Hirsch, Christian

Western Michigan University, Kalamazoo, MI, United States

The Transitions to College Mathematics and Statistics project is developing a mathematics course for the fourth year of high school. The course builds on the NSF-supported Core-Plus Mathematics curriculum and provides an alternative to the Calculus course that is now in place. The new course is being designed for students who will enter post-secondary education and will major in programs not requiring Calculus. The new course includes mathematics from a problem-solving or applications perspective, and serves as a bridge to college mathematics and statistics. Unit topics include functions, modeling, algebraic strategies, binomial distributions, and information processing.

The project is creating both a print version and a digital version of the course. Students are taught to use software tools such as spreadsheets, data analysis tools, interactive geometry programs, and computer algebra systems. These tools are embedded in the curriculum and allow students to apply the mathematics they are learning in interesting and relevant problems. The lessons include hyperlinks that allow students to have immediate access to related text. The designers are exploring the incorporation of video, access to language translation software, and the use of public domain, learner-centered software tools. One goal of the course is to increase student access to needed tools and information and to promote flexibility in how the materials are used. The project will conduct field tests of the materials and will implement an extensive formative evaluation plan where staff will visit classrooms and interview students. The summative evaluation will be conducted by an evaluator at the University of Missouri, and will focus on student achievement as measured by ACT/SAT scores, GPA, placement data, and course-taking.

The Transitions to College Mathematics and Statistics course provides a mathematics course that prepares high school students to transition into college mathematics and statistics courses that are designed to support non-scientific fields. It provides a viable, interesting, and useful technology-based course in the fourth year of high school. The course will also provide an effective way to help schools meet the college and career readiness standards that states have adopted.

(TCMS) is a problem-based, inquiry-oriented, and technology-rich fourth-year high school mathematics course. It was designed and developed to help ensure student success in college and careers in an increasingly technological, information-laden, and data-driven global society. TCMS was specifically designed for the large numbers of non-STEM oriented students whose undergraduate programs of study do not require calculus—such as business; management; economics; nursing; political science; psychology; the information, life, health, and social sciences; and many teacher preparation programs. Why TCMS? For students intending to enroll in non-STEM undergraduate programs or apprenticeship programs not requiring calculus, many high schools in the U.S. have little to offer as a transition to college-level mathematics and statistics other than Precalculus or narrow Advanced Placement courses. Consequently, many students opt out of mathematics their senior year or study mathematics that is inappropriate for their undergraduate and career aspirations. One all too frequent consequence of this situation is college placement in a remedial or non-credit bearing course. A compelling case for an alternative to Precalculus as a fourth-year capstone course is provided by data collected for the Princeton Review (www.princetonreview.com/college/top-ten-majors.aspx) as summarized below. Top 10 Undergraduate Majors in the U.S. Based on Enrollment 1. Business Administration and Management/Commerce 2. Psychology 3. Nursing 4. Biology/Biological Sciences 5. Education 6. English Language and Literature 7. Economics 8. Communications Studies/Speech Communication and Rhetoric 9. Political Science and Government 10. Computer and Information Sciences Transition to College Mathematics and Statistics is designed for use with students who have successfully completed a conventional single-subject sequence of algebra, geometry, and advanced algebra or a three-year integrated mathematics sequence. The course has been carefully field tested in high schools with students using conventional mathematics curricula and with students using an integrated mathematics program. Key themes and instructional features as outlined below have been informed by research on student learning and recommendations from client disciplines on the focus of undergraduate non-calculus-based mathematics and statistics courses. Balanced Content—Transition to College Mathematics and Statistics reviews and extends studentsâ€™ understanding of important and broadly useful concepts and methods from algebra and functions, statistics and probability, discrete mathematics, and geometry. These branches of mathematics are connected by the central theme of modeling our world and by mathematical habits of mind. Flexibility—TCMS consists of eight focused and coherent units, each of which is generally self-contained with attention to content prerequisites provided by "Just-in-Time" review tasks in lesson homework sets. The course has been organized to be as flexible as possible. The organization permits teachers to tailor courses that best meet the needs and interests of their students. Transition to College Mathematics and Statistics Unit 1 Interpreting Categorical Data Unit 2 Functions Modeling Change Unit 3 Counting Methods Unit 4 Mathematics of Financial Decision-Making Unit 5 Binomial Distributions and Statistical Inference Unit 6 Informatics Unit 7 Spatial Visualization and Representations Unit 8 Mathematics of Democratic Decision-Making Technology — TCMS is accompanied by TCMS-Tools, a concurrently developed suite of curriculum-embedded Java-based software, including a spreadsheet, a computer algebra system (CAS), dynamic geometry, data analysis, simulation, and discrete mathematics tools together with specialized apps. Included in the software are all the authentic data sets used in the text. Active Learning—The instructional materials are designed to promote active learning and teaching centered around collaborative investigations of problem situations followed by teacher-led whole-class summarizing activities that lead to analysis, abstraction, and further application of underlying mathematical ideas and principles. Students are actively engaged in exploring, conjecturing, verifying, generalizing, applying, proving, evaluating, and communicating mathematical ideas. Multi-dimensional Assessment—Comprehensive assessment of student understanding and progress through both curriculum-embedded formative assessment opportunities and summative assessment tasks support instruction and enable monitoring and evaluation of each studentâ€™s performance in terms of mathematical practices, content, and dispositions. Summing Up The highest level ITED Quantitative Thinking Test for end of grade 12 was one of several beginning and end-of-year measures assessing the effectiveness of TCMS in the six field-test sites. The test consists of 40 items focusing on thinking, reasoning, and problem-solving skills. All schools showed pre-post gains greater than expected (national) norms. One school using the integrated program made significant gains at the p = .05 level, as did one school using a conventional curriculum. Across all schools, gains were particularly notable for students in the third and fourth quartiles.

- Agency
- National Science Foundation (NSF)
- Institute
- Division of Research on Learning in Formal and Informal Settings (DRL)
- Application #
- 1020312
- Program Officer
- Karen King

- Project Start
- Project End
- Budget Start
- 2010-09-01
- Budget End
- 2014-08-31
- Support Year
- Fiscal Year
- 2010
- Total Cost
- $3,495,494
- Indirect Cost

- Name
- Western Michigan University
- Department
- Type
- DUNS #

- City
- Kalamazoo
- State
- MI
- Country
- United States
- Zip Code
- 49008