One Main Street

Houston, Texas, 77002

*Grant Number*: DUE: 9552147

The purpose of this poster is demonstrate some of the features and
uses of the software "system" called MILTON (an acronym
loosely derived from "Mathematica Interactive Library
Toolbar"). MILTON was developed by the presenters in support of
the ILI grant entitled "A Laboratory Classroom to Support an
Alternative Technology-Based Mathematics Curriculum." The
purpose of this grant was to equip (or upgrade) two laboratory
classrooms of PCs to support an alternative technology-based
mathematics curriculum that any technical major could pursue through
at least the first two years. A poster illustrating the overall
nature and goals of the grant was presented at last year's session.
For this poster, however, as the grant nears its completion, we have
chosen to focus on one of the most promising aspects of the project:
the success we have achieved in integrating the use of
*Mathematica* into lower-division courses. We feel this success
has been possible due to MILTON.

MILTON consists of two major parts: a *Mathematica* package of
functions specially designed for use at the freshman and sophomore
level, and a toolbar coded in Visual Basic that provides an
alternative to the command-line Notebook interface for executing
functions in the package. The function package consists of more than
30 so-called "high-level" functions. By
"high-level" function we mean a function capable of
processing both numerical and symbolic input, which might request or
require user interaction during execution, and which may have
complex output consisting of numerical, textual and graphical
components. Many examples of such functions will be demonstrated. At
present, students can utilize the same package for four courses:
College Algebra, Applied Calculus, Precalculus, and Discrete Math,
with more functions from the package introduced to the student as he
or she progresses through these courses. This consistency sharply
reduces the amount of time a student must devote to studying
documentation, help diminishes the culture shock that accompanies
each new semester, and furnishes a crucial unifying motif the
student can use to mentally link topics from one course to the next.
Each high-level function is centered around a particular skill,
concept or result. Functions are also used to instantiate and
manipulate models of abstract objects, such as certain types of
sets. At the most basic level, skill functions serve to simplify or
eliminate difficult computations; but these functions do not act as
mere oracles that automatically perform certain types of
computations or execute key algorithms. There is not be a one-to-one
correspondence between problem types and skill functions. Function
interfaces and outputs are organized to obligate conceptual
understanding, and there are many instances when the output from one
function is needed as input to other functions to successfully
construct a solution to a problem.

To protect novice students from the underlying *Mathematica*
syntax and to simplify the use of *Mathematica* package, we
have developed a Visual Basic applet in the form of a toolbar of
buttons and dialog boxes. Each of these buttons corresponds to a
high-level function and has a distinct and intuitive icon that
represents the function. By clicking on the button, a dialog box is
opened that allows the user to input the various parameters that are
necessary for that function to execute. The applet then constructs
the correct command-line syntax for the function and pastes this
into the *Mathematica* notebook where it is executed
automatically.

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