Teaching an Art? It’s a Science!
Bruce Holtby
Computer Systems Technology
Northern Alberta Institute of Technology
ABSTRACT
The two complaints that
seem to be made the most often by students are that their instructors can’t
seem to teach or that they don’t seem to know what they are teaching. Teaching
requires a myriad of skills that fall into two distinct areas: pedagogical
skill and technical knowledge (or skill). Teachers with excellent qualities in
both are a rarity. But both, to some
extent are required, but at what level?
This paper proposes a
framework that can be used to help determine the minimum level of pedagogical
and technical skills any instructor needs to be effective in the delivery of
any course regardless of content or difficulty level.
There has been a lot of
research done on the need for both technical skills and pedagogical skills to
be an effective instructor, but there seems to have been no one who has tried
to establish a relationship between the two.
Using a standard
mathematical inverse relationship this paper shows how using a set of easily
established variables the relationship between pedagogical and technical skills
can be calculated, plotted and then used to determine the suitability of an
instructor’s skills.
The framework has the
built in capability to cope with those courses that are “conceptual” as well as
“technical” and allows for differing levels of complexity of the material being
delivered as well as the skill set of the audience receiving the training.
Lastly, the paper uses
the empirical results of other studies to show how the framework can model
those results to effectively demonstrate the feasibility of the framework.
Keywords: pedagogical skill, technical
skill, skills framework, content expert
1. Introduction
Why is it that students
always seem to be complaining? My school age children complain about their
teachers, my work colleagues complain about their professional development
trainers, my own students complain to me about their other instructors. Why all
the complaining? My own experience shows that once we ignore all the standard
student complaints about too much work, assignments being too hard, not enough
time and so on, that the two major complaints from students seem to be that
their instructors don’t know how to teach and that their
instructors don’t know enough about what they are teaching (their
technical skills are limited).
These two complaints
raise the fundamental question of whether a good instructor must be both a
technical specialist and a pedagogical expert. These two skills have a wide
range of expertise. Any given instructor can demonstrate very little to a lot
of pedagogic skill and at the same time appear to have from technical or
content expertise ranging from none to being a master of the field. What is the
most desirable combination of these two skills to form the perfect instructor?
Does the skill set needed by the instructor depend on the content being taught,
the environment in which the material is being delivered, or the skills and
knowledge of the student body being taught?
What is needed is a
framework to help determine the minimum but optimum combination of technical
and pedagogic skills required for an instructor to teach any given course and
to be successful.
2. Supporting Ideas
The basis of the
framework is that technical and pedagogic skills cannot and should not be
separated. My experience shows that when they are combined they form a synergy
far greater than either by itself. In their paper, “Developing a teaching
style: A dilemma for student teachers”, Onslow, B., Beynon, C. & Geddis, A.
(1992) indicate that the traditional preparation of novice teachers has
concentrated on two distinct areas, “content knowledge and general pedagogical
skills” (p. 303) and that the pedagogic skills can be generic and largely
independent of the material being taught. However, Onslow et. al. also
contrast this with Shuman (1986 as cited by Onslow et. al., 1992, p.
303) who “[drew] attention to the need to abandon this simplistic assumption
and to pay more attention to the ways in which pedagogy and subject matter
interact.” Onslow et. al. also state that a teacher’s expertise can be
tied to their ability to “transform subject matter knowledge” (p. 303) such
that the students can learn it. Onslow et. al. indicate that Shuman
calls this “pedagogical content knowledge” (Shuman 1986 as cited by Onslow et.
al., 1992, p. 303). Onslow et.
al. also write:
This
pedagogical content knowledge is in some sense a result of the interaction of
content and pedagogy. It is knowledge about the content that is derived from
consideration of how best to teach it (p. 304).
Hativa, in
her paper, “Becoming
a better teacher: A case of changing the pedagogical knowledge and beliefs of
law professors” (2000) supports this idea as well. She discusses several details of
inappropriate thinking and perceptions that can reduce the effectiveness of an
instructor. A relevant misconception presented by Hativa is that teaching is
just the transmission of knowledge. She wrote, “Instructors taking this view
believe that to teach well all that is needed is good knowledge of the
material” (Berman et. al., 1988, as cited by Hativa, 2000, p. 494). This
coincides with my experience in that instructors have been hired based on their
content skills without much regard for their teaching skills. The instructors
receive their own “training” in how to “teach” but in my case it was several
months after I first began teaching my students.
