## Performance in College Mathematics Courses

How well do Core-Plus students perform in college mathematics courses?

CPMP Course 4 was field tested nationally during the 1998-99 school year. Part of that evaluation included determining how well CPMP graduates perform in collegiate mathematics courses. A study completed at the University of Michigan examined the performance of students from two Michigan high schools in the same district. For the purposes of this report, the psuedonyms Eash High School (CPMP) and West High School (traditional) will be used. In 1995 and 1996, a traditional mathematics curriculum was in place at both schools, and West High School continued to use their traditional curriculum through 1998-99. In 1997, all East High School students who had not previously been accelerated had studied the CPMP curriculum, and by 1998 all East High School students were in the CPMP program.

Computer files provided by the University of Michigan registrar were used to generate the achievement data summarized in the following table. The table includes the number of matriculants from the school under the year, the mathematics courses taken in the first year of study at the University of Michigan together with the grade point averages, and numbers of elections and the course averages in each year. The mathematics courses are 105/110 (precalculus), 115 (calculus I), 116 (calculus II), 215 (calculus III), 216 (introduction to differential equations), and honors (all honors math courses open to freshmen). The grade point averages were calculated using the University of Michigan system as follows: A+ (4.3), A (4), A- (3.7), B+ (3.3), B (3), ..., D (1), D- (0.7), E+ 0.3), and E (0).

Table 1: Mean Grade Point Averages (Number of Students) by School, Course, and Year

East High School
(CPMP in '97 and '98)
West High School
College Class 1995
(50)
1996
(74)
1997
(87)
1998
(72)
1995
(34)
1996
(57)
1997
(45)
1998
(35)
105 3.18(4) 2.29(6) 2.74(13) 2.98(6) 1.46(7) 3.00(4) 2.60(5) 2.97(3)
115 2.86(14) 2.60(19) 3.08(32) 2.89(25) 2.33(7) 2.82(13) 2.58(15) 2.87(7)
116 2.67(14) 3.33(12) 3.17(19) 3.49(12) 2.45(6) 3.21(18) 2.63(8) 2.29(8)
215 2.66(5) 3.10(4) 2.95(6) 2.99(8) 2.50(2) 3.17(11) 3.34(6) 2.34(5)
216 2.15(2) 4.00(1) 4.00(2) 3.30(2) --- 3.67(3) 3.65(2) ---
Honors --- 3.28(5) --- --- 3.30(1) 3.77(3) 4.23(4) ---
All Courses 2.76(39) 2.89(47) 3.06(72) 3.07(53) 2.15(23) 3.15(52) 2.92(40) 2.57(23)

The East High School achievement for the years 1997 and 1998 when CPMP was in place is stronger than both pre-CPMP East High School (i.e., 1995 and 1996) and 1997 and 1998 West High School achievement. Similarly, the number of East High School graduates who attended the University of Michigan for the last two years is greater than that for the previous two years at the same school. These achievement and admissions data clearly support the view that in collegiate mathematics courses at the University of Michigan, graduates of the CPMP program perform as well as, or better than, graduates of a traditional mathematics curriculum.

Graduates of the CPMP program at East High School have, themselves, commented on their preparedness for collegiate mathematics and mathematics-related fields. The following comments are from three students who studied the pilot version of CPMP Course 4. The first two students enrolled at the University of Michigan.

 Student 1: In high school, I looked forward to math as one of my favorite subjects. The way I was taught and the instructors who taught it, made Core-Plus math extremely interesting to me. My sophomore year of high school is when I developed such a love for math and science that I decided to go into engineering. In my senior year of high school, I took Calculus BC and placed into Calculus 116 [second semester calculus] here at Michigan. The Core-Plus mathematics system and the calculus class I took [in high school] gave me such a strong base in mathematics that I received an A+ in Calculus 116. The real-life examples of Core-Plus Mathematics gave me an excellent background for demanding engineering courses. Because of my Core-Plus background, I feel I am two steps ahead of students who did not take Core-Plus math in high school. ... I am able to problem solve much faster than students who do not have a Core-Plus mathematics background.

 Student 2: The first political science class that I took at U of M was Comparative Politics. I was lucky because in Core-Plus Mathematics I learned many different kinds of charts, many different data tables, and many different methods for analysis of data. While many of my peers at college were left wondering what a Pearson's r correlation was, I was asking the professor questions like, "Did you, and by what method, screen out any outliers in the data sets?" I think the biggest advantage of Core-Plus math is that the diversity of topics allows me to feel comfortable in any math setting, whether it is politics, economics, or any subject.

Comments such as the above are not unique to students at the University of Michigan. The following is a quote from an East High School (CPMP) graduate from the same class who enrolled at Stanford University.

 Student 3: It is my firm belief that my Core-Plus education in fact better prepared me for the mathematics I encountered in college, as well as for preceding Advanced Placement Examinations, than would have a traditional mathematics program. For any student who intends to study math at the level of single-variable calculus or beyond, I believe that the conceptual-based style of education stressed in the Core-Plus program will prove far more beneficial than the memorization of what would otherwise be meaningless formulas and algorithms.