My Teaching Method
Richard A. Beldin, Ph.D.
[Objectives]
[Learning Habits]
[Principles]
[Technology]
[Evaluation]
[Experience]
Objectives
[Arithmetic]
[Algebra]
[Planning]
[Documentation]
[Translation]
[Communication]
[Creativity]
Course Specific Objectives
In general, I seek to get students actively doing something rather than
passively listening to me. I have developed a list of
teaching experiments for
this purpose.
Each course of study has its own objectives. In general, I emphasize
"skills" over "understanding" when writing objectives. I can test the
skills that a student can demonstrate reliably, but "understanding" is
basically a private phenomenon which I cannot be sure I am assessing.
What are usually called tests of understanding seem more like tests of
compliance with accepted vocabulary. I tell my students frankly that they
are the real judges of understanding.
I attempt to integrate the skill based objectives with the overall
general education objectives which I discuss below. Here I list some
common objectives for the courses I have taught recently.
Statistics
Since I returned to teaching, I have been concerned with three
introductory courses in statistics which I will call "elementary",
"applied", and "math statistics" respectively. I have applied the method
to finite mathematics, calculus, numerical analysis, and programming
courses as well, but the statistics sample is more simple to describe.
Elementary Statistics
Students in Elementary Statistics normally come from the social sciences,
nursing, and physical education. They often are intimidated by the very
thought of anything mathematical or quantitative.
Computational Reliability
My primary objective for these students is to develop computational
reliability so that they both can and know they can do basic arithmetic.
Along the way, they learn some statistical description techniques.
Reading Reliability
My second objective in this course is to
develop reading interpretation reliability so that they can translate
verbal problems into precise computational forms. The section on
probability is an excellent opportunity for this because of the
convoluted form in which probabilities are often discussed.
Deception Detection
My third objective is to develop the habit of critical reading of general
media to discover any intent to deceive. I warn them that as a group,
they are too naive if they believe that any of the media are intended
just to inform.
Index
Applied Statistics
Students in Applied Statistics normally come from the biological and
laboratory sciences and the professions such as business and engineering.
In addition to computational and linguistic skills, they need more
experience in abstract reasoning in concrete problems. Their knowledge of
the world as derived from their other studies must be put to the test.
Algebraic Competence
These students are more comfortable with algebraic notation, but
frequently depend on their memory to solve problems in a familiar way and
avoid the exercise of analytic skills.
Planning Skills
My second objective for these students is to develop the ability to plan
and execute activities of reasonably long duration. They often depend on
their memories to guide them through complex algorithms. They need to
develop work habits that are practical.
Record Keeping
Many of these students have never appreciated the power of written
records for their personal success. I attempt to give them a experience
from which they can develop their personal work habits.
Index
Mathematical Statistics
These students have already committed themselves to learning to be
competent in mathematics. My objectives with these students extend those
which are traditionally mathematical in nature.
Problem Formulation
I want students of mathematical statistics to learn how to convert a
vague and imprecise problem statement into something that they recognize
as a solvable problem, one which can be attacked by the techniques they
know.
Communication via Mathematics
After applying their mathematical tools to a problem, they must be able
to express it in a form that the mathematical community can comprehend
easily. This requires that they learn to write using the conventions
they have been reading and that they discard habits picked up in early
math courses and misinterpreted as professional practices.
Creative Thinking
Once one has learned a set of tools in one context, one needs to extend
them, to find other contexts in which they will be useful. I want to
stimulate my students to explore in this way. For this reason, I avoid
premature exposition.
Index
Observation,
Reason,
Trust
I believe that there are three principle routes to learning, observation,
reason, and trusting authorities. Nearly all the experience of my
students has been with authority based learning from parents, teachers,
and religious leaders.
Observation
Students need practice in observation as a means of learning. It is all
too easy to rush along without noticing what is happening nearby. They
need to learn that observation requires planning, not just looking.
Reason
Statistics offers a good opportunity to demonstrate how reason is applied
to the process of observation and how the theories of authorities can be
put to the test.
Trust
In general, I discourage students from trusting authorities. They have
been doing that for nearly all their lives. I focus their attention instead
on designing tests of the usefulness of authorities, tests, naturally
based on statistical thought.
Index
Course Design Principles
Group Study,
Attendance,
Exercises,
Exams,
Readings,
Lectures,
Projects,
Notebook,
Presentations
Group Study
In mathematics and statistics the design of textbooks is somewhat
standardized so that the textbook is adequate for independent study. I
use the
cooperative learning model, assigning my students to review or work exercises in
groups.
More information on this approach can be found at
Cooperative Learning Classroom Research
and Kenneth Bruffee's "Collaborative Learning".
One of the common drawbacks of group study is the consequences for
reliable students of having irresponsible colleagues. I have instituted
the rule of TWO to remedy this problem. When TWO (or more) students are
absent from any group, I reorganize the groups to concentrate the
absentees into a new group and consolidate the attendees into another.
Another approach which avoids the sustained harm of irresponsible
colleagues is to form new groups in each class meeting. This is
a different environment, one which foregoes the security of a
semi-permanent environment and its potentially intense impact for a
shifting collaboration. One might think that this is a logistic
problem, but it turns out that the simple expedient of collecting ID
cards and laying them out in the desired grouping works well. The
practice of calling out the names to organize the groups also
accellerates learning students' names and faces.
