Why Interactive Texts



     During the past few years there has been much interest nationally in

the improvement of mathematics education at all levels from elementary

school to graduate school.  Beginning in tenth grade (and continuing

through college) the nation loses 50% of its mathematics students each

year.  The discussion of these issues within the mathematical community

has centered on the ability of the community to reproduce itself and, more

importantly, the fact that students who drop out of mathematics are, in

addition, dropping out of careers in science and engineering.  To combat

this trend, efforts at revitalizing mathematics instruction are taking

place at all levels. 



     Four documents have played a central role in this endeavor. Everybody

Counts: A Report to the Nation on the Future of Mathematics Education

reviewed the way that we teach mathematics and outlined a plan for action. 

Curriculum and Evaluation Standards for School Mathematics gives

objectives for school (i.e., precollege) curricula and assessment in

mathematics. Moving Beyond Myths , presents an action plan for

revitalizing undergraduate mathematics.  Professional Standards for

Teaching Mathematics provides guidance for mathematics departments to

curricula that will prepare teachers to teach the curriculum recommended

in the other documents listed above. 



     Common to these documents is the need to move away from the passive

approach to teaching, in which the student is viewed as an empty vessel

into which we "pour" information, toward an active approach in which the

student learns by doing.  Implicit in this change is the empowerment of

the student to control his or her learning environment. 



     The theoretical basis for this approach is best described by Lynn A.

Steen in a recent article.



      "Learning takes place when students construct their own 

       representation of knowledge.  Facts and formulas will not become

       part of deep intuition if they are only committed to memory.  They

       must be explored, used, revised, tested, modified, and finally 

       accepted through a process of active investigation, argument and

       participation.  Science (and mathematics) instruction that does 

       not provide these types of activities rarely achieves its

       objectives." 



The Interactive Mathematics Text Project has as its fundamental tenet the

belief that interactive texts provide an environment in which students can

fruitfully engage and explore mathematics. 



What is an interactive text? 



     An interactive text is a computer document from which symbolic,

numerical, and graphic tools can be invoked.  The results of these

computations can be pasted into the document so that each learner has an

individual record of his or her explorations.  The seminal interactive

text is the Brown, Porta and Uhl Calculus text described in MAA Notes #17:

Priming the Calculus Pump: Innovations and Resources. 



They write:



          "Imagine a mathematics text in which each example

           is infinitely many examples because each example

           can be redone immediately by the student with new

           numbers and functions.  Imagine a symbolic or

           numerical computer routine into which fully word-

           processed descriptions can be inserted at will

           between lines of active code.  Imagine a text

           whose paragraphs can be modified and added to as

           the teacher sees fit.  Imagine a text that has

           better graphics and plots than any available in

           any standard mathematics book and imagine that the

           amount of graphics is limited only by the computer

           memory instead of the cost and weight of printed

           pages.  Imagine that ... the three-dimensional

           graphics ... can easily be viewed from any desired

           viewpoint.  Imagine a text in which a student can

           launch his or her own graphic and calculational

           explorations with graphics and calculations

           appearing as the student desires.  Imagine a text

           in which the student can find as much space as he

           or she needs to solve the assigned exercises."

           An interactive text may consist of a single module used in a

           laboratory session or it may be an entire course.



Why Interactive Texts ?



In the article referenced above, Steen provides a description of

active learning.  Although the IMTP predates publication of

Steen's article, the goals of the IMTP are very similar to those

that he describes.  In particular interactive texts have the

potential to:



      Engage students: Interactive texts require that students explore

mathematical concepts.  The use of the computer makes this possible by

eliminating the drudgery required by hand computations.  Students can

explore myriad examples through numerical and graphical exercises without

having to do copious computations. Students who use interactive texts

cannot be passive receivers of information that they regurgitate on the

next exam.  Students must master the concepts and principles.  As Steen

points out and we are all aware, true learning comes from engaging a

concept and through experience gaining ownership of the concept.  This

"hand to hand" battle is facilitated by the use of interactive texts. 



      Encourage teamwork: Interactive texts will be used in computer

laboratories by groups of students.  The interplay of ideas and the give

and take of intellectual discussion are an important component of

learning.  The competitive forces of today's workplace require peer

interaction.  For too long learning has been viewed as an individual

pursuit. 



      Stimulate creativity: The industrial revolution required individuals

to master the particular tasks that were required by factory workers. 

This need is still reflected in our educational system.  The problems

faced by scientists today require imaginative solutions.  By asking

students to explore and conjecture, the mind-set for learning has changed. 

The use of the computer makes this possible. 



      Require writing:  Writing is an important component in the use of

interactive texts.  The notebook interface not only permits the author to

write but also encourages the student to make notes in his or her copy of

the text and to include written comments and explanations with

assignments.  Students must be able to communicate the results of their

investigations to others. 



      Increase breadth: Ease of computation allows many more applications

to be included in traditional courses.  Mathematical modeling involves

three stages: (1) Translation of the problem into mathematics (creation of

the model); (2) Solution of the mathematical problem; and (3)

Interpretation of the solution in terms of the original model.  Current

education in mathematics focuses on the second stage. With the

computational power of the computer available, the emphasis must change to

steps (1) and (3). Interactive texts provide an environment in which this

change in instruction can take place. 



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