Maple and MapleTA
Learning Mathematics with Computer Algebra Systems
Maple (from Maplesoft.com) is a computer algebra system (CAS) for performing mathematical calculations in pure and applied research, financial and industrial applications and in university, college and high-school education.
Post-calculus classical applied math is scattered through courses in differential equations, boundary value problems, vector calculus, matrix algebra, complex variables, and numerical methods. Most of this material can be found in texts entitled Advanced Engineering Mathematics. The mathematics in such texts is truly classical, having been available in its present format for many years, if not centuries. The apprenticeship for working in the field of classical applied mathematics is long and arduous because the apprentice must master material from so many different disciplines.
Twenty-first century software allows this apprenticeship to be both shorter and more effective. Modern computer algebra systems can be the tool of first-recourse for teaching, learning, and doing such applicable mathematics. Software tools such as Maple, Mathematica, MuPAD, and Macsyma implement nearly all the manipulations of the undergraduate program in applied and engineering mathematics. The time has come to use these twenty-first century tools for teaching eighteenth and nineteenth century mathematics.
A complete post-calculus applied math curriculum in which a computer algebra system is the primary working tool appears in [1]. In this text the software is not just an add-on to a traditional by-hands pedagogy. Instead, the software is used as an active partner in the student.s participation in applied mathematics.
We give two examples taken from [1], examples that show how use of a computer algebra system enhances pedagogy. The purpose is not to tout a particular book, but instead, to call attention to the concept that a computer algebra system can, and should, be the working tool for teaching, learning, and doing classical applied math. So, rather than talk about this approach, we give two examples and let readers judge for themselves the viability of a curriculum predicated on the ubiquitous use of modern software tools.
Quoted from the introduction to
An Innovative Approach to Post-Calculus Classical Applied Math
by
Robert J. Lopez,
Rose-Hulman Institute of Technology (retired), Maplesoft.
Note: To
view the paper you may be asked to register at Maplesoft.com.
Alternatively, request at copy by sending email to pkates@uwaterloo.ca.
References:
1. Robert J. Lopez, Advanced Engineering Mathematics, Addison-Wesley, Boston, 2001.
- An Introduction to Maple 10 (42 min)
- Introduction to the Maplet Builder (7 min)
- Advanced Engineering Applications with Maple (50 min)
- Clickable Calculus (54 min)
- Click Here to Download the Associated Maple Worksheet for
- this Seminar
- Maple T.A. Demonstration for Instructors (24 min)
- Maple T.A. Demonstration for Students (13 min)
- Maple T.A. for Blackboard. Software Demo (8 min)
- Syntax-Free Computations in Maple 10 (65 min)
- Control System Development Using System Identification (43 min)
- Technical Solution Deployment Using MapleNet 10 (34 min)
- Introduction To Global Optimization Toolbox For Maple (61 min)
- Maple in the High School Classroom (10 min)
- Modeling Multi-body Mechanical Systems With DynaFlex Pro (65 min)
- Implementing Technology in the Modern Math Curriculum (60 min)
Maple Mathematics Lessons are also available using Maple.
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MapleTA
MapleTA is an online assignment and quiz system backed by the Maple mathematics engine that allows questions to be graded using Maple to match and evaluate student answers mathematically, something most quiz systems cannot do.
MapleTA is an advance over other quiz systems because it
- mathematically compares student and instructor answers
- uses MathML for accurate mathematics display
- offers LaTeX and an online math editor for question writing
- can generate similar, but not identical, questions for each student
- uses portable, text-based question banks.
The key attraction of any quiz system is to give some indication of how well students understand their subject. A pre-lecture quiz based on advanced reading of the day's topic can prime students for a lecture. A post-lecture quiz allows the following lecture to deal with any student weaknesses revealed by the quiz results. Students can monitor their understanding with short review quizzes that give instant, automatic feedback and practice.
Many different question types are available including questions generated by templates and variables so students see similar but not identical questions. A single question template is capable of generating a very large bank of questions, released in a random order. Questions can make use of physical units, error bounds, constraint expressions, and Maple procedures. Maple graphs can be included in questions for display or for interaction with a student e.g. selecting an area of the graph or plotting points on a curve.
Questions can be created using the online math editor or with LaTeX. MathML is used to accurately display mathematics notation.
MapleTA is freely available within all departments and faculties at UW. Please request a demonstration by email to pkates@uwaterloo.ca or visit Maplesoft to see one online.
A presentation about MapleTA from the December WatItis 2006 conference (select year 2006) session A Look at Quiz Systems in Mathematical Subjects by Paul Kates and Sean Scott is available in pdf format.
Paul Kates, Mathematics Faculty LT3 Liaison, pkates@uwaterloo.ca, x37047.
This page is located at www.math.uwaterloo.ca/~pkates/LT3/Maple+MapleTA.html