What if we display learning progressions in our learning space to show a pathway for learners? After Jill Gough (Experiments in Learning by Doing) and I published SMP-1: Make sense of problems and persevere #LL2LU, Jill wondered how we might display this learning progression in classrooms. Dabbling with doodling, she drafted this poster for classroom use. Many thanks to Sam Gough for immediate feedback and encouragement during the doodling process.

I wonder how each of my teammates will use this with student-learners. I am curious to know student-learner reaction, feedback, and comments. If you have feedback, I would appreciate having it too.

What if we are deliberate in our coaching to encourage learners to self-assess, question, and stretch?

[Cross-posted on Experiments in Learning by Doing]

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Howard Phillips

August 17, 2014 at 12:24 pm

I figured that Polya’s “How To Solve It”‘ was totally relevant to this. In case you are not familiar with this I have below the summary pages from the book:

HOW TO SOLVE IT

First.

You have to understand the problem.

Second.

Find the connection between the data and the unknown.

You may be obliged to consider auxiliary problems if an immediate connection cannot be found.

You should obtain eventually a plan of the solution.

UNDERSTANDING THE PROBLEM

What is the unknown* What are the data? What is the condition?

Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory?

Draw a figure. Introduce suitable notation.

Separate the various parts of the condition. Can you write them down?

DEVISING A PLAN

Have you seen it before? Or have you seen the same problem in a slightly different form?

Do you know a related problem? Do you know a theorem that could be useful?

Look at the unknown! And try to think of a familiar problem having the same or a similar unknown*

Here is a problem related to yours and solved before. Could you use it? Could you use its result? Could you use its method? Should you introduce some auxiliary element in order to make its use possible?

Could you restate the problem? Could you restate it still differently? Go back to definitions.

If you cannot solve the proposed problem try to solve first some related problem. Could you imagine a more accessible related problem? A more general problem? A more special problem? An analogous problem? Could you solve a part of the problem? Keep only a part of the condition, drop the other part; how far is the unknown then determined, how can it vary? Could you derive something useful from the data? Could you think of other data appropriate to determine the unknown? Could you change the unknown or the data, or both if necessary, so that the new unknown and the new data are nearer to each other? Did you use all the data? Did you use the whole condition? Have you taken into account all essential notions involved in the problem?

Third. Carry out your plan.

CARRYING OUT THE PLAN

Carrying out your plan of the solution, check each step. Can you see clearly that the step is correct? Can you prove that it is correct?

Fourth. Examine the solution obtained.

LOOKING BACK

Can you check the result? Can you check the argument?

Can you derive the result differently? Can you see it at a glance?

Can you use the result, or the method, for some other problem?

The first few pages of the book, written 70 years ago, read just like Dan Meyer today.

Here is the link to a photocopy of the whole of the original book

Click to access Polya_HowToSolveIt.pdf

jwilson828

August 17, 2014 at 5:54 pm

Absolutely! Thank you for the reminder. I read How to Solve It the first year I taught, which has been a while. The Standards for Mathematical Practice are connected to so much that is good about learning mathematics.

Kristin

August 19, 2014 at 10:32 pm

Love the visual. Will you be doing that for other SMPs?

jwilson828

August 20, 2014 at 7:51 am

Hi, Kristin. Yes … we are working on them for all of the SMPs. Jill and I will both post as we get them ready.