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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 (x2 - 2) times (2x + 3), then you have to type in 2x3 + 3x2 - 4x - 6. I presume you could also type in 2x3 - 4x + 3x2 - 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.