APPENDIX I: Core Plus and the University of Michigan-Ann Arbor (UMAA)
 
 

This appendix contains the following:
 
 

       1. The posting of Kim Mackey concerning his interview with Melissa Lynn, the Core Plus response, and Melissa Lynn’s response to their response.  These
appeared in Appendix A of my original report.
       2. A memo put out by BHSD about a UMAA Math Department Study.
       3. An article by Professor Arthur Coxford of the UMAA School of Education.  I include it here because I don’t know where it may be posted or will appear.
       4. A memo by Gary Doyle concerning math placement test results for Andover graduates at UMAA; this also appeared in Appendix A..

 I will intersperse comments between some of these items.  I want to say at the outset that I haven’t been able to get hold of the UMAA Math Department Study.  It
is also referred to in the Debra Saunders’ article, which appears in the body of my update.
 
 
 
 

Excerpts from a posting by Kim Mackey on several Internet sites.[1]
 

On June 17th the Detroit News published an article about the Core Plus Mathematics Project that presented some disturbing information about student achievement
in college after taking 3-4 years of the program in high school.  I decided to contact one of the students mentioned in the article to get a better understanding of Core
Plus from a student's perspective. Information from her interview is presented here with her permission.

Curriculum Background: Core Plus Mathematics Project (CPMP) is one of five major NSF-funded secondary math programs designed to be a core curriculum for
all high school students that adheres to the NCTM Standards. The co-PI's on the initial project were Christian Hirsch, Franklin Demana, James Fey, Arthur
Coxford, and Harold Schoen. The initial sponsor was Western Michigan University. CPMP is published by Everyday Learning Corporation under the title
"Contemporary Mathematics in Context: A Unified Approach." [...]  CPMP departs from traditional texts in a number of significant ways including heavy emphasis
on collaborative groups, integration of mathematical topics both within a unit and during the year, and a reliance on guided or group discovery for student learning.
Graphing calculators are used very extensively in the course. [...]

School Background: Andover High School in the Bloomfield Hills School District is a 9-12 high school with about 900 students. Ethnicity in the district is 80+
percent white, 7 percent Asian, and about 2 percent each black and Hispanic. Median income in 1989 was 88k+ and median housing prices in 1994 was 450k+.
With a mill rate of 40, this means that a houseowner with the median house would pay 18,000 in taxes. This is significant since local taxes are overwhelmingly the
major share of the 55 million dollars utilized by the school district. 58 percent of the adult population 20 years and over has a bachelor's or higher degree. In terms of
dollars per pupil Bloomfield Hills is in the top five districts in the state of Michigan at $10,000+. Average teacher's salaries are also in the top five at $59,000+. An
overwhelming percentage of Andover graduates go on to colleges or universities.

Student Background: Melissa Lynn has just finished her freshman year at the University of Michigan. She graduated from Andover High School with a 3.97 GPA
and has the intention of entering a pre-med program. At the 8th grade level Melissa did not qualify for algebra and instead took pre-algebra at which she excelled. At
Andover Melissa took 4 years of Core Plus Mathematics. When Melissa first took her ACT exams she scored a 31 in English and a 21 in math. Not satisfied with
the math score she took 8-12 hours of tutoring and got a 26 on the retake.

At the University of Michigan Melissa was required to take a math placement exam. She did not recognize many of the types of problems on the exam and scored in
the first percentile of all students taking the exam.  When she contacted more than a dozen other students who had been in her Core Plus classes she discovered that
all had placed in the sixth percentile or lower on the placement exam. This score meant that the students were required to take math 105 (precalculus) instead of
math 115 (calculus). Melissa's particular section of 105 used the preliminary edition of the Harvard Calculus Consortium's precalculus text.

So what was the problem? Melissa feels that the Core Plus curriculum is weak in algebra, particularly symbolic manipulation using paper and pencil analytical
methods. [...].  For students like Melissa who are good at English, the necessity of providing reasons and justifications for problems in Core Plus was not difficult.
But Melissa estimates that as much as half of the class copied the work of others in their group, short-circuiting the learning process. Notebooks were required in
class and were allowed to be used on all examinations, including the semester exams. Melissa feels that the weakness she had solving for variables contributed to
making her college level science classes more difficult than would have been the case if she had taken a more traditional math class.

