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The Evolution of a Keller Plan Service
Statistics Course
RJ Brook a & P.J. Thomson b
a Massey University , New Zealand
b University of Wellington , New Zealand(formerly at Massey
University)
Published online: 09 Jul 2006.
To cite this article: RJ Brook & P.J. Thomson (1982) The Evolution of a Keller Plan Service
Statistics Course, Innovations in Education & Training International, 19:2, 135-138, DOI:
10.1080/0033039820190207
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The Evolution of a Keller Plan Service
Statistics Course
R J Brook, Massey University, New Zealand
P . J. Thomson , University of Wellington, New Zealand (formerly at Massey University)
Abstract: Since 1975 the Department of Mathematics and
Statistics at Massey University, New Zealand has been
teaching a large first year introductory statistics course
using the Keller Plan. Over the years the structure and
organization of the course have evolved to meet various
contingencies that have arisen including problems such as
record keeping, devising acceptable pacing strategies and
Constructing tests. In this paper these contingencies are
discussed together with the various measures that have
subsequently been adopted.
Introduction
The purpose of this paper is to describe the evolu-
tion of a particular Keller Plan or PSI (Personalised
System of Instruction) course. A number of
problems have had to be faced in maintaining this
large (approximately 750 students) service course
and, as a result, various solutions have been devised.
(There is a considerable body of literature on
Keller Plan courses for large groups. See, for
example, Weir and Brook (1977), Imrie, Blithe and
Johnston (1980) and the references cited therein.)
The Keller Plan, PSI, mastery learning, call it what
you wish, is now used in many universities
throughout the world. The theory is well known,
but the practicalities involved in mounting and
maintaining such courses are less well known.
It would seem to be in the interests of all who
either use such a scheme or intend to do so, to
share the ideas and differing approaches to this
teaching method.
Background and structure of the course
This Keller Plan course was first introduced in
1975. An account of the years 1975-76 is found in
Weir and Brook (1977) and of 1977-79 in Brook,
Pringle and Thomson (1981). The course syllabus
is conventional and has been based on Walker and
Lev (1969). As it is a service course, it suffers
problems due to the poor motivation of students
who have widely varying quantitative abilities and
backgrounds. Approximately one-third of the
students take the course because it is compulsory
for their particular degree programme. The remain-
der take the course for interest or to fill out their
degree requirements.
The course runs for the entire academic year of
24 weeks (three terms). It is divided into 12 separate
units each based on relevant chapters of the set
text and each representing approximately one
fortnight's work. The latter should be comparable
with the work generated by a conventional course
of four lectures and an assignment per fortnight.
Students proceed sequentially through the units of
the course at their own pace. For each unit there is
a study guide and a test.
The study guide contains guidance as to which
sections of the text to read, additional explan-
ation, worked examples, key points and relevant
formulae. An assignment is also included together
with a sample test. In the assignment, applications
of statistical methods to real data are emphasized
whereas the sample test gives the student an idea of
what to expect when he sits a test for that unit.
Unit tests are closed book with no fixed time
limit and normally consist of 20 questions. Students
may sit a unit test at any time during the four
three-hour testing sessions scheduled each week.
Typically a test takes about 30 minutes to com-
plete. When a student has completed a test it is
marked in front of him by a proctor who is usually
a second or third year student majoring in
statistics. This takes between 5 minutes and
20 minutes as the proctor has the important task
of ascertaining the points not understood by the
student and then clarifying these points. A mark of
18, 19 or 20 (at least 90 per cent) is a pass, ie is
deemed to indicate mastery. A student who fails
to attain this level of mastery is required to sit
another version of the test at some later date.
Six one-hour tutorial sessions are held each week
and these are, in the main, informal and voluntary.
They are run by staff members who can give
individual attention to problems raised by students.
In fact, not many students feel the need of these
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136 PLET, Vol. 19, No. 2 -June 1982
tutorials. Those, however, who score less than half
marks in a unit test are required to attend a
tutorial and complete some remedial work. There
are no formal lectures. The latter were found to be
of little benefit due to the students' widely varying
rates of progress through the course. (Indeed, the
Keller Plan positively encourages widely varying
rates of progress!) Since there are no lectures,
incidental course information is communicated
to the students by means of information sheets
which are distributed at irregular intervals.
In the normal course of events each unit passed
(with the exception of unit one) counts five marks
towards the students' overall assessment for the
course. In addition there are two review tests and
a project which make up the balance of the
assessment. To pass the course, a student need
only accumulate at least 50 marks from a maximum
of 100 made up of 55 (11 x 5) from unit tests,
five for the project, 15 for the mid-year exam and
25 for the final exam.
For the course about 20 student proctors are
required, each working an average of four hours
per week. Course organization requires asubstantial
contribution from the two lecturers concerned
while a number of departmental colleagues assist
with the supervision of testing and tutorial sessions.
