REFORM VS. TRADITIONAL MATH CURRICULA:*

PRELIMINARY REPORT ON A SURVEY

OF THE GRADUATING CLASSES OF 1997 OF

ANDOVER HIGH SCHOOL AND LAHSER HIGH SCHOOL,

Bloomfield Hills, Michigan,

CONCERNING THEIR HIGH SCHOOL MATH PROGRAMS AND HOW

WELL THESE PROGRAMS PREPARED THEM FOR COLLEGE MATH

Gregory F. Bachelis, Ph.D.

Professor of Mathematics,

Wayne State University

Detroit, Michigan [1]

Dedication

This report, and the six months I spent working on the underlying survey, is dedicated to the students, past and present, of Andover and Lahser High Schools.

Acknowledgment

I would like to the thank several parents and others in the West Bloomfield and Bloomfield Hills School districts, and in particular Mark Schwartz, Ph.D., for their support and encouragement during the duration of this project

STATEMENT OF PURPOSE

This survey was conducted to compare how high school students with differing high school math programs do in college. I conducted the survey in my capacity as a Professor of Mathematics at Wayne State University, where for 27 years I have taught and done research in mathematics, and more recently also in mathematics education and theoretical computer science. I conducted this survey as a public service to parents, students and others in the Bloomfield Hills School District, the West Bloomfield School District (where I live) and other districts where new programs have been introduced which have caused concerns among community members. It was also done as a service to the mathematical community, whose two main organizations[2] are closely following the evolution of these new math curricula and the effect they are having on incoming college students.

I sent the survey questionnaire (see below) along with a covering letter bearing the letterhead of the Department of Mathematics of Wayne State University. I gave my office phone number for people to call if they had any questions or concerns. There was also a stamped return envelope, addressed to my office, with which to return the survey. None of the above made it a “Wayne State Survey," nor did I imply in any of my communications with the people being surveyed that this was anything but my own research project. Nor was any implication given that Wayne State would endorse any of the research’s conclusions.

In addition, the research was not funded by Wayne State University. The stamps on the return envelopes were paid for by interested parents; I did all of the work connected with the survey -- clerical, follow-up phone calls and e-mail messages, data transcription and the like -- and I was not given release time from my usual duties in order to accomplish all this.

The report that follows is preliminary in nature. Further analysis needs to be done on the data, and this is currently being done by professors at another university. However, the report does include all the comments made by all the respondents, with accompanying information supplied by them -- GPA’s, SAT and/or ACT scores, college attended, college major, etc.-- in order to give the comments a context. Since I promised confidentiality to the respondents, I have blurred the contextual information, in a manner explained later, so as to preserve their anonymity. I have also, in a few cases, paraphrased or deleted portions of the comments in order to protect the identity of the respondent. In each case this is clearly indicated. None of the above actions detract in any material way from the information that they provided.

In closing, I wish to reiterate that this research project was performed by myself as an individual faculty member of Wayne State University, conducting a survey on what I considered to be a matter of public interest within the area of my professional expertise.

The Advent of Core-Plus in Bloomfield Hills

The Bloomfield Hills School District (BHSD) is located in Oakland County, Michigan. It is a 25-square-mile area, which is comprised of virtually the entire city of Bloomfield Hills, most of Bloomfield Township, a large portion of eastern West Bloomfield Township, and a small part of the city of Troy. The district has two high schools, Andover and Lahser, and three middle schools, West Hills, Bloomfield Hills and East Hills. The middle schools all house grades six through eight. West Hills feeds Andover, East Hills feeds Lahser, and Bloomfield Hills Middle School feeds both high schools.

In the fall of 1993, Andover High School began what would be a four-year phase-out of its (non-accelerated) “traditional” math program, which had been as follows:

· Ninth grade --- Algebra 1

· Tenth Grade -- Geometry

· Eleventh Grade --Algebra 2

· Twelfth Grade - Pre-Calculus[3]

In its place the Core-Plus Mathematics Project (CPMP or Core-Plus) was installed; it is an integrated math program using modeling, simulation and cooperative learning, which makes extensive use of graphing calculators. Core-Plus was phased in on a year-by-year basis, so that by the 1996-97 school year it was the exclusive math program at Andover, with the exception of AP Calculus and AP Statistics.[4] The latter courses are typically taken in the twelfth grade by “accelerated students,” by which I mean those who take Algebra 1 or Core 1 before the ninth grade.

“Integrated” or “Reform Math” refers at the high school level[5] to constructing the curriculum out of four “strands”:

· Algebra and Functions,

· Probability and Statistics,

· Geometry & Trigonometry,

· Discrete Mathematics.

These are woven together for a three or four-year curriculum, rather than being taught as separate courses.

Core-Plus was introduced at Andover in 1993 as a pilot project, which means that this was the first time it was used anywhere in an actual classroom setting. According to Professor Harold Schoen, evaluation Director of Core-Plus, “The pilot test was designed mainly to provide feedback to the authors from teachers and students concerning what worked well, what did not and what improvements were needed.”[6] In 1994 the field testing of Core 1 began in 36 high schools in Michigan and around the country. Core-Plus was originally intended as a three-year curriculum. However, according to Marcia Weinhold, the Outreach Coordinator of Core-Plus, “During their senior year, [the non-accelerated Andover] students studied three prototype units for a possible fourth-year course that was envisioned by Core-Plus. Thus, the curriculum these students pursued was not a complete four-year curriculum.”[7] The field testing for Core 4 started in the fall of 1998.

The Accelerated Students

A substantial portion of the Andover Class of 1997 consisted of students who had been accelerated in math, and hence had not taken Core-Plus. These students as a rule had taken Algebra 1 during the 1992-93 school year, while still in middle school. So when this group arrived at Andover in 1993, they rode the last wave of the traditional math sequence while the non-accelerated students rode the first wave of Core-Plus. Lahser, the other high school, stayed “traditional.” Core-Plus was introduced at the middle school level, so that accelerated students destined for Andover could take it in the eighth grade, in (I believe) January, 1994.

Controversy over Core-Plus

So, in June 1997, the first class having completed four years of Core-Plus graduated Andover High School. Subsequently, reports of some of these graduates having difficulties on the math placement exams at the University of Michigan - Ann Arbor (UMAA) and Michigan State University (MSU) began to surface. On October 28, 1997, a joint meeting of the Bloomfield Hills and West Bloomfield School Boards was held to discuss reform math. After the featured speaker had finished the main part of his presentation, several parents and others took to the floor to express their thoughts and concerns about Core-Plus and about how this first graduating class was doing in college. I live in the West Bloomfield School District (WBSD), which had started introducing Core-Plus, and phasing out their existing math program, in 1995.[8]

I had participated in several meetings of my school board during the preceding year, at which Core-Plus was discussed, and I attended this joint meeting. After attending a number of additional meetings organized by parents, in both BHSD and WBSD, concerning the impact of Core-Plus, and mindful of the intense scrutiny the mathematical community is giving the evolution of such reform math programs, I decided to do a survey of the 1997 graduates of Andover, in order to determine their opinions about Core-Plus and to get as complete as possible a picture of their mathematical experiences since graduation.[9]

I surveyed the entire Andover class of 1997; the reason being that I did not know a priori who had been accelerated and who had not. Also, with the accelerated students I could study how well students with a traditional high school math background do in Reform Calculus courses such as “Harvard Calculus,”[10] The latter is the flagship calculus course of UMAA; it is also taught at MSU, but on a more limited basis.[11] One of the main claims of Core-Plus and other programs of its type is that they are a better preparation for Reform Calculus courses than the more traditional curricula.[12]

The survey commenced in late April of 1998 and concluded in mid-September, as far as any activity on my part soliciting responses. The covering letter and survey questionnaire are given below in compressed form. (Most blank lines and some lines for answers have been deleted.) The original questionnaire consisted of three pages plus the optional section.

Covering Letter and Survey Questionnaire

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

College of Science

Department of Mathematics Detroit, Michigan 48202 (313) 577-2479 (313) 577-7596 FAX

April 22, 1998

Dear __________________,

I am conducting a survey of 1997 graduates of several high schools, including yours, who entered college in the summer or fall of 1997. We would appreciate your cooperation in this effort to evaluate how high school math programs are preparing students for college level mathematics. The results of this survey will be used for independent research regarding high school math curricula and individual names will be kept confidential. We are asking you for a few minutes of your time to complete the enclosed questionnaire and then to return it in the enclosed envelope. Please feel free to call me at my office at Wayne State at 313-577-3178, or to send e-mail to greg@math.wayne.edu, if you have any questions or concerns.

Thank you for your cooperation,

Gregory Bachelis, Ph.D.

Professor

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

MATH SURVEY

1. High School graduated from in 199___ ________________________________High School

2. High School GPA ______ Honors or Awards__________________________________

3. Academic interests in high school 1.______________________2._______________

3. 4. 5.________________

4. Scores on SAT Math ________Verbal ________ PSAT Math______ Verbal ____

ACT ________ PLAN _______ Other (specify) ______________________

5. Did you take any Advanced Placement tests? Yes No . If so, please specify.

Subject Score Year Subject Score Year

________________ _______ _____ ________________ ______ _____

6. Did you take any ACT or SAT prep courses? Yes No If so, please tell from whom and give dates.:

________________________________________________________________________

7. Math courses taken in High School: (Please fill in the appropriate box with the grade(s) received.)

Year

Alg 1

Alg 2

Geom

Trig

Adv Alg

Pre Calc

AB Calc

BC Calc

Core Plus 1

Core Plus 2

Core Plus 3

Core Plus 4

Other (specify)

School Name

Fresh

Soph

Junior

Senior

8. Did you receive any math tutoring while in high school? (besides SAT or ACT prep, if any) Yes No. If so, please give details on the next page. (Indicate if tutoring was private, provided in school, or by a commercial organization.)

I received tutoring in:

Subject _____________________ Year ____________ From ________________

9. Did you participate in any summer math programs during the years you were in high school?

If so, please specify subject, year, and who sponsored them.

______________________________________________________________________________

10. Did you enter college after graduating from high school? Yes No. If no, or if you haven’t taken any math courses or placement exams in college, please skip to question 16. Otherwise, please continue with questions 11 - 15.

11. Please specify any college math courses taken during the summer of 1997, or the 1997-98 academic year.

	Math Course	College/University	Grade	Text *
Summer ‘97
Fall ‘97
Winter ‘98

*Please identify the text by listing the author or first author, if there are several. (e.g. Stewart, Thomas, Finney, Hughes-Hallett, Stein, Anton, Ostebee, Ellis, Edwards, Swokowski, Varberg, Larson, Dick, Wattenberg)

12. Did you take a math placement exam in college? Yes No . If so, please tell where taken, the nature of the exam and your score and/or in what course you were placed.

______________________________________________________________________________

13. Have you sought any math tutoring in college? Yes No If so, please give subject(s) tutored in and reason(s) for seeking tutoring.

