Here's the plan:
We will complete a high speed version of a project where students create, explore, and generalize visual counting patterns (pile patterns for example). Sprinkled in will be discussions of how mathematical habits of mind (aka problem solving, aka mathematical practice) can be developed and assessed. Come prepared to do some math.
Basically, we're going to start with
and go from there...
Here's the current draft of my powerpoint (zzzz) presentation. I've never done this before (mostly because I've never been finished mostly finished putting together a presentation this far in advance). Obviously, there are lots of pieces that need to be filled in (I kind of hate powerpoints that don't have pieces that need to be filled in) but I'm hoping that I can get some feedback beforehand, send participants here during, and continue the conversation afterwards.
Here are some additional resources related to the workshop.
Supposedly there will be attempts to stream the conference for those of you that fail to scalp tickets between now and then. We'll see how well this works, but stop by if you have some time (9-3PST).
See you tomorrow, Avery. I'm looking forward to playing with patterns, and thinking about how to help students do it later.
ReplyDeleteI live in Oklahoma and I am also in the middle of crunch time at school. I really wish I could be at the conference. I will look out for how to possibly go next year (I see a grant in my future). I hope your session is broadcast.
ReplyDeleteLooks good to me. Psst... there are actually textbooks out there that center the material around mathematical habits of mind: www.edc.org/cmeproject
ReplyDeleteSorry for the blatant plug. You rock, Avery! How was the talk? I am glad you are thinking about assessment here, which can be a difficult thing to do while still maintaining a focus on HoM.
I think the talk went well (no rotten tomatoes or shoes were thrown at me), but who knows. There were some great questions and discussions that warrant separate posts (What to do with students who ask not so great questions, for one). Bowen is right (as usual), the CME textbooks do a better job than any other traditional (ie state adopted) textbook addressing habits. That said, I don't think CME goes far enough (and I don't think that it can in the current climate of what states require). I also found out that The Park School in Baltimore wrote their own Habits of Mind textbooks which is super cool and super exciting. So yes, let's reconsider my list of why not to use a textbook.
ReplyDelete1. To put a greater focus on concepts
2. To expect a greater cognitive demand (to not give too much away)
3. To supplement content not available in textbooks
4. To address habits of mind
5. To build in a more dynamic/flexible classroom
While 1-4 could be addressed with different textbooks and are (to some extent) being addressed here and there, I think difficulties in addressing #5 are inherent in the medium. I can imagine a "textbook" that talks about expected responses to a call for student posed problems, but the cool part of student-posed problems (and the field of mathematics) is that the possibilities are endless.
That high School kids are still saying that geometry is a waste of time because they can't see what possible use they would ever have for it, strikes a familiar chord. This was exactly the same conversation some forty-five years ago when I was in the tenth grade. It's amazing that after four and a half decades, no one is bothering to teach kids how to relate. So children are still asking the same question, “Why do I need to learn this stuff?” However if teachers would tell them, “Circular motion is the foundation of time and space,” it might perk some interest because it’s all about shape, which Wikipedia defines as “the external two-dimensional outline, appearance or configuration of some thing — in contrast to the matter or content or substance of which it is composed.” Additionally, the interesting thing about this concept is that despite the connotation of physical structure we seem to be able to apply it also to the realm of intangibles, so these ideas about shape are taking shape. But the point here is that shape is the foundation and infrastructure of all existence and that the key to success and joy is in the forms and structures of the universe by which we shape our thoughts into action to achieve all objectives. Thoughts, for the most part are responses to stimuli emanating from the world around us, which is a hodgepodge of geometry. Hence, the shapes of this finite world influence, impact and inspire what we think, which, in turn governs all of our actions. Some questions have answers and some don’t, but the bottom line is that we need to look at each of the basic geometric figures as they exist in our language, culture and the world around us so that we may uncover some of the secrets of life to achieve joy and success. Therefore, seeing stimulates thought, thought causes speech, speech transforms to action and action leads to success. So, look, see and enjoy. More at http://thoughts4thesoul.wordpress.com
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