In his book, “The
tutorial process”, Barrows (1988) appears to be adamant that the synergy
between pedagogic and technical skills is required. He states, “there is no
question that the ideal circumstance is for the tutor to be expert both as a
tutor and in the discipline being studied by the students” (p. 43). However,
this is not always possible, or practical. In this case Barrows wrote, “the
next best tutor is the teacher who is good at being a tutor … though not an
expert in the field” (p. 43). Actually Barrows seems to feel so strongly about
this that he states, “the skill of the tutor is the backbone … it is not
acceptable [his bolding] to have a teacher who is an expert in the
area of study, but a weak tutor” (p. 44). The implication here is that
of the two sets of skills the pedagogic skills are the more important of the
two.
So it seems apparent
that the instructor must know the content as well as be a good instructor. But
what exactly does it mean to be a good instructor? The literature indicates
that the skills required are more than just classroom management, material
delivery, and time management skills. Hativa (2000) adds that important traits
in this area include “having positive self-regard, self esteem, energy and
enthusiasm, and positive view of others; being sociable, gregarious, friendly,
and agreeable” (Feldman 1986, as cited by Hativa, 2000, p. 492). As well Hativa
indicates that Murray et. al. researched the following capabilities as
part of teaching: “leadership, … liberalism, supportiveness, intellectual
curiosity, [and] endurance” (Murray et. al., 1990, as cited by Hativa,
2000, p. 492). Hativa also describes further details of her ideas around inappropriate
thinking and perceptions about teaching. First was the mistaken belief that
adapting instruction to suit the students’ capabilities is somehow reducing the
level of the teaching. She wrote that teachers “resist adapting instruction to
the rate and level of understanding of their students because they believe that
one cannot teach good science by simplifying it for the students” (p. 495).
Second was the false impression that students are solely responsible for their
own learning. Hativa states that teachers with this impression reject any
responsibility for the success or failure of their students. These traits
obviously don’t coincide with those described elsewhere in her paper. Hativa
seems to imply that the teachers must take a very active part in the learning
of their students. She seems to indicate that they must teach at a level with
which the students can learn and also to accept some responsibility for the
student’s learning. I agree strongly with both Barrows and Hativa that to be
effective an instructor must have a suitable set of pedagogic skills.
But
what about the level of technical expertise required? My experience as an
instructor clearly indicates that the instructor must know, and be competent
at, a minimum level of content if he or she is to teach it effectively. The
students are very aware of when an instructor does not know the material.
Unfortunately, the students become skeptical of any of their instructor’s
abilities if they sense a lacking in technical knowledge. Hativa (2000) seems
to concur and relates it back to a behaviour of the instructor. She wrote,
“students may interpret teacher shyness or insecure behaviour as an indication
of having … insufficient command of the material” (p. 493).
Page, G., Pachev, G.,
& Schreiber, W. (2001) in their study of student learning and the content
expertise of the tutors at the University of British Columbia in 1997 stated
the following expectations based on current literature they had researched
(Schmidt & Moust, 1995, and others, as cited by Page et. al., (2001)
p. 1):
·
The level of content knowledge of the tutor
improves student learning and the learning process.
·
To be effective, tutors must have both
pedagogical skills and content expertise.
·
Content expertise is a pre-requisite of the
tutor performing well pedagogically as described by Barrows (1988).
I don’t believe that
this is what Barrows intended and so this statement seems to be a
misinterpretation of Barrows. Barrows (1988) as stated earlier, appears to be
adamant that pedagogic skills are more important than technical skills.
In their conclusion,
Page et. al. state “student achievement … does not appear to be a
function of [the] level of … tutor content expertise” (p. 6) and that “the
results of this study do not support those of other recent studies showing that
tutor content expertise enhances student learning” (p. 6).
In another paper based
on the same University of British Columbia study, Pachev, G., Broudo, M., &
Walsh, C. (2001) when evaluating the tutors also make reference to Barrows
(1988). It seems they also misinterpret him. Pachev et. al. state “one
can expect that tutors that are content expert will be better than non-experts
at providing guidance, modeling reasoning and critical thinking skills” (p. 1).
In their conclusion they wrote, “high content-expert tutors … were better than
the other [low-expertise] tutors in modeling and fostering reasoning and
communication skills” (p. 6). These are not content skills as I see them but
rather are pedagogic skills. I think that this study and the two subsequent
papers set out hoping to show that content is the more important of the two
skill sets. They appear to have inadvertently used pedagogic skills in support
of technical expertise. I don’t believe the study or papers achieved the goal
of showing that technical skills are the more important. However, I do believe
the study and two papers have helped to confirmed what others have already
surmised – both technical and pedagogic skill is required to tutor or instruct
effectively.
