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Teaching with aleks

Brian Rude

July 2010

Aleks is instruction by computer.
I don't know too much about it. My experience is limited to using it to teach
one course for one semester in a community college. This paper is simply a
description of my experience, for whatever it might be worth. I understand
aleks is not the only commercial method of computer instruction on the market,
but I know nothing about others.

I cannot give a great deal of
information on how aleks would be to experience as a student, because I never
used it as a student. However I do have two sources to draw on. First of all I
got feedback from my students. I will describe, as best I can, and from their
comments, how it works for a student. Secondly I learned about aleks from
pretending to be a student, as I will describe shortly. I do not know if my
experience teaching with aleks is typical, or atypical in some ways. I am
neither an advocate of aleks nor a critic. The semester is over, and I am still
left wondering whether it is a good way to learn or not.

I'll go into some of the history
of how this course was set up, what was expected, and how it took it's present
form. I do this because it has some relevance to how the course came out, and
it also gives some alternative ideas of what a course like this could be.

Originally this course was to be
a "hybrid accelerated course". To serve the target population it
needed to be an evening course, and it needed to have less than the usual
amount of class time. But, of course, it needed to cover all the material of
the regular course. It should not be diluted in any way, because students need
to be prepared to progress to the next math course. The target population is
people who would like to get an associates degree, or more, but for whom
regular college classes are just not possible, primarily because of their jobs.

The "hybrid" part of
this term refers to the idea that it would be taught half "face to
face" and half "online". The accelerated part of this term
refers to the idea that some of the courses of this fast track program would be
squeezed into half a semester or a summer. It was scheduled for Tuesday
evenings from 5:30 to 6:45, an hour and a quarter of instructional time each
week. This would allow for exactly one half of the regularly scheduled class
time for this course. A regular three semester hour course would be scheduled
for two such classes a week for the fifteen weeks of the semester, or for three
fifty minute classes a week, which would be the same amount of class time.

The fast track program includes a
number of courses that lead to an associates degree. So far as I know it is the
only course taught using aleks. The decision to use aleks was made by the
curriculum committee who set up the fast track program. I can't say that I
remember, or even know, all the reasons that led to the use of aleks. I did
have some input into that decision, and I was happy with the decision. But my
input was limited just because it was all new to me.

In most colleges, at least in my
experience, there is a basic math requirement for most majors, and the course
required to satisfy this is usually called "college algebra". It is
usually a three semester hour course. Most institutions also offer remedial
math courses for students who show by a placement test that they are not ready
for the regular college algebra course. At my school this basic math course,
our College Algebra, is Math 110. However we also offer Math 105, Introduction
to College algebra. This is not considered remedial math. We have several
courses with lower numbers that are considered remedial math. Perhaps 105
should be considered remedial, as by itself it doesn't satisfy the math
requirement for most majors or degrees. However it does give credit toward a
degree. Students do not have to take 105 if the math placement test shows them
ready for 110, and that does happen quite a bit. However it does seem that we
have two required math courses that correspond to one math course in similar institutions.

I had been teaching 105 for two
and a half years, one or two sections a semester, so the course was not new to
me. In the course as I had been teaching it there is enough time to give a
careful and thorough explanation of every mathematical topic that we are
supposed to cover in this course, but barely. In the time that I have been
teaching at this school I have formed the opinion that we try to pack in just a
little too much into this course. We would do better, in my opinion, to delete
a topic or two from the course requirements and have time to teach the
remaining topics more adequately. But that is simply my opinion, and I have
little to no influence on such things. In the regular course the class time is
such that I can expect to explain each topic adequately before assigning
homework problems or testing on a topic. But with only one half of this regular
time available that would no longer be true. Therefore students must be capable
of self study. They must be able to learn on their own from the textbook.

I participated in a training
course given by our community college system on how to teach in the accelerated
hybrid mode. However once the decision was made to use aleks all of that became
irrelevant. What remained, in my opinion at least, was that the students will
still need to be capable of independent study.