Problems and their solutions
The pre-Keller 1974 class roll of 225 students has
more than trebled over the last six years to the
1980 roll of 750. While this indicates general
satisfaction with the course by students and
teaching staff throughout the university, this
popularity poses problems in applying the principles
stressed by Keller (1968) and Keller and Sherman
(1974: chapter four in particular). For a large class,
careful consideration must be given to logistics to
encourage students conscientiously to complete
the requirements of each unit; to ensure that the
mastery tests are effective; to maintain a quick and
foolproof system to record student progress; to see
that feedback to the students from the proctors is
clear and accurate and to ensure that procrastin-
ation is kept to a minimum.
Room organization
The room currently used can accommodate up to
50 students sitting a test at any one time and,
typically, around 150 tests are processed in a
testing session, or approximately 600 per week.
On average there are seven proctors on duty at a
time. Thus the location of cupboards, tables,
proctors, students etc is a matter of some import-
ance. On the one hand, quietness is essential when
students are sitting a test, but interaction between
student and proctor is encouraged when the proctor
marks the test. If both activities occur in the same
room, they should be separated as much as possible.
Consideration should be given as to how, where
and when queues might form. If students are allowed
to pick their proctors there is a danger that they
may select the so-called easy proctors. At Massey,
the students are required on leaving the testing
area to deposit their script in a tray. The proctors
take scripts from the bottom of the same tray.
This simple device ensures strict queue formation
and randomly allocates students to proctors.
Selection and organization of the proctors
The availability of good student proctors in
sufficient numbers is a key ingredient to a success-
ful Keller Plan course. As such, selection procedure
should be sufficiently rigorous to ensure that high
standards are maintained. Selection criteria were
based on academic performance in related mathe-
matics and statistics courses. The rates of pay are
sufficient to attract and retain the best quality of
proctors. Staff endeavour throughout the year to
ensure that working conditions jure pleasant and
supportive. Proctors are made aware of the nature
of their position and the duties they are expected
to fulfil. Since they are in the 'front line' they are
encouraged to submit written and verbal criticism
of all aspects of the course. On the other hand
staff constantly monitor, on a systematic basis,
the scripts marked by the proctors to ensure
homogeneous standards of marking. It should be
noted that, through the years, the wholehearted
support, vitality and enthusiasm of the proctors
has undoubtedly contributed in no small measure
to the success of this course.
Assignments
In the period 1975-77 assignments were compulsory
and had to be completed prior to attempting a unit
test. However, a number of students who had
completed assignments and received the printed
solutions were frequently not averse to passing
these set solutions on to their more tardy colleagues.
It is fair to say that the students on the whole,
saw the assignments as an unnecessary and
annoying adjunct to the course which hindered
their more important learning; ie sitting and
mastering unit tests. The two primary aims of the
assignments were to prepare students for a unit
test and to encourage them to undertake more
lengthy real world problems than it was possible to
sit in a unit test. In 1978 and subsequently,
assignments have been optional. To guard against
inadequate or poor preparation, the unit tests are
now used as diagnostic instruments in that if the
test clearly indicates that the student concerned
has failed to grasp even the most basic ideas of that
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Evolution of a Keller Plan Statistics Course 137
unit then he is required to attend a tutorial where
remedial work under the supervision of a tutor
is undertaken. To fulfil the secondary goal of en-
couraging students to undertake lengthy statistical
analyses, an optional project has been added to the
course. Students collect data, analyse it and then
present their interpretations and conclusions. This
innovation has proved to be a most rewarding
addition to the course.
Tests
From 1975-77, there were four versions of each
unit test. Occasionally, however, test scripts were
illegally taken and, as a result, certain students
obtained access to the supposedly closed book test
material. This was a thorny problem to deal with.
Increased security was a partial, but unfortunately,
incomplete solution. In 1978 a statistical solution
was adopted — the test questions were introduced
in a random way. Computers can do this readily
but the Massey University computer does not yet
print subscripts or Greek symbols such as , etc.
Hence we decided to use the Massey University
printery. A number of schemes were devised, all
equally acceptable from a mathematical point
of view but unintelligible as far as 15 year old
apprentice printers were concerned. In the end we
devised a system acceptable to the printery and
this system has been in force since 1978. Basically
each test now comprises four pages with five
questions per page. For each page there are five
versions. The printery produce and staple together
all possible combinations (54 = 625) twice yielding
a stock of 2 x 54 = 1250 tests for each unit. The
procedure entails repeated use of an automatic
collator. Precise details may be obtained by writing
to the authors. This innovation appears to have
been an unqualified success.
