ALTERNATE LEARNING ENVIRONMENT HELPS STUDENTS EXCEL IN CALCULUS
by Jerome Dancis
This is the uncut article that I sent to the Post.
A related article may be read on my Web site at
http://www.math.umd.edu/~jnd/Treisman.txt
This year the government of the State of MD is blessed with extra
tax revenues and there is a desire to spend some of this money on
education. I suggest using some of it to finance "Treisman-type
workshops" to help students learn mathematics at all the colleges and
community colleges in MD. Uri Treisman originated his workshops at the University of
California (UC) at Berkeley, where they resulted in a significantly higher rate of graduation for
black students, especially in math based fields. Overall, the graduation rate rose to roughly 65%
for the "workshop" black students from roughly 45% for earlier black students with very similar
backgrounds. All the workshops were racially integrated; they were organized outside of and in
addition to the regular program.
At UC, Berkeley, most of the white students from blue collar and farm families and
most of the black students were not succeeding in the calculus course for engineering and science
students. Students need to understand calculus on an A or B level in order to be comfortable with
the calculus aspects of later math, physics and engineering courses; C is not sufficient. In 1973-
75, the average grade in Calculus 1A for Engineering and Science students for black students was
1.5 on the usual scale of 1.0 = D and 2.0 = C. After only 11 weeks of college, their low grades
in calculus dashed the academic aspirations of many students at U.C. Berkeley. This educational
disaster occurred in spite of the fact that these black students at U.C. Berkeley had the
characteristics which presuppose success. They were smart, highly motivated, and very hard-
working; some had been valedictorians. Many of these students had studied calculus in high
school. Each of them had at least one parent who strongly encouraged their academic pursuits and
urged them to go to college. The majority had a parent who was a teacher. Various remedial
programs were tried without success.
Enter Uri Treisman. Over several years, he developed an alternate learning
environment for training black and white students how to learn both individually and cooperatively.
Black participants in his alternate learning workshops exceeded the achievement levels of those
white students whom had not participated.
Two important reasons that many good students have difficulty with calculus is poor
high school training. They arrive at college with weak knowledge and understanding of the
algebra and trig taught in high school and with ineffective learning strategies.
In the Fall 1994, I taught a college honors beginning calculus class (Math 140H) at UMCP.
With one exception, all the students had taken calculus in high school; a few had even taken two
years of calculus. On Day 1, the homework assignment was to read Ch. 1 of the textbook (which
reviews "precalculus") and then to do the math department's precalculus(Math 115) final exam
on high school math. One third of the students scored 80% or higher. Even though these honors
students got to take this closed-book, two-hour final as an open-book, bring-it-back-tomorrow
test, one third failed. These students had difficulties with the algebraic and trigonometric aspects of
calculus, they did poorly in the course and they complained about it.
Most likely the fraction of non-honors students in calculus classes, who do not have
sufficient understanding of high school math, is higher than among my honors students. The
fraction is even higher in calculus courses at community colleges.
Thus much review and reteaching of high school algebra and trig is needed by calculus
students. The Treisman workshops provide this indirectly by including the algebra and trig in the
workshop activities.
Many freshmen use the same strategies that earned them success in high school.
Pseudo-good "study" habits often includes too much time spent memorizing too many formulas
and prescriptions for calculations and doing lots of computations with an emphasis on getting the
correct answer. These types of łgood˛ study habits are usually rewarded by success in high
school, but they can be a trap in a college calculus class. Ineffective study habits of this kind are
commonly inculcated in both black and white students in most high schools.
The question was "What contributes to the failure of college freshmen? The answer
was "The overemphasis on testing, skill development, and fact level content, etc. [in high school]
seems to have inhibited [both white and black student] interest in learning, motivation, ability to
work with and enjoy ideas, use creativity and attain satisfaction from an educational experience."
This question was raised by the PGCPSS. A series of discussions were held in 1986. The
participants were UMCP faculty members from 10 departments, together with high school teachers
from the PGCPSS and college freshmen from PGCPSS high schools (Ref #1). In a later
discussion among faculty members (mostly from departments of speech and communication in
colleges in PG county), it was noted that: "Entering college freshmen appear severely limited in
their ability to read critically, synthesize information, interact effectively with both peers and
instructors in academic settings, and participate actively in discussions." (Ref. #7) This is a natural
consequence of these activities not being included in the curriculum of most school systems.
In math, this non-intellectual approach comes from math textbooks which "never offer
intellectual challenges, or chances to build confidence and problem-solving skills" as noted by
Prof. Davis of Worcester Polytechnic Institute (Ref. #5). He also wrote: "The [high school
precalculus textbook] ... is no more mathematics than the noise made by trained seals is music.
But the trained seal approach abounds in textbooks and in classrooms. It never provides a
foundation of fundamental ideas ... ." Of course students are able to solve those math problems
for which the text has supplied cookbook-type directions, but there is little training in serious
problem-solving skills, that is solving problems that are different than the examples worked out in
the textbook. In this way high school textbooks "set-up" students with a wrong orientation for
college.
Treisman workshops provide students with extensive training on (i) how to learn in
general and (ii) how to learn cooperatively, this facilitates students replacing their high-school,
skill-oriented attitudes and ineffective study habits with effective learning habits.
Results in calculus at U.C. Berkeley. (1983-84)
For black students whose S.A.T. math scores were 550 or higher:
Average grade. % earning A's,B's. % earning D's,F's
Workshops 2.8 71 0
Non workshop 1.7 24 30
..................................................................
Average S.A.T.math scores Average grade
Workshop black students 500 2.6
Non-workshop white students 640 1.9
Also, the group of black students whose S.A.T. math scores were less than 460 and
lower but participated in the workshops had a higher percentage of A's and B's (30%) than the
non-workshop black students (24%) whose S.A.T. math scores were 550 or higher. The D's and
F's rates for non-workshop white and first generation Chinese-Americans students were 15% and
10% resp.
There is a watered down version of Treisman project called "Close Contact (C^2) Calculus
at UMCP; it achieves watered down results. Also it is only available to students who start calculus
in the fall, not to those who start in the spring or summer.
The state would be wise to fully finance these workshops at all campuses of the Univ. of
MD as well as at all community colleges.
References
1. Report by Prof. Jim Greenberg, then Director of Office of Outreach Programs [to public school
systems], Univ. of Maryland. (May 26, 1986).
5. Paul Davis, Teaching mathematics and Training seals, SIAM News (the newsletter of the
[professional] Society for Industrial and Applied Math.), (March 1987) page 7.
7. John L. Brown, Curriculum Dialogues, Prince Georges County Public School System, Upper
Marlboro,MD