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This page provides a short guide to the main technical innovations
which I have implemented or plan to incorporate into MathForLife.
The course home page
outlines my pedagogical rationale for the organization of the course highlighting
my principal aims and how my approach differs from that of existing terminal mathematics courses.
Currently implemented features are shown with black headings, planned features with
gray headings.
I should emphasize that while the implemented features involve several novel
programming elements and represented the key missing elements in creating the MathForLife site.
The planned ones involve only standard web programming
(mainly HTML and PDF
forms and some CGI scripts) interfacing to currently available tools. However, the planned
features will be somewhat dependent on the final course server platform
so I prefer to wait until I have a publisher and these choices are final before beginning implementation.
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A Hyper-
textbook
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MathForLife is based on what I call a hypertextbook.
By this I mean both a traditional
printed text and a coordinated set of enriched hypertext pages - one for each section in the book to
keep downloading delays to a minimum - which also
serve as an interface to supporting tools (symbolic calculation programs, cgi-scripts etc.)
running on a remote server. Here I will simply list the main types of enhancement provided: for more details
see the online Help! file in the sample chapter.
The online version of the course provides a dense web of cross-references to provide the
constant review of basic concepts which the target audience must have if it is to reach
more complex applications. Every reference to a formula, principle or problem can be followed
back to its source instantly and novel uses of important concepts link to the course index
where the student can review earlier occurences. Global materials like the contents, index and help file
are accessible from every page.
Color and type style are used to highlight important passages and classify other material (as exposition, example, problem...)
and to indicate the locality and type of links (within section, within chapter...). Many off site
links are included as starting points for independent research by the student to carry out more substantial course projects.
All graphs, pictures and other graphic elements are scalable: the student can zoom in on particular features at scales
far beyond what is possible on a printed page.
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Common sources,
common appearance,
one-click creation
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I have spent much of the past year developing a system which allows a single
collection of common enriched TeX source files to be compiled into both a traditional linear book and into the
online hypertext pages.
The book and online versions use different page sizes but are otherwise
are essentially identical so that the student who switches
between them will be able to do so seamlessly.
The basic text is the same - even
to the numbering of definitions, formulas and problems. Both use the same
professional quality page layout and mathematical typography, the same color keying,
and common EPS files for graphical elements.
A master frame file is used to assemble these elements into the book in one
TeX implementation. The source files can also be compiled individually in a second
TeX implementation to produce a collection of small PostScript files which when passed
through the Acrobat Distiller emerge as a collection of PDF files for the individual sections
of the book plus supplementary files to collect global material like the contents and index.
A third option (not shown on this site) collects all the small files into a single large PDF
file suitable for use as an offline interactive companion to the book.
All three options can be produced from the common sources by double-clicking a single
build script.
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Testing
services
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From teaching terminal students, I have learned that they very often try to work problems
before mastering the ideas, definitions and formulas which will be needed.
The resulting waste of time and frustration is a major reason for their hostility towards math.
Every section of the online MathForLife will contain one or more Self-Tests. These are links
in the text leading to a CGI tool which uses a database of multiple choice and short answer questions
to serve forms containing short tests.
The student completes the test and submits it, and the CGI tools then grades it in real-time and reports
back the student's results. The student can find out the right answers to questions incorrectly answered and get
help as to the likely error from the database. The student then knows whether he or she is ready to work the next set of problems
or needs to review the material covered before proceeding.
Once again, tools of this type are currently available. It would be possible to serve and grade end of section quizzes
containing more substantial problems but the thrust of the course is to replace such tests with more
open ended and substantial group projects.
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Monitoring
and
reporting
services
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Each instructor at a school which adopted MathForLife would be given
an area on the server and a set of passwords to distribute to his students.
The students would use these passwords to enter the online site and when
they did so their interaction with the site (pages served, tests taken,
tools used...) would be logged. The instructor would be able to request the site to
prepare reports from these logs.
At the most basic level, the site would provide grades derived from the student's scores
on the self tests or other online tests assigned by the instructor, freeing the instructor
to look only at the more substantial group projects turned in by the students.
More sophisticated reports would provide overall activity summaries, summaries for each login,
or full activity logs. These would allow
the instructor to assess the overall effort of each student in the course.
Conversely, the knowledge that their work is monitored and the need to prepare and submit substantial projects
gives students with a powerful motivation to work on a consistent basis and not just to cram before tests.
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Tools for
calculations
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The online pages will link to a variety of general and special purpose computational tools.
Basic, general purpose tools will include a scientific calculator and a graphing tool probably
implemented as Java applets.
Custom elements will include forms to perform more complex calculations on values entered by the student (for
example, to perform a complex financial calculation from rates, term and amount). My plan is to use online forms to provide
simplified user interfaces to specific functions within a symbolic calculation tool such as Maple or Mathematica: the form
calls a PERL script which wraps the student's values in a call to the symbolic calculator, unwraps the answer and serves
it via a dynamically generated HTML page back to the student. I have implemented proof of concept pages of this type using Maple.
This approach has three major advantages over using the same tools in a computer lab setting.
First, the student can use sophisticated tools without having to learn their complex command syntax; in effect, the
course site provides a simplified user-friendly interface. Second, a few copies of an expensive tool running on the
course server suffice for many students; there is no need to purchase a copy for every seat in a lab. Third, the tools
remain available to the student working at home, or in a library or dorm and not just to one working in the lab.
Finally, I plan to collect URLs which offer interesting computational aids developed by other scholars which can be used in
working with the material in the course and to provide links to these external tools in the online pages.
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Out-of-class
help services
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The MathForLife web site would provide each course
using it with a list server to which students could submit queries
or raise difficulties in the course and via which they could receive
feedback from their instructor and other students in the course. Again,
this is already a common feature even of many traditional lecture courses.
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