______________________________________________________________________________

14. What is your intended major? _____________________________________________

15. Please answer the following two questions, when applicable, on a scale from 5 to 1.

a) Math courses I had in high school, other than calculus (if taken), helped me with my

college math courses (circle one)

5 4 3 2 1

very much somewhat not at all

b) Calculus I took in high school helped me with my college math courses. (circle one)

5 4 3 2 1 (Does not apply)

very much somewhat not at all

16. Please give any additional comments you wish to make concerning your math experiences in high school or college. ______________________________________________________________________________

______________________________________________________________________________

Thank you for your cooperation. There is an optional section on the next page. When you have completed this questionnaire, please return it in the enclosed envelope to

Professor Gregory Bachelis

Department of Mathematics

Wayne State University

Detroit, MI 48202

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

OPTIONAL SECTION

NAME ___________________________ AGE _________ SEX : M F

HOME ADDRESS________________________________________________________

COLLEGE ADDRESS (if different from above) _________________________________

May we contact you to obtain any further comments? Yes No

TELEPHONE NUMBER(S) ________________________________________________

E-MAIL ADDRESS __________________________________

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

In the eighteen months prior to my decision to conduct the survey, I had spoken out about Core-Plus. I was skeptical of the claim being made that it was suitable for all students, and I was critical of the fact that it was being implemented at certain schools to the exclusion of almost the entire previously existing math courses; the latter was the case at Andover and at West Bloomfield High School, the sole high school in WBSD. I felt qualified to speak out, since I have been a mathematics professor for over 30 years, and I have taught, at one time or another, all of the subjects that are included in these new integrated curricula. I felt that it was impossible to do these subjects justice by cramming them into a three or four year high school curriculum

However, I do not feel that my voicing criticisms and concerns disqualified me from conducting the survey. Certainly I am capable of wearing different hats, and people doing surveys are entitled to have opinions on the subject under study. The key point is whether the survey is conducted in a fair and impartial manner. In this regard, note that the tone of the letter and questionnaire is quite neutral. There are no “loaded” questions. My follow-up phone calls and e-mail messages, encouraging people to respond, were also quite neutral in tone. I knew none of those surveyed beforehand. Also, only a few of them attend Wayne State, which has about 17,000 undergraduates. For these reasons there was no pressure on them to respond. In any case, the respondents to this survey were not analogous to a jury being picked prior to a trial. They had had the course, so to speak.

The Control Group

In surveys of this type, there is a lot of “noise” that needs to be filtered out. If the Core-Plus graduates were the treatment group, then who to use as controls? It would not have been fair to the Core-Plus group to use the accelerated Andover students as controls. Virtually all of the latter had taken calculus in the 12th grade, and it had been determined that they were among the better math students in their class - by exams, grades or other means - or else they wouldn’t have been accelerated in the first place[13].

I decided to survey the 1997 graduates of Lahser, the other high school in the district, which had stayed traditional. I could then use the non-accelerated Lahser students, or perhaps the Lahser students who didn’t take Calculus in the 12th grade (which includes the non-accelerated ones), as controls. With the remaining Lahser students I could study the same question as with the accelerated Andover students, concerning Traditional vs. Reform curricula. I could also compare these Lahser students with the accelerated Andover students, pre-Core-Plus.

I believe my choice of control groups was a reasonable one. The populations of the two high schools are similar socioeconomically, they are in the same school district, and one of the middle schools even feeds both of them. In 1993, when Core-Plus was introduced at Andover, students in the district could in fact choose which high school to attend. I have only anecdotal evidence as to what effect, if any, the advent of Core-Plus had on traffic between Andover and Lahser, or out of the public system entirely to private schools such as Cranbrook Academy or Detroit Country Day School, or to parochial schools such as Marian High School or Brother Rice High School. In 1997, choice of high schools in the District was ended for the time being because of an imbalance in favor of Lahser.[14]

Survey Mechanics, Population Size and Rate of Response

In 1997, there were 228 graduates of Andover High School, and 258 of Lahser High School.[15] I determined the size of the population being surveyed and response rate of each high school as follows:

Andover High School

· 1997: 228 total graduates

· one exchange student -- returned home

· at least four other students had left the country

· probable valid addresses for all but one of the remaining students

Therefore student population size = 228 - 1 - 4 - 1 = 222

· 112 total replies

Response rate = 112 total replies/222 population size = 50%

Lahser High School

· 1997: 258 total graduates

· one exchange student -- returned home

· probable valid addresses for all but six of the remaining students

Therefore student population size = 258 - 1 - 6 = 251

· 75 total replies

Response rate = 75 total replies/251 population size = 30%.

In late April and early May the questionnaire and covering letter were mailed to all 1997 graduates from both high schools. A stamped envelope with my return address at Wayne State was included. The initial mailing was followed up by phone calls or e-mail messages (when e-mail addresses could be determined). These follow-up contacts were made by me, so that there would be consistency in the messages being sent by e-mail or left on phone answering machines, and in the phone conversations. Based on these contacts, a second questionnaire was often dispatched, as its predecessor had been misplaced or discarded for sundry reasons. I have communicated in the ways indicated above with over 80% of the 473 graduates (or in some cases, family members) who were being surveyed.

One can only speculate as to the reasons why some graduates did not respond to the survey. The non-respondents might include those who

· for one reason or another, never received the questionnaire;

· were apathetic, busy, etc.;

· objected to a survey in the first place;

· didn’t want to revisit high school issues.

SOME WORDS OF CAUTION

I wish to make the following three points.

1) I want to stress that I was not trying to determine how well the various curricula were taught. This is certainly an issue, especially with a radical new curriculum like Core-Plus. I was simply trying to find out how the various curricula, as taught, prepared the students for college math, their reaction to their high school math experiences, and also how much extra help, such as tutoring, they sought.[16]

2) The information is only that provided by the respondents, and has not been independently verified. They were promised confidentiality by me, and I believe they made a good faith effort to give accurate answers to the questions. Certainly a number of the comments were quite candid.

3) Many schools besides Andover High School have phased in new math programs like Core-Plus, mainly in response to the promulgation of the 1989 NCTM Standards[17], although some of these schools have also kept the traditional track, thus allowing for “choice” and for comparison of the two curricula.

SOME STATISTICAL ANALYSIS

The Andover respondents fall naturally into two groups:

· I: non-accelerated (Core-Plus), and

· II: accelerated (virtually all of who took Calculus).

The Lahser respondents fall naturally into three groups, since a lot of the accelerated students did not take AP Calculus, although a number of them did take AP Statistics. These groups are

· I: non-accelerated,

· II: accelerated, no Calculus, and

· III: accelerated, with Calculus [18]

The answers to 15a) of Andover I are compared to those of Lahser I and II in the following table. Recall that question 15 was:

15. Please answer the following two questions, when applicable, on a scale from 5 to 1.

a) Math courses I had in high school, other than calculus (if taken), helped me with my college math courses (circle one)

5 4 3 2 1 very much somewhat not at all

b) Calculus I took in high school helped me with my college math courses. (circle one)

5 4 3 2 1 (Does not apply) very much somewhat not at all

We have the following results.

Group Mean response Standard Deviation Number of Responses

Andover I 1.78 0.94 53

Lahser I 3.39 1.09 23

Lahser I&II 3.46 1.05 35 ________

Table I: Answers to 15a) for Andover I, Lahser I, and Lahser I&II

Assuming linearity of the response scale, this means that the Lahser students without calculus thought their high school math was approximately twice as helpful with college math than the Andover Core-Plus students did.

I should mention that a number of respondents appear to have been confused about 15b) and to have thought that the word “calculus” applied to college rather than high school. So, for example, all of the respondents in the above three groups should have circled “Does not apply” in 15b), and this was not the case. The answers to 15a) and 15b) for Andover II and Lahser III are now compared.

______________________________________________________________________

Group Question Mean response Standard Deviation Number of Responses

Andover II 15a) 3.81 1.13 36

Andover II 15b) 4.01 1.34 35

Lahser III 15a) 3.50 1.24 28

Lahser III 15b) 3.80 1.30 30

______________________________________________________________________

Table II: Answers to 15a) and 15b) for Andover II and Lahser III

This means that all groups who had high school calculus answered between 3.5 and 4 on average, when asked about the helpfulness of high school calculus or of high school math before calculus, and that Andover was slightly more generous than Lahser. Considering both tables, we see that the average answer of each of the groups, except Andover Core-Plus, was roughly 2 times more than Andover Core-Plus.

Further statistical analysis of the data is needed, and this is currently being done by several professors at Stanford University.

The Comments

I have decided to report all the comments verbatim, subject to the following protocol. I have corrected spelling errors and expanded abbreviations. In a few instances I have deleted a word or phrase to protect the confidentiality of the respondent. These deletions are denoted “[...]”. In a few cases I have added a few words or paraphrased. Such paraphrasing or additions are enclosed in square brackets.

I have given the answer and accompanying remarks to question 13 about math tutoring in college, when there were remarks made that were worth noting, since this question did indeed generate a lot of comments. I have also included those parts of answers to question 12, which asks whether a math placement exam was taken in college, that relate to the score received and the resulting placement, since this is a matter of some controversy.[19] I have also included affirmative answers to question 8 about math tutoring in high school, and excerpts from the answers given, since this too has been a matter of some interest; to wit, did Core-Plus generate more than the “usual” amount of math tutoring. In this regard, I have included affirmative answers to question 9 about summer programs when they relate to summer school as opposed to summer “math camps.” In addition, I have given the answers to question 15a) for Andover I and Lahser I&II and to questions 15 a) and b) for Andover II and Lahser III.

Besides the above, in order to give the comments more context, I supply some information about the respondent, blurred somewhat so as to preserve anonymity. This “blurring” is accomplished as follows: High School GPA’s, and SAT and/or ACT scores, when given, are reported in a certain range, rather than by exact value.

Colleges, except for UMAA (The University of Michigan - Ann Arbor) and MSU (Michigan State University), are reported by category, these being:

Michigan-Public,

Non-Michigan-Public,

Private,

Private-regional, and

Other (specialty schools, no college attended, or college unknown).

College majors are also reported by category, these being

Science (which includes mathematics and psychology),

Engineering,

Business,

Education,

Nursing (which includes medical technicians and physical therapy),

Design,

Fine & Performing Arts;

Pre-professional (which includes architecture),

Communications (which includes journalism),

Social Science, and

Liberal Arts[20].

Unfortunately, I cannot supply an indication of grades in high school math classes, because a lot of respondents, in answering question 7, merely put X’s in the grid to indicate which courses they took, without listing the grade received, as was requested. In some cases this was no doubt because they couldn’t remember the actual grades. I don’t see the purpose of supplying information that can only be done so sporadically.

I want to make it very clear that I did not solicit comments beyond what people wrote in their returned questionnaires. In a few cases respondents sent e-mail messages with comments prior to sending in their questionnaires, and I have included these where they were not duplicated by the written comments. In a number of cases, during the course of my phone calls subsequent to the mailing of the questionnaires to encourage people to respond, graduates or their parents gave opinions. In these cases, I said that I could not do the survey over the phone, and I encouraged them to send in their questionnaires. I made no written record of such conversations.

A majority of the respondents chose to answer the Optional Section and to answer “Yes” to the question asking whether they could be contacted for additional comments. In these cases I thanked them, by phone or e-mail, for responding to the survey, and I encouraged them to get other graduates to respond. In some cases I also sought clarification to their answers to one question or another, and in a few of these cases, comments were made by respondents which I then added to their written comments (and these additions are so noted); but as I said above, I did not solicit comments beyond what the respondents had chosen to write.[21]

Some Conclusions

I will let the reader draw his or her own conclusions as to the validity or reliability of the comments. One conclusion I wish to make is that, if some of the Lahser comments give the reasons why curricula such as Core-Plus have been developed to try to make mathematics more meaningful and accessible, then surely a preponderance of the Andover comments - even some by people who were not in the program - indicate that the cure is much worse than the disease for students who need to take additional math courses in college, and perhaps for others.

