. (2007).
Guidelines for assessment and instruction in statistics education (GAISE) report: A pre-K–12
curriculum framework. Alexandria, VA: American Statistical Association. [essential resource]
Garfunkel, S., Godbold, L., & Pollak, H. (1998). Mathematics: Modeling our world—ARISE Course 4.
Cincinnati, OH: South-Western Educational. [NSF-supported 4th-year high school textbook]
Moore, D. S., & McCabe, G. P. (2006). Introduction to the practice of statistics (5th ed.). New York:
W. H. Freeman. [now in 6th edition, a source for a non-AP high school statistics textbook]
Senk, S. L., et al. (1998). Functions, statistics, and trigonometry (2nd ed.) [University of Chicago
School Mathematics Project]. Glenview, IL: Scott Foresman Addison Wesley. [a post-Algebra II
alternative to Precalculus]
Sevilla, A., & Somers, K. (2007). Quantitative reasoning: Tools for today’s informed citizen.
Emeryville, CA: Key College Publishing. [NSF-supported college textbook]
Souhrada, T. A., & Fong, P. W. (Eds.). (2006). SIMMS integrated mathematics: A modeling approach
using technology, Level 4 (3rd ed.). Dubuque, IA: Kendall/Hunt. [NSF-supported 4th-year high
school textbook]
Yoshiwara, K., & Yoshiwara, B. (2007). Modeling, functions, and graphs: Algebra for college students
(4th ed.). Belmont, CA: Thomson Brooks/Cole. [college textbook with applications appropriate for a
4th-year high school mathematics course]