## Saturday, June 20, 2015

### Saturday Sayings: Empowered

Last week I met up with a real life math problem. I don't recall the context, but without a calculator, paper, or pencil, I needed the answer to 14 x 3. I split the 14 in half since I already knew 7 x 3 = 21. Then of course I doubled the 21 to get the answer 42.

It might sound silly, but I was so proud of myself. Being a past valedictorian, one wouldn't think a celebration would be in order for such a simple problem, but when it comes to math, it was my studious nature and study habits that led me to As, not my superior understanding. I was taught mathematical rules and procedures, and I obviously used them well enough that my grades made it look as though I knew what I was doing. For sure I would not have even considered solving 14 x 3 like I explained above. Now over twenty years later, I'm finally seeing math through the lens of number sense instead of a lens of rules and procedures.

If I could sit down with parents (and some teachers) who are distraught about the current state of math instruction, I'd want to share the above quote with them. Teaching algorithms straight up without the prerequisite understanding of number sense debilitates our mathematicians. Computation then equals the following of rules, rather than the understanding of numbers, and I can say this from personal experience. I am a product of that style of "learning" math.

The authors of Young Mathematicians at Work shared a problem similar to this one: 999 + 1341. If my younger self had seen this problem, I would have immediately stacked the numbers vertically and put an algorithm to work. Now when I look at this problem, I actually see the numbers and as a result, I also see the ridiculousness of trying to borrow and carry. Instead, it's empowering to transform those numbers into 1000 + 1340 and know the answer in an accurate, flexible, and fluent way. That is exactly how I want today's young mathematicians to feel.

1. Yesterday I was thinking that I needed to think more about my approach to math. I'm not kidding! I spend most of the summer thinking of ways to make my Language Arts more engaging, but rarely math. This summer I'm going to think mathematically! Do you have a favorite math resource? I have Math Their Way memorized. I'd like to broaden my mindset. Thanks for the inspiration!!
Jenny

1. Jenny, I think many of us have math on our minds. It's sure on mine. I'm reading several math books this summer. I'll be posting about them. So far my favorite is Number Talks. I'm excited about that one! I love Math their Way by the way. It's been my foundation for most of my career.

2. We must have been the same kid! I totally aced math all through high school and also took two years at the university level, but like you, I was missing some fundamental understandings.
But I have to say...I find it quite hard to teach the "Fosnot" way. I'll keep working at it though, 'cause I know how important it is.

1. Barb, I'm guessing there are many out there just like us who aren't as math literate as our grades make us out to be. It's good to know I'm in good company!

3. I was raised on math rules too. Not so much of the how and why this makes sense but follow the rules. Your math instruction would have benefited me so much!
Lori
Conversations in Literacy

1. Lori, I know we all still have much to learn about great math instruction, but I too wish I had learned math differently than I did. I think I'd feel much more confident about numbers if I had.

4. Well, I would have done 10x3, plus 4x3! I like your way too! I want to keep working on this in my room too. I tried this year to have students explain and share their strategies more, but I can do better. Thanks for always inspiring me to be a better teacher!

Crystal
Teaching Little Miracles

1. Crystal, I also thought of that strategy. Years ago, I wouldn't have thought of either. :)