The other matter I would like to comment on is the performance of Core-Plus graduates on the placement tests at UMAA, MSU, as well as other colleges. A lot of them complained that they did not do well because of their lack of knowledge of basic algebra, and some said they did not do well even in the courses they were placed into. Now it is all well and good to say that people are just having a bad day when they do poorly on a placement test, but as someone who has taught remedial algebra for more years than I care to remember, let me assure you that there is a big difference between learning basic algebra and then forgetting most or all of it, and never having learned it at all. Core-Plus appears to have created a new category of students who land in remedial math courses - courses that were not designed with such students in mind.

Further Work

This is after all a preliminary report, so I welcome any suggestions or corrections, and I will make appropriate changes where indicated. As I mentioned above, more analysis of the data is being carried out. In this report I have chosen not to study in detail the issue of high school math vs. reform calculus in college; however some of the comments of the students do shed some light on this.[22] Parenthetically, I wish to point out that the comments made by the respondents about the T. A.’s at The University of Michigan (called GSI’s for Graduate Student Instructors) are probably not much different than those that would be made by students at any other major university in the U.S.

There are also other groups that should be surveyed. For example, the accelerated group that graduated from Andover in 1998 after 4 years (or maybe 3 and 1/2) of Core-Plus followed by one year of AP Calculus should be studied. I tried to get information about this group, but I only have a few anecdotes about how they are doing. Also, non-accelerated groups a year after graduating whom had field-tested Core-Plus, as opposed to pilot testing and testing prototypes, could be studied. West Bloomfield High School now has a hybrid version of Core-Plus, in which certain Core modules have been deleted in favor of algebra drill.[23] (The courses being taught at that high school this year are one year past field testing, except for Core 4.) Groups having had this type of curriculum could be studied as well.

I leave such surveys to others, as I am not up to an encore.

The Comments in Context[24]

Andover Group I Students {non-accelerated (Core Plus)} who made Comments about Core Plus[25]

Andover 4. 2.75-3.25; SAT M 400-500 V 500-600; Michigan-Public; Education

· Core Plus was a waste of my time. I have very few math skills, and none of them helped me with Algebra I in College.

Math placement exam? Yes. I suppose I didn’t pass because I was placed in 110, the second lowest.

Math tutoring in college? Yes. I have never understood Algebra because of Core Plus math in

High School. I went to the tutor lab 3 times per week and I still did poorly.

15a) 1

Andover 8. 2.75-3.25; SAT M 500-600 V 500-600; ACT 18-20; Michigan-Public; Business

· With the new program of math at Andover I did not feel prepared to enter the level I was placed at in the University.

Math placement exam? Yes. I was placed in Intermediate Algebra.

Math tutoring in college? No. I decided that I should prepare myself by taking a couple of math classes at a community college before I go and take it at [my university].

15a) 1

Andover 14. 2.75-3.25; ACT 24-26; Michigan-Public; Business

· [Core Plus] was probably the most horrible experience I have ever gone through in high school.

Math tutoring in high school? Yes. 1996.

Andover 16. 3.25-3.75 ACT 24-26 UMAA Communications

· Should not use notes for test, because you can’t at college.

Math tutoring in high school? Yes. Math. On and off throughout High School

Math placement exam? Yes. I got a 6%

15a) 1

.Andover 17. 3.75 - 4.0 ACT 21-23 UMAA Social Science

· Helped me learn new way of thinking, but high school math should have taught more basic math concepts

Math tutoring in high school? Yes. Basic Math. 1995-96.

Math placement exam? Yes. Got 0/10 because knew no traditional math.

Andover 19. 3.75-4.00 ACT 18-20; UMAA Communications

· I hated Core Plus; thought it was a waste and very boring.

Math placement exam? Yes. 29%. pre-calc.

Andover 20. 2.75-3.25; SAT M 500-600 V 600-700; Michigan-Public; Fine & Performing Arts or Education.

· I thought math would be really easy at [...] because [...]. But High School did nothing for me. It seems all I took from High School math was how to use the TI-82.

Math placement exam? Yes. I placed into Normal.

15a) 2

Andover 27. 2.75-3.25; ACT 21-23; Michigan-Public; Design

· Core Plus has got to be one of the worst math programs. We were never taught any of the basics and most are suffering in college math courses

Math tutoring in college? Yes. College Algebra, because I did not learn (was not taught) in high school.

15a) 1

Andover 31. 2.75-3.25; SAT M 400-500 V 500-600; ACT 21-23; MSU Communications

· The math I received in high school did not prepare me for the math I received in college. I was expected to know many things in my college course that I do not feel the Core Plus program prepared me for. I was very behind in my knowledge of mathematics upon entering my college math course [Intermediate Algebra].

Summer School. Before freshman year. First-level Algebra.

Math placement exam? Yes. I [had] a raw score of 5 right and was placed in the lowest level of math, 1825 [Intermediate Algebra].

15a) 2

Andover 40. 3.25-3.75; ACT 24-26; UMAA Business

· Core Plus focused on theory instead of numbers whereas calculus at U of M focused on numbers [and] then explained the theory behind it.

15a) 1

Andover 42 3.75-4.00 UMAA Undeclared

· Even with having an excellent teacher and being self-motivated I felt unprepared. Core Plus needs to focus more on teaching basic skills before diving into applications. The program was similar to calculus and pre-calc at Michigan in terms of group homework and story problems - but fundamental concepts need more attention!

Math tutoring in college? Yes. Made use of the math lab (free tutoring) while taking calculus to get help with new concepts and prevent being behind.

15a) 3 (pre-calc) 1 (calculus) [Count as 2 for statistical analysis.]

Andover 43. 2.75-3.25 Other Unknown

· 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.

Andover 45. 2.75-3.25 ACT 18-20; Michigan-Public; Social Science

· The reason I have not taken any math courses in college is because the math I learned in high school does not apply to college math. I used the TI-82 for linear programming and colleges do math by hand which is very tedious. Colleges all need to change to the new math.

Andover 53. 2.75-3.25; SAT M+V 1000-1100 (better in verbal) MSU Science

· I feel let down by the integrated math program. I felt as if there was a great deal of skills they assumed us to already have.

Math placement exam. Yes. Lowest math class for no credit.

Math tutoring in college? Yes. Algebra, I was not taught a lot of the “basics.”

15a) 2

Andover 54. 3.25-3.75; ACT 24-26; Non-Michigan-Public; Communications

· The math program at Andover sucks, and f____d me in my first year at [the] university and did not prepare me for [the] ACT at all.

Math tutoring in college? Yes. Trig, had no high school background.

15a) 1

Andover 55. 3.25-3.75; ACT 21-23 MSU Nursing

· The concepts I learned were interesting but did not prepare me for standardized tests or, more importantly, for college mathematics.

Math placement exam? Yes. My score (8, I think) placed me into remedial math (1825)

Math tutoring in college?. Yes. Math 103 (College Algebra). Did not learn adequate algebra concepts in high school. Therefore I was extremely behind.

15a) 2

Andover 57. 3.25-3.75; SAT M 500-600 V 500-600; ACT 21-23 MSU Business

· My math experience in high school was terrible. I used to be an excellent math student in middle school, but when I took Core Plus Math my math skills went downhill. It is a terrible pro gram. I wouldn’t recommend it to my worst enemy.

Math tutoring in high school? Yes. Core Plus Math. 1996

Math placement exam. Yes. [results not given]

Math tutoring in college? Yes. Math - I was having trouble keeping up with all the work [in Finite Math]. I didn’t understand half of it due to my terrible high school math program.

15a) 3

Andover 60. 2.75-3.25 ACT 18-20 MSU Education

· I believe that the Core Plus program was horrible. I was not prepared for college math courses, and I am now struggling in a course I am attending for the next 7 1/2 weeks at OCC. My scores on my ACT were all high except for math, which brought my overall score down.

Math tutoring in high school. Yes. Math (Core Plus). All 4 years

Math placement exam? Yes. I was placed in 1825, which is a non-credit class, but I needed it to take 103 (which is a basic algebra class).

Math tutoring in college? Yes. It was for 1825 [Intermediate Algebra], and I received help from [another] student, who [was] a math major. I needed help because I was lost in the class.

15a) 1

Andover 63. 3.75-4.00; ACT 24-26; MSU Business

· I think Core Plus is the worst math program I’ve ever been forced to take. Traditional math courses are what high schools need to teach to prepare kids for college.

Math placement exam? Yes. I placed into Math 120 but chose to begin in 103[College Algebra].

15a) 1

During subsequent phone conversation: The algebra class I took in high school was the only thing that helped in college math.

Andover 64. 3.75-4.00; SAT M 700-800; V 700-800; ACT 27-29 UMAA Science

· Core-Plus math stinks. It did not help me as much as other courses would have and should have. Do your best to end it.

Math tutoring in high school? Yes. Algebra. 1995

Math placement exam? Yes. Scored in the 20th percentile.

15a) 3

Andover 68. 2.75-3.25 ACT 21-23 MSU Communications.

· Because of the Core Plus Program I am completely unprepared and have no way to understand college math. I have to take Math 115 (High School Math) at OCC during the summer [which is] equivalent to 1825 [Intermediate Algebra] at MSU for no credit toward graduation in order to go forward into math courses at MSU. I have been extremely frustrated and disappointed with the “math” I took in High School.

Math tutoring in high school? Yes. 1994-97.

Math placement exam? Yes. I do not remember the score, but it was low. I placed into 1825 [Intermediate Algebra].

Math tutoring in college? No. I was not going to take a math course because I was so unprepared.

15a) 1

Andover 70. 3.25-3.75 ACT 21-23 Michigan-Public; Business

· I did very well in all my years of high school and got A’s and B’s in all my math courses, but when I tried taking 090 [Intermediate Algebra] at [my university], I was totally lost and didn’t know even the most basic concepts. I took a W for the class and have made arrangements with the head of the Math Department to retake the course under his tutoring next fall.

Math placement exam? Yes. Low, below avg. score. Placed into Math 090.

Math tutoring in college? Not yet, but I’m pretty sure I’ll have to.

15a) 1

During subsequent phone conversation. My high school math helped me in my Statistics course.

Andover 73. 2.75-3.25; SAT M 500-600 V 600-700; ACT 21-23 UMAA Fine & Performing Arts

· I’m not going to take and math courses in college because, although I did well in High School math, I feel I don’t understand basic math concepts well enough to keep up in college.

Mathematics courses during 1997-98 school year. None taken. Don’t feel prepared enough.

15a) 1

Andover 74. 3.25-3.75; SAT M 400-500 V 600-700; ACT 21-23; UMAA; Communications

· Andover Core-Math Program does not prepare a student entering college the sufficient basic skills that are necessary to function within college level courses.

Math placement exam? Yes. Placed in the lowest math possible.

15a) 1

Andover 77. 2.75-3.25; ACT 21-23 MSU Undeclared (maybe Communications)

· I liked how we did group work a lot of the time, and the material we were to be taught was taught in a very small amount of time. Like, I think we learned algebra for 3 days. It takes practice, but we did it anyway in 3 days. That doesn’t work.

Math placement exam. Yes. It was kind of easy and I passed. I was placed into Mth 103, 116 or 132 .

15a) 3

Andover 83. 3.25-3.75; SAT M 500-600 V 700-800; ACT 27-29; UMAA Social Science/Science

· I enjoyed my high school math class because it was neither overly difficult nor frustrating. However, it did not prepare me sufficiently for standardized tests such as the ACT/SAT and college placement exam. My high school math did somewhat help me in college. My problem in college math [Pre-Calc] was not so much about poor preparation as it was about poor teaching. My GSI was very difficult to understand. He spoke little English and drew incomprehensible diagrams on the blackboard. Also, the grading of exams was somewhat questionable.

