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Before getting into it, I want to make a few qualifying declarations: my primary background is in science education. I'm not a mathematician, and the highest level of math that I've taught formally (so tutoring notwithstanding) is 10th grade. I can't honestly pretend to have a firm read on the pulse of math education, and attempts to get such a read have been a challenge.
For instance, a common thread in some of the literature I've tried to digest on Math Ed Reform is that research comparing progressive practices frequently involves teachers expertly trained in the methods being researched in the study, compared against control groups with teachers using traditional practices. No mention is given to the level of expertise of the control groups in their own methodologies (how are we to be certain some of these aren't just generally bad teachers?), nor is a group studied involving teachers receiving a "typical" amount of training that might be offered a rank-and-file teacher through professional development within the context of an existing career. In other words, I'm not totally sure I trust all the conclusions I read about progressive methodologies or their practical applicability. Moreover, I don't have to look very far to find conflicting claims (as in the fourth article of this journal) by other research groups or by comparing our methods to those in countries that score well in international math assessments.
Additionally, my perspective is fairly limited to high school math education. My sense of what's going on in elementary and middle/junior high schools is limited to a cursory appreciation of the curricular objectives, tidbits of professional literature, and in experiencing elementary math through the lens of a parent with kids in primary school (grade 6, grade 2, and grade 1, with a fourth kiddo still bumping around in diapers).
So now that we have established that I don't have much business telling math educators how to do their jobs, why then, would I pick this as a spot to weigh in on math? A few reasons:
- It's saucy. What's a revolution without some controversy in it? I don't think any issue in Ed Reform has gotten more mainstream media screen time than changes in math teaching. This is especially true across the border where American backlash to their national Common Core standards have received considerable attention and opposition.
- Math test results evidently carry a lot of weight in the international scene. Sorry humanities teachers! The bean counters and politicians don't seem to give a rip if students in China are crushing us in Sonnet Deconstruction, but show them another dip in our annual PISA results and just watch the panic button take another beating. Debate its merits at your leisure, but it's a pretty entrenched view that a nation good at math is a nation good at money.
- There's no right answer (ironic, hey?). I have no doubt I'll have some opposing opinions come my way, but no one can definitively say they know what needs to happen in Math Ed within the context of our existing education system. It was declining scores and lack of math engagement that pushed for reform (which has arguably not worked) in the first place. Debate me all you like, but proving me wrong is going to be a tall order.
- Just because we don't clearly know WHAT to do, doesn't mean we don't agree that something needs doing. Math scores are still declining (Alberta is particularly guilty here, and recent pedagogical shifts have come under scrutiny similar to that of the Common Core backlash), math and computer science enrollment has taken a beating, and Canadian students are less likely to take math-related programs than international students studying here. We are most definitely NOT in an "if it ain't broke, don't fix it" head space.
- It is interesting to me partly because some of the most insidious challenges appear to have solutions that require, at least in part, some manner of structural or design changes to the way we educate. Imagining novel ways for schools to operate is a fun exercise (well... at least for weirdos like me). Ironically, for all my bluster about the need for ground floor changes in my first post, this is an area where we might need a little help from the bigwigs to get just right.
- It's the area in which I personally diverge in my views most significantly from progressive teaching ideology. This is not because I don't believe in progressive ideas generally. I just feel that embracing them in totality is throwing the baby out with the bathwater, at least insofar as math is concerned. Why that is the case will become clear as I continue.
- I like math, and I like teaching math. It absolutely kills me to see kids step into my classes on day one having long ago decided that they suck at it, that they hate it, and that they will NEVER get it. I will also add that getting a kid to turn a 180 on at least that last one is honestly one of the most satisfying things a teacher can experience.
For now, the challenges:
Challenge #1:
Math has an incredibly high degree of internal dependency. Early learning (or lack thereof) is highly determinant of the degree of learning (or lack thereof) in later stages. A single year of bad math experiences for a student can be enough to derail their outlook on the subject permanently. There are only two other subject areas (that I can think of) that can compete with math's degree of level dependencies: learning to read (literacy) and second language learning. The similarity of learning numbers and learning words should not go unnoticed here.
Teachers of other subject areas have tried to debate me on this point, but none of them have even come close to convincing me that their subject areas require the same degree of mastery in prior courses as that of math. I can learn about plant biology without having first studied chloroplast functions. Understanding World War II is not critically dependent on understanding the American Civil War.