Independent study is nothing new.
My perspective on what might, or should, be meant by independent study comes
from my past experience. I have taken a number of "correspondence courses"
in my life. Before the age of the internet a correspondence course consisted of
a textbook, some general information about what to do, and a list of
assignments. The assignments are mailed to the instructor one at a time as they
are completed by the student. The instructor corrects each assignment, giving
feedback as needed, and then the student takes the final exam under supervision
at a local college or whatever can be arranged. Independent study worked for me
a number of times. I took an introductory statistics course that way when I was
young. I also took, for reasons I cannot now recall, a course in social
anthropology. A few years later I took two courses in physics. I also took
statics and dynamics, which are basic engineering courses. When I began to
think about going to graduate school in math I took a correspondence course in
vector analysis. I made good grades in all of these courses and felt that I
learned pretty much the same as I would if they were regular courses.

So I know by personal experience
that self study works. The key, it seems to me, is to put in the time and
effort that it requires, and it is a substantial amount of time and effort. It
worked for me because I was interested in the subjects and never counted the
hours. I also became aware over the years that probably the completion rate of
correspondence courses is pretty low. I started a correspondence course in
criminology that I never finished, and I was aware of an instance or two of
friends starting a correspondence course that they never finished for one
reason or another. If a course is not enjoyable, if the student just wants to
get it over and out of the way, I can imagine how it would be daunting.

And of course we should not
consider that there is a sharp distinction between independent study and a
traditional college course. In either case you have to put in a lot of study
time with the textbook and paper and pencil. But a traditional college course
has a number of advantages over independent study. Perhaps the most important
advantage is also an important disadvantage - the lockstep nature of a regular
college course. The simple fact that lectures come on a regular schedule, and
homework and tests come on a regular schedule can be an important motivation to
students, and an important obstacle for those who just can't keep up.

But we are in the age of the
internet now. Correspondence courses still exist in their old form, I presume,
but "online courses" are now the thing. I have no experience with
online courses. I would expect that they can take a variety of forms. One form
would be pretty much the same as the old correspondence course. You get a
textbook, some general information about what to do, and a list of assignments.
Instead of mailing in the assignments as they are completed, you probably send
them by email. As in the old correspondence course, you are self paced. The
only time requirement is a general requirement that it be completed in one
year, or something similar.

Another possibility of an online
course, is that students are connected to a teacher and other students by some
sort of closed circuit television or computer linkage. In this situation time
is not flexible. There is a definite time to log on and participate in class.
This would be much more like a regular course than a correspondence course. I
have no experience in this sort of thing, but I believe it is common now and
successful for a reasonable number of students.

And perhaps there are other
possibilities of what might be meant by an online course. Before the idea of
using aleks was brought up my course was going be a "hybrid", part
online and part face to face in a regular classroom. To me this always meant
that I would have time to explain some of the math in the usual lecture format,
but still the students would have to be capable of learning a lot on their own.
I would have only half the regular amount of time for this course, so I
couldn't explain every topic. The training I took had some good ideas, but
never seemed to alter the basic fact that students must be capable of
independent study. Students must learn much of the material without my
explanation and help. The "online" part of this course was never
envisioned as a time that you must log on and participate in a class by a
technological connection to some remote location. So the online part of the
course must be basically a list of assignments, a list of topics that must be
learned from the text, just like the old correspondence course.

But once it was decided that
aleks would be used all this changed.

"Interactive instructional
software" might be an appropriate label for aleks. I will describe it as
best I can. As I mentioned one way I learned how aleks works was by pretending
to be a student. A few weeks before the semester started I was given two log in
names and passwords. If I wanted to log in as the instructor my user name was
brude. But in order to learn the system I could log in with the user name
brude2. When I do this the computer doesn't know I am a teacher. In this
account I am just another student. I put in a total of about eight hours
working on alecks as a student. (Aleks keeps track of your time logged on.) So
this is what I will describe at the moment.

The first thing a student gets is
a brief tutorial of how to enter answers on the computer to the questions and
problems that will be given. This is pretty simple. Typing in words or numbers
is just like in any other computer application. But there is a bit to learn
about typing in exponents, to plot points on a plane on the computer screen, to
draw a line on a graph, to enter algebraic fractions, and so on.

At the very beginning I wondered
if aleks would present only multiple choice questions and problems. I was
pleased to find out that is definitely not the case. For example, if the
problem is to multiply (x^{2} - 2) times (2x + 3), then you have to
type in 2x^{3} + 3x^{2} - 4x - 6. I presume you could also type
in 2x^{3} - 4x + 3x^{2} - 6, and that answer would also be
recognized as correct. This, it seems to me, is a big step beyond multiple choice
responses. However this is still a long way from what a live teacher can
respond to, and I will have more to say about this shortly.