Math placement exam? Yes. I placed in the 6th percentile. Therefore I was placed in 105 (pre- calculus).

15a) 3

Andover 84 2.25-2.75 Other

· I am currently working and feel that I cannot even do basic math calculations. I am missing too many fundamentals

Andover 91 2.25-2.75 MSU Education :

· Andover’s math program was not helpful at all.

Math placement exam? I was placed in Math 1825 [Intermediate Algebra].

15a) 1

Andover 94. 3.75-4.00; SAT M 500-600 V 700-800; ACT 24-26; Michigan-Public; Pre-Professional

· The Core math program has given me a weak math background.

Math tutoring in high school? Yes. 1996-97.

15a) 1

Andover 95. 3.25-3.75 SAT M 500-600 V 500-600 UMAA Science

· I am concerned with the direction math has taken in Core classes. Math has become second nature [read “secondary”] to learning to write about math. I am embarrassed and not the least bit confident with my math ability. I am upset that I was ever placed in a Core class!

Math placement exam? Yes. Math 105 (pre-calculus).

15a) 3

Andover 100. 2.75-3.25 ACT 24-26 MSU Communications

· When it comes to my mathematical ability here in college, I feel second compared to other students. My high school is a nationally recognized institution and while I do feel as if I’ve been well prepared in other areas, I feel that the Core-Plus math courses were a waste of four years.

Math placement exam? Yes. Placed in MTH 1825, an algebra class for no credit (towards graduation requirement[s].)

Math tutoring in college? Yes. MTH 1825 Visit[ed] Math TA (teaching assistant) during office hours for help on class material..

15a) 2

Andover 107. 3.25-3.75 SAT M 500-600 V 500-600 UMAA Social Science

· My math courses in high school barely prepared me for college. I was very behind when it came to competitiveness and dealing with the difficulty of taking a college-level Math course. [Respondent took Math 105, Pre-Calc.] I was taught difficult math ideas in high school but was never taught the fundamentals!

Math placement exam? Yes. Placed in the 5th percentile.

Math tutoring in college? Yes. Repeatedly went to office hours for special attention from my teacher, a GSI.

15a) 2

Andover 112 3.75-4.00; SAT M 500-600 V 600-700; ACT 24-26; Non-Michigan-Public; Fine & Performing Arts

· My math experience in high school was not advantageous. Although I received good marks in the courses, they did not help prepare me for the SAT or ACT . I can also positively affirm that I remember almost nothing from those courses (Core-Plus). I am very fortunate that I do not have to take any seriously math based courses in college. My major does not require me to do so. The Core-Plus math program did not help me remember the elements and forms of algebra, calculus, geometry and trigonometry for the long term. Also, there was no permanent index to the formulas and equations used. If I needed to look back on something, I could only depend on my own notes. I guess no one took it into consideration the fact that students might miss a few things in their note taking.

I learned the math and I studied it. The key, however, is that I learned it the way the Core-system presented it to me. Years of solving long word and statistical problems does not seem to help on the SAT’s. In the SAT booklet you will find a few letters (A, b or c), a few numbers, and possibly a chart. There are no words and no real-life situations presented. I’ve never been superb at math, but Core-Plus didn’t make me learn and retain it any better.

Thankfully my parents read to me as a child. I can read, write and spell very, very well. A skill I desperately needed for those standardized tests.

Andover 126 2.75-3.25 ACT 24-26 MSU Business

· At Andover High School I was required to take Core-Plus when I was a freshman. The class has not prepared me for anything in college. I am currently finishing a math class at MSU that I will not receive credit for [1825]. In this class we only use our calculators to solve simple computations. It is not acceptable to give answers produced by advanced calculator programs as we were taught in high school. By participating in the Core-Plus program I was essentially handicapped when I went to college. I don’t know where this survey will take you, but it seems to me that a positive effort is being made [by this survey] to evaluate the current situations. Please keep me informed of your progress.

Math tutoring in high school? Yes. Only to prepare for a test that contained subjects that I did not understand. I went, probably once a month.

Math placement exam? Yes. Placed into Math 103 [College Algebra]

Math tutoring in college? Yes. Tutoring for everything. I have much difficulty understand[ing] math.

15a) 1

Andover 128 2.75-3.25 SAT M+V 900-1000 SAT 18-20 MSU Business

· I received A’s B’s and a C in math [in high school], but I still didn’t know anything in the lowest Math class at State.

Math placement exam? Yes. I placed [by?] one point into regular Algebra, but they advised me to go into Intermediate Algebra.

15a) 2

Content of an e-mail message sent in response to an e-mail query of mine.

I never received the questionnaire and would like to take it. I will also tell you this, Not one person who took the Math Core program is even close to prepared for college level math, not even the Intermediate Algebra at MSU (unless they received help from a tutor, or took extra math classes at OCC) I feel the Math Core Program at Andover is the (excuse my language) dumbest thing the Bloomfield Hills School District has ever done. Most students who graduated from Andover do not even know simple Algebra. I find it idiotic that a school like Andover who has a 99% graduation record and about a 95% future college bound body changes their math program to one for students planning not to go to college.

Last year, a math teacher at Andover told his Calc. class that this was the last year Andover had any chance of doing good in the Quiz Bowl because of the new math program. He then turns around and tells our class that the Math Core program is great and will prepare everyone for college. Excuse my language but that was a bunch of bull %$&#. As you can see, I am a little bit sour about this whole thing. As you will see if you haven't found out yet, is that Andover screwed everyone who was forced to take the Math Core program, and is costing parents extra money on math tutors, classes that shouldn't be needed (like MTH 1825 at State)...etc. It also wastes students’ time. I must go, but if you need anything else just ask.

Andover 132 3.25-3.75 ACT 21-23 MSU Business

· The Core Plus program was a poor excuse of a math program. Because of it, I am well behind all other students in Math at MSU, and have struggled to the point where I have now failed a math class.

Math placement exam? Yes. I was placed in algebra.

15a) 1

Content of an e-mail message sent in response to an e-mail query of mine.

I seem to have misplaced the questionnaire that you sent. You can send me another if you like, but I will tell you right now that I am going to tear the math class to pieces. I am going to give it all the lowest marks because it was the most ridiculous class, that made the majority worse math students than at other schools, and has been the primary factor behind the failure of many students in math thus far in college.

Andover 133 3.25-3.75 SAT M 600-700 V 300-400 ACT 18-20 MSU Education

· Math has been my strong subject. I could simply understand whatever I learned in math classes. So I never spen[t] [a] long time studying for math, even before exams.

Math placement exam? Yes. The score was 18. Placed into MTH 201, math investigation[s].

15a) 4

Andover 145 2.25-2.75 ACT 21-23 Michigan-Public Pre-Professional

· I think the Core Plus program does not help especially when you get to college.

Math tutoring in college? Yes. Failing class, was not able to keep up with other students.

15a) 1

Andover 146 2.75-3.25; ACT 21-23 Michigan-Public Undecided

· Andover math left me totally unprepared for college math.

Math tutoring in college? Yes. Trouble with Intermediate Algebra.

15a) 1

Andover 148 3.25-3.75 SAT M 700-800 V 500-600 UMAA Undecided

· I didn’t really like the new [math] program we had in our high school. It didn’t prepare me well for college calculus.

15a) 1.5

Andover 150 3.25-3.75; SAT M 400-500 V 500-600 ACT 21-23 MSU Business:

· I was not properly prepared for College Math from the Core Plus program. I never completely grasped the concept of Algebra in college because of a lack of experience in high school.

Math placement exam? Yes. Placed into Algebra I.

Math tutoring in college? Yes. Algebra I - did not understand material..

15a) 2

Andover 152 3.25-3.75 MSU Liberal Arts/Business

· I feel that the preparation I received in High School with Core Plus was hardly adequate enough for College Algebra. I struggled with many basic mathematical principles that I should have mastered in High School.

Math tutoring in college? Yes. Algebra, because my High School Program was so weak and I was having a hard time with Algebra.

15a) 1

Andover 154 2.75-3.25 SAT M 400-500 V 500-600 ACT 21-23 MSU Business

· The Core Plus system was horrible to my learning. I don’t know one person who was happy with it besides the teachers.

Math placement exam? Yes. I placed in College Algebra.

15a) 2

Andover 159 2.75-3.25 SAT M+V 900-1000 ACT 24-26 MSU Pre-Professional:

· I sometimes regret that I hadn’t taken math very seriously over the past years. I hear from my graduat[ing] class that Core Plus did not help in their college math courses. I am planning to go into the [...] field so I am going to take math more seriously.

Summer School. Algebra. 1996.

Andover 162 2.25-2.75 ACT 21-23 Michigan-Public Social Science

Math tutoring in college? Yes. Math, because I was not adequately prepared.

15a) 1

Andover 163. 3.25-3.75; SAT M 600-700 V 600-700; ACT 27-29; Michigan-Public; Business

· Core Plus taught me math well; however, it did not teach me how to show my work. Because of that I failed college math.

Math placement exam? No. ACT placement.

15a) 3

Andover 164 3.25-3.75 ACT 30-34 MSU Science/Pre-Professional:

· Core Plus was useless. It helped me very little for college level calculus.

Math tutoring in high school? Yes. Just 2 sessions prior to ACT.

Math placement exam? Yes. Received a 36 out of 40.

15a) 2

Andover 168 2.25-2.75 Other

· I don’t think the Math was any good. It’s like going to a restaurant and sampling every item from the buffet table and not having any main course.

Math tutoring in high school? Yes. Junior year.

Andover 178 3.75-4.00 ACT 24-26 UMAA Social Science:

· My high school math program stunk. Andover should be ashamed for hindering the futures of their students.!!

Math tutoring in college? Yes. This semester because I am not comfortable with my math ability.

15a) We’ll see!!

Andover 187 2.75-3.25 ACT 18-20 MSU Pre-Professional

· The Core Plus math program is the worst thing I could have taken. I learned nothing I needed to know for college !!!

Math placement exam? I placed into the lowest, Math 1825 [Intermediate Algebra]. I scored a zero.

Math tutoring in college? Yes. Intermediate Algebra by my math teacher there.

15a) 1

Andover 189 3.25-375 ACT 24-26 MSU Education

· The high school math program was good. The problems arose because colleges haven’t restructured their math programs accordingly.

Math tutoring in high school? Yes. 1996-97

Math placement exam? Yes. Scored below primary math course. Had to take 1825 which is no credit towards graduating.

15a) 3

Andover 190 3.25-3.75 ACT 27-29 Private Science

· High school math was easier to apply to situations outside of the class. College math [Respondent took College Algebra] has been completely abstract.

15a) 3

Andover 191 3.25-3.75 SAT M+V 1100-1200 UMAA Business.

· I have never been so disappointed in a type of schooling such as this course. I am the epitome of mathematical ignorance in a top ten [high] school with a 4.0 in math.

Math tutoring in high school? Yes. 1996-97. Also audited Algebra classes at OCC, 1996-97.

Math placement exam? Yes. Pre-Calc.

Math tutoring in college? Yes. My Pre-Calc. Class has far surpassed my capabilities and under- standing in Math.

15a) 1

Andover 204 3.25-3.75 ACT 21-23 UMAA Nursing

· The math program in high school did not sufficiently prepare me to continue in college level mathematics!

