First, find a fantastic middle school Algebra teacher.
Second, ask them what are the most important skills necessary for learning Algebra.
Third, have them teach you Algebra, highlighting skills the student should already know.
Fourth, find a fantastic high school Calculus teacher.
Fifth, ask them what are the most important skills necessary for learning Calculus.
Sixth, have them teach you Calculus, highlighting skills the student should already know.
I STILL get pissed at my fourth grade teacher (who I otherwise loved) because she told me I had to do fractions vertically instead of horizontally! I still think this was/is the stupidest math lesson ever! In every subsequent math class I took, all the way through calculus, equations are done across the page (horizontally) and can sometimes take over the entire whiteboard. Learning to do fractions vertically was really a stupid waste of time!
Of course, math equations are solved by continuing vertically down the page, but even then, the combinations (which can include items that are division problems, which are what fractions are!) are done on a horizontal basis. You work across and bring the answer down.
In high school, I got annoyed with my friends’ teachers of years past because they’d come to me with pretty basic algebra problems and be completely thrown by the variables. While a blank is okay for lesson one, lesson two should be that x, y, and z are all alternatives to the blank and the blank should be quickly weaned away in favor of proper variables.
One of the most important things a math teacher ever told us was that stuff you learn in math class will only make sense 2 or 3 years after you first learn about it because that is when you learn to apply it to the real world. Too bad this was my Calculus teacher talking and I was nearing the end of my journey with math. I think we are misguided to try to save kids interest in math by keeping them away from the bigger picture while they learn the basics.
Telling or showing kids why they’re learning a skill is THE single most important thing you can do as a teacher. “Because it’s important” is a crappy cop out answer that should be banished from your vocabulary! If you do not know WHY you are teaching your students a skill, you should NOT be a teacher!!
My dad would chant: “fractions, decimals, money, they’re all the same thing” whenever my homework was on one of these topics. I didn’t understand him because I was too focused on giving my teacher exactly what she wanted.
Now, I literally go from fractions to decimals in the seconds between measuring and cutting (the paper cutter uses decimals, my line gauge fractions).
1 flippen 32=.031
And yes, I will sometimes need to go even smaller to get a border to match! .005 movements aren’t fun!
Oh! One of the interesting byproducts of this quick mental conversion I use at work is that when I’m writing down my measurements I will seriously write: 8. 5/8. You see that superfluous decimal point? Yeah. Honestly, I can’t for see how that hurts anything when teaching fractions and decimals because it really means the same thing. 8 and five eighths? 8 point five eighths? 8 point one two five? I wouldn’t make a point to teach this this way because it is messy and you CANNOT have messy in calculus, but it would be a good bridge between fractions and decimals, which is really all just division!
As for metric, my favorite machine uses these. I just flip my line guage over because it has that scale on it, but a coworker took the time to do the conversion with the same results (of course ☺). I don’t use millimeters often enough to use them in everyday life, but I do like that everything is in whole numbers when I measure for this machine. There’s two reasons for that: the machine doesn’t accept fractions and a half a millimeter is too small to make a difference on this machine. Still, mremorizing fractions of millimetres on the line gauge are EASY: 6/10= 0.6; 1/10=0.1 😉
I still have trouble memorizing 7/16=.467? No. I checked; it’s .4375. The paper cutter can do a four function calculator’s job, so I usually just add up the pieces until I get it memorized because of repetition. Or in this case, I’d probably do .5-.062, but I don’t do math in my head, especially subtraction. Being quicker like that does NOT mean you’re smarter! It is only one skill that not everyone has. So long as we all get the right answer eventually, life is good.