Math Forum Discussions

Jonathan Groves

Posts: 2,068
From: Kaplan University, Argosy University, Florida Institute of Technology
Registered: 8/18/05

Re: Direct Instruction Wins
Posted: Apr 21, 2011 9:28 AM

Plain Text

On 4/20/2011 at 5:31 pm, Robert Hansen wrote:

> Jonathan wrote...
>
> "Direct instruction is usually all or almost all
> lecturing. And a curriculum
> that is lecture-driven is, by definition, one that is
> taught using lecture
> as a primary way of delivering information in the
> classroom."
>
> If you are going to use that strict definition then
> why are we even discussing this? I can vouch for 30
> to 40 years ago and by your definition that only
> occurred once in high school (a calculus teacher) and
> in selected later classes in college which by there
> very nature involve only an instructor workng through
> problems. For example, if it is a course on linear
> algebra, what else is the instructor to do but show
> you how to apply mathematics to problems involving
> linear algebra? A course in electromagnetic fields is
> a course in applying calculus and various physical
> laws to problems involving fields. Other than a few
> demonstrations to say "See, it works!" the whole
> purpose of the course is to say "See, it works!" with
> calculus and the laws of physics. I suppose maybe you
> mean that a course in topology should show clever
> animations. But those clever animations don't teach
> topology. In fact, they don't teach anything. At the
> end of the day the instructor has to go up to the
> board and show them how it is done.

Robert,

First, isn't this what the article Wayne posted defines as direct
instruction? In other words, don't the conclusions attempt to
explain what happens when the teacher increases lecture time in
the classroom?

Now that I think about it, here is a question that this study
does not seem to answer, at least not in its conclusions:
Is there a point of diminishing returns? In other words, suppose
class discussions and problem solving activities are supplemented
by lecturing and that increasing lecture time helps to increase
student performance (which does not always translate to increased
learning). But does that mean that increasing lecture time to
nearly 100% (ignoring time for tests and quizzes) maximizes
student performance? Not necessarily. This relationship could
be quadratic in that student performance increases with increased
lecture time up to a certain point and then begins decreasing
after that. As far as I could tell, this issue is not even
addressed in any way.

Second, these courses you mention in these examples are pretty
high-level, especially for K-12 and even early college. Most
of these students are already generally well motivated and
generally good thinkers anyhow. Of course, there are exceptions
no doubt, but exceptions in those courses are relatively rare.
Though analyses of teaching in such courses are worthwhile,
this study does not attempt to say anything about advanced
college courses, only eighth-grade math and science. And I'm
not even attempting to say anything about these advanced
courses either, especially given that the students I have
described are a rather poor description of the students
taking these sorts of courses you have mentioned here.

> When you get to a certain level in the material,
> there is really very little show-n-tell left that
> equates to learning. For the most part we are
> entirely past intuitive notions and the few
> activities left aren't there for pedagogical
> purposes, they are there simply to have a freaken
> break.

Once again, this is a description of more advanced courses,
not courses in K-12 or early college level. Even then,
more advanced courses can still discuss developing intuition
but not normally developing intuition for basic concepts
but instead developing intuition for more specialized concepts
that generally only math or science majors in college or
graduate school ever see. The reasoning that these courses
attempt to foster are more advanced reasoning, not basic
reasoning about elementary mathematics or elementary
physics that is needed for more advanced work. These courses
generally assume that the students have already developed
this basic reasoning anyway. Again, that is not necessarily
reality for all the students taking these courses, but that
is a different question.

> I think you need to be more specific Jonathan. I am
> going through an inventory in my head of all past
> classes and only a couple were done poorly enough to
> fit your strict definition. You need to make a list
> of classes that are direct (even your form)
> instruction entirely by nature (like those I
> mentioned) and those that are not. You will find few
> transgressions. Which is probably why mazur is
> spending decades trying to get someone to listen to
> his lectures on lecturing. It just isnt applicable.
> Either the class is entirely direct by its nature or
> it is open for discussion and operates like I
> described.

If the classes you are examining here are like the classes
described above, then you have missed the point entirely.

In reality, I do care more about what is taught in a class and
how learning is tested and what the goals of the class and the
teacher are, especially in K-12 and early college where the
students are often not fluent thinkers yet in the subjects
being taught, than about specifics of whether the teacher
lectures or not. I would rather see a teacher relying more
on lecture but teaching a meaningful class and insisting on
understanding going beyond mimicking solutions to worked examples
or quoting facts than a teacher using problem-solving based
approaches but spending all the time chasing after trivalities
and memorization and mimicking canned solutions to exercises
or leading discussions and activities that end up going nowhere
or are so badly monitored that hardly anything worthwhile is
being discussed in class.