After this tutorial on how to
enter answers on the computer aleks gives a diagnostic test. I think there are
about 30 questions in this test. Aleks gives a problem. The student works out
the problem and then either enters the answer, or clicks on the "I don't
know" button. As I recall, aleks doesn't give you any feedback when you
enter an answer on this diagnostic test, or on later assessments, it just
presents the next problem.

I also can't remember just what
my strategy was on this initial diagnostic test. What's the best way to find
out about aleks from a student's point of view? Should I just answer every
question right? Should I answer a few wrong and click "I don't know"
a time or two?

I didn't make 100%, by whatever
strategy I used. I probably made a simple mistake a time or two, and there were
a few problems in which I was not sure if what I thought was the best way to
answer was what aleks thought was the best way to answer. And I think I
answered a few with "I don't know" just to see how that works.

After the diagnostic test was
done the actual instruction is begun. At any point in aleks, except when you
are taking a test of some sort, you can click on your "pie". The
aleks "pie" is important. It is the organizational center of aleks
instruction. This is a pie chart on the computer screen of the student‘s
progress, divided into the broad categories of topics that make up the course.
Each segment is notated as to how many topics are completed in that category
and how many topics remain to be done. The initial pie, of course, showed the
results of the diagnostic test. So to continue I simply clicked on one of the segments,
which brought a short list of types of problems that I had not gotten right on
the diagnostic test. I would click on one of those types of problems, and the
instruction begins.

The goal is to get all the types
of problems of each category done. When beginning a new session of aleks the
student logs in. Aleks responds with what it considers the next problem. The
student can work on that problem, or go to his pie and choose another type of
problem to work on.

Aleks presents a problem and a
place to enter the answer. If the student does not know how to answer he can
click on the "explain" button. Aleks then provides a page of
explanation and perhaps a sample problem. The student then goes back to the
problem and tries again. (It will not be the identical problem, but a problem
of that type.) When the student figures out an answer he types it in and
presses "enter". Aleks responds. It may say the problem is incorrect
and it gives another problem to try. If the answer is correct aleks will respond
with something like, "Correct, do one more problem correctly and this
problem will be added to your pie." Or it may say "do two more
problems correctly and this problem will be added to your pie."

This is the basic idea of how
aleks works. And it did seem to work.

Some problems come from what I
like to call "briar patch problems". You may understand the math and
know how to do the problem, but if there are numerous steps it can be hard to
get the right answer. You can get lost in a briar patch of details. Or you can
make a simple mistake in the middle of the briar patch, and, of course, your
answer comes out wrong. Even in my very limited exposure to aleks there has
been several times when I would work out a problem, type in the answer, and
then hesitate to press "enter". Maybe I spent only a few minutes on
the problem, but that seems like a long time. If I made a simple mistake again
and get the answer wrong I have to repeat the whole process. I didn't want that
to happen, so I should check over my answer. But that too can be a little
frustrating. It takes about as long to check it over as it did to do it in the
first place. This can become a bit demoralizing. It seems more like I am
fighting the system than learning math . But how would I know? I am not
learning the math. I am learning about aleks. It is hard to say that I really
experienced aleks as a student would. But I learned the basic mechanics of
dealing with aleks.

It is not only with aleks that
briar patch problems can be frustrating. But it seems that the impersonal
mechanical all-or-nothing nature of aleks can increase the frustration. In a
briar patch problem on homework in a regular course a student may make a
mistake and lose a point when it is graded, but still get confirmation that the
method and understanding are correct. In a briar patch problem on a test the
same thing can happen. Teachers normally give partial credit when a problem has
a simple mistake but understanding is apparent. But with aleks not only is
there no partial credit, but such a problem can totally stop progress, at least
in that category of problem.

