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.