NCTM11 - Teaching for Reasoning and Sense Making

The first session I attended at NCTM was "Teaching for Reasoning and Sense Making: How Does it Work?" and Fred Dillon, Jenny Salls, and Christine Thomas were the presenters.  I have seen Fred Dillon before and that was part of the reason I chose the session. The other reason I chose it was because the title intrigued me. The pdf of the slides for this session can be found here.

Basically what reasoning and sense making does is puts the mathematical skills into practice.  It fits right in with Race to the Top and the Common Core  practices.  I think I remember Fred saying that this really fits in with the first one on the list.

We proceeded to work through a problem about fish dying off in a lake and the lake being restocked each year and we were to figure out how many fish were in the lake at the start of the 2nd, 3rd, and 10th years and when it reached zero. Fred had taken a "typical" problem from a textbook and modified it to this. The problems that Fred talked about creating (like this one) have multiple entry points and can be done arithmetically and have multiple representations. There were five he listed but I didn't get them all written before the slide went off the screen. Three of them are Algebraic Formula, Graph, and Table.

The biggest problem that we have as teachers is when we tell students we will help them with the first step or tell them how to figure it out step by step.  We need to let the students struggle, for we are not really helping them by telling them what to do. (see more on this in my next post on my 2nd session).

As students are working through the problem and asking questions, things to think about include "How do we handle this? Does it matter?" (at the time it was in reference to decimal values). The most important thing to do is try it and see - encourage students to explore and not to worry about mistakes.

Fred also mentioned that other similar type problems to this one could include compound interest, exponential decay, and half-life of medicines. Once students have completed this type of problem once, you can consider these related problems to see how they can apply their reasoning to similar, but differing situations.

Some other thoughts from what Fred had to say include:
Reasoning and sense making should occur every day. I can see this - it is the main part of math (non-content wise) that can help our students do well beyond schooling.

Reasoning and sense making is NOT a list of topics to be covered.

I have a note about "productive ways of thinking that have become customary" but I have no idea why that is there.

Things that should happen as a part of Reasoning and Sense Making:
**Good Questioning Techniques
**Adequate wait time (and we never give enough of it - we think it's 30 seconds and it's only been 10)
**Resist the urge to tell students everything

How can you get started?
**Recast the material as questions. The opening problem was a typical textbook example.

The other two speakers walked through examples with finding x- and y- intercepts, graphing linear equations, and difference of squares (factoring).

Here's where I am at with this sesssion -
Great topic.  I needed to hear this.  I need help in how to make it happen in my classroom. I picked up 3 of the Reasoning and Sense Making books from NCTM (25% discount yay!) and they move to my reading list.

But I need to learn how to be less helpful.  I know we've talked about this in the math blogosphere and I probably need to search through Dan Meyer's blog to find it. Anyone else have suggestions on how to be less helpful and how to do these types of problems?

Here's the other thing - I still don't get how I am supposed to handle covering the content I am supposed to in my class. When does the teaching go on? Or do the kids figure it out from the problems? How does this all work? I guess that's my biggest issue on "rich problems." I think they're great, but how do I incorporate them into class and still get the content covered that I'm supposed to? Do any of my readers have any insight into this or know of someone who has blogged about it? Any and all help is appreciated.