[OS X TeX] Latex for beginning math students

[Maarten Sneep]

On 25 aug 2004, at 1:11, Alain Schremmer wrote:

> I believe that there is a misunderstanding as to who my students are. 
> I certainly don't mean for them to learn LaTeX but only to give them a 
> means of communicating their problems, such as they are, to their 
> teacher. It is a fact that they won't do it in class and not even face 
> to face in an office.

As far as a user interface that puts up no barriers, in my experience 
nothing can beat a stack of paper and a pencil. (admittedly my 
experience is mostly with physics students). The problem is that paper 
doesn't travel well over email.

[snip]

> The usual fare these students are given in "remedial math" is "show 
> and tell and drill". There is no attempt at helping them figure out 
> why things are the way they are. It is: "Now, don't bother to think, 
> just do as I say. See? It's easy!"
>
> Out of 1,000 such students, at most one will pass Differential 
> Calculus.
>
> While it is convenient for us to think that that is just the way 
> things are, TIMSS (and logic) would seem to indicate that this is not 
> necessarily true. I am interested in showing that many of these 
> students, given a certain mathematical environment in which things can 
> be tried, discussed and retried, etc can actually learn to behave 
> mathematically, at least to a certain extent. This is why, for many 
> years now and with varying measures of success, I have been involved 
> in the design of such mathematical environments. (And why I am now 
> learning LaTeX.)

So let's make sure I understand you correctly: you want to have a 
(very) limited set of mathematical notation, and have them put the 
pieces of the puzzle together to form a solution (with the possibility 
that there are more pieces than needed). If you have the experience to 
design such environments, you could probably tell us what it should 
look like --- don't forget to test a prototype of such a system, one 
way of doing that is shown here, with links to IBM with further 
details. http://www.sum-it.nl/enprotot.html

After a prototype has been tested, one could conceivably create 
something in AppleScript Studio, or with interface builder and Python.

> The problem is that only so much can be done in class. What I am 
> looking for is a tool with which I can correspond with the students. 
> For instance, say a student adds two three digits numbers and makes a 
> mistake. Or, to take another example, say a student investigating the 
> behavior of a rational function near +3 "forgets" that the division 
> has to be done in ascending powers of h.

How much to you want to have automated? Adding numbers could be done on 
a web-page, with JavaScript based feedback, others items require more 
AI than is easily available: human intervention is required.

> It would be nice for me to see what they have done, mistake and all, 
> and, since many of these mistakes have a very small number of sources, 
> to have macros for me to give them an expanded hint as to what may 
> have happened and/or to "remind" them of the consequences of what they 
> have chosen to do.

Pencil and paper (provided you instruct them very clearly that you want 
to see it _all_) provide just such a track record.

> The idea would be for them to download one package with the 
> appropriate class already in there.
> Then, New would open a new file with the preamble already there and 
> with begin document and end document already there and no way for them 
> to write anywhere other than inbetween.

Don't show the TeX code at all, get it LyX like. Having any code on the 
screen is another possibility to scare a student, make mistakes, ...

Possibly an interface similar to the recently discussed Publicon might 
work (simplified, but similar).

> Then, the student wanting to do the addition would hit the macro 
> addition that would give him the appropriate tabular to enter the 
> digits

Tabular to enter digits: they do have a numeric key-pad, right? One way 
to driving them crazy is to force them to do everything with a mouse... 
Of course, you know your students, so you should be able to tell. I 
know I would not use such a tool...

> (Of course, a graphic interface would be nice but probably 
> unattainable at this point.)

IB is not that hard... the hardest bit is to come up with the right 
idea for an interface. I think that France and Germany have some 
GNU-GPL software for use in education, maybe there is something at that 
level (possibly platform independent, server/web based).

> Hence my request about if any such thing would be at all "feasible" 
> and, if so, of the kind of knowledge that would be necessary.

Knowledge of the level of the students, the material they should 
master, and a really good idea on the UI. Personally I'm not yet 
convinced that an on-screen numeric key-pad will make a huge 
difference. One thing you could do is write software that records every 
step (including deletions, as they show the thought process, and that 
is exactly what you want to train in the first place.

Also keep in mind that your efforts have to beat the zero-level barrier 
of pencil and paper; although some students might be intimidated by an 
empty sheet, and for them some hints on how to solve a problem can be 
helpful to get them started.

Maarten

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