Challenge #2:
There are a significant number of professionals teaching math who have no formal training in math, little to no training in math education, and their own negative dispositions toward mathematics. Linda Pound, in her book Supporting Mathematical Development in the Early Years found this to be both commonplace and measurably impactful on student success in math.
Challenge #3:
There is a very pervasive undercurrent of thought that some kids (some people in fact) simply "can't do math." A few very specific learning disabilities notwithstanding, this is verifiably false.
Challenge #4:
This one has endured a while: Technology has the ability to stand in for foundational math skills and reasoning. When a kid grabs a calculator to do 5 x 6, it has the potential to be far more detrimental than a failure to reinforce the memory of one small square on the multiplication table. It eventually strips away the meaning of what it is to multiply. If I don't understand what multiplication IS, later when I need to calculate area or volume, or isolate for a variable in algebra, the calculator isn't going to tell me when I should be performing that operation instead of dividing or adding. Too often, I have seen students blindly pecking away at their calculators hoping that an answer will magically appear without any clue whatsover as to why they are pressing the buttons in the first place. And the worst part of it all is that I frequently see math resources (textbooks) and instruction that explicitly reinforces this broken pedagogy. When technology moves beyond simply being a tool for efficiency and instead becomes something akin to magic, progress in math becomes seriously impaired.
Number sense is one of the most fundamentally critical components of math learning, and it has been utterly eroded by little mechanical boxes and, more recently, the dulcet tones of Siri, who will cheerfully answer my math questions without my needing to think OR type. (By the way, if you've never asked her what zero divided by zero is, you're going to want to give that a go.)
Challenge #5:
The spectrum of math ability among students, particularly in high school, can be vast. One size-fits all models of instruction and assessment only serve the slice of students roughly in the middle of the ability scale. Advanced students go unchallenged to seek out their genuine potential, while weak students are further outpaced and marginalized.
Challenge #6:
Progressive learning models applied in math have received highly mixed reviews, show conflicting (or no) empirical data with regards to efficacy, and resist incorporation with other advanced learning models. Inquiry-based models and discovery learning can be highly engaging to already skilled learners, but can reach a ceiling with students who do not have a fully developed library of tools with which to approach the inquiry.
I recently visited High Tech High in San Diego, where I witnessed not only the deepest foray into progressive teaching and school design I have ever seen, but also (by far) the most effective. This school was recently the subject of a tremendously interesting documentary, Most Likely to Succeed, and I cannot adequately express the importance of seeing this film if you are a high school teacher wondering what else school might look like.
While there, I had the good fortune of meeting with math teachers and observing classes in action. There, teachers articulated the challenges of including math in cross-curricular project-based learning (PBL). The most significant of these challenges was that projects that had to be married with other disciplines were limited in terms of how far the math could be taken before they simply outstripped the meaningful connections with the other subject. Additionally, there was the significant challenge of exhibiting (a crucial component of PBL) projects to a public audience who does not have a similar level of understanding or appreciation for the subject matter.
That said, among the activities that I saw kids undertaking at HTH was good old fashioned worksheets. When I asked one student about her experiences, she described it this way: "our major project uses a lot of what we're doing in math, but some things we just have to do the 'old-fashioned way.' I actually like it, though, because it's the one time of day where we don't have think about this huge project that's going to happen weeks from now. I can focus on this one small thing for a little while and it's not so overwhelming." Ironic that in her school it's the math class where she goes to escape the overwhelming.
Challenges 5 & 6 Taken Together:
Traditional "Drill & Kill" models are not effective in the cultural environment of North America (and many other western countries). Progressive models, however, have failed to prove themselves to be the superior alternative. Either a third model that hybridizes the best of the two or some completely new paradigm entirely is required.
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That is by no means an exhaustive list of the difficulties facing math education. They are the most pressing ones, however, that I feel I can frame an agenda for what direction I'd like to see math education take, both for me as a teacher and for my own kids as learners.
Next up, what we might do about it all.
TL;DR: Math is a big deal. It's self-dependent, sometimes poorly taught and supported, challenging for kids once they get off track, impaired as much by technology as helped by it, traditionally serving only the median, and progressively serving only the gifted, and it still needs fixing after at least 30 years of apparently needing fixing.
Vive la resistance?
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