Math has always been a vitally important subject in any school curriculum and High School math is no exception. In recent years we have been made aware of a rather alarming trend among some of the High School students – some of them are not doing their level best in learning this subject and as a result are not faring satisfactorily in their math work. And quite a number of these low- and under-achievers in Math are even considering dropping the subject if at all allowed by the school authorities.
One cannot just point an accusing finger at the Department of Education, and specifically school administrators and teachers for any declining standard in math. The reasons for such a sad state of affairs are manifold: low student moral and little motivation; shortage of trained and experienced teachers; teaching overload; ineffective teaching and possibly a lack of sufficient funding, among others.
Granted that it is never an easy task teaching school children, including High School students, in any discipline, and especially math, I would like to share some of my experiences as a math teacher of over a decade in the hope that they will be of help to our suffering teachers who I believe have been working very hard and doing their best in the circumstances.
To be able to teach math effectively to High School students will take an average teacher some years of hard work and perseverance, plus good fortune and dedication and overall support from the school administration. Most importantly this requires students who are enthusiastic, responsive, motivated and who are willing to learn. Other than that, I propose the following strategies which I believe will help the beginning math teacher.
1. TEACH FROM THE SIMPLE TO THE COMPLEX: FUNDAMENTAL TO ADVANCED
Of course the math teacher is in a way constrained by the syllabus, if there be one sanctioned by the local educational authorities. But even so I still think the math teacher has some leeway around every unit of the syllabus content. So assuming that our target group is the cohort of Grade 11 students, it is probable that a typical math program will comprise the following math topics, viz Algebra, Trigonometry, Geometry, Statistics and Calculus. I would recommend that the teacher start off with either Algebra or Statistics. High School algebra is usually not very involved and the teacher can build on the students’ prior knowledge and math skills obtained during the earlier Grade years – techniques of algebraic multiplication and division; algebraic expansions and factorization, simultaneous equations in 2 or 3 unknowns, series and sequences, to name a few. More advanced algebra topics like matrix algebra and linear systems are usually studied at college. Statistics is probably not a brand new topic to the students either – they probably have gained some rudimentary knowledge of this topic when they learned terms like mean, median, mode and simple histograms in their Junior High School years.
Geometry is about moderately difficult but most students would find Calculus and Trigonometry much more challenging: with new and somewhat abstract notions like the derivative, anti-derivative and slopes of a curve, etc, Calculus can prove to be the most intellectually difficult math subject and likewise Trigonometry can be confounding too as many High School students complain of being confused by the various trigonometric ratios of sine, cosine, tangent, cotangent, secant and cosecant.
2. SUGGESTED WAYS TO TEACHING TRIGONOMETRY AND CALCULUS EFFECTIVELY
To teach Trigonometry effectively, the teacher first has to introduce very carefully and systematically the definitions of the various trigonometric ratios and try to explain how these ratios come about and how best to memorize the formulae for them. At the beginning some rote memory is perhaps unavoidable but the teacher can make this less onerous by using some common mnemonics or even by creating his or her own aids to memorizing trigonometric formulae. The values of the sine, cosine and tangent of angles of any magnitude should be taught after the students have mastered the values for angles less than 90 degrees. This could be followed by the teacher covering the trigonometric identities and techniques of solving trigonometric equations. From my experience this latter part of the trigonometry course is the part that students find most difficult.
For evaluation of the course objectives, the teacher has to assign work of course – either during class or giving work for students to do at home. Short quizzes and tests must be given on a regular basis and the students’ performance monitored. Students who under perform have to be given some form of remedial teaching; perhaps the teacher could see the students concerned to have a heart-to-heart talk to find out exactly what are their learning problems. I realize that this is really a tall order to ask of the teacher but it may not be a bad idea if the teacher squeezes some time before class begins or at the end of the lesson proper to tutor these students.
Calculus is another possible mine-field from the teacher’s perspective. I would recommend a more ‘historical’ approach in that before teaching formally the various concepts a brief outline history of the discovery ( by Newton and Leibniz ) of this important math unit is presented to the students. Of course nowadays the math teacher has at his/her disposal many teaching aids – computer aided educational tools, electronic boards and other devices that aid teaching. In addition there is the world wide web of Internet resources where the diligent and discerning teacher could choose and select the appropriate websites for the students’ benefit. I emphasize the historical approach because this is an excellent opportunity to show to the students that the studies of math need not be dull and boring- it could be intriguing and even dramatic.
Other than presenting the various formulae for finding the derivatives of algebraic and trigonometric functions together with associated rules for finding the same for products, quotients etc, the teacher could make the studies of Calculus more interesting and meaningful by emphasizing the applications of finding these derivatives. Techniques such as solving differential equations, finding the rates of change of one variable with respect to another – all of these could find applications in many fields of Physics, Chemistry and Engineering and even Economics.
3. OTHER STRATEGIES/SUGGESTIONS THAT COULD MAKE TEACHING MATH MORE EFFECTIVE
While this article is not written to cover comprehensively all possible avenues for more effective math teaching, I submit that some of the suggested methodologies and strategies would work equally for math topics which have not been specifically mentioned. In addition I would venture the following courses of action on the part of the math teacher that I figure might help him or her in achieving the noble objective of more effective math teaching:
3.1 Maintain a cheerful and pleasant disposition even in the event that your efforts do not bring about expected results immediately.
3.2 Always reflect on what you have been teaching to the students to see if you have engaged them meaningfully.
3.3 As far as possible try to be innovative in your approach to teaching ( especially a new sub-topic ); modify the approach for greater effectiveness if necessary.
3.4 Learn new and novel teaching methodologies and strive to improve your professional knowledge.
3.5 Persevere, remain enthusiastic and characterize your teaching life with optimism.