The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy). by http://www.corestandards.org/Math/Practice/
I know many people are not happy with “Common Core Math.” However, I just want to share my life experience with math. I spend very little time lining up columns, borrowing numbers, carrying the one, and coming up with a final product. I do, however, spend lots of time playing with numbers in my head. This is exactly what Common Core tries to teach kids. They want kids to have number sense so they can figure out solutions in a variety of ways. This is how I use math:
- When I am running I have a constant math conversation with myself. I’ll share a script from running a marathon. It goes like this. “Ok, I’m at mile ten and I’ve already been running for an hour and thirty-five minutes. That means I’m running a 9:30 pace. But, I want to finish the marathon in four hours I need to run a 9:09 pace. So, that means I need to run the rest of the race in 8:something minutes per mile. That isn’t going to happen. Ok, so if I run at 9:30 that means that 20 miles would be 20 miles at 9 minutes or 180 minutes plus 20 miles at 30 seconds each which is 10 minutes and I add those together and that makes 190 minutes divided by 60 is, well, three hours plus 10 minutes. Then, I have six more miles so that is 54 minutes plus 3 minutes and that total is 57 minutes. I add those all up and I get, more or less, four hours and a little less than ten minutes. I need to run faster.”
- I used a lot of math when I was having my babies. “Ok, the contractions are 90 seconds long and they happen every two minutes. That means I only get 30 seconds off. I’ve been in labor for 12 hours and the last baby came in 18 hours and 18 minus 12 makes to many hours and I think I’m going to die.”
- Vacations are a great time for math. “We’ve been driving for four hours. We still have 72 miles to do and if we drive sixty miles an hour we will get there in a little over an hour. But, if we hit traffic and only drive thirty miles an hour that means it will take us more than two hours and then we’ll get there after 7 p.m. and that is too late for the kids to eat so we should stop now and eat or at least pick up food and if we do it in ten minutes then we will arrive between 6 and 7 p.m.”
- I do it with my age as well. “I had my first child at 34 so when she’s in college (18) I’ll be 30 plus ten or 40 and I have to add 4 plus 8 which is 12 so that means I’ll be 52.” I’m always separating my numbers into manageable chunks, no matter what math I’m doing. Who ever has a pencil and paper when you need to do math?
- I play with numbers like this in the grocery store, when I’m paying bills, when I’m figuring out how much we’ll have to pay to send kids to college. I do it when calculating vacation costs, times, and distances. I do it when I have a kid awake at night and I’m figuring out how much sleep I’ll get before the alarm goes off.
Real life numbers are estimations and calculations and moving numbers into places that make it easier for us to understand them and use them. Numbers and number sense help us make sense of where we are and where we are going. Doing math in your head is also a great distraction (see marathon and labor above). I love common core math partly because I never understood why all those columns and calculations worked out the way they did. I was taught to carry the one and I did, but I didn’t really understand why. But, figuring out numbers in your head is fun! I would have liked my classroom a lot more if we had spent more time doing that instead of just practicing problems on paper over and over and over again.
Because, math is really a treasure hunt, a scavenger hunt, a mystery to be solved. It should be fun and exciting as you figure out how to get to the end. It’s also flexible. If you are running slowly and won’t get to your target time to finish the race, then speed up and recalculate! If you don’t have enough money to buy all those groceries, put something back and recalculate. It’s fun!
How do you play with numbers in your head?