Geometry is, year in and year out, one of the topics that our Grade 10 to 12 students find the most challenging and the most intimidating. Many will even tell you that they ‘hate’ it in the most dramatic way. And let me tell you that as a teacher… I sympathise. To be brutally honest, sometimes I HATE it too.
The geometry we cover in our school curriculum is specifically Euclidian geometry. It is the study of 2-dimensional shapes, such as circles, triangles and quadrilaterals (fancy word for squares and rectangles), based on the proven theories of the mathematician Euclid.
It’s an enormous body of work. It took Euclid a lifetime of study to compile it all, and because it was such an impressive achievement (and so far ahead of its time), it is now known as Euclidean geometry in his honour. As a result of its breadth, it is often treated as a separate topic from Algebra or Core Math in many international curricula.
In South Africa, Euclidian geometry is presented as an integrated part of the Mathematics school curriculum.
It’s still a tremendous lot of work for our teenagers to absorb, even in its abridged form… the time frame is quite tight, and they need to get it done. It is recommended that students spend 9 weeks studying Euclidean geometry between the ages of 10 and 12. At the end of this period, students should have been exposed to and should be able to explain and apply at least eleven of Euclid’s theorems or propositions. Understandably, our students would feel anxious facing such a formidable obstacle.
Another part of the geometry struggle is that it is a branch of mathematics vastly different from the other topics in our curriculum. If we think of algebra, functions, financial mathematics and calculus, these topics use identifiable and recognisable algorithms and formulas. For many learners, the trick is just to match the algorithm to the question.
Geometry has no formulas or algorithms. Each problem presented to the learners can be vastly different from the previous one. There are no helpful keywords that can make the learners ‘see’ the diagrams in a different light or that indicate the best-suited approach. Geometry uses the learners’ problem-solving skills, which is a high cognitive demand. It is uncomfortable and can be messy and frustrating – all factors pushing a learner to disengage and give up because it is ‘too hard.
So, what can we do about it?
Well, I like to think about the age-old saying what doesn’t kill you makes you stronger. The more geometry problems our learners tackle, the more they develop their spatial awareness and problem-solving skills. We can develop the tools to slay the beast only by facing the beast. Our learners cannot be cramming for a geometry test – they need to look at one or two problems daily.
The key is to first try it by yourself.
Often, we get stuck and absorbed in the problem, and we simply cannot find the solution. At this point, the learner should walk away from the problem. More often than not, taking a mental break and coming back to look at the problem with fresh eyes helps the learner see bits of information they may have missed before. They should ask a friend or teacher for help if they still cannot manage.
The more problems the learners work through, the more comfortable they will become with geometry. It took me a couple of years, but once the bulb lit up, it stayed on, and the beast was slayed.
For the love of math,