Disclaiming the Cultural Psyche of Social Promotion
Visiting Instructor of Mathematics
Education Doctoral Student at the
It is easy to teach a college mathematics course when your students have
the prerequisites to handle the new material. The course syllabus
becomes your teaching guide. You can convince yourself that your job is
merely to present the syllabus material during the semester. You only
need to check off that you covered the various topics without worrying
much about whether the students fully grasped the concepts. This
scenario is disquieting because I guesstimate that only twenty-five
percent of my students are ready to immediately start learning new
material. Hence, the decision becomes do I only teach those prepared
students or do I develop some way to reach my passing goal of eighty
percent or more of my class?
Intuitively we want to think of the eighty percent of students who need
background enhancement as merely an academic problem. That thinking
would ignore the cultural identity problem that many of these students
possess where they may view failure as being okay. They obviously need
to undergo a Mainstream American acculturation program where they accept
success as their norm.
Some anti-mainstream traits I have observed in students over the years
are they:
1)
Never learned to read
mathematics textbooks
2)
Give up when things get
difficult
3)
Accept failure as the
norm
4)
Have no disciplined work
habits
5)
Become masters at coming
up with excuses to explain away nonperformance
6)
Do only enough to pass,
seeking excellence as the exception rather than the rule
7)
Exploit teacher
intimidation techniques either overtly or covertly to induce teachers to
use social promotion techniques to pass them
8)
Have low self esteem
9)
Demonstrate poor
performance on tests
10) Cut Friday classes
11) Get grades without honest effort
12) Fall asleep in class
A holistic look at these problems suggests that they are the under
girders of a culture of failure. This means that they must be attacked
first before any serious mathematics can be taught.
Sarah J. McCarthey offers a glimpse of American teachers’ background and
mindset. “Like the majority of teachers in
Since my focus will be on
Before I start into methods to remedy some of the problems listed above,
I need to make it clear that I feel many of the above problems are
underpinned by remnants of the age of the life-adjustment curriculum.
John L. Rudolph offers a feel for the life-adjustment curriculum. “The
life-adjustment curriculum was essentially an extension of the
vocational education model to general education. By making preparation
for life rather than preparation for work (or college, which some viewed
as preparation for professional work) the objective of schooling, the
proponents of the new curricular program seized the common ground shared
by all secondary students despite the diversity of their ultimate
vocational goals and, in doing so, sought to extend their authority over
the entire school program. … With its focus on training students for
this ‘job of living’ the life-adjustment curriculum was little more than
a variant of earlier social efficiency curricula prominent in the early
1900s, which were similarly designed to fit individuals to the emerging
social order of the time.” (Rudolph, p. 18-19)
Clearly, there exists a chasm between some students’ mindset on merely
sliding through the system and what teachers view as getting up to
mainstream standards. I view this as a cultural divide that requires a
classroom modus vivendi to create an atmosphere of learning. Over the
years, I have developed some classroom operating principles that all of
my students must adopt in the first two weeks of the semester or it is
too late to help those students needing background enhancement to make
significant mathematical progress. My operational principles evolved
empirically through addressing the problems listed above, so I will
speak to remedies from that mindset.
Classroom decorum is established the first day for everyone including
the teacher. Men must remove their hats and head rags prior to the start
of class. Cell phones must be turned off or put on vibrate in class. No
one is permitted to eat food or drink liquids during class. Students who
go to sleep in class will be asked to leave for the day. Haughty-eyed
displays of emotions will get students asked to leave for the day.
The teacher must truly
believe that all of the students can learn.
There may be varying levels of initial preparedness in the classroom,
but the goal is to find the untapped potential and ignite passion in the
student to rise to the level of expectation for the course.
This means avoiding the enchantment of perceived ideas on student
capabilities. Barbara Levin offers some chilling thoughts on some
teachers’ perception: “… Some teachers ignore misbehavior or a student
who is not learning as expected until they figure out what to do about
it. Some teachers even think that some students cannot learn, are not
motivated to learn, don’t behave appropriately at school, or cannot
learn because of their home life.” (Levin, p. 242 – 243)
I recently heard a college professor offer similar emotions in a
bucket-dumping session over difficulties teaching modern college
students.