Few Lectures
I give only a few lectures, typically one at the beginning of each new
chapter in a statistics course. I choose those topics which I believe
will enable a student to quickly learn from the assigned text and
exercises. Lectures are sometimes supplemented by computer demonstration
programs or overhead transparencies which I try to make available for
student review.
Course Readings
Although I publish a reading list as part of the syllabus, I do not
emphasize it greatly. Rather I depend on the obligation to work the
exercises as a stimulus to read the textbook. This is not always
effective, naturally. Occasionally I have to respond to a question by
simpling identifying the section of the textbook that answers it.
Exercises and Exams
Each group will present at least one exercise in each class unless
preempted by a lecture or examination. They may use any method of
presentation they wish, completely oral, chalkboard based, handouts, or
with overhead transparencies. Several groups prefer to prepare graphs on
poster board which they tape to the chalkboard for display.
After each presentation, the rest of the class is prompted for comments
and questions which are handled before I provide feedback. My feedback
falls into one of several categories:
-
positive (ranging from "good" to "excellent")
-
neutral clarifying remarks which explain alternative but equivalent
approaches
-
critical comments which refer to incorrect interpretation of the
exercise, unconventional data presentation techniques, incorrect
computations, invalid assumptions, overlooked conditions etc. When I make
critical comments, I remind the students to correct the exercise before
posting it in their notebooks.
Examinations are considered incomplete until a student has achieved a
100% score. I generate the exams on a computer using random number
generators to obtain five versions and the key for each. On examination
days, I distribute exam versions so that everyone has a different version
from any any neighbor. As students finish the exam, I grade it
immediately. If they did not achieve 100%, they will have to retake it.
Usually, the first exam requires two or three trials which are handled
just as any makeup exam except that I reserve time in the schedule for
one in-class makeup.
I focus my three exams differently. The first exam is a pure
computational exercise in which the students are required to calculate a
variety of descriptive statistics from raw data.
The second exam poses problems which require careful reading and
interpretation of verbal problem statements. (One of my favorite ones is
based on finding the probability of selecting students of different types
in a random survey sample.)
My third exam presents several innocent and/or deceptive analyses. I ask
students to either agree with the analysis or explain why they believe it
is incorrect or deceptive.
Course Notebooks
All materials are saved in the groups' notebooks which I review four
times (unannounced) during the semester. This includes handouts,
exercises the group has prepared, attendance lists, and incomplete exams,
as well as any deliverables associated with course projects.
In the Applied Statistics course I use research projects to give students
both the responsibility of planning and executing a plan and experience
in real observation. I require a proposal during the first three weeks of
class, an outline by week ten and reserve time for each group to present
its project during the last two weeks of class.
The proposal must describe the methodology in prospective form, with
estimates of effort and completion date and assignment to a group member.
I critique the proposal in terms of what seems practical, giving
feedback on how long some typically underestimated activites are likely
to require.
Index
Use of Technology
I do not expect that the use of today's technology is likely to be a
significant aid in teaching statistics because that technology is
changing far too rapidly. Whatever technology students learn to use today
will be obsolete within five years of their graduation.
In the Applied Statistics and Math Statistics courses, I do expect the
students to use the computer laboratory for at least some exercises. In
all cases I require students to bring a
Calculator
to exams. Any five-function (including square roots) calculator is
acceptable. I describe what is available locally in department stores and
some of the trade offs of sophisticated calculators vis-a-vis the
traditional table driven analysis. I warn my students that a
sophisticated calculator that they don't understand is a handicap.
I store my slide presentations with notes in my portable computer.
If a VGA projector is available in the classroom, I can use it to display
the information. If not, I resort to demonstrations before each group
separately or use the traditional chalk board. Group presentations have the
additional benefit that students can actually supply the parameters for
the demonstration programs.
Index
Evaluation
Currently, I give three examinations in each course
valued at 100 points each. These are the exams that the students must
retake until they master them. Each of the four
notebook reviews is valued at 25 points and all
members of the group receive the same score. The Final Exam is also
worth 100 points giving a total of 500 points. I consider 451-500 an "A",
401-450 a "B", and 351-400 a "C". There is no excuse for anyone with less
than a "C".
In the applied statistics course, I use only two exams and a research
project as described above.
I plan to increase the dependence on the notebook in future terms to
determine its proper weighting. It might turn out that Notebook Reviews
would replace Examinations as an evaluation technique.
Index
Student Reactions
When I describe this method to the students, their faces typically light
up when I mention the requirement to repeat any exam without a 100%
score. In reality, some of them get quite frustrated when they have
repeated an exam three or four times. By then, of course, they are doing
their makeups during office hours and I have a chance to give them
coaching and encouragement.
After the course, some students have remarked that this was the first
time they ever had an opportunity to master anything in their lives and
that they appreciated it. In the anonymous faculty evalutation sheets, I
usually end up as well as anyone else. What is the most telling evidence
is that students (for whatever reason, I don't kid myself too much)
frequently try to enroll in another course with me.
I conclude that I am successful because I observe the following:
-
Students actively work on the exercises.
-
Students demonstrate the skills cited above.
-
Students' fear of mathematics and statistics appears reduced.
-
I expend less effort to achieve these results than do my conscientious
colleagues using more traditional approaches.
Index
This page was last updated on Friday, March 07, 2003