"A day without math is like a day without sunshine." -- my friend V's mom

[mrissa]

The state of Minnesota is having another go-round with its high school graduation standards, particularly in the area of math. We set up a math test people would have to pass to graduate high school. Surprise! People didn't pass it. Lots of people didn't pass it. Surprise again! There was a great deal of uproar, because what were we to do with these high school juniors who didn't pass?

High school graduation the supposed skill certification and high school graduation the social ritual have become inextricably intertwined in our culture. So it's no surprise that people are up in arms and saying things like, "These kids ought to be able to graduate." I even agree with them, but not in the way they think: I don't think high school graduation is most useful when it's a certificate of attendance. But I do think that if you don't know enough or can't do enough to meet graduation requirements, you should be getting feedback to that effect. The idea that you would have passed all your classes and yet not know the things they feel you should know at that point seems like something has gone wrong, and I doubt that there would be this much uproar if we were talking about kids who hadn't passed their classes--for whatever reason, we are culturally on board with the idea that if you fail math, you don't graduate. But these kids are failing at learning math, and they're not failing math, and that, to me, is a big problem. Sure, we're not talking about students who are passionately committed to mathematics here; not every student is or should be. But we are talking about students whose best indications on whether they know an acceptable level of math for a high school student is that they do, and those best indications are, apparently, wrong.

I'm sure there are people who are totally okay with a math test but not with this math test. But that's not what we hear every time this issue comes around. It starts to boil down to, "But math is hard! You don't really need math! And it's hard!" And at that point, well, what do you really need from a high school education? What can't you work around? There's not a heck of a lot, on the level they're talking about here. If having to calculate the area of a room from its dimensions is too much to ask of high school graduates, I'm starting to think that the people constructing these arguments are, in fact, arguing for a high school diplomat to be a certificate of attendance, a verification of age.

One of the things we are not willing to say in this discussion is that people who can't do math are missing out. They're missing out on ways of protecting themselves, sure, on a measure of independence that comes from being able to do some rough calculations yourself. But they're also missing out on something wonderful. Something beautiful. I know I'm talking to some of you about yourselves, and yes, I'm sorry: you're missing out. That dimension of understanding is worth cultivating. It is worth having. Some of you can't do math the way a person who is completely tone-deaf from birth can't learn to identify a piece of music upon hearing it, but the vast majority of you who can't do math are more like someone who doesn't know any songs because no one ever taught you any. It doesn't make you a worse person. It doesn't make you an unintelligent person. But it's still a damned shame to induce disabilities in people who don't have them to begin with.

I believe that math-related learning disabilities are real. I absolutely do. I do not believe that irremediable math-related learning disabilities are as prevalent as people who were taught math very, very badly, often by people who did not themselves know how to do math.

I don't really know what to do about that. Saying, "Yes, fine, go on ahead and get out of here; it's not like we have any real preparation to teach you math from here anyway," seems practical in the short-term but distinctly suboptimal in the long-term. It treats the problem as one of what to tell the students--yes, you are a high school graduate, or no, you are not--rather than what to do to fix a system that "should have" done something but did not.

It allows us to keep on with math education the way we have been. And on the one hand, we sort of have to. And on the other hand, we sort of can't.

Comments

[mmerriam.livejournal.com]

I do not believe that irremediable math-related learning disabilities are as prevalent as people who were taught math very, very badly, often by people who did not themselves know how to do math.

Seems like I was involved in a conversation about this just a few days ago...

[akitrom.livejournal.com]

Do you have a link to the particulars of the high-stakes math test in question?

I'm looking to return to the secondary math teaching field, after a couple of years as a Test Development Associate, working on End of Course tests at ACT. And I can tell you, there are good reasons to have an EoC test that's independent of, and not scored by, the classroom teacher, but that independence makes it very difficult to test curriculum-specific skills well.

Added to all the normal issues (The kid is sick on test day, or her parents had a fight the night before...) are issues like notation (a kid might know how to answer a question, if only it were phrased in the terminology that his textbook and teacher use), time (the EoC test from ACT comprised 38 multiple-choice questions, and we expected students to complete the test within a 45-minute class, which pretty much messed up students who were used to carefully solving problems and showing all their work), and a half-dozen other variables.

[mrissa.livejournal.com]

Here (http://www.startribune.com/local/stpaul/47047072.html?elr=KArksUUUU) is the most recent Strib article, others available for the Googling or the link-following.

To my way of thinking, when we're talking about a test for leaving high school, if students know math if it's phrased very narrowly, they don't know math. The outside world will not be nearly so careful with phrasing.

And sure, there will always be slow workers and kids who are sick. But 40% failure is no longer looking like, "A is very methodical and B was coughing up a lung on test day." It's looking a great deal more like, "Many of these kids cannot pass this test."