In discussing the Core Plus math program, Melissa did think it had good qualities mainly centered around the aspect of requiring reasoning and justification of
answers. Melissa came across as the kind of student many teachers look forward to seeing in their classroom: bright, articulate, hard-working and self-motivated to
excel. Advocates of reform like to point out that many traditional students fail placement exams at major universities. True, but I would still submit that when a
student the caliber of Melissa Lynn scores so dismally on a math placement exam, the curriculum she was exposed to in high school needs to be seriously looked at
to discover why it fails to prepare the best and the brightest for college level work in mathematics. If Melissa's story becomes typical of students in Standards-based
reform programs around the country, it is likely that the backlash from parents and students will raise serious doubts about their efficacy.
************************************************************************

Excerpts from an e-mail message sent by Marcia Weinhold, in response to Mackey’s posting.  (Weinhold is the Outreach Coordinator for Core-Plus.
These excerpts deal specifically with the Andover situation.)

Date: Tue, 14 Jul 1998 14:15:29 -0500 (CDT)
From: marcia.weinhold@wmich.edu
To: Multiple recipients of list <amte@csd.uwm.edu
Subject: Core-Plus Mathematics -- Adding Balance

A recent [7/10/98] posting by Kim Mackey on the Core-Plus Mathematics Project (CPMP) and its preliminary testing at one of 35 national field test sites appears,
on the surface, a rather factual account from a distant correspondent. What's missing?

CURRICULUM BACKGROUND

The original NSF-grant to CPMP in 1992 was for the development and evaluation of a Standards-based three-year core mathematical sciences curriculum for all
students -- not a complete four-year program. Each of the three courses has gone through a multi-year process including: research and development, pilot testing,
revision, field testing, and further revision prior to publication by Everyday Learning.

In September 1997, CPMP received a second NSF grant to develop and evaluate a fourth-year course for college-bound students.  Initial (pilot) testing of Course
4 was completed in May 1998 and revisions are underway.  [During the pilot test CPMP received reports of selected students (not accelerated in eighth grade)
successfully completing AP Statistics or AP Calculus concurrently with Course 4.] The national field test of Course 4 begins in September 1998. Based on the field
test results, further revisions and enhancements will be made before final publication. Thus, students completing field-test (not final) versions of the complete CPMP
four-year curriculum will first arrive on college campuses in Fall 1999.

MATHEMATICAL CONTENT  [...]

INSTRUCTIONAL APPROACH  [...]

ANDOVER BACKGROUND

Students graduating in 1997 from Andover High School in Bloomfield Hills, who were not accelerated in eighth grade, participated in the initial (pilot) testing of the
CPMP three-year curriculum. During their senior year, these students studied three prototype units for a possible fourth-year course that was
envisioned by CPMP.  Thus, the curriculum these students pursued was not a complete four-year curriculum. [Emphasis added. G.B.]  Each of the first
three courses studied was a preliminary version two stages removed from the final published texts.

School reports from Andover indicate that the distribution of students placed into precalculus and calculus at the University of Michigan in fall 1997 was similar to the
distributions in previous years when a traditional curriculum was in place. According to school reports, the student discussed in Mackey's posting "placed into
precalculus, and possibly calculus."   The student elected to take precalculus.
Mackey fails to report that the student in question actually received an A in the UM precalculus course.

Is it unreasonable that some students who have not had a complete precalculus course in high school might be placed into a precalculus course in college without
ascribing failure to the math program?  What about the students of the same math program who placed into calculus at the University of Michigan?

We agree with Mackey that the CPMP curriculum "needs to be seriously looked at."  In fact, we would encourage reviewers to actually work through investigations
in the curriculum.  Clearly, just "hav[ing] copies of student and teachers texts" was not sufficient for Mackey to convey an accurate description of the curriculum.
-------------------------------------------------------------------------
Marcia Weller Weinhold
Outreach Coordinator
Core-Plus Mathematics Project                                               (616) 387-4589
Western Michigan University
-------------------------------------------------------------------------
************************************************************************

An e-mail message sent by Melissa Lynn, the person interviewed by Mackey and one of the people in the group I surveyed, in response to the above
excerpts of Weinhold’s message.

