I have to tell you, I definitely felt like I learned a lot at the conference I keep telling you all about. I discovered a lot about my own teaching and how I’m doing a lot more right than I thought, but also found stuff that I need to work on more diligently. I suppose if I’m going to be in this as a career, I should learn a few things here and there.

Like I mentioned before, I took copious notes at the conference, hoping to not only remember what I was taught but also share with mi gente. I’ll try to make it brief and all notes are available in full if you ask, but here’s my summarized top ten:

1. Teachers don’t do a good enough job helping kids understand abstractly as well as concretely. (courtesy of Greg Tang, author of The Grapes of Math)

I totally see this. For the first decade and a 1/2 of my education, I knew what place value was, but I didn’t understand how it worked until I got into college, when I started learning more about binary systems as a computer science major. We need to push the kids’ thinking, and try to help them become more abstract thinking and give them a foundation for that thinking.

This man’s also the one that said, “What’s the 8th planet in our solar system? What, you don’t know? It’s Planet of the Eights! It’s a joke, don’t you get it?” Well done.

2. One person’s self-evident truth is another person’s unfounded theory. (courtesy of Julian Weissglass)

Weissglass used a historical analysis of the Constitution to concretely explain the last statement. If we understand the Constitution as it was written, then we’ll see that it didn’t apply to a huge section of America’s constitution. In other words, what some at the time may have considered a basic assumption for living may not have been so for another person. Actually, I want to write more about this later on (presses pause until Thursday).

3. Math, art, and technology mesh much more readily if we think a little more deeply. Just ask Leonardo daVinci. (courtesy of Nikki Blair)

4. Not only are we in the business of pushing kids to be better, but making it harder for them to be average. (courtesy of Larry Bradsbury)

If we want to become better teachers, we need a more systematic approach, by defining skills that we want the kids to learn, diagnose student needs, provide appropriate activities, evaluate student learning, reteach if need be, and maintain better student records.

5. Good feedback isn’t an easy task. (courtesy of Laura Maly and Sharon Kolade)

Just like the comments we leave in blogs, writing good comments on posts can change how the original writer improves or understands the task at hand.

6. Sometimes, it’s the kids that are at the highest levels that need the most help. (courtesy of Dr. Joyce Fisher)

With regards to ELLs (English Language Learners), sometimes they’ll be really good at doing math in their own language, but they’ll have a hard time translating that math knowledge into English because not every concept in Spanish has a cognate in English.

7. Broaden the question so more students have entry into the discussion. (courtesy of Marian Small)

This applies to everyone, but if we look at differentiated instruction, sometimes asking a specific question can really limit who will participate in the conversation. For some purposes, it may be good to target the question for a specific answer, but in general, making the question accessible to every student will allow even the low-level students to feel engaged in the conversation. So, for example, instead of asking, “Is 6 a factor of 54?” we might ask, “What relationships can we make between 54 and 6?”

8. Be careful with too many cultural references in your exams. (courtesy of Carol Caref)

Unfortunately, when it comes to tests, they’re often culturally biased without people even realizing it. Those biases can make the difference between students who excel in their tests, and those that understand the math but can’t grasp it because they don’t know what the dimensions of a house look like or how a mortgage works.

Also, I got to see David M. Schwartz work his magic with How Much Is a Million? and Nora Ramirez, president of TODOS (a group for teachers who teach Latino / Hispanic students) not only demo a lesson on proportions, but also explain the values of going her math teacher organization. The conference also gave me a good indication that, overall, I’m on the right track. I just need to keep plugging away.

I was actually a little disappointed that I didn’t see any of the prominent edubloggers either go to the conference or present at the NCTM, but I suppose with time that too shall pass.

jose, who will finally start using his SmartBoard …