Howard Gardner offers comments I believe help the public school teachers
understand their role. His comments are also appropriate for teaching
university level mathematics where students may need some background
enhancement. He writes, “… Education is primarily a realm of value
judgments. What we teach and how we teach reflects our notions of the
kinds of persons we want our children to become and the kinds of minds
that we want them to have …” (
Over my ten years of teaching at the college and university level, I
have observed that students understanding of the course material is very
addictive. Its addictive nature appears to have the greatest impact on
the students needing the most background enhancement because they
suddenly taste the power that comes with controlling ones own lot in
life. This means that the course needs to be highly focused on
understanding with a presentation of the material at a rate that does
not overwhelm the students in the initial phase of the semester. I teach
on an exponential curve where I move slowly in the first half of the
semester whilst the background enhancement is occurring and move
aggressively in the second half to cover the material in the syllabus.
At this background fill-hole stage, “… the students must
understand that you will be a teacher and not their pal which means that
you will make decisions based on their long term needs and not worry
about merely making them feel good at the moment.” (Miller 1999, p.
307)
What is emerging is that the teacher must become a primal leader and not
merely an android dispensing knowledge in some rote manner. Daniel
Goleman, Richard Boyatzis, and Annie McKee offer guidance here. “In any
human group, the leader has maximal power to sway everyone’s emotions.
If people’s emotions are pushed toward the range of enthusiasm,
performance can soar; if people are driven toward rancor and anxiety,
they will be thrown off stride.” (Goleman, Boyatzis, and McKee, p. 5)
It is incumbent, therefore, to be forthright with the students and give
them an honest assessment of the educational journey they are about to
undertake. I am upfront offering, “The brain is like other muscles,
and it hurts when you first start to use it; but it gets keener with
regular exercise, making the mind perform at an extraordinary level.”
(1996 Miller, p. 37) I often ask students to speak to what happens at
the first few practices if they played sports in high school. They
usually corroborate my assertion by telling stories of the aching
muscles in the first few practices until they get into shape.
Now let me turn my attention to the anti-mainstream traits list. Since
the above problems may not occur in isolation, I will offer my remedies
in categories:
1.
Course Objectives
My mathematics course syllabi state that a course objective is to learn
to read the textbook. In algebra, each definition is written on the
blackboard and parsed, so that the students understand what is being
said. Students learn that definitions are the rules of the game in
mathematics and must not be violated. As long as they can work within
these definitions, they can use their own creativity in problem solving.
In higher-level courses, definitions are also put on the
blackboard, but these courses also use team examinations and personal
presentations to demonstrate mathematical understandings. Team and
presentation format examinations also are gauges to assess the students’
ability to comprehend textbook material without instructors’ aid.
As an example, students in the introductory statistics course
have to read 100 pages of new information to complete a team examination
because they do not know which team member will be called upon to
present the team’s findings in the oral phase of the final examination.
2.
Student Perseverance in Course
Some students take and drop courses many times until they finally
complete the required courses for their major. This means that their
graduation date is very fluid. I use the “Modified Bragg Grading
Method;” the
3.
Negativity Not Permitted
Students are not permitted to say anything negative in the classroom. I
tell them, “There will be enough people trying to tell you how bad
you are. You don’t need to be your own worst enemy.” I chew out any
student who puts her or himself down in front of the class. There is
always a positive feeling in the classroom and it seems to make it much
easier to deal with difficult issues because people know I have their
best interest at heart. The intent is to subtly purge the enchantment
with failure out of the students’ minds and to improve their
self-esteem.
4.
Student Credibility Through Understanding
A very difficult undertaking is to get students to knuckle down and get
assignments completed. I use the blackboard to assess who is doing
homework assignments in mathematics courses beyond algebra. When people
are called to the blackboard to solve a problem, they do not get to sit
down until they fully grasp the concept. I will make up problems for
them until I feel comfortable that they understand the lesson. Not
letting students sit down until they understand makes going to the
blackboard a positive experience and the student gains credibility
through understanding the material.
5.
Purging Mediocrity
Excellence must be demanded at all times. I will make a student rewrite
things that are illegible on the blackboard or speak up louder when it
is clear that all of the class cannot hear him. When students understand
that you will not accept mediocrity, they come up to the level of
expectation you place upon them. In finite mathematics and business
calculus where team final examinations or individual presentations are
common final testing techniques, the level of excellence in students’
effort elevates on the second day of testing once it is clear they are
being marked on an industrial standard. Students see mediocre
performance called down and they are informed, “In industry you only
get one chance to make a first impression. It is also very difficult to
clean up a bad impression.” The quality of work between day one of
testing and day two often goes up one quantum level.
6.