Date: Sun, 19 Jul 1998 22:52:53 EDT

Being that many publications have used my name as a case in point, I wuld like to take a moment to comment on the "Core Plus Controversy."  I was placed into the
Core Plus program without any say in the matter.  I requested a switch into the traditional math program, but was denied permission to do so numerous times.  Even
though I felt that Core Plus had strong points, it was evident that the costs outweighed the benefits.  There was a strong emphasis on expanding mathematical
knowledge into other aspects of life, but this was done at the cost of teaching the essential algebraic manipulations.  I realized right away that you cannot expand
upon information without learning the basics; you cannot expect a baby to be able to run before he can even crawl.

Needless to say, I continued the Core Plus program through my senior year.  I received a high A throughout all of my math classes.  Thus, I found it somewhat ironic
that I received a 21 on the Math section of the ACT the first time that I took it.  When I took the ACT, we had not yet covered trig in math class. The following
week, however, we began to learn trig.  Whoops--that was only one mistake that could easily have been avoided.  I then sought out a math tutor to help me raise my
math scores for the ACT.  I managed to do so, but not without wasting precious time and money that could have otherwise been spent in more productive ways.

When I discovered that I was in the first percentile on my math placement exam, I decided to enter into precalculus.  This was the path that was recommended to me
by my academic advisor.  Thus, I had to take math 105, a remedial course in mathematics.  I wasted precious time and money once again.  I potentially could have
placed out of math 115 if I had been in a traditional math program; this is two semesters of math.  I did receive an A in my precalculus class, but I did so in spite of
Core Plus, not because of Core Plus.

Also, during my general chemistry class, I had to seek extra help simply so that I could learn the correct manner in solving for a variable when given a specific
situation.  The hard part should have been figuring out what equation to use.  For me, it was the method necessary for solving the equation.

 It angers me to hear other people justifying Core Plus by using my situation in Kim Mackey's report.  The fact that I received an A in my college Math course is due
to my efforts, not to Core Plus, in any way, shape or form.  The fact that Andover did not even have the complete four year course of Core Plus makes a mockery
out of education.  Instead of aiding me in my academic goals, I was hindered.

I understand that the past remains in the past, and is out of reach.  The Board of Education should realize their mistakes, and make a positive change.  They are so
concerned with winning the battle that they have lost sight of what the battle is about.

This was a small write-up on some of my thoughts.  I am speaking only for myself; I believe that if other students chose to verbalize their thoughts, they would concur
with my sentiments.  Thank you for your time.

          Sincerely,
                             Melissa Lynn

************************************************************************

I would like to interject here that much has been made of the fact that Melissa Lynn couldn’t have scored in the first percentile, because the scores aren’t reported
that way.  But this is beside the point; the point is that she got a low score, whereby she had to take pre-calculus, and that her score had no correlation with the math
grades she had gotten at Andover.  This was the case with other Core-Plus students as well.  For Chris Hirsch to say that that wasn’t REALLY Core-Plus they
were taking serves to reinforce Debra Saunders’ argument that these students were being experimented on.
 
 
 
 
 

                                            U-M Math Study:

                             Bloomfield Hills CORE+ Students Well-Prepared

 The math department at the University of Michigan has received many inquiries concerning
 the preparedness of freshmen coming from high schools using "reform" (CORE+) math
 curricula. Because of the amount of concern, the department recently analyzed the first
 semester college grades of two groups of students entering the University from comparable
 high schools in southeastern Michigan. The profiles of both groups were very similar in
 terms of their high school GPAs, math SAT scores, and last high school math class (and
 grade therein). Only their math curricula were different; one was reform (CORE+) and one
 was more traditional. The students included in the study were those who came in either the
 fall of 1997 or 1998 and elected Math 105(Precaiculus) or Math 115(Calculus I) during their
 first college term.
 

