e:\doc\web\99\02\coreplu2.txt Just hunted down a post of a documented NTCM math horror story where an ELITE high school adopted reform math and resulted in students who were relagated to remedial math instead of Calculus where it was supposed to leave them. This is the standard that the 1209 EALRS were written to enforce on all state high schools. "Outcomes Analysis for Core Plus Students at Andover High School: One Year Later", by R. James Milgram, Department of Mathematics, Stanford University: ftp://math.stanford.edu/pub/papers/milgram/andover-report.html txt: \clip\99\06\coreplus.txt htm: \clipim\99\04\coreplus\coreplus.htm Outcomes Analysis for Core Plus Students at Andover High School: One Year Later R. James Milgram1 Department of Mathematics Stanford University Summary: Andover, one of the best high schools in Michigan replaced the traditional sequence of G9=algebra I G10=geometry G11=algebra II G12= precalculus with 4 year NSF funded Core Plus integrated program. Students who completed Core Plus reported that not only were most relegated to taking remedial math, and not even ready to take college algebra, rather than Calculus, which was the logical freshman year sequence before. Students who went directly in the workforce said they either didn't learn any practical math, or learned it outside of school. Students who were 75th percentile in verbals, or in math in the traditional courses scored only 50th percentile on the SAT. Highlights: Andover had, at that time, a group of accelerated students who finished their high school education with calculus, because, currently, all students at Andover take Core Plus. Core Plus was phased in over a four year period. the results are not encouraging. ..almost all the Andover students were severely critical of the program, many bluntly blaming it for their difficulties in university level courses. .. by every measure such as ACT scores, SAT Math scores, grades in college math courses, core plus students fell short of Lahser students. [... even when compared with students who did not even take pre-calculus] useless for real life? the two Core Plus students at Andover who reported entering the work force directly after high school. The first of them says "The math program was good and bad. It tried to apply math to real life - but it didn't make a great attempt. I live on my own in [....], use math in all my taxes and bank account things, and I learned all that outside of the math program." other "I am currently working and feel that I cannot even do basic math calculations. I am missing too many fundamentals." "I feel that the preparation I received in H.S. with Core Plus was hardly adequate enough for college Algebra. The students were quite emphatic about where they felt Core Plus failed them. .. they did not feel it adequately prepared them for college mathematics classes. .. their basic math skills were too weak, three others felt that all they had learned from four years of Core Plus was how to use a TI 82 calculator. Median Percentile SAT-MATH SAT-VERBAL Andover, Core Plus 49 74 Lahser, Group 1 76 79 [two groups are comparable in verbal, but not in math] ----------------------------------------------------- Five years ago Andover High School in the Bloomfield Hills School District in Michigan2 was selected as one of 36 test sites for the NSF funded four year integrated mathematics program, Core Plus Mathematics Project3. In June, 1998, Prof. G. Bachelis of Wayne State University in Michigan collected data from 50% of the class that had graduated the year previously and 30% of the students at Lahser High School, the other high school in the Bloomfield Hills District4, which had been using a traditional mathematics curriculum: Algebra I, Geometry, Algebra II, Trigonometry, Pre-Calculus5. A copy of the survey is included as Appendix 4, and Appendix 5 by Prof. Bachelis explains more about it. The 67 non-accelerated mathematics students at Andover who replied to the questionnaire had participated in the entire four year Core Plus program, and at the time of their responses all but two of them had completed one year of college work. Consequently, the data collected there represents a unique view of the outcomes6 for Core Plus students after one year of college, especially when the results are compared to those of a similar group of 41 students from Lahser High School. These are the students at Lahser who did not take calculus courses in high school. The data represents the first glimpse -- to the best of our knowledge -- of how students trained in this new way perform in a university environment, and, frankly, the results are not encouraging. First, almost all the Andover students were severely critical of the program, many bluntly blaming it for their difficulties in university level courses. Moreover, there was no measure represented in the survey, such as ACT scores, SAT Math scores, grades in college math courses, level of college math courses attempted, where the Andover Core Plus students even met, let alone surpassed the comparison group of Lahser students. This held true even when the group of Lahser students was restricted to those who had not even taken a pre-calculus course in high school. It is worth noting however, that both groups had virtually identical grade point averages in high school: 3.23 for the 67 Core Plus students at Andover, and 3.29 for the 41 comparable students at Lahser, or 3.30 for the 25 Lahser students who did not take a pre-calculus course at Lahser. College Math Courses Taken by the Andover Core Plus and Lahser, Group 1 Students Here are the first comparisons: the displays below show the first college math courses taken by the Core Plus students and the non-calculus students at Lahser. Perhaps the most dramatic comparison is between the students who succeeded in taking calculus as their first college course versus those who had to take a remedial course: college algebra, basic mathematics, or trigonometry. First College Calculus Remedial Course Andover, Core 2 46 Plus Lahser, Group 11 18 1 [Image][Image] In the display above we included all the students at Lahser who responded to the survey and had not taken