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 this, 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 one 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 learned in math that was really necessary. I became sad, due to some teachers who had made math as a dry subject, devoid of excitement of learning and discovery; our children are in grave danger of loathing it!
This is my conflict with how math 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) Math is just taught for its sake alone, no mention is made of it’s vital role in preparing future architects, engineers, scientists and more.
It is time to reinforce the connection between the tangible and the symbolic—math 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, as well as in our science classes, awesome connections can be made, all subjects have connections to math in one way or another.
When I taught middle school- grades 6-8; (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 memorize “P = 2 x L + 2 x W” and “A = L x W” and then solve problems. They solved the problems alright but often got them muddled up; perimeter for area and vice versa. One day I had the idea to break down the concepts in reality. I brought rulers, measuring tapes and lots of strings/ropes for measuring. I divided the students into groups and gave them chalk 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, wall to wall (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 skipped through making what the concepts mean in actuality to get straight to the meat of the lesson, but we miss great teachable moments and engaging the minds of our students entirely. 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.
I am blessed that my first peer mentor/coach and role model was a seasoned Math 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 math 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 my lessons off by asking my students questions about what they were going to learn, glean their own 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.
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 learned 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 about the interconnectedness of what we taught. In the real world, you don’t know if the solution of the day will come from math, physics, chemistry, or just as likely human behavior or the quality of product instructions.
Adetola Salau; Educator / Speaker / Author/ Entrepreneur