Using Connected Curriculum Project Modules - Technology: help or hindrance?

Author(s):
John Hannah

Ideally the browser and the helper application will be transparent to the student, as they are primarily a means of getting the student to understand and engage with the mathematics.  Despite an initial hostility to an unfamiliar operating system (Unix instead of Windows), and perhaps an unfamiliar browser (Netscape rather than Internet Explorer), most students settled quickly into using the browser pages of the CCP materials.

The Maple worksheets that accompany each CCP module have most of the necessary commands already entered, and most of the exercises can be answered by copying and pasting these commands to new command lines, and making minor modifications to them. One student had a colorful way of expressing the advantages of this approach:

#43: Not too much emphasis on knowing the exact commands to input for Maple which means time is well spent on the actual mathematical concepts not pissing around trying to get it to work.

Some sensed a temptation inherent in this approach:

#30: Useful tool for learning concepts. Perhaps it was too easy just to follow the instructions without actually understanding it, but still an effective method of learning.

to which other students succumbed:

#20: . . . I feel I didn't learn a lot as we seemed to be just pressing enter, so when it came to explain what we learned, it was difficult.

but others felt the approach worked in their case:

#96: Often with computer learning it is easy to race through the exercises just pressing the enter key, but these labs often made me stop and think.

Just pressing the enter key led a few students astray in the fifth module, Experiments with Fourier Series, where about 10% of pairs commented on the convergence of the Fourier series approximations (Part 2, Step 5) using just the plot with n = 1, the value supplied by the original worksheet, as their evidence. (By this stage many students had discovered the Execute Worksheet command in Maple's Edit menu, and they didn't always look very carefully at the resulting output.)

Where more than copying and pasting was involved, students needed to be more or less familiar with the basic commands and syntax of Maple. There are hints of the problems some people experienced in the responses above (see #43 and #85 on page 5). Some students seemed almost philosophical about it:

#46: Good. Although you can get a bit distracted from the task at hand due to trying to figure out how to work Maple, ie syntax etc . . Can get a bit annoying.

But others became quite angry about the experience:

#93: BAD. Maple is both boring and aggravating, and doesn't seem particularly useful either. The assignment took ages, and most of it was trying to get Maple to execute commands which we'd left a bracket out of or something, who really knows where. All the difficult bits we just worked out on paper anyway.

Bookman and Malone also offer several examples of how exasperating the Computer Algebra System can be and, as they found, the problems with Maple can lead to problems with time management too:

#76: Useful for understanding concepts but the interface is so user-unfriendly, unpredictable and unreliable that on several occasions we have spent the entire hour in tutorials fighting with computers crashing or just taking 10 minutes to load a large file. This leaves us no time to ask the tutor questions and as I cannot attend any other tutorials this means I cannot ask for help! Don't get me wrong, this is a useful tool for visualising complex ideas but maybe we could shift across the hall to a (slightly) more reliable computer lab.

Some of the students' problems can be put down to unfamiliarity with Maple. Although most of the students would have met Maple in their first year courses, only a few had used it intensively. I offered an introductory Maple session at the start of my course, but only a third of the students attended. In the first survey (before the CCP modules), 36 of the 96 responding students said that they had either never used Maple or hadn't had time to use it during this course. A further 18 students voiced negative feelings about Maple (either from experience in a previous course, or from trying to use it in the first part of my course). As Bookman and Malone  report (see their Vignette 6), sometimes even the tutor can't figure out why Maple isn't doing "the right thing," and the only option is to start all over again. So it is not too surprising that even after the CCP modules were completed there were still 18 students in the second survey who either disliked Maple or felt that syntax problems had hindered their progress.

JOMA

Journal of Online Mathematics and its Applications