Another Math Problem
Structural Engineer –
I am 35 years old. I have no kids and no intimate knowledge of the education system. As the country transitions to the “new common core curriculum” I am observing it with passing curiosity, specifically as it relates to math.
Math is important to me because I am a structural engineer. I have completed courses in algebra, geometry, calculus, linear algebra, and differential equations. Math mostly comes easily to me. Mostly, not always.
Knowing algebra allows me to simplify complex problems and find an answer. See the picture to the left. The series of gears that transition from the second wheel to the hour wheel can be written as an algebra problem. How many teeth are required on each wheel to link a wheel rotating one time per hour to another wheel rotating sixty times per hour?
For the home improvement weekend warriors out there, have you ever used a 3:4:5 triangle to square a deck when laying it out? Geometry can be used for a myriad of reasons, but for me it is useful to understand how different pieces of a building fit together.
I may start to lose some of you with calculus, but what a great tool. Effective use of calculus can optimize systems to gain efficiency. What is the ideal number of gears in the wooden geared clock to minimize the amount of material used to make the gears? If I am making thousands of clocks, this may be important to improving my bottom line.
Linear algebra allows us to solve huge systems of equations efficiently. If we want to write a computer program to determine the forces in a building roof that has thousands of structural members, we better be able to efficiently solve thousands of equations.
Although the courses above were not necessarily easy, understanding how each of these subjects could be used in the physical world allowed me perspective on the problems I was solving. It gave me the incentive and curiosity to work hard and learn the subject matter. It also gave me insight to understand if the answers I was finding were likely wrong or right.
For me it broke down at differential equations. To this day I have no idea what the point of differential equations is. I don’t understand how to apply any of the formulations to anything in the physical world. In my mind this simply math for the sake of math. I didn’t do well in differential equations.
Have you ever known someone freakishly good at math? The kind of person who can multiply two (4) digit numbers in his/her head? (I am not one of these people.) Ever ask them how they do it? They don’t multiply the way you learned in third grade. They break the numbers down, regroup them and reassemble them. They have a feel for numbers. In their mind they can see different paths to solve the problem and can choose a path they can complete in their head.
As an adult, have you ever tried to do math on two large numbers in your head? Perhaps not to get an exact number, but to get an approximate number. How do you do it? Do you do the math the way you learned in grade school? Or do you start to break the numbers down and then put them back together? Try it.
Imagine you are at the grocery store and a jar of salsa costs $5.97 for 16 ounces. A larger jar is $11.88 for 30 ounces. Which jar do you buy?
Or you are buying gas, you purchase 10.3 gallons. Looking at the odometer you see you have driven 327 miles. Roughly how far have you driven per gallon?
Or you are watching the evening news and they mention the CEO of a company makes $7,500,000/year and the average line worker makes $50,000/year. You wonder how many times the average worker’s salary the CEO makes.
- I get a little over 150 times as much (let the indignation abound). How did you do it?
- Did you break out a pad and paper and complete a long division problem?
- Or, did you say there are (20) groups of $50,000 in $1,000,000. (20)x(7)=140+(20)*0.5=10 140+10=150 +/-
- Or did you think (as my wife did), there are (20) groups of $50,000 in $1,000,000. That would mean there are (200) in $10,000,000. $7.5 mil is ¾ of $10 mil and ¾ of (200) is (150)
- Or did you divide in your head 75/50 and add back some zeroes?
- Or some other way?
I like to think adults do this daily without thinking.
One of my friends recently shared this picture (below-right) on her Facebook page.
This makes me sad. Should math be taught as a rigorous set of instructions to achieve the correct answer? Or should number sense and theory be taught that is tied to actual real life problems?
I work with a lot of engineers. People who are very good at math. 9 times out of 10 if you ask any of them to add two numbers two things will happen in no particular order: 1) They will reach for the calculator (myself included) and 2) They will quickly check with an approximate answer from their head Why? Because if I need an exact answer I can use my calculator or computer. But I need to have enough number sense to understand if the answer I am getting is likely to be correct.
If you reflect back to your school years, how did you look at math at the time? Did you look at math as formulas and operations that needed to be manipulated in a specific order and with great precision as instructed by your teacher? Did you understand how those operations could be related to the physical world? Did you ever step back and look at the numbers outside the minutia of the math operation? Did you take time to play with the numbers, understanding what each operation did to the result and how the full system fit together? How did you do in your math classes? Did you struggle or do well?