 Here are the results:
 

 1.  Both high schools turned out very strong students, approximately 60% of whom had
   taken an AP calculus class in high school. Many of these students used their advanced
     placement to begin their college studies in Calculus II or above.
  2.  Students from the reform curriculum who elected Math 115(Calculus I) in their first fall
   received grades which were nearly half a letter grade higher than students in Math 115
   coming from the traditional curriculum.
 3.  Students from the reform curriculum who elected math 105 (Precalculus) in their first fall
    received grades which were slightly higher than the students in Math 105 coming from
   the traditional curriculum.
 4.  More reform students than traditional students got low scores on the U-M placement test
    (algebra skills), and hence were recommended to take Math 105.
 

 In summary, pursuing the CORE+ curriculum did not diminish a student's chances for suc-
 cess in either precalculus or calculus at the University of Michigan. However, the reform
 students who came to college without prior calculus seemed to have had more trouble
 "passing" the place exam regardless of their high school performance in CORE+. Since the
 decision about how to place incoming students is a difficult one, colleges with large entering
 classes must often resort to doing a quick test of routine skills. This means that it is impor-
 tant for successful reform programs to set up mechanisms (such as the new exercises
 CORE+ has recently introduced) which will encourage students to maintain their mechanical
 skills.
 

 CORE+ appears to have allowed students to succeed in U-M's entry level math courses.
 Although they were at some disadvantage in terms of mechanical skills, they had the advan-
 tage of having been taught in high school classes which were taught in much the same
 manner as those at U-M.
 
 

Mathematics Achievement for Andover and Lahser

Students at the University of Michigan 1995-98

Arthur F. Coxford

The University of Michigan

There has been some concern expressed by parents and others regarding the Core-Plus Mathematics curriculum implemented at Andover High School for graduates for 1997 and beyond. Gregory Bachelis, a critic of improving mathematics in the schools, collected opinions from some 1997 graduates of Lahser and Andover high schools regarding the way their mathematics programs prepared them for collegiate mathematics. The general view expressed by Bachelis and Milgram, who applied statistical methods to the data, was that the Andover program did not prepare students for collegiate mathematics. Since they provided no achievement evidence supporting their views, I decided to test the validity of their position by collecting achievement data for University of Michigan matriculants from the two schools. I asked the registrar to provide anonymous academic records of all matriculants from Lahser and Andover high schools for the years 1995 - 1998. In the years 1995 and 1996 the Andover students completed a traditional mathematics program while in 1997 and 1998 a contemporary program was in place at the school. Lahser's program was similar for all four years.

Computer files provided by the registrar were used to generate the following tables. Each table includes the number of matriculants from the school in the title line, the mathematics courses elected in the first year of study at the University of Michigan in the second line, the grade point average and numbers of elections for female and male students in the next two lines and the course averages in the last line. 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).
 

Please note that the information in the following two tables is for the Fall semester only. Data were not available for the Winter semester since the semester was just concluding.

Arthur F. Coxford

acoxford@umich.edu
 

Notice that in Coxford’s article I have been promoted from being a "critic of reform math" to a "critic of improving mathematics".  Also note that
Coxford seems unaware that the Class of 1997 was split between those who had Core Plus and those who didn’t (the accelerated students).  Also, he says that a "contemporary program" was in place in 1997, whereas Marcia Weinhold in her message above says they were trying out different prototypes.

This confusion over the class of 1997 persists with the Core-Plus directors.  In a recent letter to the editor of the Detroit Free-Press in response to a recent Debra Saunders’ column, Hirsch and Coxford state that there were 72 Core-Plus graduates who entered UMAA as freshmen in 1997.  This is clearly absurd, since this is about one-third of the entire graduating class, so the number 72 must also include the accelerated students.  In fact, in Coxford’s article above he gives the number of freshmen taking math courses their first year as 72, and the total number of matriculants as 87.  (Of course 72 could include multiplicities if a student took two math courses.)    This is also consistent with the following memo from Gary Doyle wherein it states that 67 of those freshmen took the math placement exam.

Even if all 87 matriculants where freshmen, and given that 52 Andover freshmen at UMAA responded to my survey (20 from the Core-Plus group, 32 not), this means the response rate for UMAA freshmen from Andover was virtually 60% or more.

[1] Mackey is a high school teacher in Valdez, Alaska, who has been closely following the progress of new math programs such as Core Plus.