But not all
instructors can be great both technically and pedagogically. However, they all
do fit on the continuum of technical and pedagogic skill combined. Where an
instructor fits will depend on their skills and knowledge. Hativa (2000) wrote that
“university professors tend to be differentially suited to different types of
courses rather than uniformly effective or ineffective in all courses” (Murray et.
al., 1990, as cited by Hativa, 2000, p. 492) and that this “compatibility
of teachers with courses is determined in part by personality characteristics”
(ibid).
3. The Framework
So exactly what does
this continuum of technical and pedagogic skills look like?
3.1 The Continuum
Figure 1 shows the
continuum, which depicts a two-dimensional context that shows the cross between
pedagogic and technical skills. Pedagogic skill is shown as low at the bottom
of the continuum increasing until it becomes high at the top of the continuum.
Similarly, technical skill is low to the left and increases to the right. Where
the two lines cross in the middle of the continuum an instructor could be
considered average in both skills.
3.2 Minimum Skill Levels
The literature seems to
indicate that a minimum level of pedagogic skill is required (Hativa, 2000, and
Barrows, 1988). This level of skill is shown in Figure 2 by the dotted line
labeled “Minimum Pedagogy”. This level is arbitrary and needs to be set based
on the material being delivered and the student body receiving it. An
instructor with skills less than this level would be unsuitable or unsuccessful
as an instructor for any course requiring this minimum level.
Similarly, the minimum level of technical skill is also shown on the continuum. This level of skill is shown by a dotted line on Figure 2 and is labeled “Minimum Technical”. Again, anything less than the minimum would be insufficient.
Hence, the gray area in the
continuum indicates where an instructor’s skills must lie in the continuum if
the instructor is to be successful for any course requiring those two minimum
levels.
3.2 The Skill Sets
This continuum can be
tailored to suit any teaching context such as workplace, college, or school. It
is independent of the material being taught and so can be adapted to any course
or learning situation.
Having said this, the
minimum skill levels need to be established according to both the learning
setting and the material to be delivered.
The pedagogic skills
include those cited by Hativa (ibid) and include, but are not limited
to:
· Positive self-regard
· Self esteem
· Energy and enthusiasm
· Positive view of others
· Sociable, gregarious, friendly and agreeable
· Capable leadership
· Liberalism
· Supportiveness
· Intellectual curiosity, and
· Endurance.
The minimum level of pedagogic skill can be
measured on a scale of one to ten (1 – 10) and is made up of the aggregate of
ratings for the skills listed above. This minimum level can then be plotted on
the continuum.
The minimum technical skill level is more difficult
to describe here other than to say that it is content specific and must be set
by the content experts assigning or preparing the material for each specific
course. Note that the same aggregate rating of these skills can be used to set
the minimum technical level on a scale of one to ten that can then also be
plotted on the continuum.
3.3 Variations in Minimum Skill
Levels
Not all courses require
the same skills sets. Not all courses or material to be taught require the same
level of detail either. Some courses may be more technical but not necessarily
more difficult. For example there are courses that I will call “technical” such as computer programming,
structural engineering, science (especially chemistry), medicine, and many
others. These types of courses tend to rely more on rules, formulas and
calculations, and tend to be inflexible in their technical content and
knowledge requirements. At the other end of the content spectrum there are
courses that are very much “conceptual” based. These include content such as
management, leadership, counseling, customer / personnel relations, arts,
liberal arts, and the humanities, as well as many others. These courses
typically have fewer rules, and are more flexible in the way the material is
taught and learnt.
The continuum supports both
types of courses through shifts in the levels of minimum pedagogic and
technical skills. Figure 3 compares two courses with differing levels of
“technical” and “conceptual” contents. For clarity, the minimum level lines
(dotted) have been removed.
The “technical” course has
a much higher minimum technical level but lower minimum pedagogical level. This
means the course will concentrate more on rules and fixed skills. In contrast
the “conceptual” course has a much higher minimum pedagogic level and lower
minimum technical level and will concentrate more on the flexibility of
concepts rather than rules. Note how this changes the shape of the gray
defining areas for an acceptable instructor.
Also note the overlap of
the two gray-hatched areas showing the two skills sets. An instructor in this
area would be able to teach both courses successfully.
