Surrounded by teachers who think their students don't have the ability to think...

This last Wednesday I went to a meeting with about 20 math teachers from around the district that I work in. The following problem was posed to us:

When we had all finished the problem we reconvened as a group. The person leading the meeting asked us "is this a fair question for our students?" I looked around me and saw 18 stone faces... and saw one of them began to speak. He said "No. Our students can't think like this." Others nodded in agreement. I sat with a perplexed look on my face and timidly raised my hand. I mentioned how I had given my students a problem that looked almost exactly the same, however as this was supposed to be a summative assessment, I used my activity as a precursor to a unit on percents. I mentioned how our students can absolutely think like this, and that the more we push them to actually do the thinking, the more likely our students will be to think. The co-presenter was sort of amazed that I would speak up about this, but agreed with me.

I left the meeting in awe... if such a small fraction of our district's math teachers felt this way, I wondered how the others felt. How many of us actually have faith in our students? I'm quite disturbed over the prospect that most of the teachers in our district don't have faith in our kids.

I have some cards in my pocket...

This year as I struggled to teach set-builder notation to one group of students I thought "seriously what's the point? They're going to forget it by the end of the year anyways, it's not like we use this anywhere else in the mathematics we're going to cover each year." I decided that I should move this to the end of the year so that it is fresh in their minds come exam time. Then my next group of students came into my classroom. They were playing cards and really giving the attitude to me like they didn't want anything to do with math. I looked at them with a huge smile and told them they could play two hands of the game they were playing while I quickly set something up. I found a deck of cards lying somewhere around my classroom (little known detention center facts: there are usually more packs of cards than children present at any given time in a detention center) and got to work. I stuck a sets of cards in each of my pockets (thankfully rocking 4-pocket jeans on this dress-down day) and put the above statement/questions on the smart board. Prior to finishing their last hand, the girls looked up and said...

So I made life a little tougher for them and introduced symbols they have barely seen up to this point...


They thought about it for a second, and then told me that I had the 10, Jack, Queen, King, and Ace of Spades in my pocket. I asked why. They responded "they are all spades because you told us and that shows you have cards between 10 and ace." After she said it, the of the girl said, "maybe she doesn't have the ace..." I asked why? and she responded "because you don't have the little line under the less than symbol." I probed further, "what does that little line mean?" The girls got it then, and the original girl answered "oooooh, you have the Jack, Queen, and King of Spades." I asked why and she was fully able to explain to me why. This was working out great, so I took a leap and gave them the thing that I was really trying to get at...

The girls got it almost immediately, still struggling with the meaning of < and <. After some "why's" they figured it out on their own. I put up about 5 more of these, varying in difficulty. I put a few up with "or" and they were stumped at first, but quickly figured it out. Lastly, I put up the following: . To my surprise, the girls understood what it meant (they had forgotten what the Z stood for, but after looking through their notes remembered) and were able to list off the numbers. They rocked through a set-builder worksheet as class-time was coming to an end. Overall, I'd say this is one of the most successful lessons that I have taught this year!

A word of warning...

I have started a blog numerous times in the past; if this one takes off I will be extremely surprised. Here is what usually happens:

1. I get all excited and blog 50 times in one week.
2. I get bogged down by work at school and graduate studies.
3. I stop blogging entirely.

Will this time be different? Maybe. But the probability is slim as I am busier than ever at school, and am taking six grad credits this semester, and perhaps even training for a marathon. Anyways, here I go...