Do you feel that the overwhelming majority of people who graduate from high school know as much math as you would consider a good, reasonable idea for that stage of life/education?

[aamcnamara.livejournal.com]

As a completely irrelevant note to the topic of better math education (which is definitely needed), I'm fairly certain that they didn't have a good baseline for this test--my class was the try-it-out class, last year; we were told we had to take it, but as we'd taken the MBSTs and passing the MCA didn't have anything to do with graduating, a lot of people skipped school/doodled pictures instead of answering questions/filled in random bubbles/turned in blank sheets of paper. And I would believe someone who told me that my school was pretty typical in that regard.

However, since I know nothing about test-judging standards, I may be completely off base here. Maybe they adjusted for that.

And certainly there are many and numerous problems with how a lot of math classes are run. (Though I would argue that standardized testing is also not the best way to test abilities for a lot of students.)

... this comment sounds like I am disagreeing with you. I am not. I am agreeing with you. Just... sideways agreement.

[mrissa.livejournal.com]

I'm not convinced that standardized tests are The One True Way or even A Pretty Good Way, either. But I'm wary of people (not you!) who go from that to, "And therefore the way we're teaching math is probably fine." Because it mostly really isn't.

[redbird]

On the other hand, a lot of standardized tests will, if anything, make it look as though the students know more math than they do, because they're multiple choice with no penalty for wrong answers. So the students are, reasonably, encouraged to guess.

(Hints like "if there's no penalty for a wrong answer, guess" and suggestions on ways to guess well don't even count as teaching to the test.)

Conversely, there's no way on a multiple-choice test to give partial credit for someone who shows their work and clearly understood most of it, but absent-mindedly turned a plus sign into a minus sign when copying from line 3 to line 4; it looks the same as someone who had no idea of what's being asked.

[I'll spare everyone the bit about "real world" problems that nobody in the real world ever addresses except if they're interested in numbers for their own sake, like the surface area of the leftover three slices from a medium pizza. [at this point, the bailiff stuffs redbird into a sack, head-first, and deletes the rant about pizza area before posting the comment.])

[stillnotbored.livejournal.com]

Having crashed my computer trying to read the article you linked to (the site's fault, not yours) and googling but failing to find what I wanted, could you please tell me what is on this math test? Is it basic math or is it advanced math?

[mrissa.livejournal.com]

It's what I would consider basic algebra and geometry. No trig, no calc: the idea is that this is the minimum for high school graduates, not the minimum for college prep or for someone who considers herself/himself pre-engineering or anything extravagant like that. It was the level of math I had mastered by seventh grade at the latest.

[snickelish.livejournal.com]

High school graduation the supposed skill certification and high school graduation the social ritual have become inextricably intertwined in our culture.

This, to me, seems the key to the entire debate. The skill certification and the social ritual are put in conflict, and many people prioritize the social ritual.

[cissa.livejournal.com]

I know that when my daughter was in secondary school, and refusing to do any work, we BEGGED the teachers to flunk her for not doing the work. And they wouldn't. So she learned that doing the work is, in effect, optional.

And she can't do math, even though both of us her parents like math and use it a lot.

I think if her math teachers had given her the F she had earned, her pride would have been tweaked and she might have learned some math. Maybe not- but they sure didn't help, passing her- with good grades even!- when she knew NOTHING.

I'm a metalsmith, and I use math daily- couldn't work without it. When I was teaching, it was really amazing how many people freaked out about having to do even simple calculations that had been spelled out on a worksheet, and to help with which they had a calculator. Honestly- not hard... and pretty important.

Math is not only beautiful in and of itself- but it's key to everything from household budgeting (at one level) and being able to enter some technical fields; it's a shame that so many people cut themselves off, and are cut off, from basic competence.

I know many of my elementary school teachers had little grasp of math or science, and that made them boring. I'm reading now that teachers can be certified as competent to teach- including math and science- without answering one math question correctly on their exams. I think this shows, and it needs to change.

[mrissa.livejournal.com]

Yes. "My friend V's mom," the person I quoted in the subject line, is a grade school teacher who loves math and teaches it well, but she's very rare, as far as I can tell. I know that all of my grade school teachers were of the "this is the formula and you follow it" approach to math and couldn't explain anything beyond that. Secondary school teachers were somewhat better, as they had to actually choose to be math teachers and not some other kind of teachers. But by then a lot of people were already terrified of math, and were already behind in it.

[akitrom.livejournal.com]

Cissa, very rarely does a young woman go into elementary education because she loves math. Typically, it's because she loves working with kids, and secondarily because she likes dinosaurs and storybooks and caterpillars and art.