3.4 The Optimum Instructor Line
It is not enough to have
a “gray area“ in which an instructor falls. The continuum further provides a
line of best fit for determining the optimum combination of pedagogic and
technical skills required by the successful instructor.
This line is
mathematically equivalent to an inverse function. It is based on the framework
variables already identified as well as those of the instructor being rated
against the continuum. The Optimum Instructor Line is determined as follows:
PSR – MPS = CD / (TSR –
MTS) (which represents the inverse
equation of y = 1 / x)
Where:
PSR is the
Pedagogic Skill Required by the instructor
MPS is the Minimum
Pedagogic Skill for the material being taught
CD is the Content
Difficulty of the material being taught (see next section)
TSR is the
Technical Skill Required by the instructor
MTS is the Minimum
Technical Skill required for the material being taught
As previously shown the
Minimum Pedagogic Skill (MPS) and the Minimum Technical Skill (MTS) need to be
established by the developers of the material in concert with the assessors of
the success of the training. These values could conceivably be different for
every course or set of materials being delivered.
The Pedagogic Skill
Required (PSR) by the instructor and the Technical Skill Required (TSR) by the
instructor can be established by rating the instructor using the same
instrument that was used to set the course minimum requirements.
Figure 4 shows the
continuum with an Optimum Instructor Line shown.
3.5 Course Content Difficulty or
Learning Level Expectations
There will be courses
where the minimum levels of the two skill sets are consistent but the difficulty
of the material being taught is different. An example of this may be two
courses where basic mathematics sets the minimum technical level but one course
is teaching a higher level of mathematics while the other course is teaching
the mathematics required for a nuclear physics degree.
Also the expected level
of learning by the audience may vary for two courses that have the same minimum
requirement levels. An example would be where the one course is expecting the
audience to leave with an understanding of the new material while the second
course expects the audience to be expert and the end of the course.
The continuum supports
these two variations through its Content Difficulty parameter in the Optimum
Instructor Line equation. This parameter shift the Optimum Instructor line
either up or down depending on the necessary requirement. Figure 5 shows
several different Optimum Instructor lines with varying Content Difficulties
but which all have the same minimum pedagogic and technical skill levels.
3.6 Comparing Instructors and
Courses Using the Optimum Instructor Lines
The following table
describes three instructors teaching two different courses and how they compare
to each other based on their places on the Optimum Instructor Lines. The
instructors are shown as A, B and C on Figure 6. The three instructors are
fictitious and have been set to demonstrate the various aspects of the
framework.
Note that both courses
have the same minimum pedagogic and technical skill requirements.
|
Content Difficulty
Line |
Comparisons |
|
Line 1: Higher content
difficulty of the two courses. |
Instructors A and B
both lie on this line and so would potentially have the same success at
teaching this level of content difficulty. A has less technical skill than B
but has more pedagogic skill. Conversely, B has more technical skill but less
pedagogic skill than A. Note that both have more than the minimum required
for both pedagogic and technical skills. Instructor C has the
same technical skills as A, but has less pedagogic skills than A. Similarly C
has the same pedagogic skills as B but less technical skill. Hence in both
cases C would not be as successful in teaching the same content difficulty as
A and B. This is shown on the continuum in that C is not on the same content
difficulty line as A and B. Note that C lies to the left and / or lower than
the line on which A and B lie. |
|
Line 2: Lower content
difficulty of the two courses. |
The line on which
Instructor C lays shows a continuum of pedagogic and technical skills at which
C would potentially be successful as an instructor. In contrast, A has the
same technical skills as C but much higher pedagogic skills. Similar B has
the same pedagogic skills as C but much higher technical skills. In both
cases A and B would be better instructors for this level of content
difficulty. This is shown on the continuum in that both A and B are to the
right and / or above the line on which C lies. |
Another aspect of the
continuum is the concept of the law of diminishing returns. This basically
means that even a large increase in either pedagogic or technical skill only
allows for a much smaller decrease in the corresponding skill. The opposite of
this is that if a particular instructor has only a slightly lower level of
technical skill than a colleague then the first instructor must have
significantly more pedagogic skill to overcome this deficit to be an
equivalently competent instructor. This is shown on the continuum by taking
away a small amount of technical skill from Instructor C (move left along the
Optimum Instructor Line) and see how quickly C moves up the pedagogic skills
axis. By the time C reaches the same height as A the increase in pedagogic
skill required is about three times the level of technical skill lost. This
also applies in the opposite direction where a small loss in pedagogic skill
would require a significant increase in technical skills. This relationship is
directly related to the inverse properties of the continuum. The two skill
sets, pedagogic and technical, are not interchangeable and depending on the
instructor’s location on the Optimum Instructor Line determines the
relationship between the two skill sets. As an example, an instructor who is
average in both skill sets (lines in the middle of the line) can substitute a
small change in one skill set with a similar small change in the other skill
set. However, as the instructor moves further in one of the skill sets the
corresponding change required in the other skill set grows inversely.