Excusers
Some students ought to win an Oscar for their performance in conjuring
up excuses to explain why they didn’t come to class or complete their
assignments. I tell people, “Just because you are not in class does
not mean you are not held responsible for what happens in class. You are
held accountable for the class material whether you are here or not.
Furthermore, I don’t accept excuses unless you are in the hospital.”
I make it clear that in industry if you bring in a lot of excuses you
will lose your job because you are unfit for industrial employment. I do
excuse athletes who are on scholarships since their coaches send me
letters to document their absences.
7.
Teacher Intimidation
Some students attempt to exploit overt or covert teacher intimidation in
hopes that their teacher will acquiesce from their teaching
responsibilities. These intimidators seem to hope that the professors
will succumb to social promotion at the college or university level. I
challenge these misguided students and make it clear that my early
childhood was spent growing up between two public housing projects, so I
do not give in to teacher intimidation. I expect everyone to get his or
her work done-period. Once I correct a couple of people, discipline
problems are few for the remainder of the semester.
However, sometimes it requires discussions with the errant
students after class where they must understand that their behavior is
unacceptable to remain in my class.
It is very important that I keep in mind that teacher intimidation is a
very real concern today. The US Department of Justice reported, “In the
1999—2000 school year, 9 percent of all elementary and secondary school
teachers were threaten with injury by a student, and 4 percent were
physically attacked by a student. … This represented about 305,000
teachers who were victims of threats of injury by students that year and
135,000 teachers who were victims of attacks by students.” (US
Department of Justice, October 2003) Once I had to intercede when I
overheard a male student outside of my office verbally abusing a female
teacher. I felt this student’s action was unacceptable, so I chewed out
this chap for disrespecting the teacher. We got an understanding that
this bad behavior would not be tolerated.
It should be noted that discipline problems come from traditional
students and any problems with nontraditional students will be a rare
event.
8) Testing
Algebra
When I turned my attention to test anxiety, I learned that
nontraditional students were really stressing out over taking the
departmental final examination. At this point, I do not have a full
appreciation of this test anxiety problem with the students who take a
computer-aided format course and then are required to be tested in a
standard format for the departmental final. (Wright) Today, I attempt to
discuss written test taking in a low-key manner to avoid causing a great
deal of unnecessary stress. This technique did not work well in calming
the test anxiety of this first group of computer-aided algebra students
who took the mathematics departmental final examination. My plan is to
examine this test anxiety in a future effort.
Finite Mathematics
In addition to giving only one examination prior to midterm, a review of
the algebra fundamentals is a key element in the finite mathematics
course. The goal is to establish a mathematical literacy, similar to the
thinking of E.G. Hirsch’s cultural literacy, on which to develop the
class. (Hirsch, 1987 April 15) The initial emphasis is on blackboard
assignments where student capability can be assessed. One of the hidden
agendas in the blackboard assignments is to get students to believe in
their own capability, thereby diminishing their propensity to seek out
schemes that they think will help them to pass the course without
putting forth any effort.
The Cornell University School of Engineering testing technique of
allowing students to bring in one sheet of paper full of equations used
for tests is adopted in all of the mathematics courses above
computer-aided algebra. This system also further dampens the student’s
feeling for a need to rely on other people’s answers on examinations
because it puts her or his fate in their own hands.
Tests are made at a high degree of difficulty and the final grade is
based on a curving system. The usual curve begins with finding the class
average. If it is less than seventy-five, then the difference between
that average and 75 is added to each student’s raw test score. Then
students are graded on the standard grading system. However, if the
class average is above seventy-five or below forty, the students get
whatever their raw score happens to be.
An effort is made to reduce test anxiety by giving the students choices
on problems they work out. The tests are always made up of seven
problems. On the first test students get to pick any five problems to
do, but they must circle which ones they want marked. This process
forces students to learn to make decisions for which corporations will
be paying them to do. If a student fails to circle problems to be
marked, the worst problems tried on the test will be graded on her or
his behalf. Students are required to solve the first two problems on
tests two and three, and then pick any two or three other problems
depending on whether the test is a five- or four-problem set total. The
final test is a formal oral presentation where the student must use some
of the mathematics learned over the semester to solve a real world
problem. The oral final examination allows the student to show what he
or she can do, unaided, to his or her peers and occasionally invited
members of the faculty. These oral final examinations are marked toughly
which implants mainstream standards in the minds of the class.
The finite mathematics course uses the textbook, “Introductory
Mathematical Analysis.” (Haeussler & Paul).