I did not have the opportunity to
talk with other teachers who had used aleks, but from second hand information I
got the idea that some students don't like aleks. It may work okay for a while,
but then somehow it lets you "spiral down", so that you actually lose
ground. I didn't hear any details on this but I can imagine that these briar
patch problems might be the problem. A student may successfully complete a
certain type of problem and think he is done with it. Then, however, aleks will
give another assessment. The student will make some little mistake on a problem
and get a wrong answer. As a result that topic is taken off the student's pie,
and the student must attempt it again. If the student gets it right, I think,
aleks presents the usual feedback. Aleks replies: "Correct. If you answer
one more problem of this type correctly this topic will be added to your
pie." But if the student makes a mistake on the next problem, the message
changes. After you answer a problem incorrectly aleks informs you that you must
get two more problems correct before you are done. This can be daunting even if
you know how to do the problem.

I am conjecturing on second hand
information here. Perhaps this is not what was meant by "spiraling
down". Or perhaps there is this, and a number of other ways to spiral down
in aleks. As I say, my experience with aleks is very limited. Things might look
quite different when one teaches with aleks a second or third time.

Alek's feedback is limited. It
tells you if your answer is right or wrong. As a teacher I am accustomed to
giving a lot more feedback than that, and a lot more perspective than that. As
an example consider the following problem.

Mary leaves town in her car at 54
miles per hour. John waits one half hour and then follows Mary at 66 miles per
hour. When will John catch up with Mary?

When I taught problems like this
in a regular class I emphasized that a solution by trial and error was of no
interest to us. We needed to learn how algebraic ideas and methods could be
used to solve a problem like this. Therefore, I emphasized, little credit will
be given on either homework or tests for an answer, correct or not, that did
not show the algebraic method. To enforce this, of course, took a lot more work
on my part than just looking for a correct answer. However to do anything less
would be for me to fail on what I considered the essence of my job, to teach math,
not just a collection of recipes for getting answers.

For this type of problem I make a
big deal of "declaring the variables". Start out with "Let x =
the time John travels", and then "x + 1/2 = the time Mary
travels". Actually in distance problems we customarily use a chart to
declare variables:

distance
rate time

Mary
54(x+1/2)
54 x + 1/2

John 66x 66 x

Then we set up an equation. John
and Mary both travel the same distance, so the equation is

54(x
+ 1/2) = 66x

At this point we can stop
analyzing and just solve the equation. This is an algebraic solution to the
problem, and the general method is applicable to a very wide variety of
problems. Perhaps even more importantly this general algebraic method is a
beginning point for many other mathematical ideas and methods.

It can be claimed that aleks does
much of this. All you have to do is click on the "explain" button.
That is true. But aleks cannot tell the student that they will lose points if
they do not show the algebra, or that the student will get no credit for an
answer by trial and error. Aleks will present the problem and evaluate the
answer as either right or wrong.

A little side note here, one of
the ideas in what we might call "reform math", or "fuzzy
math", is the idea that students may find other ways to solve a problem
than the way being taught at the moment. This is taken to be a sign of the
creativity of students, and a sign of good teaching. By this perspective
finding alternative methods of solving a problem is something to be celebrated.
But the reality, it seems to me, is not so attractive. Very often students can
indeed find a different way of solving a problem, and usually that way is trial
and error. In a word problem such as this it often takes only a minute or two
to try a few different answers and zero in on the correct answer. However
finding an answer by trial and error is not learning algebra. It is avoiding
algebra. A few years ago when I first started teaching college algebra I became
aware of this. Sometimes on a test a student would leave a very clear paper
trail of the trial and error calculations that led to the correct answer.
Suppose this problem was a five point problem on a test. Should I give the full
five points if the answer is correct even though there is no algebra shown
whatsoever, only some scribbles that show trial and error was used? One
response to this situation on tests, which I have used extensively, is to give
the answer in the problem, but to ask for the algebra. If I used the above
problem on a test I would word it like this:

"Mary leaves town in her car
at 54 miles per hour. John waits one half hour and then follows Mary at 66
miles per hour. When will John catch up with Mary? (The correct answer is 2.25
hours after John leaves. You will get no credit for a solution by trial and
error. You will get full credit an algebraic solution. Declare your variables
in a chart, as we did in class, write an equation the represents the problem,
correctly solve the equation and explicitly state the answer. 5 points)"

I explain this to students in
class when we work on these types of problems. They seem to understand and
accept it. I explain what I mean by declaring variables and setting up an
equation. In practice I am pretty generous with partial credit, but if a
student gives the correct answer with no algebra at all I will give no more
than one point out of the possible five. And I have had numerous occasions to
do exactly that. But more commonly students will have something algebraic
written down that I can give a point or two for.

