Since the advent of Computer Algebras Systems (CAS), educators have had to overhaul the mathematics curriculum taught in schools, and even drastically change the way in which homework assignments, class tests, and national examinations are conducted.
The term CAS encompasses a wide variety of software that can interpret and manipulate mathematical expressions, perform tasks such as expansion and factorization of algebraic expressions, plot graphs of functions, compute integrals and derivatives, carry out complex operations with matrices, and even employ statistical techniques such as hypothesis testing or regression analysis. CAS includes computer software such as Mathematica and R Studio, online web tools and applets, web sites such as WolframAlpha, and graphing calculators that most junior college and university students use nowadays.
The merits of such tools are obvious — they allow both teachers and students to quickly solve tedious math problems such as incredibly difficult integration and differentiation questions that would otherwise be intractable. These tools enable rapid visualization with graph plotting utilities that are able to plot detailed and precise graphs of functions, as well as find their turning points, asymptotes, intercepts, and other pertinent features. Graphing calculators in particular also allow teacher to pose computational problems in statistics, calculus and matrix algebra that would otherwise be all but impossible for students to accomplish with pen and paper alone.
But with the introduction and rapid rise of CAS, there is a real danger than students can become fixated on using these tools and neglect acquiring essential mathematical skills that can only be honed by rote practice. It is already widely known that graph plotting utilities such as those found on graphing calculators has resulted in many students being unable to sketch graphs using their own understanding how different mathematical functions such as logarithmic, exponential and trigonometric functions behave.
Teacher as well as tutors have had to rethink how homework assignments, take home quizzes and tests, and online examinations are conducted. With a suite of powerful computational tools at the students’ disposal, tests and exams that are conducted online, or in which graphing calculators are permitted, must be structured in a manner that is fair to all students, and at the same time, demands the same or even higher level of rigour than before.
Since it is clear that CAS is here to stay, it is now up to lecturers and tutors to make full use of these tools to raise the scope and quality of mathematics education, and at the same time, ensure that students do not abuse these tools. Essential mathematical skills such as algebraic manipulation must still be mastered to a high degree of dexterity in spite of the availability of these tools. Mathematics educators must ensure these tools complement, not compromise, their curriculum