An epiphany is a sudden and profound understanding of something. In this blog, I would like to share some of my moments of sudden and deeper understanding of a math concept. A “profound” understanding is probably a stretch.
I was fortunate to have had Vivian Jones as my math teacher at Moline High School in 1959. Vivian could teach math to a post. I will remember some of the things she taught me until the day I die because they made intuitive sense to me.
• To find the area of a trapezoid, multiply the height by the average of the two bases. Of course, this method works for a rectangle, but it also works for a triangle! A triangle is a trapezoid with the length of one base equal to zero.
• To find the sum of the first n terms of an arithmetic sequence, multiply the average of the first and last term by the number of terms.
• When doing polynomial division, and you are at the subtraction step, change the sign of the term and add. Like all math teachers, Vivian knew that students are much better at adding than subtracting positive and negative numbers.
• To find the area of any polygon when the x-y coordinates of each vertex are known, use the Surveyor’s rule which is a really slick algorithm. Every math team coach should teach the Surveyor’s rule. Shoelace algorithm, shoelace formula and Gauss’ area formula are other names for the Surveyor’s rule procedure.
Vivian could explain concepts by asking simple, penetrating questions that got the point across. For example, she taught me the difference between a rational number and an irrational number by asking 3 simple questions:
• Question 1 – What is the square root of 2? My answer – 1.414
• Question 2 – What kind of number is 1.414? My answer – rational
• Question 3 – What kind of number is the square root of 2? My answer – irrational
Did you have an influential math teacher? What were your moments of math epiphany? Feel free to share your stories about how teachers added to your understanding of math concepts.