Statistics
The testing scheme for statistics is similar to finite mathematics, so
only the difference will be discussed. Statistics in-class tests are
based on giving only two tough problems. In the first test, students
select any two problems from the four offered for solution. The
Students are required to do problem 1 on tests two and three, then
select another problem from the other three offered.
Test 3 is an open book and open notes test that is designed to
favor people who have good class attendance. The final examination is a
team examination where student teams are given one week to solve two
challenging problems on material that has been only briefly touched in
classroom lectures.
The team final requires students to read one hundred pages of material
in one week and solve problems with this knowledge. A team member is
selected to present the team finding only on final examination days.
Student teams are given two difficult problems with a week to solve them
and turn in one completed examination from each team. Then members from
each team are selected to discuss the problems at the blackboard. If the
team has it right and the person selected does not, the team gets credit
and the presenter fails. The team format allows the stronger students to
help the weaker ones to learn the material.
The goal of this team test system is to mimic what may happen in an
industrial setting during a crisis period where students will have to
demonstrate that they can read a book to dig out enough understanding to
solve a real world problem.
Students like the two-problem test format for in-class examinations
because it does not appear to overwhelm them, although there can be
subparts to each question that really amounts to four tough problems. In
the two statistics courses that have utilized the two-test problem
format, the class average was above 75 so the raw scores became the
grading score. Students also are required to give the business
significance of their test answers and not merely make some mathematical
calculations.
The statistic course spans over calculating samples sizes and ending on
hypothesis testing in the Introductory Statistics book by Perm S.
Mann. (Mann) The underpinning idea is to get the students feeling that
they are capable of operating in the economic mainstream as soon as they
graduate from college. The drop out rate is less than 10 percent and
often students ask to get into the course.
Business Calculus
Business calculus modus operandi is also similar to finite mathematics,
so only the differences will be discussed. The final examination is a
team final where student teams are given two difficult problems with a
week to solve them and turn in one completed examination from each team.
The course focuses on differential calculus presented in “Introductory
Mathematical Analysis” by Ernest F. Haeussler, Jr. and Richard S. Paul
(Haeussler & Paul). The
final examination is made up of all word problems that span from limits
to curve tracing to differentiating complex exponential functions
divided by algebraic equations. Students are required to give the
business significance of their answers and not merely make some
mathematical calculations. The student drop out rate is less than 10
percent and often students ask to get into the course.
SUMMARY
In summary, we have looked at some worrisome traits observed empirically
in some of today’s students, especially people needing background
enhancement. We offer some remedies to college or university mathematics
professors to alleviate these problems. Holistically, we are attempting
to define elements of a new culture that encourage students to seek
success as the norm versus being enchanted with failure especially if
the student’s high school exploited some form of social promotion in
teaching their courses.
However, we would be remiss if we did not call attention to problems
that testing might cause students attending Historical Black Colleges
and Universities from the fallout of ill-fated experiences with the SAT
examination that may have helped to shape these students’ valuation of
themselves. It is therefore disquieting to read Deborah Meier’s
statement on SAT questions development that worked against Black
students’ academic persona in the view of the economic mainstream.
“Test items that appear—on the surface, mind you—to be equally
good discriminators of math or vocabulary skills and that show a ‘black
preference’ (meaning that blacks get them right more often) virtually
never make it into the final test.” (Meier, p. 149) This comment is
troubling because I worry that these covert actions work to destroy any
potential of African Americans gaining self-confidence on mainstream
tests. With a mindset of failure, my concern is that Black students may
become overly stressed on examinations where their performance suffers.
Works Cited
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Haeussler, E. and Paul, R. (2002). Introductory
Mathematical Analysis for Business, Economics, and the Life and Social
Sciences. Prentice-Hall, Inc. Upper Saddle River, NJ
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(1987 April 15). Education Week
Levin, B. (2003). Case Studies of Teacher Development: An in-Depth
Look at How Thinking About Pedagogy Develops over Time. L.
Erlbaum Associates Mahwah, N.J.
Mann, P. (2004). Introductory Statistics. John Wiley & Sons.
Inc.
McCarthey, S. (2002). Students’ Identities and Literacy Learning.
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Delaware, Ltd.
Miller, S. (1999) America’s Golden Riffraff. Library of Congress: Txu-920-578
Miller, S. (2004 publication expected). Reversing the Effects of
Social Promotion (College Algebra for
Rudolph, J. (2002). Scientists in the Classroom. St. Martin’s
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Wright F. (2004). Intermediate Algebra. Hawkes Publishing.