Tuesday, February 7, 2017

Making Explorations Successful

In a fit of perhaps excessive caution, the district cancelled all after school activities today despite the snow being almost completely melted.  So I'm tabling my plans for Math club for this week.  I really look forward to working with the kids so I'll have to work some of that energy out with my own children instead. I'm particularly fond of watching Numberphile videos as a family.

In the meantime, I saw a quote that I wanted to bounce around:

"If you group kids by "ability", those who are struggling may never see the pattern. Groups need to be mixed"

My first reaction to this idea was contrarian. For one,  if you don't really believe in ability i.e. quote the word to signal skepticism, then why does it make a difference if you mix the kids or not?  If ability doesn't matter groups are basically random already.  Kids should succeed anyway based on their own potential regardless of which peers they are with.  If it does matter, then what kind of learning is happening exactly in these situations?  My fear would be that basically you end up with a set of kids forging ahead and a second set copying what the others have learned. For me this is a poor man's version of direct instruction.  Rather than having an adult who has specialized in instruction showing the way, you devolve to peer to peer tutoring.  And having a reasonable amount of experience, I can safely say even kids who really get a concept are usually not nearly as good at communicating it.

So how does this relate to my Math Club?  First, I do have semi-random groups since I let the kids self select who they work with. The clusters tend to be gendered as a result and split along lines of friendship not necessarily skill. The kids obviously have volunteered to join the club which correlates mostly to some passion for math but in practice there are differences among them that are still probably comparable to a classroom.  When we do non-trivial explorations or tasks which is most of the time, kids discover concepts at vastly different rates.   This is one of the great weaknesses of this structure. In a one on one setup, I could slow down and scaffold just the right amount to let each individual "get it".  In a group, I'm always balancing the needs of the many against each other.

I try to compensate for this by having group discussions where everyone shares and by working individually with clusters during any activity.  I also work really hard to focus on having everyone participate. Those mitigate to some extent, but I still don't achieve a truly even amount of learning. Some kids still regularly have more breakthroughs than others. In a way, I think this shows the need for individual tasks. There needs to be a space, where everyone can struggle with a problem without having  it short-circuited by a peer finding the answer.  I'm sensitive when giving advice to not do all the work. Friends on the other hand jump right to the answer.

But in the end of the day, group inquiry based learning works best for me the more level the playing field to start off with and I'm not sure I've found an entirely satisfying way to resolve the issues that arise when it really isn't. And in thinking about this more, to me this is the crux of why teaching is non-trivial in general.


  1. My parents are visiting from WA and keep grinning whenever a friend posts a snow picture on facebook. My family is about to move back to the US northeast, though, so I'm not smug about the snowy winter.

    I don't know if there is innate ability or not, but it is undeniable that there are differences of background experience that can be huge, even by first grade. For a variety of reasons, there seems to be a positive feedback loop, with the kids who are ahead getting farther ahead.

    Here are some of the things we do in our classes:
    (1) a series of related activities with difficulties something like 1, 2, 5, 10.
    Everyone gets the level 1 activity, those who finish first jump to level 10, then the next cluster to level 5, then the next cluster to level 2. This idea comes from Gordon Hamilton at Mathpickle.com.

    (2) Have activities that can be judged on two levels, usually one dealing with the basic mechanics and the other about structure or strategy. For example, we recently played factor capture in our classes. Most of the kids were thinking about what factors mean, finding factors of a given number. Some kids were thinking strategically, trying to optimize their moves. Other kids were thinking about the structure of the game, what happens on differently sized/shaped boards.

    Ultimately, this is one of the reasons I like games so much, there are usually many levels of thinking that can happen at the same time in the class.

  2. I use some of the same strategies although I've been doing multi-leveled or multiple activities less. That's because I've also been trying to emphasize more group discussions which require everyone to mostly be on the same task. I don't have a great structure for doing talks with say half the room at once while the rest works and keeping everyone moving forward. I'm definitely thinking about this more I'm most of the way through agreeing to take on a full blown middle school club. That would mean 6th-8th graders and an even huger spread.