Granted, there will be lots more structure put in place when I do this with my sixth graders next year, but I'm curious (especially for the people who are NOT math teachers)...

Assuming you're one of those students who does what he/she is asked to do, how would you respond to this question if it were, say, a homework problem?

Would you respond any differently if I just gave you the picture (in the context of this being part of your math homework)?

Thanks Heather for the suggestion to put this out here front and center.

## Thursday, May 27, 2010

## Thursday, May 20, 2010

### What Makes a Problem Great

I've put together an ever evolving list of characteristics of rich math problems. Anything you'd add, subtract, or edit? These are in no particular order...

1. The problem should be accessible. It should minimize vocabulary and notation, have multiple entry points, and include ways to collect data of some sort. It should have multiple methods that promote different learning styles and celebrate different ways of being smart.

2. The problem should be deep. It should be rich enough to spend hours, days, weeks, months, or years working on variations, generalizations, and extensions. It should lead to and connect as many different aspects of mathematics as possible, as this can then be the motivation for developing procedures, vocabulary, notation, and mathematical concepts.

3. The problem should be able to scale sideways so that students can explore related ideas in different contexts to reinforce concepts.

4. The problem should be captivating. This does not mean that it has to be a “real world” problem and it really shouldn't be a contrived real world problem (please explain to me how in the world I would know the number of total animals and feet I had on my farm, but not the number of cows and chickens). It might mean that it leads to a surprising result. It might mean that it feels like a puzzle waiting to be solved.

5. The problem should be mathematical. Progress should be able to be made by using problem solving heuristics and resources. The language of mathematics should benefit the student in solving the problem.

1. The problem should be accessible. It should minimize vocabulary and notation, have multiple entry points, and include ways to collect data of some sort. It should have multiple methods that promote different learning styles and celebrate different ways of being smart.

2. The problem should be deep. It should be rich enough to spend hours, days, weeks, months, or years working on variations, generalizations, and extensions. It should lead to and connect as many different aspects of mathematics as possible, as this can then be the motivation for developing procedures, vocabulary, notation, and mathematical concepts.

3. The problem should be able to scale sideways so that students can explore related ideas in different contexts to reinforce concepts.

4. The problem should be captivating. This does not mean that it has to be a “real world” problem and it really shouldn't be a contrived real world problem (please explain to me how in the world I would know the number of total animals and feet I had on my farm, but not the number of cows and chickens). It might mean that it leads to a surprising result. It might mean that it feels like a puzzle waiting to be solved.

5. The problem should be mathematical. Progress should be able to be made by using problem solving heuristics and resources. The language of mathematics should benefit the student in solving the problem.

## Monday, May 17, 2010

### Probably the only teaching blog that has ever started in May

Ok, so I think I want to make a real go of this blogging thing (boy do I sound old...maybe even older than I actually am). I've blogged for a grad school class and for my own personal journal keeping, but I have yet to share any of this with the general public.

The thing is, I have found that there are just too many incredible math teachers out there not only doing innovative and thoughtful things in their classroom, but finding the time to share and talk about these ideas with others.

I have a selfish desire to be part of that.

I am also going to be embarking on a very new experience next year: teaching and research.

While I've been learning to teach math for 11 years, I'm now lucky to have the opportunity to teach and conduct research (for my dissertation) and I have a feeling I'm going to want/need input from whomever is interested.

The thing is, I have found that there are just too many incredible math teachers out there not only doing innovative and thoughtful things in their classroom, but finding the time to share and talk about these ideas with others.

I have a selfish desire to be part of that.

I am also going to be embarking on a very new experience next year: teaching and research.

While I've been learning to teach math for 11 years, I'm now lucky to have the opportunity to teach and conduct research (for my dissertation) and I have a feeling I'm going to want/need input from whomever is interested.

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