What Was He Thinking?

A few days ago I gave my kiddos this problem:

We had been reviewing percents and so I tossed this on to a quiz.  I figured they would use either a proportion or change the percent to a decimal first and then multiply.

However, one young man wrote this: (this is my handwriting, recreating what he wrote)

It was 9 p.m. by the time I got to his paper, so I just wrote:  "I think you know what you are doing, but I cannot follow your thinking.  Will you explain it to me?"   

The next day I got together with him and he explained it to me.  It was a simple piece of brilliance.

"First of all," he said, "you have to ignore this."  He pointed to the proportion.  "I was just thinking about stuff."

"Oh, good," I said, relieved.  "You DO know that those are not equivalent, right?"

"Yeah, yeah.  So I knew that 8 of every 100 kids were sick.  So in 600 kids that would make 6 groups of 8 kids, or 48 kids.  Then that also means that in a group of 50 kids, there would be half as many kids sick, so instead of 8 kids, that would be 4 kids.  48 kids and 4 kids would be 52 kids out sick."

I nearly melted.  I absolutely LOVE it when kids have these great ways of seeing things.  

We also worked all week (in our warm ups and review questions on homework) on taking 10% of a number in our heads, which led to taking 20%, 30%, and even 15% in our heads.  One kid asked if we could practice more on finding out how much tip to leave at a restaurant, which also led us to a discussion of why we leave tips, what it means to have a living wage, and the types of bills their parents have to pay.  It was an amazing week with those students!

A Message for TMC First Timers

To all of you who are headed out to Twitter Math Camp (#TMC17) for the first time:  hang on to your hats... you are in for the ride of a life time!

First of all, I will not be attending this year, so I am sorry I won't get to meet you in person.  There are many reasons for this (two other times away from family already this summer, being chief among them), but also because one of the great things about TMC is the intimacy of it.

Deciding to keep the numbers down means more interaction among more people.  I was blessed to attend this most fabulous of professional development 3 years in a row (thanks to the administration in my school, who supported me professionally and financially), and met some fabulous people with whom I stay in touch via Twitter.  I wanted to make sure I wasn't going to take up a spot that maybe should go to a first timer.

So, First Timers:  go for it! Jump in and learn and share.  You have a lot to contribute, so don't be shy (this coming from a MAJOR introvert).  Be sure to tag along when someone announces a bunch of people are going to dinner.  This is how I met Brian Bushart (@bstockus) and Meg Craig (@mathymeg07).  OR hang around the hotel lobby or restaurant, which is where I got to meet Sarah Martin (@Sarah3Martin) and Max Ray-Reik (@maxmathforum).  Max!..... whose book I had just finished reading on the plane, and who eventually came to my school. He helped me change the way I teach: a small adjustment which has resulted in BIG changes in the way my students and I learn and share.

I even got to meet some of my heroes (and was brave enough to ask for pictures):

But more importantly, I had the opportunity to meet people who live in my geographic area so we could get together for fun and for brain storming!

I hope in the near future, more of this great professional development at TMC will be video taped so others can benefit from it!  (Yes, @cheesemonkeysf, I sure would like to see your morning sessions at TMC17!).  What an amazing library of professional development that would make!  But be sure to visit the wikis and the archives from previous Twitter Math Camps.  They are full of fantastic materials and ideas.

This school year is going to be a real challenge for me.  It is the end of July and I still don't know what courses I will be teaching.  Because of some dual enrollment courses, I will no longer be teaching my favorite Honors Pre-Calculus classes (I don't have the requisite majors/Masters), and may end up teaching some courses I have never taught.  My teaching load will also be increased.  AND we have two new staff joining our math department, to whom I will want to be sure to be available .

But I will not be alone. In addition to the great math faculty at my school, I have a huge Professional Learning Community in the Math Twitter Blogosphere (be sure to go explore it!)  I may be shouting out for help along the way.  Thank you, in advance, to members of MTBoS past, present, and future, for your help!  I will be reading your tweets and posts (especially during TMC 17 time).

One final piece of advice:  Go forth and have a blast, First Timers!

My Math Autobiography

Once upon a time, math and arithmetic was fun for me.  I enjoyed it, I found it easy and fun.

Then integers happened toward the end of junior high school.  And suddenly nothing made sense.  Well, that isn't TOTALLY true.  Multiplying and dividing integers had a very simple pattern: easy to catch on to, but adding and subtracting integers?   Why not just teach me Chinese....while speaking Russian?  That's how much sense it made to me.

And my teacher had only one way to "explain" it... using a horizontal number line.  Being spacially dyslexic, this was the worst possible way for me.  It was his ONLY tool.

When I got to Algebra 1, I was supposed to already be fluent in this integer-speak.  I learned process quickly.  I absolutely understood how to do and undo.....except I couldn't add or subtract with those integers!  I was just guessing!!!

Midterms came.  I studied so hard: practiced by doing and re-doing old homework assignments and tests.  Our teacher called us up to his desk during silent work time to "stage whisper" our exam grade to us.  I didn't hear him say "C" a grade I was expecting...it wasn't an ssss sound.  Could all my hard work have paid off?  "Excuse me?" I said.  His reply came through loud and clear, and in the silence all could hear him say:  "D.  As in Dumb."

I wanted to die.

I was truly crushed.  And for a while, I was convinced he was right.  But I knew I was good in other subjects, REALLY good, so this just didn't make sense that I was Dumb in Math.

I muddled through that year, and Geometry was better.  I think I saw all those proofs as puzzles.  But then I got an Algebra 2 teacher who asked me if I could read (I asked for help on several word problems everyone else was too afraid to ask about).

I snapped.  I was done being called stupid.

"Yes, Ma'am, I can.  There is a sign down the hall that says "Guidance" and I think I will take myself down there."  This from skinny, timid Tina  The whole class fell silent as I gathered my books and bag and left.  I had never, ever done such a thing in all the years we had been in school together.

I deposited my stuff in Guidance, told the secretary I would be right back to see my counselor, and then went to my Assistant Principal's office to let him know I had just walked out of my math class.

"Come in, Tina," the Assistant Principal said.  "What seems to be the problem?"

"Well, I just walked out of Mrs. O's class, Dad, and I wanted to let you know.  I was not disrespectful, but I did walk out and will serve whatever detention she or you feel I should get for that.  But I will not go back to that class.  I am going to Guidance to have my Algebra 2 class switched.  You can talk with her and let me know what my consequences are."

Dad nodded, told me to go on my way and he would talk to Mrs. O.  He asked me to close the door on the way out.  I was nearly in the hall when I heard him erupt in laughter.

It was a long, slow climb back to some semblance of confidence in my math ability.  Some decent college experiences helped, but I still stayed away from math as much as I could.

I was trained to teach reading, and it was because of students with learning disabilities who came to me for reading help that math and math education returned to my life. Turned out many of my tutees also needed math help.  These students all struggled with concepts I had struggled with.  Together we came up with ways that helped them or I would think and think and think of how to make this more visual or more hands on for them.  Sometimes they showed ME things that someone else had showed THEM.

In the end, it was my students who made me a better math student, and eventually a better math teacher.  I am forever grateful to them, as my students continue to challenge me and make me grow.