Obviously aleks can't do anything
along this line. Aleks can present a problem, accept an answer that the student
inputs into the computer, and respond with feed back that the answer is correct
or not. Aleks would require that you type in the answer 2 3/4 hours. Aleks
doesn't care of you got the answer by applying algebra, by trial and error, by
letting a friend do it, or anything else. Of course aleks could be programmed
to require a more complete answer, "t = 2 3/4" hours. And aleks could
be programmed to respond as correct to a number of answers, such as

2.75

2.75
hr

2
3/4

2
3/4 hours

2
3/4 hr

t
= 2.75

t
= 2.75 hours

t
= 2.25 hours after John leaves

t
= 2.75 hours after Mary leaves

and possibly hundreds of other
ways to state the answer. But all of these answers still do not require that
the student show an algebraic method.

For more perspective on how I
like to teach written problems in algebra see http://www.brianrude.com/writpb.htm.
I think this will show how limited aleks is in comparison to the feedback that
a teacher can give.

To be fair I think a bit more was
built into aleks than I have described so far. It was programmed to give a
prompt in some situations, after the student enters an answer, though I don't
recall just what those situations were. I think an example would be if a
student gives only one correct solution to a quadratic equation aleks would
prompt for the other solution. But this is still far less than a response from
a live teacher. Aleks goes beyond multiple choice, but not by far. You type in
the answer and aleks tells you whether that answer is right or wrong.

I began this course wondering how
aleks would work for actual students. Will they learn? Will they learn what's
really important in the subject? Or would they learn how to game the system
without learning the important mathematical ideas. Would it be motivating for
students? Would it be frustrating or demoralizing at times?

Aleks did seem to work, but how
it worked changed over the course of the semester.

For the first few weeks of the
class, indeed until close to midterm, class was very simple and easy for me.
Students worked individually on their computers. (We met in a room with 24
computers available, but a few students brought their own laptops.) I would
generally have a few things to say at the beginning of the class period. That
would just take a few minutes. Thereafter for the rest of the 75 minute class I
would circulate around the class talking with individual students. Sometimes
there would be math questions to answer, but not too often. I would ask each
student what they work working on, and ask to see their "pie". This
would give me a general idea of how things were going for them.

There was plenty of enthusiasm
from the students about aleks. Time and again a student would say, "I just
click on "explain", and it shows how to do the problem . . ." I
was heartened by this positive response, and students did seem to be learning.
Students did not speak much of frustrations.

My usual custom is to grade 70%
on tests, 15% on homework, and 15% on quizzes. I explained from day one that
aleks would be the homework. The quizzes and tests would be the same as I use
for my regular 105 class. "Aleks is for learning the math", I told
them,. "Aleks will be the workhorse of this course. But to get credit you
have to demonstrate that knowledge on the same written tests that I use in my
regular 105 class." There are four hourly tests in the regular course, and
the final exam. It was agreed early on in the planning of the course that these
tests, not just aleks topics completed, should be the basic requirement for
getting credit in the course.

So until about midterm things
went smoothly. Students seemed to be learning, and seemed to be satisfied. But,
I wondered, what about the pace? Are students learning fast enough? Will they
be able to learn all that is required, and then pass the tests, in the time
available.

And I also wondered about the
quality of the learning. It would seem possible that students might learn, in
ways that I do not understand, to respond successfully to aleks but still fail
to learn the math in some ways. I still consider this a possibility, but I
can't say that anything in my experience with aleks gives evidence of this. And
again we can compare to a regular course. Is it possible that students in a
regular course somehow learn what they need to pass tests and yet somehow fail
to learn the actual math? Yes! Absolutely! I have been thinking that for a long
time. Indeed, I have become increasingly aware that almost everything I teach
is high school math. Did the students learn this math before and forget it? Did
they never learn it, in spite of making satisfactory grades in math courses
that purportedly cover this material? That is a subject that I think needs a
lot of investigation.