calculus in High School, regardless of whether they started with geometry or algebra. This is our control group, and this choice is justified in Appendix 1. However, the results do not change significantly when restricted to those Lahser students who started with algebra: First College Calculus Remedial Course Andover, Core 2 46 Plus Lahser, Algebra I 7 11 The c 2 statistic for the first table is 14.687 with a P value less than .00013. The c 2 statistic for the second table is 13.402 with a P value less than .00026. The critical value for significance for both tables is less than 5. [Image][Image] For the entire group of Core Plus students at Andover and the entire group of non-calculus students at Lahser we have the following distribution of outcomes: All Calc Pre-Calc Other Remedial No Work No Outcomes Math Response Andover 2, 3% 3, 4% 2, 3% 46, 70% 3, 4% 2, 3% 9, 13% Core Plus Lahser, 11, 3, 7% 2, 5% 18, 44% 2, 5% 0, 0% 5. 12% Group 1. 27% The Students' Views of their High School Math Experiences It is revealing to see how the students, themselves, view their high school mathematics experiences. One of the questions on the questionnaire, 15a, asks the students to grade (on a scale from 1 to 5 with 5 being the highest) their high school mathematics experience: a. Math course I had in high school, other than calculus (if taken), helped me with my college math courses (circle one) Here are the averaged responses: High School Math Usefulness of Standard Deviation Courses Andover, Core 1.75 .945 Plus Lahser, Group 1 3.46 1.07 [Image] In more detail, here is the comparison of all the responses to 15a by these two groups of students: This is a very significant difference in perception. It fits well with the fact that only two of the Core Plus students reported even attempting Calculus as their first mathematics course in college. It also fits with the grades reported by these students in their first college mathematics courses: [Image]Taking account of +'s and -'s, the Grade Point Average for those Andover Core Plus students who reported grades in their first college mathematics courses was 1.90, less than a C. On the other hand the average for the comparable Lahser students reporting scores was 2.6, which is equivalent to a B-. Here W, F, I denote withdrawn, failed, and incomplete, respectively. Also, it should not be forgotten that the courses being taken by the Lahser students are, on average, more advanced than those being taken by the Andover Core Plus students. SAT-I Scores for the Andover Core Plus and Lahser, Group 1 Students There has been some discussion about the effect of integrated mathematics courses on college entrance exams such as the SAT's. Here we have the following table of sample means: Average Test Scores SAT-MATH SAT-VERBAL ACT Andover, Core Plus 531 585 23.35 Lahser, Group 1 590 611 25.09 The ACT scores were not broken down in the survey so we cannot use them to differentiate between the mathematics scores and the verbal scores and it is not possible to say much here. However, the SAT scores are significant. Here are the median percentiles for these students [Image] Median Percentile SAT-MATH SAT-VERBAL Andover, Core 49 74 Plus Lahser, Group 1 76 79 In Appendix 3 we give the entire distributions of the SAT-MATH and SAT-VERBAL scores for both groups to give a better appreciation of the actual differences rather than just the difference reflected in the medians and sample means reported above. It is worth noting that the entire distribution of scores for the Andover Core Plus group in math is markedly different from the distributions for the other three data sets. Details All of the colleges and universities reported as being attended by the Core Plus students except the University of Michigan at Ann Arbor offered courses more basic than ``pre-calculus'' such as intermediate algebra, finite mathematics, or mathematics for education majors. Michigan State University, in particular offers Math 1825, a basic algebra course, which is the lowest level mathematics course they offer, but it receives no college credit. Of the 23 Core Plus students who reported attending Michigan State, 15 were required to take Math 1825, and two others who had tested into the next highest course, Math 103, Intermediate Algebra, withdrew from 103 and ended up taking Math 1825. In total, five placed into 103, one placed into the next course in the algebra sequence, Math 110, and one placed into a finite mathematics course. Only one of the 23 placed into the regular pre-calculus course. By comparison, seven of the Lahser students reported attending Michigan State. Only one started with Math 1825 (grade A), four started with 103 (grades A, B, B, B-), one started with Math 110 (grade B), and two started with calculus (grades A, B). Since the lowest level course offered at the University of Michigan, Ann Arbor is Math 105, Pre-Calculus, it was more difficult to decide if a student taking Math 105 was taking it as a remedial course or not (though if we are to take the description of Core Plus given on their web site at face value7, students should be able to start their university work with calculus after having successfully completed the Core Plus program). Fortunately, most of the 13 Core Plus students who reported attending the University of Michigan at Ann Arbor included details of their placement exam scores. Seven of them scored below the 10th percentile. They were counted as taking remedial courses. Two reported their scores as above the 20th percentile. They were counted as taking pre-calculus. One placed into the regular calculus course. Of the remaining three students, two indicated in their comments that they regarded their preparation as inadequate so they were also counted as taking remedial courses. The final student was counted as having made no response since it was impossible to decide in which category he or she belonged. Of the nine students from Lahser reporting on having taken mathematics at the University of Michigan, Ann Arbor, five successfully took calculus as their first course, three placed into Math 105, and one placed into Math 115, Calculus, but elected to start with Math 105.