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MathForLife is
an innovative one semester terminal mathematics course
intended to replace existing core or terminal
courses ranging from "math-for-poets" to Finite Math whose
primary audience is the undergraduate majoring in the humanities or
social sciences. Its goal is to convince this
difficult group of students - generally hostile to mathematics
and poorly prepared by high school standards - of the enormous
practical importance of mathematics, to reintroduce them to the
power of mathematical thinking, and to give them a working command
of those topics they are most likely to find useful in their later
lives.
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An online course
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These goals pose enormous pedagogical challenges and I am convinced
that to realize them MathForLife must adopt radically different
strategies from those traditionally employed in other core courses.
MathForLife introduces many innovations, not just in the choice of topics
covered but in how they are presented and in
how the students are asked to study them.
The most fundamental novelty
is to cast the student as an actor rather than a spectator in every aspect
of the course. MathForLife moves away from passive lecture and textbook format
to a much more interactive model in which students work both independently and in small groups
under the guidance of their instructor. To make this possible,
the course is delivered online through a collection of densely linked
hypermath pages supported by a range of interactive tools which provide
computational, diagnostic and monitoring services to both student and
instructor.
The current development version of the MathForLife provides
proof-of-concept of the course framework but many projected components are
not yet live. For an overview of the infrastructure which will be provided on the published
site, please visit the course features page.
The missing pieces are external to the curricular materials. You can see the full range of
hypertext features in the course by browsing the online
sample chapter.
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Relevant material
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"First get their interest, then close the sale." is a basic marketing maxim.
MathForLife will interest its students
though effective use of color, hyperlinks, and other interactive elements. To close the sale
it must convince them to put in the real effort needed to achieve a working command of
the course material.
To sustain the interest of the student, the MathForLife curriculum focusses
on two topics which students will be able to apply throughout their lives,
the mathematics of finance and the elements of probability and of inference from observations.
Wherever possible we start from an interesting real-life question,
often one we all have to ask ourselves
at some point in our lives, and then introduce the mathematics
needed to answer it. Here are a few sample questions:
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The table of contents page shows
the mathematics to which such questions lead in MathForLife.
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Depth and mastery
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Current terminal courses provide
many problems but, since these consist of many (often 20 or 30) repetitions of a small number of
ruthlessly simplified calculations, they
don't begin to equip their students to answer questions like those above.
Answers to such realistic questions demand first that the course cover the corresponding
mathematical topics covered in realistic depth and second that the students
develop a working mastery of these topics.
In MathForLife, small groups of problems
are interspersed frequently with the text, leading the student gradually from
easy cases to problems of practical interest.
Once they have mastered the basic mathematical elements,
students will apply them in group projects. Projects are
independent investigations into real-life problems, often calling for research into
areas likely to interest terminal students
(business, economics, sociology, medicine, archeology, physics...),
and often providing an external web site as a starting point. The sample chapter
Time is Money on mathematics of finance
shows in detail how this strategy is implemented.
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