In other words, seriously botched attempts with alternatives to
lecture and students working on exercises and problems individually
can end up with results worse than lecturing, which probably explains
why these alternatives have not made significant headway on a
large scale. On top of that, if the class consists mainly of
students who don't want to do their own thinking in class or
feel that they cannot do their own thinking and simply want the
teacher to do show-and-tell the entire class period can truly
thwart the teacher's attempts to do anything more than lecturing.

So lecturing is better than chaos resulting from seriously
botched attempts to do anything beyond lecturing. A teacher
who cannot use these alternatives effectively are better off
lecturing, but that doesn't mean that they can't eventually
learn to teach using these alternative ideas. And, of course,
teaching using these alternatives doesn't necessarily mean
abandoning lecturing entirely (though it could, and some
can teach effectively without lecturing).

But I do find that most students tune out during lecture or end up
being so lost that they might as well be tuning out. And it can
be very easy to get so involved with the lecture itself that we
fail to realize that the majority of students are lost. And
lectures often focus on presenting canned mathematics that almost
all hints at their development are lost, which is especially
problematic for students who already believe that solutions to
mathematical problems are supposed to come out of mathematicians'
heads and their own heads in this canned form. I have little
reason to believe that most students who struggle with math don't
believe this, especially when they look at a problem, cannot make
sense of it right away, and then begin panicking. And many of
them also feel that their first attempts at a written solution
are supposed to be good enough for a final presentation of the
problem's solution. Sounds like that kind of thinking to me,
the kind of thinking that solutions are supposed to come out
already in canned form. Now where do we suppose they got that
notion?

And this brings me back to what I had said before, which you
did not address yet:

But the problem is then that all such activites are relegated to outside
the classroom only. So why not instead use class time to work more on these
things so that the teacher and classmates can help monitor each other's
development of these good habits rather than relegating them to outside class
only where many have no one to help encourage or monitor their development
of these good study and thinking habits? Why use a lot of precious class
time to deliver information that students can try to get themselves
and this effort to get this information helps them practice their reading?
Many struggle with reading, and much of that problem is that they are
rarely encouraged to read anyway. So what should we expect? Of course,
they will struggle some with this reading, but they will need to know
how to learn by reading. And class time can be set aside to ask
questions about the reading.

And the teacher will serve students well by demonstrating to them their
own thinking on problems rather than simply delivering what is clearly
no different from a rehearsed presentation of the solutions to problems.
Many students have trouble getting started on problems, and teacher's
presentations often do not help because the teacher is delivering a solution
that he or she has already worked in advance! That is, the teacher does
not need to think of possible ideas to start and then struggle by testing them
and trying to make them work and trying to think of new ideas when current
ones are not working because the teacher already knows the solution!

Of course, lecturing does not have to be avoided entirely, but a heavy
dependence on lecturing is a big waste of precious class time that can
be used to foster good thinking habits. Most students will need to work
on these habits consciously and with a lot of encouragement and guidance
from their teachers and classmates before they master them, and heavy
lecturing eats up that time they need.

> You are right about students not reading. And
> students need to read the same whether the nature of
> the class is direct or not. I disagree with your
> reason though. I don't think students don't read
> because the class involves lecture. Only stupid
> students would even begin to compare 3 hours of study
> to 1 hour of lecture. I think they don't read because
> they are not interested in the course or lazy.

Of course, bad textbooks don't exactly help encourage students to
keep up trying to read and decipher the mess or even help encourage
students to try to get started if they already know that their
textbook is impossible to read and decipher. And many elementary
math books are not written to be read seriously, just to consult to
mimic canned solutions or to look up that fact the students can't
remember. So, yes, lecturing is not the only reason they fail to
read their books.

Another reason is that many of these students don't associate learning
with reading but with listening to a teacher talk. So where do we
suppose they get this notion?

But if their books were well written and they knew that but if the
teacher is going to lecture on just about everything in there, many
probably won't read anyway because the lecturing provides a shortcut.
And students will tend to use any shortcuts that we seemingly provide
because of their many other duties besides our class that they must
attend to. It is human nature to prioritize our tasks if we have
many to do based on formal deadlines or other short-term consequences
for not doing them soon. If we have many other things to do or at
least we feel that we do, then it is easy for us to ignore or not
even see long-term consequences if we see no short-term ones.
In other cases, we might see those long-term consequences but may
tell ourselves that we can still avoid them but that we don't have
to work right now to avoid them--that is, avoiding these is not an
issue right now, only later. So my point is that teachers will
probably need to provide short-term consequences rather than relying
on natural long-term ones--which the students might not even see till
much later down the road, if ever--for not doing the reading.

Jonathan Groves