Mathematics

It is a fallacy to assume that we can achieve competence in what we term critical subjects by narrowing the breadth of education. By creating artificial walls between subjects, we are attempting to teach in a manner that mimics how the teachers may have learnt their subjects late in their academic careers — but it is not an effective way to learn.


Mathematics is the most beautiful and most powerful creation of the human spirit – Stefan Banach

I am an engineer and a scientist. I am also an educator. Beyond all of these, I am a mother. Last night, I was teaching my son how to calculate the surface area of a triangular prism. I didn’t like how his teacher taught it, I also didn’t like how the textbook solved the problems. So, I proceeded to do what I do best: I found a real life model of a triangular prism and explained what the surface area was. He then made a statement about whether surface area mattered in the real world and how much of what was learnt in maths was really necessary. I became sad, due to the below par effort of some teachers who had made maths as a dry subject to him, devoid of the excitement of learning and discovery. This puts our children in grave danger of loathing the subject!

This is my conflict with how maths is taught traditionally, especially here in Nigeria and, I daresay, Africa as a whole. (I’ve seen what is done in other West African schools during my foray in consulting across our borders.) Maths is just taught for its sake alone, with no mention made of it’s vital role in preparing future architects, engineers, scientists and more for their career lives. It is time to reinforce the connection between the tangible and the symbolic — maths comes alive when numbers appear as dimensions that you can see and touch. Shapes and angles are observable, and how they meet, fit and feel is appealing to the senses. In our Basic Technology classes, where engineering drawing is taught, awesome connections can be made, as well as in our science classes, with all subjects having connections to maths in one way or another.

When I taught middle school — grades six to eight (primary 6, J.S.1, and J.S.2), it was a harrowing experience getting my students to grasp the concepts of area and perimeter. At first, I expected them to memorise formulas, “P = 2 x L + 2 x W” and “A = L x W” and then solve problems. The thing was they solved these equations but often got them muddled up subsequently, with ‘perimeter’ being taken for ‘area’ and vice versa. One day, I had the idea to break down the concepts in reality to them. I brought rulers, measuring tape and lots of strings/ropes for measurement. I divided the students into groups and gave them chalks to measure different parts of the room. Then we calculated how much carpet it’d take to cover up parts of the floor (in essence the area of those parts of the room.) Then we discussed how much rope we’d need to cordon off the wall, from one end to the other, and completely (perimeter in it’s true understanding.)

When we actually solved problems later that required calculations of how to use perimeter to build a fence and area to buy carpet, it actually connected mentally for them. The formulas made sense to them now beyond just being letters. Usually we skip through making what the concepts mean in actuality to get straight to the meat of the lesson, and great miss teachable moments and engaging the minds of our students in entirety. By really getting students to understand the physical embodiments of distance, space, science, and the connectedness of the world, we miss the big picture for them.

The major task of early learning is to build a robust mind-bridge between the tangible world and the symbolic world of words and numbers that we later use as a means of building more complex models.


I am blessed that my first peer mentor/coach and role model was a seasoned maths educator who truly loved teaching, and her whole life was about that. She had seen a lot of changes in the system but didn’t lose sight of what mattered most; teaching maths for it to make sense to our students. Mrs. Vogel, thank you for listening to the fears of a newbie and encouraging her to keep striving for the best for our children.

She taught me to start lessons off by asking my students questions about what they are going to learn, to glean their understanding of the concepts and incorporate what we hoped to achieve by the end of the lesson. In the famous words of Stephen Covey; “Begin with the end in mind.”

The major task of early learning is to build a robust mind-bridge between the tangible world and the symbolic world of words and numbers that we later use as a means of building more complex models.

foraminifera

It is a fallacy to assume that we can achieve competence in what we term critical subjects by narrowing the breadth of education. By creating artificial walls between subjects, we are attempting to teach in a manner that mimics how the teachers may have learnt their subjects late in their academic careers — but it is not an effective way to learn. It may seem efficient to getting through the curriculum mapped out for the school year but it’s effectiveness is debatable as students return the following school year, having forgotten most of what they were taught already. Lists of independent facts without a network of connections are hard to follow and harder to retain. An analogy I read was of the problem of trying to dig a deep, narrow hole in dry sand. As the hole goes down, the sides collapse and fill it back in. It is possible to dig a deep hole, but only if it stretches out to the sides.

I once brainstormed with a couple of STEM teachers such as myself at a Professional Workshop in North Carolina and we discussed the importance of teaching our students the interconnectedness of what we taught; as in the real world you don’t know if the solution of the day will come from maths, physics, chemistry, or just as likely from human behaviour or the quality of product instructions.

Adetola Salau, Carismalife4U@gmail.com, an advocate of STEM education, public speaker, author, and social entrepreneur, is passionate about education reform.

Image credit: questionsuniverse.com