Math placement exam? Pre-Calc - failed - 4%

15a) 3

Andover 205 2.75-3.25 ACT 18-20 MSU Education

· I took Core Plus all through high school and it did not prepare me at all for college math. I should have learned basic algebra in the 9th grade and because of this program, I learned it this past year. I know that many others also struggled in college math and ended up in low math classes because of Core Plus

Math tutoring in high school? Yes. 1995-96.

Math placement exam? Yes. I was placed in Math 1825 or Intermediate Algebra.

Math tutoring in college? Yes. I received tutoring in College Algebra, because I had never learned the material in high school.

15a) 1.5

. Andover 206 3.25-3.75 SAT M 500-600 V 500-600 UMAA Social Science:

· I’m horrible at math and do not intend on taking any math courses in college. However, I think it has much more to do with my interests and little to do with my high school math background.

Math placement exam? Yes. I fell into the 0 - 1 percentile (the last percentile).

15a) N/A

Andover 207. 3.75-4.00; SAT M 500-600 V 500-600; ACT 27-29; UMAA; Science

Math placement exam? Yes. Placed into Precalculus. Scored 1- %tile.

Math tutoring in college? Yes. Algebra, through the free tutoring through the University. I didn’t know algebra.

15a) 1.5

Andover 209 3.25-3.75 SAT M 400-500 V 500-600 MSU Pre-Professional

· My experience of math in high school was a waste of my time! The only reason I did good [in College Algebra] at MSU was because I took math courses at OCC for audit.

Math tutoring in high school? Yes. 1994-97.

Summer School Algebra, 1996 and math at OCC, 1996, to get me ready for College Algebra at MSU.

Math placement exam? Yes. Do not remember the score, though I ended up guessing on a lot of the questions.

Math tutoring in college? Yes. Math. (College Algebra), to improve my understanding of the course.

15a) 2 (only helped me by teaching me how to use the TI-82 Calculator)

Andover 213 2.75-3.25 ACT 18-20 MSU Undecided

· I did not enjoy Math at Andover High School. I feel it did not prepare me for College Math.

Math placement exam? Yes. 3%/100%

15a) N/A

Andover 220 225-2.75 ACT 18-20 Michigan-Public Education

· I did not have much success in the Core Plus Math Program in High School. Since it wasn’t regular algebra or calculus, it was difficult.

Math placement exam? Yes. Beginner course. I will take [exam] over again (didn’t take the class).

Andover 224 3.25-3.75 SAT M 600-700 V 600-700 UMAA Liberal Arts

· Core Plus may be a good idea for non-college bound students - but almost 100% of Andover’s [graduating] classes go to college. I feel like I was screwed over.

Summer School. Algebra 1, summer before freshman year.

Math placement exam? Yes. Received < the 10th %tile; placed in 105 (pre-calc).

Math tutoring in college? Yes. Math - I had no idea what was going on.

15a) 1

Andover 228 3.25-3.75 ACT 21-23 Michigan-Public Fine & Performing Arts

· My class (1997) was the first class to use Core-Plus, so the kinks were still being worked out. However, I do not feel I can hold a conversation about math problems, using math vocabulary, due to the lack thereof using Core-Plus.

Math placement exam? Yes. Placed in entering freshman math (basic).

15a) 3

Andover 229 3.25-3.75; SAT M 500-600 V 700-800; ACT 27-29; Michigan-Public; Communications

· My Math teachers seemed to make math a chore, rather than a subject to be learned and studied. I always ask “why” and “how”, and in math, those questions were never answered. It was always “Just do it!” That is a large part of why I do not take an interest in math.

Summer School? Yes

15a) 1

Remaining Andover Group I Students {non-accelerated (Core Plus)}

Andover 5 3.25-3.75 ACT 24-26 UMAA Social Science

· Calculus at Michigan is not hard, but the TA’s that teach it make it hard. Exams are extremely difficult.

Math placement exam? Yes. Placed in Calc. 115.

Math tutoring in college? Yes. Instructor was a Teaching Assistant [and] was incapable of teaching material well.

15a) 5

Andover 102. 3.25-3.75; ACT 21-23 MSU Pre-Professional

Math tutoring in high school? Yes. 1993-95

Math placement exam? Not yet (I want to start from the lowest.)

Andover 109 3.25-3.75; SAT M 500-600 V 700-800 UMAA Liberal Arts

Andover 182 2.75-3.25 MSU Social Science

Math placement exam? Yes.

15a) 1

Andover Group II Students {accelerated} who made comments about Core Plus[26]

Andover 37 2.75-3.25 ACT 27-29 UMAA Liberal Arts

· The new math program has made math difficult for many college students.

15a) 3 b) 3

Andover 41. 3.25-3.75; SAT M 600-700 V 500-600; ACT 30-34; UMAA Pre-Professional

· I was [one of few] to ever take both Core Plus and “regular” math at Andover High School. Thus making me a “guinea pig” in this heated debate. I have a lot of good views on this so feel free to contact me. PS I saw the article in the News and I believe I can add to what was said.

Math tutoring in high school? Yes. Geometry 1993-94. Pre-Calc 1995-96

Math placement exam? Yes. Placed into Calc. I. I think I was the only Andover student who took a Core-Plus class to place into Calc I (Math 115).

15a) 5 b) N/A

Content of subsequent e-mail message. My views about Core Plus are not necessarily negative but I think more constructive if anything. There are some things about the program that are better than "traditional" and some that aren't and vice versa.

First, and I have thought this since the beginning, I don't think that the high schools are in the authoritative position to initiate a major change in the way that math is taught. The biggest argument when Core Plus (CP) first came aboard was that it wouldn't complement what colleges were teaching. That proved right, and the educators who were firmly behind CP neglected to hear out and respect the students’ and their parents' worries. An alternative route would have been to work in conjunction with universities and maybe have the universities change first and then the high schools would follow. I remember that I was told in the beginning that CP is the new wave of mathematics and that it is the way everything will be in the future...including colleges. Well, guess what, I'm in college and there isn't a CP program here, although some people claim that “Harvard Calculus” (Math 115-116 here) is a good fit with CP. I will have to check this out further, but that still leaves the schools that don’t feature reform calculus, and there are many of those, including many top schools.

I found that CP was interesting, much more interesting than "Hey, let's do 1-99 odd and look in the back of the book for the answers". It explained the “How”s, “What”s, and “Why”s of the math problems. Though what it forgot to do is emphasize the mechanics of the problems. The important steps were never really emphasized. It seemed almost like they were steering away from directly solving the problem. Why beat around the bush? I found myself a lot of times using my past knowledge from traditional classes to solve CP problems. Maybe that's where I go wrong but hey, a math program isn't supposed to make the student make adjustments to it, it should be flexible enough for anyone to respond to it. Working in groups was often a bonus. Though a lot more teamwork and feedback is produced during group work, it is also easy to have some members trail off into no man's land, and thus hindering the group's performance, and their own.

From the start of my CP class, I found the material quite insufficient. No practice problems, examples, and insufficient explanations were all what I found as a problem with the thin color coded packets. Sometimes you would have to rely on the explanation of your group but then would have to question if the explanation was correct or not. Thus, slowing down the learning process.

In conclusion, I want to be clear that I am not trying to insult the program. I do think that it could be a useful method in Mathematics if presented correctly. I have a lot of respect for my high school and for what they strive to do. I believe that Andover is amongst the elite sec-ondary schools in the nation, and for that I am proud of it. The faculty of Andover has always striven for the best, though it seems as if they are selling themselves short with CP.

Andover 50 2.75-3.25 SAT M 600-700 V 500-600 UMAA Pre-Professional

· The traditional math courses in high school helped me tremendously in my college calculus course. I cannot understand how someone without these basic skills can take a college level calculus course. In high school I had many friends in the Core-Plus program and by senior year they could not even factor or do other basic mathematics which I learned in 8th grade! And there were above 3.5 GPA students. Personally, from experience and observation of my peers, I don’t think there is a way to get around learning basic math skills. For example, when teaching a child to tell time one does not need to impart the interworkings of a clock. The explanations of the “Why”s come much later. after the fundamentals are in place.

It seems to me that this whole Core-Plus movement is geared toward the “laziest” common denominator. It discriminates against those who want to excel in math and take the time to learn/memorize the basics. Where is the common sense in all of this? It is non-existent. Where else would you teach advanced concepts without the fundamentals? In life you have to start out with a base and then move on to greater and more complicated things.

Do you teach a child thermodynamics when teaching them not to touch a hot stove? No. You just teach them that the stove is hot, don’t touch. 2+2 is 4 and 8x7 is 56. There’s no way to talk around it. One just needs to memorize it. If one doesn’t have this base, how can one move on to greater things like calculus. In college-level courses one can explain why certain answers are arrived at, but at lower-level courses, explaining why 4+5 equals 9 is completely unnecessary!

Some people don’t seem to realize how this new approach has sealed the fate on many students. They are so far behind that I doubt they will ever be able to make up for what has been lost. I found the U of M placement test to be very basic. Any student with the fundamentals of algebra and geometry should be able to either pass the test or at least get most of the problems correct. However with many of my “Core-Plus friends,” this was not the case. Some, even 3.9 students, received a near 10% score, if that, on their placement test.

It seems quite obvious that many of the Bloomfield Hills Core-Plus students are ill-prepared for higher level learning. Shame on the Bloomfield Hills School District.

Math placement exam? Yes. I was placed in Calculus 115.

15a) 5 b) 3

Andover 59 3.75-4.00 SAT M 700-800 V 700-800 UMAA Liberal Arts

· I think the Core-Plus program stinks! It babysteps around the true concepts of math and instead kids learn a ‘watered-down” version which they can’t really use. I feel very fortunate that I did not have to take Core-Plus classes. If you would like to reach me for additional comments you may do so through e-mail [...]. Thanks.

Andover 62. 3.25-3.75 SAT M 600-700 V 600-700; Non-Michigan-Public; Business

· 99% of my circle of friends were part of the new math program implemented by Andover. My knowledge is that they are having an extremely difficult time with college math courses and their SAT math scores were very low. I feel that Andover should return to the standard math curriculum and teaching of it.

Math tutoring in high school? Yes. Calculus. 1996-97.

15a) 5 b) 1

Andover 113 3.25-3.75 SAT M 700-800 V 700-800; ACT 30-34 UMAA Engineering

· I found that taking High School Calculus helped a great deal when I took Calculus II. I also found that I performed much better on standardized math exams than my peers who took Core Plus.

Math placement exam? Yes. Score = 80%. Placed into Calculus II.

15a) 3 b) 5

Andover 116 2.75-3.25; SAT M 600-700 V 700-800; ACT 30-34 Other Fine & Performing Arts:

· I enjoy math and enjoyed the classes I took, but because I am going to an Art School, I am not required to take Math courses. In eighth grade, because ours was the first class to start the Math Core program in high school, we were given a choice. If we got into the advanced class, Algebra 1, we would continue on in the original, classic Math program. I had no interest in entering into a new experimental program, and so [I] worked extra hard to get into the Advanced Algebra 1 class. Luckily, I made it.

15a) 1 b) 1

Andover 151 3.75-4.25; SAT M 700-800 V 600-700 ACT 30-34 UMAA Engineering

· I attended Andover during the transition from the traditional math program (which I took) to Core-Plus. As a student at the UM College of Engineering, I firmly believe that Core-Plus does not adequately prepare students planning to enter any field that requires math (math, science, engineering, etc.). Students [in Core Plus] depend too heavily on calculators, due to the fact that they have no knowledge of the fundamental aspects of algebra. True, “Core-Plus” may tie math in with “real-world” situations, but problems in fields that require math are seldom “real-world” situations.