When I log on to aleks as the
instructor I have data available on what each student has done on aleks. One
important statistic is the total amount of time a student has logged on to
aleks. Several times a week I would check this out, and on Tuesday afternoons,
before the class, I would print out the results to have at my fingertips when I
talked with students. The hours logged on varied a great deal. There were a few
students who logged on so few hours that it was very doubtful that they would
ever get anywhere unless things changed. It was not unheard of for the hours of
a student one week to be identical to the hours from a week ago, meaning they
had not done a thing that whole week. I could usually confirm this by looking
at the last log-on date. Most students logged on a substantial number of hours,
but early on I didn't have too much idea of what to consider a substantial
number of hours.

It was about the fourth week, as
I recall when I began to form an opinion on just what a "substantial
number of hours ought to mean." At that point, as I recall, one or two
students had logged on forty or more hours. Most students fell short of this.
Forty hours of effort in a month's time is about ten hours a week. How does
that compare with students in a regular class? There is an old rule that
students should expect to put in two hours of outside study for every hour of
class time. Obviously lots and lots of students do considerably less. A regular
three semester hour course would have three hours of lecture a week. Add on
twice that, six hours, of outside study and you get nine hours a week. So any
aleks student logging in ten hours a week compares very favorably with what
students would do in a regular class. If they are learning efficiently, they
should be in good shape. but are they learning efficiently? How can we know.
And what about the students logging only four or five hours a week? Will they
be okay?

Another important statistic
available from aleks is the number of topics each student had completed. This
varied greatly. The entire course consisted of about 250 topics (each topic
being a specific type of problem). One student may have logged in 22 hours at a
certain point in time and completed 65 out of 250 topics. Another student who
also logged in 22 hours at the same point in time may have completed 145 out of
those 250 topics. Is the second student learning at twice the rate of the first
student? Or did the second student get a lot more topics out of the way on the
diagnostic test than the first student did?

Can we say that if a student has
completed 125 topics, about half of them, then that student is half way through
the course? Or could it be that the second half of the topics are much more
difficult and will require a lot more time than the first half of the topics?
Or maybe it would work out the other way. Maybe the first half of the topics
are more time consuming because they involve learning difficult basic concepts,
and the second half of the topics would go much quicker because they just apply
the earlier ideas.

I knew that out of those 250 or
so topics some needed to be weeded out. Some of those topics were appropriate
for Math 110 rather than Math 105. And perhaps other topics needed to be weeded
out for the opposite reason. They weren't worth the time that it took the
students to do them. It was not until the end of the semester that I pretty
well had accomplished that weeding job.

I concluded that there was no
good way to judge progress early in the course. Until students start passing
tests it would be very difficult to know if things were going well or not. This
is quite different in a regular class. In a regular class the first test, about
four weeks into the semester, normally would show very clearly how the students
were doing. A student who makes 80% on test one will likely do okay in the
course. A student who makes 50% on test one is very unlikely to do well in the
course. There are plenty of exceptions of course. If there were not we could
just hand out final grades for the course after test one and save a lot of
work. But the point is in a regular course students get a good idea of how they
are doing early in the course. With aleks that is much less the case.

At the last class meeting before
the midterm break I told the class that I was putting practice test one on
"D2L". D2L, which is an abbreviation for "desire to learn"
is a computer course management system that we use at our school. It uses the
internet. Teachers use it in different ways, I presume. I use it is primarily
as a bulletin board. I can post any documents that I want to be available to
students. Students can go on the internet anytime anywhere and see what I
posted for their class. I made students aware of D2L at the beginning of the
semester.

As I recall at that time, right
before midterm, no student had even taken test one yet. That would mean we were
not on schedule. There are four tests plus the final. However there is not an
explicit connection between the aleks problems and the topics covered on the
written tests. It would be good if I could give the students a specific list of
aleks problems to complete before test one, and so on. But I never had time to
actually do that. So long as students seemed to be making good progress on
aleks, there was no immediate concern that we are getting behind. A student
might do many topics on aleks before realizing that he or she ought to go ahead
and start getting tests out of the way. I explained all this at the beginning
of the term, but by midterm it was time, I thought, to remind them of this.
It's time to start taking tests, I told them. I expected to put practice test
two, and subsequent tests, on D2L shortly thereafter.

I discovered several years ago
that posting a practice test is very valuable to students. Previously I had
always tried to give out a "study guide" before each test, a short
discussion and listing of the topics and types of problems that they needed to
study. But when I started providing practice tests the students' responses
indicated this was of more value than a study guide. In most math courses it is
generally quite possible to tell students just what will be on the test.

