To sing a song, you have to know the words. Too many of our teachers do not have the necessary content background to teach math effectively and efficiently.
While almost all of the math teachers in the Clark County School District know how to operate with different number sets and know rules, many can’t explain the “why” behind those rules. For instance, you can’t divide by zero — any number to the zero power, except zero, is equal to one; you invert and multiply when dividing fractions; when you subtract numbers with consecutive even or odd numbers in the units’ column, the answer is 8 or ends in 8. Just teaching rules that don’t make sense standing alone makes math look like magic.
Listening to many teachers or observing lessons, I find it clear that many students are not shown how the relationships in secondary math are related to elementary concepts and algorithms. How operations with fractions are related to decimal operations — multiplying polynomials uses the exact same algorithm as multiplying in third and fourth grades. Or that finding areas of squares in right triangles results in the Pythagorean theorem, which becomes the distance formula and later the equation of a circle as well as a basic trig identity.
Learning becomes so much easier for students when new topics are introduced through previously learned math using familiar language. Plus, it allows teachers to review and reinforce those topics. But when students ask “why” they are learning this, many of our teachers can’t address the question with much depth because they do not have a math degree — their electives in college were generally made up of science and engineering courses.
It would be nice for students to have some idea of the importance of math in any field. Knowing the size of a tire (circumference) has impacts on speedometer and odometer readings in a car might surprise some. The same with knowing that the characteristics of a parabola (directing sound and light waves) can be related to flashlights, headlights, lasers, amphitheaters and satellite dishes.
Math is important in almost all fields of endeavor.
So going back to knowing the lyrics to be able to sing a song. This is analogous to being properly prepared to teach math. In Clark County, we have hundreds of teacher vacancies, hundreds of substitute teachers and hundreds of alternatively licensed teachers coming from colleges of education and organizations such as Teach for America. While these teachers are hardworking members of our community, they should not be good enough for our students unless they have more solid backgrounds.
As an example: Those with business degrees typically graduate having taken either pre-calculus or the watered-down calculus for non-math majors, and Nevada recognizes them as licensed to teach high school math. They typically don’t take many science or engineering classes to learn applications of math. An introductory class for math majors typically begins with a full-blown calculus class. So how can a business major qualify to teach high school math? That’s not fair to our students.
Does our community continue to settle for inferior teachers in subjects such as math, then continue to complain about the results? Or do we realize that, to do better, our students need teachers who not only know and understand their subject matter but also see the relationships and applications of the math they teach and know how to teach it in a way that increases student interest and understanding?
Most Americans understand the importance of paying for talent in sports. It’s time they understand that same importance in education. This can’t be done if you can’t recruit math teachers with subject matter expertise (talent) and working conditions that suggest we are aiming for excellence. We need to really set our students up for success and stop pretending that we are currently doing it.
— Bill Hanlon, who has served on the Nevada Board of Education, is president of Mathematical Systems Inc. and former coordinator of the Clark County School District’s Math/Science Institute.