Further to the previous
discussion on the variations between “conceptual” and “technical” courses, the
proposed framework supports the integration of these two types of course
materials very well. Consider the locations of instructors A and B on the
continuum shown in Figure 6. Both lie on the same content difficulty line and
so could potentially teach the same course regardless of content. But let’s
look at their positions with respect to pedagogic and technical skills.
Instructor A has many more pedagogic skill but less technical skill and so
would seem to be better suited to the “conceptual” types of courses which rely
less on technical details. In contrast, Instructor B has higher technical skill
but fewer pedagogic skills and so may be more suited to teaching the more
“technical” subjects where rules and details are more important. This seems to
be supported again by Hativa (2000) when she states “university professors tend
to be differentially suited to different types of courses rather than uniformly
effective or ineffective in all courses” (Murray et. al., 1990, as cited
by Hativa, 2000, p. 492).
Grasha (1994), in his
paper “A matter of style: The teacher as expert, formal authority, personal
model, facilitator, and delegator”, describes five teaching styles that he had
developed through his studies of college teachers. These five styles seem to
fit very nicely on the continuum and are described in the following table (p.
9-10).
|
Expert: |
“Possesses knowledge
and expertise that students need. Strives to maintain status as an expert among
students by displaying detailed knowledge and by challenging students to
enhance their competence. Concerned with transmitting information”. |
|
Formal Authority: |
“Possesses status
among students because of knowledge and role as a faculty member. Concerned
with … establishing learning goals, expectations, and rules of conduct for
students.” |
|
Personal Model: |
“… establishes a
prototype for how to think and behave. Oversees, guides, and directs by
showing how to do things, and encouraging students to observe and then to
emulate the instructor’s approach.” |
|
Facilitator: |
“Emphasizes the
personal nature of teacher-student interactions… Overall goal is to develop
in students the capacity for independent action and responsibility.” |
|
Delegator: |
“Concerned with developing
students’ capacity to function autonomously… The teacher is available at the
request of students as a resource person.” |
As Grasha (1994) notes
(p. 2), it might be tempting to categorize teachers into the five styles but
this is actually not the case. Rather he says, “it became apparent that all
teachers possessed each of the qualities … to varying degrees … [and] they
could be blended together” (p. 2). This seems to fit very well with the
continuum framework. Grasha (1994) then grouped the five styles into what he
called “clusters” (p. 2) that show the way in which the styles are blended with
some being used more often than others. The four clusters Grasha describes are:
·
Expert and Formal Authority. Grasha said
that this blend sends the students the message that the instructor is in charge
and sets the tone as neutral or “cool”. This matches the continuum area of high
technical skill but low pedagogic skill where the “technical” course
instructors would tend to lie.
·
Expert, Personal Model, and Formal Authority
·
Expert, Facilitator, and Personal Model
·
Expert, Facilitator, and Delegator. On the
other end of the spectrum, Grasha said that this combination lets the students
know that the instructor is there to consult and advise. The tone then becomes
“warm” and open to discussion and participation. This matches the higher
pedagogy range of the continuum relating to the “conceptual” courses.
It is very interesting
that Grasha included “Expert” in all four groupings. This could indicate that
having technical skill is a requirement of all instructors, which fits well
with the continuum. The four groupings also cover the range of variations in
pedagogic skills that lie along the continuum.
Grasha (1994) also seems
to further support the concept of “technical” and “conceptual” courses. As part
of his research he had asked the question “What influences your teaching
style?” (p. 3). Many different responses were received but those I see directly
relating to the continuum include: “The subject matter (hard sciences versus
humanities), [and] Level of students (freshmen, seniors, graduate)” (p. 3).