I expected students to make use
of the practice test. But I did not expect that everyone would abandon aleks,
but that is about what happened. This was very evident from the statistics
provided by aleks. Students who had been putting in eight or ten hours a week
were suddenly putting in only two or three, or none whatsoever. It was apparent
that they perceived that the practice tests were what to work on. They were
what counted. Aleks apparently was not very appealing any more.

Is aleks a good way to learn?
Before midterm it appeared to be working very well, but I have nothing to
quantify, only subjective opinions. After midterm, everyone abandoned aleks, or
at least gave it second priority. So how can we make any judgments about
whether aleks works well or not?

If aleks was abandoned, what took
its place? That is not clear. Part of the answer was that students thought that
working on the practice tests would take the place of aleks. But that is short
sighted. The practice tests are very good for review and to focus the students
attention on specific problems, but they are certainly not a primary means of
learning math. That requires doing a lot of problems, not just a few on a
practice test.

A textbook, along with a list of
problems and a little guidance can be an effective way to learn math. Indeed
that is the old style correspondence course. A week or so after I put the first
practice test on D2L I told the class that I would also start putting on the
homework assignments from my regular course. A homework assignment in my
regular course, of course, is a list of problems. I told them that these
assignments were purely for the students convenience. If they proved to be a
good way of learning, use them, if not, stick to aleks.

In my regular course homework
assignments are provided. People learn math by doing problems, and homework
provides for that. But there is much more. I collect and grade the assignments.
That provides feedback, which I hope is valuable, and I hope also provides
motivation. That would not transfer to the fast track course. I didn't want to
require these homework assignments. I had said from the start that aleks would
be the homework in this course.

So the first half of the course
was marked by total reliance on aleks, but little quantifiable data. The second
half of the course was marked by an abandonment of aleks and nothing definite
to take its place.

However the results, I felt, were
not bad. About one third of the class finished all four hourly tests plus the
final in the regular semester. Another third of the class took a grade of
"I", incomplete, with plans to finish up during the summer. Another
third of the class drifted away.

This "drifting away" of
students is not good, but it's not a disaster either, and it doesn't reflect
much on aleks, in my opinion. It happens in all courses, so far as I know. At
least it has always been a regular part of any of my regular courses. Some
students will have poor attendance for a few weeks or a month or so, then just
disappear. Sometimes such a student will come to see me and have good
intentions of catching up, and indeed sometimes such a student will catch up.
However it seems just a part of the type of students that a community college
caters to that the attrition rate is high. Many students come with the
intention of giving college a try. They have the attitude that it may or may
not work out. Often, I think, when a student disappears it is a sign that they
gave it a try, and are finding out that college is not working for them. . When
they stop coming to class it doesn't necessarily mean that they have
consciously decided that it didn't work out, but they are not far from that
point. I suspect some of these students are thinking they'll try again the next
semester, and some of them do. Others, I presume, at some point simply conclude
that college is not for them. They gave it a try, it didn't work, so they move
on.

I am guessing to quite an extent
in this. I would like to know a lot more about what our students expect from
college and how they interpret their experiences. But the point here is that it
was not unexpected that about a third of the class would drop out.

I wish I could explain exactly
how those successful students, about a third of the class, accomplished their
success. I could go back, perhaps and analyze the data provided by aleks and
perhaps learn something. But I think that would be inconclusive. I think it is
true in general that after midterm students stopped working on aleks as the
essence of the course. The successful students probably used a variety of means
to learn the math. I will guess that some of them found the old fashioned
method of studying out of the book was the most efficient way to learn.

One student discovered that class
time of my regular 105 math course would fit into her flexible lunch hour. She
started coming to this class, and was enthusiastic about it. I had mentioned
sometime about midterm that students were welcome to do that. But I didn't
think it was very important. If they could come to the regular class they
wouldn't have taken the fast track course in the first place. I have always
felt that giving a careful, thorough, comprehensive explanation of the math is
very important, so in my regular class that is exactly what I do, as best I
can. This one student gave me some confirmation of that importance.

