One comment I’ve had from a classroom observer lately is while I may have a clear classroom objective posted, say —
I can isolate a variable in an equation.
— I hadn’t made clear why students would care about such a thing in a first place. Here I was stuck: while I have some lovely activities that interest even 13 year olds, to get to them we needed to tread through some math which motivates some more math which motivates some more math and THAT leads to application projects.*
I don’t know about your students, but no amount of emotional appeal or explanation of how it fits into the larger picture of mathematics would lead mine to care about
Isolate the y: 2x + 3y = 14.
until I did this:
This is essentially project goal oriented sequencing where I make totally explicit what hurdles still need to be leaped before we get to the Stuff My Freshmen Actually Care About (the football lesson is still one of my most popular activities ever).
* It would be lovely to get them interested in the mathematics for its own sake, but some topics are hard to redeem. Even mathematicians don’t get worked up about isolating a variable in simple algebra.
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The Number Warrior 
My schools math department spends almost no time actually teaching algebra (explicitly) Instead they go on to geometry, trig and such, and algebra inevitably comes up in these problems.
Firstly, I’d love to hear more from the anonymous commenter. Where do you work?
Second, I get what you’re saying about showing them what it takes to get what they want, and I’ve definitely done the same. The whole question of motivation is really troubling, and the ideal is entirely intrinsic drive to know, master, conquer, use, and create mathematics. Mathematicians possess this. That’s not most people.
On the other hand, this is as close as it gets to carrot and stick, and it feels slightly painful to me. (Then again, I just torture myself over this stuff with perhaps less success.) You haven’t given up the good fight though, right?
I love your blog, and totally respect you, so please don’t think I’m being too harsh.
It’s more like carrots all the way down. The pitch puts everything into one big swirl of awesome as opposed to some kind of obstacle course.
Most kid’s don’t like math, or piano lessons. But if you must teach kids something they don’t like, then I don’t see any alternative to the carrot and stick. Paul identifies the problem when he says…
“The whole question of motivation is really troubling, and the ideal is entirely intrinsic drive to know, master, conquer, use, and create mathematics. Mathematicians possess this. That’s not most people”
I recently did a deep dive into Finland’s system of education…
http://mathforum.org/kb/thread.jspa?threadID=2340957&tstart=45
http://mathforum.org/kb/message.jspa?messageID=7663681&tstart=45
and I was surprised to find that half of the students don’t go to academic high school with its algebra, geometry and calculus. They go to vocational (trade) schools. They have over a 100 main categories to choose from and when you break out the sub categories they number over 300 choices. This realization prompted me to write this (which was addressed to a different paul)…
http://mathforum.org/kb/message.jspa?messageID=7663493&tstart=45
When Mr. Salomon asks…
“You haven’t given up the good fight though, right?”
I don’t think this is a good fight. It is more like a holy crusade.
half of the students don’t go to academic high school with its algebra, geometry and calculus.
This is exceedingly common. I find trying to extrapolate truths about US education from international statistics to be painful for this very reason.
My favorite example is how Israel ranked #1 internationally in math in a 1964 study and afterward sank to the middle. The 1964 study excluded Arabs (11% of the population at the time).
I wonder if there is a way to use the football lesson as a context through which students grow to understand and conceptualize the mathematics you intend as opposed to a context in which they just practice what they have already been exposed to? In other words, put the football lesson first and embed the individual lessons within it?
I did try that once with the football specifically. It didn’t work too well. I think this has more to do with 13-year old psychology than pure curriculum constraints: they were too pumped up from going outside etc. that they had trouble building new mathematics afterwards.
One lesson that did work well in the manner you suggest is a bit with unit conversion where I have the students reproduce Oliver Smoot’s feat of using their body as a measuring stick. I guess the relation between the math and the activity was easier to see?
[…] (and possibly why I feel compelled to write this tonight): Jason Dyer’s post on building objectives towards and overarching activity/project. All of my objectives and knowledge should be building towards some meaningful mathematical […]
I’m curious: What software did you use to generate your project goal oriented sequencing diagram? Do you update it as you progress in a more-or-less automatic way?
I just drew by hand in my paint program. Given I had no idea it would even work until recently I’ve been updating by hand (now that I know it does, I might consider making something automatic).
[…] is the link: https://numberwarrior.wordpress.com/2012/02/29/project-based-objective-posting/ This entry was posted in Uncategorized by lholm. Bookmark the […]