Grasha collected
empirical data from teacher surveys and statistically tabulated the results of
his research. He then compared teaching styles and types of courses. The following
table lists some of Grasha’s results (p. 13) that I feel particularly support
the proposed framework. Note that the results are on a scale of one (1) to
seven (7) where seven (7) means “very important”.
|
Discipline |
Expert |
Formal Authority |
Personal Model |
Facilitator |
Delegator |
|
Humanities |
3.92 |
4.73 |
5.16 |
5.12 |
3.77 |
|
Applied Sciences |
4.29 |
4.70 |
5.29 |
4.96 |
3.82 |
|
Mathematics and / or
Computer Science |
4.66 |
5.11 |
5.23 |
4.28 |
3.29 |
These results seem to
support the framework concept of “technical” and “conceptual” courses. The
humanities and social sciences have higher requirements in the Facilitator and
Delegator areas implying that they are “conceptual” courses whereas mathematics
and the computer sciences have higher expert and formal authority numbers
implying them to be “technical” subjects.
3.7 A Few Worked Examples
Based on the Optimum
Instructor Line equation:
PSR
– MPS = CD / (TSR – MTS)
the Pedagogic Skill
Required (PSR) and Technical Skill Required (TSR) are the variables in the
equation. That is, they are the values that pertain to each individual
instructor rather than to the course.
As an example, consider
a course where the Minimum Pedagogic Skill is 3, the Minimum Technical Skill is
6 (this being a technical course) and the Content Difficulty is 5 (a moderately
difficult course) then the equation would become:
PSR
– 3 = 5 /(TSR – 6)
Applying some known
instructor values we could calculate their acceptability as follows:
|
Instructor |
Technical Skills |
Pedagogic Skills |
|
A |
With a skill level of
8 |
Requires a skill level
of 5.5 |
|
B |
Requires a skill level
of 7 |
With a skill level of
8 |
This example
demonstrates the power of the framework. With a technical skill level of 8
Instructor A only requires a pedagogic skill level of 5.5. In contrast,
Instructor B with a pedagogic skill level of 8 still requires a technical skill
level of 7 and not the 5.5 that may have been expected. This is because the
minimum technical skill level of 6 is much higher than the 3 of the minimum
pedagogic skill level required.
Compare this with
another course described by the equation:
PSR
– 5 = 4 /(TSR – 4)
This course, from the
numbers, would be a moderately difficult “conceptual” course with some
“technical” content.
Applying the same known
instructor values we could calculate their acceptability as follows:
|
Instructor |
Technical Skills |
Pedagogic Skills |
|
A |
With a skill level of
8 |
Requires a skill level
of 6 |
|
B |
Requires a skill level
of 5.33 |
With a skill level of
8 |
Being a slightly less
difficult course (4 rather than 5) Instructor A now still only requires a
pedagogic skill level of 6 (rather than 5.5) even though the minimum required
has increased from 3 to 5. Similarly, Instructor B now only requires a
technical skill level of 5.33 (rather than 7) because the minimum is now only
4.
Note, in contrast to the
first course, this course has a higher minimum pedagogic skill requirement and
so Instructor A now needs more pedagogic skills than B requires in technical
skills. This is the opposite of the first example.
4. Conclusion
In conclusion, this
paper proposed a framework for establishing the minimum but optimum combination
of technical and pedagogic skills required for an instructor to teach any given
course and to be successful. Current literature was reviewed and used to
support the idea that it is not possible or practical to separate the technical
skill levels from the pedagogic skill levels of the instructor, nor to try and
look at each in isolation. It would seem appropriate that, because instructors
must know the material well enough to know how to teach it but also must be
able to teach regardless of how well they know the material, their pedagogic
and technical skills must be considered together.
A continuum of pedagogic
and technical skills was proposed in concert with content difficulty and a
formula for plotting the continuum was offered and explained. Several examples
were explored and compared to studies reviewed in the literature. The framework
and the continuum appear to be viable. Further research is needed to determine
the means and methods of determining the values used in the formula – but that
will have to wait for the doctoral dissertation.
References
Barrows, S. (1988). The tutorial process. Springfield, Illinois:
Southern Illinois University School of Medicine.
Grasha, A. (1994). A
matter of style: The teacher as expert, formal authority, personal model,
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Hativa, N. (2000).
Becoming a better teacher: A case of changing the pedagogical knowledge and
beliefs of law professors. In Instructional science: An international
journal of learning and cognition, vol 28, nos 5-6 (pp 491-523). Dordrecht,
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Bruce Holtby
Computer Systems Technology
Northern Alberta Institute of Technology
11762 – 106 Street, Edmonton
bholtby@nait.ab.ca