Math placement exam? Yes. Placed into Calculus. [Took higher level course due to AP test score.]

15a) 5 b) 5

Andover 165 3.75-4.00; SAT M 600-700 V 700-800; ACT 30-34; UMAA; Science/ Pre-Med

· I feel like I was one of the lucky ones who escaped the horror of Core Plus. I’m not a math person and luckily I was able to do well enough in high school to avoid as much [math] as possible in college; but if I was a math-oriented student and I had had a Core-Plus background, I’d be in BIG TROUBLE.

Math placement exam? Scored in 80th percentile. Placed into Calc 115. (AP credit placed me out of Calc 115/116, though)

15a) 5 b) 5 (I haven’t taken a math class yet, but I assume it would have helped.)

Andover 185 3.75-4.00; SAT M 700-800 V 700-800 ACT 30-34 UMAA Undecided

· I really believe that having specialized math classes (i.e. geometry, calculus, algebra, etc.), rather than Core Plus classes, truly helped me in preparation for standardized tests.

15b) N/A

Andover 222 3.75-4.00 ACT 24-26 UMAA Business

· My experiences have led me to believe that my high school math program prepared me for college and SAT/ACT much better than [the] Core Plus Program.

Math placement exam? Placed in Math 115/116 [Calc I/II]

15a) 5 b) 5

Remaining Andover Group II Students

Andover 1 3.75-4.00; SAT M 600-700 V 700-800 ACT 30-34 UMAA Science

Math placement exam? Yes. [Passed]

Andover 2 3.25-3.75 SAT M 700-800 V 700-800 ACT 30-34 UMAA Engineering

· Very good program [at Andover]. Calc. teacher taught at and involved with U of M, so he taught appropriate subjects and style for intended U of M students.

Math placement exam? Yes. Calc 116.

15a) 5 b) 5

Andover 15 3.75-4.00 SAT M 600-700 V 600-700 UMAA Liberal Arts

· For the above two questions (#15) I was considering physics a “math course” since I have not taken any others in college.

Math placement exam? Yes. Placed into Math 115, which is Calc. I.

15a) 4 b) 4

Andover 26 3.75-4.00 SAT M 600-700 V 700-800 UMAA Pre-Professional

Math placement exam? Yes. Placed into Calc I (115).

15a) 4 b) 2

Andover 28 3.75-4.00 SAT M 600-700 V 600-700 ACT 27-29 UMAA Science

· I [was] definitely not impressed with the quality of grad. student instructors (GSI’s) at the U of M. There was a communication barrier and I believe that the courses [Calc I&II] lacked a lot.

Math tutoring in high school? Yes. Calculus BC. 1997

Math placement exam? Yes. I placed into Calculus 116. I opted to take Calc. 115 instead so I would be more prepared.

15a) 3 b) 4

Andover 29 3.25-3.75 SAT M 600-700 V 600-700 UMAA Engineering

· My 2nd Semester Calculus course [Calc II] was identical; to my AP Calculus course [AB Calc.] in high school.

Math placement exam? Yes. [No score given. Took Calc. II and Calc III]

15a) 3 b) 5

Andover 35 3.25-3.75 ACT 27-29 UMAA Social Science

· Because of taking calculus (traditional) in high school and because of my teacher (Dr. Shelly), I was able to slide through Calc 115 - I barely studied while others failed - you were expected to teach yourself

Math placement exam? Yes. Placed into Calc. 115. Don’t know scores.

15a) 5 b) 5

Andover 44 3.75-4.00 ACT 30-34 UMAA Business

· Dr. Michael Shelly was an excellent Calculus teacher (Andover High School). U of M need[s] more GSI’s that speak English.

Math placement exam? Yes. Score - ?; Math 115.

15a) 3 b) 5

Andover 46 3.25-3.75; SAT M 600-700 V 600-700 ACT 27-29; UMAA Engineering

· The division of subdivisions within math helped my focus. Furthermore, it helped me identify each subdivision in more complex math courses.

Math placement exam? Yes. Top 5%.

Math tutoring in college? Yes. Math 116, problems with integrals.

15a) 5 b) 5

Andover 48 3.25-3.75 ACT 27-29 UMAA Science

Math tutoring in high school? Yes. Algebra. 1995

Math placement exam? Yes. Placed into Calc. 115, but because of AP’s, I went into 116.

15a) 5 b) 5

Andover 58 3.25-3.75; SAT M 600-700 V 600-700 UMAA Business

· I was able to get by in High School courses with severely limited knowledge and still pull a “B”.

Math tutoring in high school? Pre-Calc. Junior year.

Math placement exam? Yes. Placed in low level course. [Took Stat. 100].

15a) 2 b) 1

Andover 61 3.75-4.00 ACT 30-34 UMAA Pre-Professional

Math placement exam? Yes. I placed into Math 115 or Calc. I. [Took Calc. II.}

15a) 3 b) 5

Andover 85 3.75-4.00; SAT M 700-800 V 600-700; ACT 30-34; Private; Science

Math placement exam? Yes. Calc.I/II Placement Test: Calc. II

15a) 3 b) 5

Andover 88 2.75-3.25 SAT M 700-800 V 700-800 Other

Andover 96 3.25-3.75 SAT M 600-700 V 600-700 ACT 27-29 UMAA Science

· The U of M Math department is terrible.

Math placement exam? Yes. Placed into Calc. 115. The highest possible placement without AP credit.

15a) 3 b) 3

.Andover 103 3.75-4.00; SAT M 600-700 V 700-800 ACT 30-34 UMAA Liberal Arts

· Calculus BC was the most exciting and interesting course in high school. Although I think I would do well, I don’t plan on taking any math courses in college.

Math placement exam? Yes. I placed out of Calc. I and II.

15a) N/A b) N/A

Andover 104. 3.75-4.00 ACT 30-34 Private Business

· My high school math teachers were wonderful. I learned more from them than I did from my college professor. Dr. Shelly was able to successfully explain concepts of calculus and make it interesting at the same time.

15a) 5 b) 5

Andover 117 3.75-4.00; SAT M 700-800 V 600-700; ACT 30-34 Private Social Science

· I placed out of the calculus courses that a majority of my college peers took freshman year.

Math placement exam? AP tests served as placement.

15a) N/A b) N/A

Andover 119 2.75-3.25 ACT 24-26 Private-regional Engineering

Math placement exam? Yes. Scores were not revealed but I was suggested to take Pre-Calc.

15a) 3 b) 3

Andover 127 3.75-4.00 SAT M 700-800 V 500-600 ACT 27-29 UMAA Science

Math placement exam? Yes. Calculus placement.

15a) 4 b) 5

Andover 138 3.75-4.00 SAT M 600-700 V 600-700 ACT 27-29 UMAA Business

· My math experience in high school was satisfactory; I was very fortunate to have had good teachers. As for college, I enjoyed Math 115 [Calc. I] because the teacher was very thorough, but I disliked Math 116 [Calc. II] because the teacher was very disorganized and didn’t seem to enjoy teaching. Teachers (rather than the curriculum) play such a crucial role in my math education. I would like to add, though, that I had no complaints about the traditional math program.

Math placement exam? Yes. Score 88%. Placed into Calc. I.

15a) 4 b) 5

Andover 140 3.25-3.75 SAT M+V 1100-1200 ACT 27-29 Other Fine & Performing Arts

· We had 3 levels of Math achievement. I was placed in the accelerated class and could never keep up!

Math tutoring in high school? Yes.

Summer School? Algebra.

Math tutoring in college? I will attend U of M in the Fall and will need a math tutor.

15a) 3.5 b) 3.5

Andover 156 3.75-4.00 SAT M 600-700 V 700-800 UMAA Social Science

· [A complimentary remark, by comparison with other teachers, about Miss Cathy King.]

Math placement exam? Yes. I was placed in 115. .

Math tutoring in college? Yes. Calc. To prove that I was at least making an effort at trying to perform better on the exams.

15a) 2.5 b) 1

Andover 158 3.75-4.0 SAT M 700-800 V 600-700 ACT 30-34 UMAA Science

· I had 3 excellent years of traditional high school math and one fair year of [...]. I was very well equipped to handle college math, which was perhaps easier than that taken during high school.

Math placement exam? Yes. [Doesn’t give score. Placed in Multivariable Calculus because of AP score.]

15a) 5 b) 5

Andover 161 3.25-3.75 SAT M 700-800 V 700-800 ACT 30-34 Private Science

· College math classes (including calculus) and high school math, I believe, are entire[ly] different endeavors. Although high school math should be the basis and is necessary for further education in higher math, it does not necessarily help in college math (taking into account only the curriculum).

15a) 1 b) 4

Andover 166 3.25-3.75; SAT M 600-700 V 500-600; ACT 24-26; Private; Social Science

· Math has always been one of my favorite subjects and I’ve enjoyed it throughout high school and college.

15a) 5 b) 5

Andover 176 3.25-3.75 SAT M 600-700 V 500-600 UMAA Science

· I was lucky enough in high school to have pretty good math courses with good teachers. These math classes prepared me for college math classes because I had a stable math background coming into college.

Math placement exam? Yes. Placed into Math 115.

15a) 4 b) 4

Andover 179 3.75-4.00 SAT M 70-800 V 700-800 Private unsure

15a) 4 b) 5

Andover 181 3.25-3.75 SAT M 700-800 V 500-600 ACT 27-29 Private-regional

Social Science

· I found the math courses prior to Calculus AB fairly easy.

15a) 3 b) 4

Andover 183 3.25-3.75 SAT M 700-800 V 500-600 ACT 24-26 UMAA Business

· I was forced to memorize math concepts in High School and it wasn’t valuable to my learning. College math [Calc. I] has taught me to learn and apply ideas. More beneficial.

Math tutoring in high school? Yes. Geometry. 1994.

Math placement exam? Yes. I placed into Calc. 115

15a) 4 b) 4

Andover 198 3.25-3.75; SAT M 600-700 V 500-600 ACT 27-29 Non-Michigan-Public Science

Andover 219 3.75-4.00; SAT M 700-800 V 500-600; ACT 27-29; UMAA; Pre-Professional or Education

Math placement exam? Yes. 94th %tile

15b) N/A

Andover 221 3.25-3.75 SAT M 600-700 V 600-700 ACT 27-29 UMAA Liberal Arts

Andover 232 3.25-3.75; SAT M 700-800 V 700-800; ACT 30-34; UMAA Social Science

· Calculus class [was] very good at Andover. Michigan math program is embarrassing. It is the worst thing I have ever been a part of. The math base [in Calc II] was ignored and short cuts were taught. The program is horrendous.

Math placement exam? Yes. Basic Algebra. 90th percentile?

Math tutoring in college? Yes. Calc. 116. From GSI to get better grade.

15a) 4 b) 5

Lahser Group I Students {non-accelerated}

Lahser 10 325-3.75; SAT M 600-700 V 600-700; ACT 27-29; Private-regional; Science/Engineering.

Math Placement Exam? Placed in Calc. I

15a) 4

Lahser 11 3.25-3.75 ACT 21-23 MSU Liberal Arts

· I dislike math. I feel as if I will never use any of it in life later on. When will I ever use Descartes’ Rule?

Math tutoring in college? Yes. Math 1825 and 103, very bad in math.

15a) 3

.Lahser 34 2.75-3.25 ACT 21-23 Other Nursing.

