What ARE We Teaching?

Today I attended a hub.  If you don't know what that is, here's the quick & dirty explanation:
Small groups of teachers, from various schools, meet up monthly for a day to inquire about learning.

Being inquiry based, we start with some sort of a plan, and led by fearless leaders, we go into a classroom and observe the students.  Then, we come back to the table, discuss what we saw, and usually make some minor changes to the lesson, and try it all again.  Today we really got into looking at "what comes next?"  I'm happy about that.  I needed to know what came next.  I feel comfortable with the classroom climate, student voice and problem based learning in my classroom.  What I need as an adult learner now is just that - now that I have this data, what do I do next?  And am I really seeing what I think I'm seeing?

Today revealed some amazing things.  We were in a Gr. 7 classroom, and the whole learning continuum really presented itself today.  The students were looking at a problem with fractions, but the question didn't explicitly state that it was about fractions.  I wonder if some of them even knew it was?  As we let them tackle the problem, we realized that there were some missing pieces.

This group found out from another that they could divide the two numbers to find the decimal.  But, they didn't have enough fundamental understandings to be able to identify what each number meant, or what to do once they'd found every decimal.  For this problem, and for their fractional understandings, that's a big gap that we can now fix, because we found out about it.

We reconvened and discussed the triumphs and struggles.  We got into smaller groups and presented our own observations, and then categorized them.  My group came up with headings like "Classroom Climate," and "Assumptions," and "Misconceptions" and "THE Math - Number Sense."  It was fairly obvious that as a whole, the class was missing major fundamental pieces, which were required in order to do THE math.

Working together to look at our observations, wonders & student quotes to find some common themes.
Quotes like "I'm so confused ... I'm getting mad.  I'm gonna spazz out!" were very telling, and informed us that some students are putting up walls ... so how do we target that now for them, and how do we target that for students who are beginning to feel that way now, in primary & junior grades? 

After our small group sharing and categorizing, we got together to see if we could group what we'd found:
were there common themes happening?  And then, how could we possibly target them?
WHAT COMES NEXT?

After much tribulation, we went back in with the prompt:

Design something to help the Gr. 4 students at (my school, not the highschool) learn about fractions.


Well.

It was a dud, I would say.  While some groups had some ideas, I think it is fair to say that they couldn't access the information without going to the internet.  That's a great strategy, except ... I don't think they were doing much other than regurgitating the information they'd found.

So now I'm left with these wonderings ...

- What ARE we teaching in primary & junior?
- Why AREN'T the fundamental concepts sticking with them?
- Is our teaching and their learning TOO compartmentalized?
- Is this because of text books?
- Is this because many of us have a discomfort with things like fractions, so we spit out the words, they "parrot" it back (to borrow the term from one of the resources we looked at today!), and then we say "Check! Moving on!"?
- Is this because the climate surrounding math has been, as a whole, stuffy?  Overwhelming?  Anxiety-ridden?  Why?
- Is this because they just can't remember?
- Do they have the language to get to the language or strategies that they need to understand it all?
- Are they worried about using the right words and pictures to please the teachers?
- Do we even know what kind of understanding we want to see from them?  I'm not sure I did.

I wonder if manipulatives (for those non-teachers reading, I mean the thingies they use to solve problems, like counters and blocks and so on) are the issue, too?  Do the kids stop using them in junior, and then not want to use them in intermediate, because it means that they're unable to solve the problem with their heads?  If that's it, we've got some major work to do around our classroom cultures.  I wonder if manipulatives looked cooler and more "adult" (maybe metal or polished fine wood blocks and counters instead of primary red, yellow and blue), would older kids be more comfortable with them?  I wonder if these kids were uncomfortable because the problem wasn't the kind that they are used to, and so they have trouble accessing the strategies that they need to solve it?  I don't know - I'm not the teacher and I don't work in the school.  I wonder if the kids would be more able to solve the problem if there was something more motivating about it?  I don't know - I don't know them and I don't know what motivates a 13 or 14 year old - I've only taught up to 11 years old.

So many wonders.  So little time.