The Things People Say About Math
Once in a great while, I hear someone say, “I Love Math!” or “I enjoyed my math classes,” and it gives me a warm, comforting feeling inside. Sadly, what I often hear people say is, “I hate Math!” or “I could never do Math!” or “I was never any good at Math.” I attribute much of the disdain for mathematics to the way that math is being taught. More times than not, I see math taught very procedurally and using an algorithmic approach. Of course, mathematics needs to be taught with procedures and algorithms. But, it also needs to be taught in context, with understanding and meaning.
The Most Important Skill
The number one most important skill everyone needs to learn from mathematics is ESTIMATION (this will be the focus of a future blog post). Estimation is unfortunately being left out of most teachings of mathematics from what I have observed. This is a big contributor to the negative comments I hear about learning and doing math.
Estimating and questioning what an answer or solution might look like should be asked at the start of most math lessons. This gives the learner an idea of what the mathematics they are doing will produce. Without estimation, the learner will not have any idea or clue what the answer will be or even look like. Without estimation, calculations and mathematics are just a bunch of steps that you must remember correctly to produce a correct answer. Without estimation, someone else must verify the answer is correct since the learner has no idea if their solution is correct or even reasonable.
Who Uses That Skill?
When I was a full-time classroom teacher, I would job shadow people who used lots of math to perform their jobs. One summer, I job shadowed an incredible person who held both a PHD in Engineering and a PHD in Mathematics and was the lead Engineer at an Engineering firm. I asked them how much they actually used the math they learned over the years for their job. The response surprised me. They said, “I rarely formally use the math I learned for my job.” I was dumbfounded! I asked them to please explain. They said calculators and computers do almost all of the mathematics required for the job and that the most important skill they did use was estimation! They had to be able to estimate what a reasonable calculation was going to be in order to know when the calculations and numbers for the job were not correct. They finished by saying that in order to estimate properly, you have to understand what is happening when the mathematics are being done. I could not have agreed more with their response.
How to Use Estimation
To be able to estimate, you must have a basic understanding of what is taking place using the mathematics, even in simple calculations. For example, what is the product of 37 and 43? The first question a teacher should ask the students would be, “What is a reasonable number that the product of 37 and 43 might be NEAR?” Hopefully the students know that this answer should be somewhat near 1600. Regardless, the responses will let the teacher know if the students even comprehend what the problem is asking them to do. Once the students have an idea of what the answer should look like, then the procedure and/or algorithm can be taught.
I am sure you all have seen the algorithm for this problem. If I asked someone to work this problem the first thing most people would do is reach for their phone or grab a calculator to do the multiplication. But what if I told you that by understanding the problem and knowing the basic Algebra skills EVERYONE was taught in high school, you could easily do this problem in your head?
Let me show you… 37 is close to 40 and 43 is close to 40 so the answer should be close to 1600, like we estimated earlier. 37 is 40 – 3 and 43 is 40 + 3. That makes this the “Difference of Two Square” that is taught in Algebra 1. Thus, 40 x 40 is 1600 and 3 x 3 is 9. The answer to this problem is 1600 – 9 which equals 1591. Check it out on your calculator. Pretty cool isn’t it! Now you try it. Multiply 65 times 55. Did you get 3600 – 25 which equals 3575? And this doesn’t just work with numbers that are symmetrical around a multiple of 10!
I truly believe EVERYONE can do Math. Over the next few weeks, I am focusing my blog on Estimation, Calculations, Algebra 1, Understanding, and Teaching Mathematics in Context. Through the sharing of ideas and best practices, we CAN change the attitudes students have toward math. My goal is to hopefully get people to stop saying “I hate Math” or “I can’t do Math” or “I was never any good at Math,” and start saying “Math may not be my favorite subject, but I can do Math,” and “I understand Math.” The ultimate response would be “I Love Math.” I can always dream!
Written by William (Bill) Reed