Math Placement Exam? Yes. Normal level for my grade.

15a) 4

Lahser 38. 3.25-3.75; SAT M 500-600 V 600-700; ACT 24-26; Non-Michigan-Public; Communications

· I lacked basic knowledge of Calculus or Trig. [Respondent took neither in H.S.]

15a) 4

Lahser 46. 3.25-3.75; SAT M 600-700 V 600-700; ACT 24-26 UMAA Social Science/Business

· The Math. Dept. at U of M doesn’t know how to teach. It is all applied non-memorized tests. [Respondent took Calc 1.] The stuff in high school is so easy and basic - you do problems that are all the same. In college it is taking a deeper understanding of that simple problem and using it in combination with others for something complex.

Math Placement Exam? Yes. I was placed in pre-calc. (105).

Math tutoring in college? Yes. Math Lab - for homework question help.

15a) 2

Lahser 54 3.25-3.75; SAT M 500-600 V 500-600 ACT 24-26 UMAA Pre-Professional

· I thought my high school prepared me well for all of my non-math classes at U. of M.; however, the math classes at U of M are supposed to be very hard, and I have heard people did not feel prepared for the math classes at U. of M.

Math Placement Exam? Yes. Placed into Math 105, which is equivalent to pre-calc.

15a) 3

Lahser 64 2.25-2.75; SAT M 500-600 V 400-500; ACT 21-23; Michigan-Public; Business

· I feel that I had a good math experience in high school, but I think the math placement test given by [my University] was poor and did not place me correctly into the math class I should have been in. [Respondent evidently felt placement was too high, judging by grade received.]

Math Placement Exam? Yes. I was placed into finite math. 15a) 4

Lahser 68. 2.75-3.25; SAT M 600-700 V 600-700; ACT 21-23; Michigan-Public; Undecided

Math tutoring in high school? Yes. Alg. II 1995-96.

Math Placement Exam? Yes. College Algebra.

15a) 3

Lahser 96 3.25-3.75 SAT M 600-700 V 500-600 ACT 24-26 UMAA Social Science

· High school math course needs to teach students how to solve and get right answer. Not just getting the answer. [Respondent took Calc I].

Math Placement Exam? Yes. Placed in Math 115 [Calc. I]. Passed exam with 95%.

15a) 4

Lahser 117 3.25-3.75 ACT 21-23 Michigan-Public Nursing

· Although I placed into only Intermediate Algebra in College, I found the class to be very easy and not challenging at all. I am sure I would have done fine in regular College Algebra, but instead I have to take it this year.

Math placement exam? Yes. Placed into Intermediate Algebra.

15a) 5

Lahser 136 2.75-3.25 Michigan-Public Education

· I hate, hate, hate math! I think that some Math courses are pointless and will never be used.

Math tutoring in high school? Yes. Algebra. 1993-94.

15a) N/A

Lahser 141 3.4 ACT 21-23 UMAA Design

· It was really hard for me to understand some things in Math, but when you get a great teacher that will take the time to help me, I can finally understand.

Math tutoring in high school? Yes. Algebra 2. Sophomore year.

Lahser 148 3.25-3.75 ACT 27-29 MSU Business

15a) 3

Lahser 154 3.25-3.75 SAT M 500-600 V 600-700 ACT 24-26 MSU Fine & Performing Arts

Math Placement Exam? Yes. I was placed into Math 103 [College Algebra], the lowest credit math course.

15a) 3

Lahser 170 3.25-3.75 ACT 24-26 UMAA Education

· I just had a hard time in Pre-Calc. but had a very easy time in Algebra II. I think it was the teaching style.

Math Placement Exam? Placed into 105 or 115.

Math tutoring in college? Yes. I went in for math help from my teacher during Math Lab and office hours.

15a) 4

Lahser 175 3.75-4.00 SAT M 600-600 V 500-600 ACT 24-26 Private Science

Math tutoring in college? Yes. Calc 140 - At [my college] there are 3 levels of calculus. I had the requirements for the middle level; however, due to the extreme demands of the upper level (whose requirements were one year of calculus) the majority of those students dropped down a level into my section. My professor then stopped teaching to the level of the students (like myself who the class was intended for) and taught only to the students that had already learned the material. Therefore the original students (approx. 20) worked with the math intern assigned to our class. (Of the 20 of us, 13 changed our class grade to pass/fail because we had no idea what was going on. [Respondent passed.]) I have now just finished a summer class at OCC and have learned what I was supposed to have [learned] last year.

15a) 1

Lahser 195 2.25-2.75 ACT 18-20 Michigan-Public Engineering

Math tutoring in high school? Yes. Algebra 1. Freshman year.

Math tutoring in college? Yes. Math 110, tutoring to get help pass class.

15a) 4

Lahser 198 2.75-3.25 SAT M 500-600 V 500-600 Private Business/ Design

· Minimal math - didn’t prepare me well - need to catch up in college. [Respondent took only Algebra 1 and Geometry in H.S.]

15a) 2

Lahser 206 [not given] ACT 24-26 Other Fine and Performing Arts.

· I am an art major - no math in college.

Lahser 212 3.25-3.75 Non-Michigan-Public Fine & Performing Arts

· It was fun.

Math Placement Exam? Yes. Basic Math.

15a) 4

Lahser 219 3.25-3.75; SAT M 500-600 V 700-800 ; ACT 27-29; MSU Communications/Business

· I think there is still a sex bias in which men are driven into the areas of math and science here and encouraged to more than girls.

Math tutoring in high school? Algebra I 1992 (8th grade). Pre-Calc. 1997.

Math Placement Exam? Yes. I received an 11/20 - Placed in Math 110.[College Algebra and Finite Math.]

15a) 4

.Lahser 222 2.75-3.25 ACT 18-20 Private-regional Education

15a) 3

Lahser 230 2.25-2.75 SAT M 500-600 V 500-600 Michigan-Public Nursing

· It was overall pretty good; I know that I’m bad at math, so my grades reflected the fact that I didn’t try too hard. I need to put in extra time for those classes.

Math tutoring in high school? Yes. Spring, 1997, Pre-Calc. Fall, 1997, College Algebra

Math placement exam? Yes. I was placed in Intermediate Math

Math tutoring in college? Yes. College Algebra, because I was doing poorly in the class and I wanted to improve my grade.

15a) 5

Lahser 233 3.25-3.75 SAT M +V 1100-1200 ACT 24-26 UMAA Science

Math placement exam? Yes.. Math 105 (Pre-Calc). [Took Stat 100.]

15a) 3

Lahser 241 3.75-4.00 ACT 24-26 Michigan-Public Science and Liberal Arts

15a) 5

Lahser 250 2.25-2.75; SAT M 300-400 V 600-700; ACT 18-20; Non-Michigan-Public; Liberal Arts

· I am a horrible math student (I have had trouble all throughout schooling.), but in high school I was in advanced English.

Math tutoring in high school? Algebra I, 1994. Geometry, 1997.

Math Placement Exam? Yes. It was 30 questions. I failed.

15a) 1

Lahser Group II Students {accelerated, no calculus}

Lahser 14 2.25-2.75 Other

Lahser 17 3.25-3.75 ACT 24-26 MSU Business

· I believe that by taking AP Statistics senior year I scored poorly on the math placement test in college, because I had not used general algebra for quite some time, but once I took algebra in college [Math 103: College Algebra], it was very easy.

Math placement exam? Raw Score: 10. Eligible to enroll in Math 103, 110, 116 or 120.

15a) 5

Lahser 20. 2.75-3.25; SAT M 600-700 V 700-800 Non-Michigan-Public; Communications

· High school math departments need to encourage, not discourage, girls to succeed and continue their mathematic[al] careers.

15a) 4

Lahser 60 3.75-4.00 SAT M 600-700 V 600-700 ACT 30-34 UMAA Business

Math placement exam? Yes. I scored in the 60th percentile and was placed in Calculus.

15a) 4

Lahser 62 3.75-4.00 SAT M 600-700 V 500-600 ACT 24-26 UMAA Science

· The tests in college (at least at U of M) are MUCH harder than high school tests [Respondent took Calc I&II], which test only the concepts in a way already studied. College tests test the application of the concepts through story problems, ones different from any already in the text.

Math tutoring in high school? Yes. Algebra II, 1994-95. Pre-Calculus, 1995-96.

Math placement exam? Yes. Placed into Calculus I.

15a) 4

Lahser 74 3.75.-4.00 SAT M+V 1100-1200; ACT 27-29; Michigan-Public Business

· Math was definitely not my favorite class in high school. However, I have really enjoyed the math courses I took in college. I like math a lot more now.

Math placement exam? Yes. I don’t remember my score, but it was not high enough to place into Calculus.

Math tutoring in college? Yes. Attended Supplemental Instruction right after class, for group study and review.

15a) 4

Lahser 87 2.75-3.25 SAT M 600-700 V 400-500 ACT 21-23 MSU Engineering

15a) 3

Lahser 92 3.75-4.00 SAT M 600-700 V 700-80 ACT 30-34 UMAA Liberal Arts

Math Placement Exam? Yes. Placed into Pre-Calculus.

Lahser 101 2.75-3.25 SAT M 500-600 V 500-600 ACT 24-26 MSU Science

· College TA’s have been more detrimental to my learning than helpful. Most of my work has been on my own. High School math was completely unhelpful.

Math Placement Exam? Yes. [Score not given. Took Intro. College Algebra and College Algebra.]

15a) 2

Lahser 108 2.75-3.25; SAT M 600-700 V 60-700; Private-regional Social Science/Business

· High school math teachers (at Lahser) were far better than those at [my college].

15a) 5

Lahser 127 3.25-3.75 SAT M 500-600 V 500-600 UMAA Science/Liberal Arts

· In high school I learned in math more from the teachers than in college. However, I overall learned more in college because of tutoring. I think that the math program at U of M needs improvement. I along with many others did not learn anything without help from others.

Math tutoring in high school? Yes. Pre-Calc. Junior Year.

Math placement exam? Yes. Pre-Calc.

Math tutoring in college? Yes. Pre-Calc., because they don’t know how to teach math at all.

15a) 2

Lahser 142 3.25-3.75 SAT M 600-700 V 700-800 ACT 30-34 Other; Liberal Arts

· I didn’t do well in pre-calc. Because, well, I didn’t really like it. So I didn’t do my homework. (Isn’t that terrible?) That’s why my grades went down.

Lahser 178 2.75-3.25 ACT 24-26 Non-Michigan-Public Liberal Arts

15a) 3

Lahser 186 2.75-3.25 ACT 21-23 Michigan-Public Science/Education

· Math classes taught do not always apply back to life; because of that it is hard to learn what can’t be applied.

15a) 3

Lahser 243 2.0-2.25 Michigan-Public Engineering

· Teachers who are enthusiastic about their subject get a better response.

15a) 4

Lahser Group III Students {accelerated, with calculus}

Lahser 2 3.75-4.00; SAT M 700-800 V 700-800; ACT 30-34; Private; Science

· Calc. BC gives excellent preparation for Multivariable Calc., other applications. I think it is very reasonable to cover Algebra II/Trig/Pre-Calc. in three semesters instead of the traditional four, leaving room to introduce Multivariable Calc. in Senior Year, if desired.

Math placement exam? Yes. Credit received for Probability and Statistics. Score around 130/200.

15a) 5 b) 5

Lahser 18 3.75-4.00 SAT M 700-800 V 500-600 ACT 27-29 UMAA Science

Math placement exam? Yes. Placed in the 97% percentile or out of Calc. 116 [Calc. II].