Pacing strategies
Procrastination in PSI courses is very common and
many attempts have been made to reduce it — see
Semb et al (1975) and Boud et al (1975). The
approach we have adopted is perhaps contentious
but has been very effective. In 1975 and 1976
students were required to complete units four, seven
and nine by the end of the first, second and third
terms respectively. In 1977 this was amended
slightly so that students were required to complete
units three, seven and nine by the ends of the
relevant terms. However, a large number of students
were clearly having difficulty organising their time,
giving rise to long queues at the testing sessions in
the last week or two of each term. This placed an in-
tolerable burden on the system, not to mention the
students themselves. To meet this problem a course
planner or timetable was devised and has been in use
since 1977. It contains all the relevant information
concerning the course together with a recommended
study schedule. Unfortunately this proved to be
only a partial success. We thought of offering some
sort of reward for rapid progress but felt that there
were enough rewards built into the system as it was.
After some thought and debate, a new deadline
system was adopted in 1978. Full marks deadlines
were specified for units two to eight. These
deadlines represented a minimal rate of progress.
Any unit test passed after its deadline scored
four, three, two, one and nought depending on
whether the test was passed in the first, second,
third, fourth or after the fourth week following
the deadline. The students were warned that this
assessment scheme would not be relaxed for any
reason. Thus, students were able to travel through
the course as fast as they desired but were
penalized for a very slow rate of progress.
This penalty system contrasts somewhat with the
more positive features of the Keller Plan. However,
the results were excellent. It proved to bean easy
system to administer and was accepted without
criticism by the students. In fact, a survey of the
1978 class revealed that more than 90 per cent of
the students found the system reasonable and/or
helpful. In 1979 the system was further amended
to the extent that any unit test passed after its
deadline scored four, three or two marks depending
on whether the test was passed in the first, second
or after the second week following its deadline.
The minimum mark on a unit test was now a little
under half marks. The results were again excellent.
This system has been in operation since 1979 and
has found favour in the sense that, as in 1978,
more than 90 per cent of the students replying to
our questionnaires found the system reasonable
and even helpful.
Record system
Extensive use is made of the computer and a
computer card filing system to record the progress
of the students. Each week the computer master
file is updated with the week's transactions and a
complete report of the status of each member of
the class, the number of units he or she has
attempted, marks to date, review test and project
marks is produced. At the end of the year the
computer is used to assist in the task of scaling,
summarization and in general with returning marks
on the university scale. It is fair to say that such
record keeping systems are an indispensable tool
for a course of this size and structure.
Conclusions
This Keller Plan course continues to find favour
with students and staff alike. However, to maintain
a course of this type and size, a certain amount of
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138 PLET, VoL 19, No. 2 -June 1982
modification or compromise with regard to some
of the Keller Plan principles (see Keller, 1968) has
been necessary. Our pacing strategies are perhaps
the most contentious. However, some form of
pacing is necessary if only because the course must,
in the normal course of events, be completed in
any one academic year. We believe that our
approach with regard to this matter presents a
workable pragmatic and acceptable solution to
this particular problem.
References
Boud, D. J., Bridge, W. A. and Willoughby, L.
(1975) PSI now -- a review of progress and
problems. British Journal of Educational Tech-
nology 6, 15-34.
Brook, R. J., Pringle, R. M. and Thomson, P. J.
(1981) Modifications to a large PSI course. New
Zealand Journal of Educational Studies 16, 2,
198-9.
Imrie, B. W., Blithe, T. M. and Johnston, L. C.
(1980) A review of Keller principles with reference
to mathematics courses in Australasia. British
Journal of Educational Technology 11, 105-21.
Keller, F. S. (1968) Goodbye, teacher . . . Journal
of Applied Behaviour Analysis 1, 79-89.
Keller, F. S. and Sherman, J. G. (1974) The
Keller Plan handbook. W. A. Benjamin, Reading,
Massachusetts.
Semb, G., Conyers, D., Spencer, R., and Sosa, J. J. S.
(1975) An experimental comparison of four pacing
contingencies. Reading 24, Behavioural Research
and Technology in Higher Education, Johnston,
J. M. (ed.).
Walker, H. M. and Lev, J. (1969) Elementary
Statistical Methods. Holt, Rinehart and Winston,
New York.
Wire, B. S. and Brook, R. J. (1977) PSI for a large
service course. New Zealand Journal of Educational
Studies 12, 2, 176-81.
Biographical notes
Richard J. Brook taught high school in Australia
and East Africa. In 1972 he completed a PhD in
statistics at the North Carolina State University.
Since that time, he has been a senior lecturer at
Massey University.
Address for correspondence: Department of Mathe-
matics and Statistics, Massey University, Palmerston
North, New Zealand.
Peter J. Thomson studied mathematics for a BSc at
Otago University, then moved to the Australian
National University and completed a PhD in
statistics in 1972. After four years of teaching at
the University of Nottingham, UK, he took up a
position of senior lecturer at Massey University.
In 1981 he moved to the Victoria University of
Wellington.
Address for correspondence: Department of Mathe-
matics, Victoria University of Wellington, Welling-
ton, New Zealand.
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