The results of that other third
of the class, those who are trying to finish up during the summer, will be
unknown for a while. In the discussions in setting up the course the issue of
time was given some thought. I felt that some students who are capable of
completing the course might not be able to do it in the regular time. I brought
up the idea that giving a grade of "I", for incomplete, would
probably be needed in some cases. The grade of "I" is used sparingly
in regular courses. It is to be used when a student is doing okay in a course
but special circumstances arise that make it impossible for that student to
finish everything on time. When a "I" is given the student has a
specified amount of time to finish, but the grade automatically reverts to a
failure if the work is not finished. I felt that under the circumstances, a new
course delivered in a new way, we should be more flexible than in a regular
course. This idea seemed to be accepted by all involved.

As I write this in July about a
third of the class are ostensibly planning to finish during the summer. I
suspect that several will, but I also fully expect that several will find it
just doesn’t happen. They’ll probably procrastinate for most of the
summer and then make a last minute effort but be overwhelmed by the amount of
work that it would take to pull it off.

So, is aleks a good way to learn?
I still don’t know. My conclusion is that aleks can be a valuable tool for
learning math, but it is not magic. Students who have the ability and are
willing to put in the time and effort it takes can make aleks work. Does it
work better than a textbook and a list of problems, the essence of the old
style correspondence course? I think it probably does. But my experience
provides only anecdotal and subjective evidence.

What lessons can be learned from
this experience? I am no longer teaching, so I won't have the opportunity to
try to improve on this experience. But I can give a few conjectures.

I can only guess, but my guess is
that aleks and similar instruction will probably not displace conventional
instruction., at least in the foreseeable future. I think as time goes on this
type of instruction will be seen as a valuable addition to conventional
instruction. Conventional college instruction works also. It has for many
years. And it has some very real advantages.

I see my job as a college teacher
as providing the means by which capable and conscientious students can learn
math. In a regular class the means is primarily a careful and thorough
explanation of the mathematical ideas and a careful and thorough explanation of
how those ideas are applied to problems. It can be argued that aleks does this
also. But I'm not sure anyone would argue that it can do as well as a live
teacher. In addition to lecturing I see an important part of my job is giving
individual help when needed. In a sense aleks does this also, but again I don't
think as well as a real live person can do.

However that is not the point.
The advantage of aleks, I would think, is economy. Once an aleks course is set
up the marginal cost for each additional student is practically zero. Thus
aleks has the potential for being very cheap. It doesn't have to be as good as
a real live teacher. It simply has to be good enough so that students who are
capable and willing can make it work. That certainly seems to be the case to
me.

But when we talk about efficiency
and economy, we should not look only from the perspective of providing the
instruction. We should also look at the efficiency from the view point of those
receiving the instruction. As a hypothetical situation imagine that some type
of aleks-like computer instruction charges a student $100 for a course. In
comparison to that suppose the regular cost of instruction is $600 per student.
I chose that figure because I think that is approximately the tuition charged
for the courses I teach. If these figures are reasonably accurate then there is
certainly a tremendous motivation for a massive move to aleks type instruction
at all levels for which it works. However suppose after a few years it becomes
apparent that successful students will put in twice the amount of work for the
same course. I have mentioned the ideal that students spend two hours outside
of class preparing for each hour of in class time in a regular college course,
but that is an ideal that is often stated, but impossible to enforce or even to
judge. I suspect many students scrape through many courses on a lot less time
Therefore a three hour college course meeting three hours a week for 16 weeks,
a total of 48 hours of class time, would entail about 144 hours of total time
for successful conscientious students. Let's suppose that research shows that
successful students in a regular college course put in a total of 100 hours of
effort, but that equally successful students in aleks put in 180 hours. Now
where does the optimum lie? Student time is valuable, is it not?

But it could be more complicated
than that. Perhaps further research comes in that shows that with computer
instruction students put in about as much time as students in a regular course,
but are substantially more likely to discover as they progress in their chosen
field that somehow aleks instruction is faulty, that students learned how to
respond to aleks without learning the basics of the subject. But, as I have
already said, there is plenty of evidence that that happens with regular
college instruction also. There would still be trade offs to be made. Suppose a
college could offer a course with instruction by aleks and charge only one
sixth of the normal tuition, as in the figures I mentioned above. Would that be
a good trade off even if there is statistical evidence that the quality of the
instruction is less than by conventional lecture?

I can't answer these questions.
My guess is that aleks, and aleks-like instruction, are here to stay,but I
don't expect a revolution in college teaching is upon us.