15a) N/A b) N/A

Lahser 30 3.75-4.00 ACT 30-34 MSU Engineering

· I think there are gap[s] between High School and College Math level[s].

15a) 1 b) 3

Lahser 32 3.25-3.75 SAT M 600-700 V 600-700 ACT 27-29 UMAA Science/Pre-Professional

Math placement exam? Yes. Score of 99th percentile.

15a) 5 b) 4

Lahser 71 3.25-3.75 SAT M 600-700 V 500-600 ACT 24-26 UMAA Science

· Math in high school was very easy and did not go very in depth. In college we covered a broad variety of topics and went into greater detail. Teaching in college math courses are [read “is”] very poor.

Math placement exam? I scored in the top 20% of students and was placed into Calc. II because of the high score and AP test score.

15a) 3 b) 5

Lahser 77. 3.75-4.00 SAT M 700-800 V 600-700 Private; Science/Liberal Arts

· Math is based on rules whereas some other subjects (e.g. English) are based on connotations; therefore, math needs to be taught (at least in the beginning) in a format stressing rules rather than interconnections, which may be interesting, but are confusing to the beginner.

Math placement exam? Yes. More a test of ability than for placement.

15a) 5 b) 5

Lahser 83 3.25-3.75 SAT M 600-700 V 600-700 MSU Engineering

Math tutoring in college? Yes. Help from my T.A.

15a) 4 b) 5

Lahser 95 3.75-4.00 SAT M 600-700 V 700-800 Private Science

15a) N/A b) 5 (I received 2 semester’s credit for Calculus.)

Lahser 106 3.75-4.00 SAT M 700-800 V 600-700 ACT 30-34 UMAA Engineering

15a) 2 b) 4

Lahser 118 2.75-3.25; SAT M 600-700 V [not given]; ACT 21-23; Michigan-Public; Business

Math placement exam? Yes. Placed into Algebra 2.

15a) 3 b) 1

Lahser 120 2.25-2.75 SAT M 600-700 V 500-600 ACT 27-29 MSU Business

· Math was much harder in High School than college.

Math placement exam? Yes. I placed into the highest math, Calc. 132

15a) 5 b) 5

Lahser 139 2.75-3.25 SAT M 700-800 V 500-600 ACT 27-29 UMAA Business

Math placement exam? Yes. Placed into Calc. 116.

15a) 3 b) 5

Lahser 153 3.25-3.75 ACT 24-26 MSU Business

15a) 2 b) 4

Lahser 161 3.25-3.75 SAT M+V 1200-1300 ACT 21-23 UMAA Undeclared

15a) 4 b) 4

Lahser 162 3.75-4.00; SAT M 600-700 V 700-800; ACT 30-34; Non-Michigan-Public; Education

Math placement exam? Yes. Placed into Statistics.

15a) 2 b) 1

Lahser 165 3.25-3.75; SAT M 700-800 V 700-800 Non-Michigan-Public; Science and Fine & Performing Arts

· I feel that I learned almost all of my high school math during Freshman and Sophomore years. [I did not mesh with my advanced math teacher’s ] teaching style, which was more concerned with “Did you get the right answer?” than “Do you know the method to get the right answer?”.

15a) 5 b) 2

Lahser 172. 3.75-4.00; SAT M 700-800 V 700-800; ACT 30-34; UMAA; Science, Liberal Arts, Engineering

· I wish we had learned Abstract Algebra in High School, because it is the basis for many substantial theoretical math courses in college (for math majors).

15a) 2 b) 3

Lahser 174 3.25-3.75 ACT 30-34 Non-Michigan-Public Pre-Professional/Business

15a) 4 b) 4

Lahser 181 3.25-3.75; SAT M + V 1200-1300; ACT 27-29; UMAA; Social Science/Science

Lahser 182 325-3.75; SAT M 600-700 V 600-700 ACT 27-29; Non-Michigan-Public Science

15a) 4 b) 5

Lahser 185 3.75-4.00 ACT 27-29 Michigan-Public Science

Math placement exam? Yes. Placed in Calc. I

15a) 5 b) 5

Lahser 191 3.75-4.00 ACT 27-29 UMAA Science

I hate numbers and formulas. I only like people. T. Koehler was my teacher Senior year. Per his absence most of the year, I was not able to expand and strengthen my already feeble math skills Math placement exam? Yes. If you can’t tell, I hate math and have a very bad memory. I don’t keep track of scores either. I almost passed into Calc, but not quite per placement exam. [Took Calc. I]

15a) 1 b) 1

Lahser 201 3.75-4.00 SAT M 700-800 V 700-800 UMAA Social Science

· Math 115 [Calc. I] at U of M SUCKS. My graduate student instructor hardly spoke English and never properly prepared us for exams.

Math tutoring in high school? Yes. Geometry Honors, 1993-94. Calculus AB, 1996-97.

Math placement exam? Yes. Placed into 185 Calculus but only took 115 Calculus

15a) 3 b) 3

Lahser 202 3.25-3.75 SAT M 600-700 V 600-700 ACT 27-29 MSU Engineering

· My school district has changed [its] math program (doesn’t offer Algebra 1 in BHMS) [the middle school that feeds both high schools], and I’m very displeased since I don’t think kids will be as well prepared for math classes at college. I know of kids that came from Andover High School who had a change in their math program, and those kids are having a hard time at college math. I also know of kids who came from other areas that required taking 2 math classes for 1 year (usually geometry and algebra), or that took Algebra 1 sooner than the rest, and I think that’s a great idea. Personally, I think teachers should concentrate more on math than they do, and try to help everyone to excel at it, (although this is hard to do). Maybe having more math teachers available from grade school on?

15a) 3 b) 5

Lahser 207. 3.75-4.00; SAT M 700-800 V 700-800; ACT 30-34; Private; Engineering

· High School math did not prepare me for the rigor of college math. [...]

15a) 3 b) 4

Lahser 209 3.75-4.00; SAT M 700-800 V 700-800 ACT 30-34 UMAA Social Science

· Pre-Calculus and Calculus were a good foundation. The entrance exam as well as the AP exam was approachable because of the good math foundation I had Junior and Senior year, largely due to the teacher’s capabilities.

Math placement exam? Yes. Placed out of Calc. 1 & 2.

15a) 4 b) 4 (I didn’t take a specific math course, but I did take courses for which I had to recall and apply high school math.)

Lahser 220 3.25-3.75; SAT M 700-800 V 500-600 ACT 27-29 UMAA Engineering

· I had some great teachers. Mr. Dobosinski and Mr. Koehler. They helped me a great deal, although to be truthful, math has always [been] quite easy for me.

Math placement exam? I got 97, give or take 3%.

15a) 3 b) 5

Lahser 236 3.75-4.00 SAT M 600-700 V 700-800 ACT 30-34 UMAA Liberal Arts

Math placement exam? Yes. Calc. II.

15a) N/A b) 2

Lahser 242 3.25-3.75 SAT M 600-700 V 500-600 ACT 24-26 MSU Business

15a) 3 b) 3

Lahser 245 3.75-4.00 SAT M 700-800 V 700-800 ACT 30-34; Private Science

· My AP Calc. BC and AP Statistics courses were very well taught and have really prepared me!

Math placement exam? No. The AP’s were our placement tests.

15a) 4 b) 4

Lahser 252. 2.75-3.25; SAT M 600-700 V 500-600; ACT 21-23; Non-Michigan-Public; Business

· I’ve always been good at math. I like math. To me it just makes sense, and that is exactly why Finance will be my major.

Math placement exam? Yes. I placed right below Calculus.

15a) 5 b) 3 (so far)

. Lahser 254 3.25-3.75 SAT M 500-600 V 700-800 ACT 30-34 UMAA Undecided

· Calculus at UM really was not a good experience. [Took Calc. I] Syllabus and method need revamping.

Math placement exam? Yes. Placed into Calc. 115.

15a) 5 b) 5

Lahser 255 3.25-3.75 SAT M 700-800 V 600-700 ACT 30-34 Private Science

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* This is the original report, as issued in November 1998. An update will appear shortly. (G.B. 11/15/99)

© 1998, Gregory F. Bachelis

[1] Address: Department of Mathematics, Wayne State University, Detroit, MI 48202

Telephone: 313-577-3178; e-mail: greg@math.wayne.edu

[2] The American Mathematical Society and the Mathematical Association of America

[3] Another designation would be Trigonometry and Topics in Advanced Algebra.

[4] AP = Advanced Placement. Students taking these courses can then take AP exams, which, depending on their scores, entitles them to place out of college courses. There are two levels of AP Calculus courses, AB and BC.

[5] There is also “Reform Calculus” at the college (or high school) level, such as “Harvard Calculus”. However, it cannot be described as “Integrated,” since it strives to cover fewer topics than traditional calculus.

[6] This is from a letter from Harold Schoen to me concerning the difference between pilot and field-testing. The entire letter is in Appendix A.I.

[7] This is from excerpts of an e-mail message sent by Marcia Weinhold; the excerpts can be found in Appendix A.II.

[8] WBSD is adjacent to BHSD and contains the greater part of West Bloomfield Township, plus the cities of Orchard Lake Village and Keego Harbor.

[9] BHSD did a survey of Andover parents’ opinions about Core-Plus. See Appendix B.

[10] “Harvard Calculus” is a product of the Consortium based at Harvard. There are several versions. The one used at UMAA is Calculus, Single Variable 2nd ed., by Hughes-Hallett, Gleason et al. There is a pre-calculus sibling, also used at UMAA: Functions Modeling Change: A Preparation for Calculus, by Connally, Hughes-Hallett et al. The publisher is J. Wiley & Sons.

[11] Course descriptions for some lower division math courses at UMAA and MSU can be found in Appendix D.

[12] I don’t think that “Harvard Calculus” is “Core-Plus goes to College,” as some would have you believe. For one thing, the former doesn’t integrate a lot of topics, and there is some pencil and paper algebra. The two do have some things in common, such as extensive use of graphing calculators, cooperative learning and “real world” problems.

[13] Of course other factors enter into advanced placement, but it is safe to assume that the accelerated students were, on average, better in math than those who weren’t.

[14] Detroit News, 1/27/97

[15] Birmingham Bloomfield Eccentric, 6/12/97

[16] In retrospect, I should have asked a question about how well they felt their high school math courses prepared them for college science courses, since this is a non-trivial issue as well.

[17] The Curriculum and Evaluation Standards of the National Council of Teachers of Mathematics. They are currently under revision.

[18] Recall that “accelerated” refers to people taking Algebra I (or Core 1 in subsequent years at Andover) before the ninth grade.

[19] See Appendix A.I

[20] Since Social Science is considered part of Liberal Arts, when someone gives two majors, one in the former and one in the latter but not the former, they are reported simply as Liberal Arts.

[21] The Comments in Context are reported in a separate section following this one.

[22] See e.g. the comments in Andover 40, 42, 83, 107, 148, 5, 35, 138, 232; Lahser 46, 96, 62, 127.

[23] I don’t think that injecting algebra drill is a viable solution to what I consider to be the problems with Core-Plus, in part because of the vast differences in approach of Core and the traditional method.

[24] Please note: I have included all responses. Even those which had no comments. The first line contains GPA, SAT, ACT,

college, and college major information. If comments were given in response to item 16, then they start on the second line, preceded by a “bullet” and written in boldface. Successive items are labeled. Other comments may be highlighted in italics or boldface.

[25] See also Appendix A.II.

[26] See also Lahser 202.