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.
As I mentioned in my last blog, I will be offering three main lines of software on my website, mathteachersresource.com. Available now is the first program, Basic Trig Functions, version 3.6. As the title indicates, the main emphasis is on teaching trigonometry at the high school and college level. However, teachers of high school algebra, college algebra and pre-calculus will also find many features of the program to be very useful.
Basic Trig Functions has two modes of operation. The first is circle and trig mode. Use it to:
- explore standard trigonometric angles, radian measure, arc length, sine, cosine, and tangent functions.
- create a variety of trig-circle diagrams, which teachers can use to create handouts and test questions.
- find and graph the powers of a complex number in either standard a + bi or polar format.
- find and graph the roots of a complex number in either standard a + bi or polar format.
- graph a wide variety of X-Y variable relations. When the user moves the mouse near a point of intersection, min/max point, or x-intercept, the X-Y coordinates of these points can be found with a click of the mouse.
- graph polar functions. Users can see how polar points are graphed with the click of a mouse.
- explore the Mandelbrot Set. Users can graph the orbit of a complex number and a mini-graph of the Julia Set of a + bi with the click of a mouse.
The second mode of Basic Trig Functions allows teachers to easily demonstrate the geometry of the trig functions and special features of the tangent, cotangent, secant and cosecant functions, and investigate special geometric properties of these functions.
I invite you to visit our website to view screen shots that demonstrate the capabilities of the program. Users can copy all program output to the clipboard to be used in the creation of their own materials.
All the best,
Welcome! I’m glad you’ve joined me for this exciting launch of mathteachersresource.com. My mathematics teaching career has covered over 40 years. I have taught courses ranging from general mathematics through calculus, and I am currently teaching College Algebra and Elementary Statistics at my local junior college. Over the years, I have developed software programs that have helped me do a better job of teaching algebra, trigonometry, pre-calculus, calculus and statistics. It is my core belief that teachers should help students understand math concepts from both an algebraic and geometric point of view, and these programs are designed to do that.
The tools found on my website fall into two major categories. The first includes three main lines of software. The second category includes free teacher-created handouts. The first offering of handouts are those created by me; my future goal is to add to this inventory of handouts and to invite other math teachers to share their handouts through the website. More information on this will be coming in future blogs.
My software offers many unique features that make it easy for teachers to give dynamic presentations of core concepts in mathematics. Please visit my website mathteachersresource.com to see some of the possibilities of my program, Basic Trig Functions.
Thank you for joining me for this launch. Feel free to contact me with feedback, and I hope you’ll join me for more in the weeks to come.