[fidelioscabinet.livejournal.com]

I did usually did well in math classes, and enjoyed them, but did very badly as a high school freshman, because the woman teaching the class was very bad at teaching a subject she loved and was knowledgeable about. There are so many reasons why math and the sciences are handled badly in our schools (although I have to say that I think we handle English, foreign languages and history just as badly at times--but math and the sciences are harder to fake your way through, and harder to pick up on your own.)

I went to a high school in a small town that had a science and engineering-focused university in it, and so, thanks to parental pressure, these subjects were taught fairly well. Public demand has a definite effect on how well things are taught, and people who have the expectation "My kid should be able to learn these topics well enough to get into MIT" are in a really good position to shape the argument when dealing with their local schools. Part of the problem is that enough parents aren't really sure why their children need to learn these things well, and so aren't in a position to make useful arguments about why the schools aren't doing this as well as they could, and how to do it better.

[mrissa.livejournal.com]

Picking up on your own is something I've watched people try to do. It's possible with math. But it's not always easy, particularly when people have learned a fear of math as well as not learning how to do it. I once spent half an hour with a student who could not understand that if T - W = 0, T does not in general = -W. The basic algebraic steps were beyond him. He was trying to learn physics (granted, in a class for the non-major, but still). I was glad to be a gatekeeper preventing him from going farther in pre-med until/unless he learned math, because that level of math ignorance is not okay in a doctor. But it was ridiculous that he'd gotten that far in the first place.

[mkille.livejournal.com]

Apparently this problem (passing math classes without actually learning math, or at least, not retaining what is learned more than a month after the end of the year) is a massive headache for community colleges (http://suburbdad.blogspot.com/2009/01/remedial-sequences.html). Among the other many practical and moral implications.

[mrissa.livejournal.com]

Four-year institutions as well. I have friends who are on the front-lines of this problem in math and in the humanities.

It really is one of those, "You can do it right the first time or keep paying and paying to do it wrong," situations.

[dichroic.livejournal.com]

I believe that math-related learning disabilities are real. I absolutely do. I do not believe that irremediable math-related learning disabilities are as prevalent as people who were taught math very, very badly, often by people who did not themselves know how to do math.

This is a tragedy too, since so many of the people in the second group really have no way of knowing that is the problem, and think of themselves as having inborn disabilities.

There are people who will persevere in learning something important (or finding workarounds) despite inborn disabilities (like my dyslexic husband, who turns out perfectly proper writings for work) but it's very very hard. I think there might be a lot more people who would be willing to put out the effort to learn something where they have the ability but were badly taught - but only if they know that's the situation.

[eposia.livejournal.com]

Math was my favorite subject as kid. I was in magnet programs from elementary school on and had finished all available math classes by Jr year of high school (including calculus). But it quit being my favorite subject in 8th grade (supplanted by the science classes) after an abysmal Algebra teacher made our class's lives hell. The death blow to my math enjoyment came in first year of college, where my college calculus teacher was teaching the same material I *had already learned* two years previously and teaching it so very badly that I found myself with less understanding of the concept by the end of the class than I had had in high school.

I had some crappy English teachers, and never had a good history teacher until college, and in neither of those areas did the bad teaching do nearly as much lasting damage to both my interest and further ability to easily learn the subjects as did the two bad math teachers. I agree with most of the expressed problems with standardized testing, and I'm certainly not bashing all teachers as I have great respect for those fine soldiers in the learning trenches, but I definitely think that the ways we teach math could use a serious overhauling in many, many cases. Also, those who hate both math AND young people should perhaps consider other career options...

[mrissa.livejournal.com]

I was greatly relieved when I turned up at college and blew through the calc test-out exam and then said to my advisor, "I also did calc 2," and he said, "Fine then," and routed me straight into diff equs. It said good (and accurate!) things about our advisor/advisee relationship for the four years to follow.

I keep repeating this because it bears repeating: nobody who does well in geometry and algebra should do badly in calculus, because it's not the "shift" point in addressing math differently. The fact that so very many people who do well in geometry and algebra are completely baffled by calculus is evidence of stunningly bad teaching.

[dd-b.livejournal.com]

Algebra and geometry are necessary for plumbers, carpenters, landscapers, gardeners, farmers, masons / cement workers. Also drivers ("How long will it be until we get back to Randy's place in Lakeville?"). Anything anywhere near construction or any form of transportation. Anybody who owns a power strip or an inverter. Anybody involved in medicine (including pharmacists). Athletes. Auto mechanics.

And anybody who runs a pizza restaurant. We had to explain to them that they really shouldn't charge us twice the cost of an 18" pizza for a 36" pizza.

Lots of this stuff came up casually over the road-trip this weekend. Math (not just arithmetic) is basic to lots of ordinary every-day life.

[scoopgirl.livejournal.com]

After I moved from Ohio, they put in a statewide exam to get your diploma. To get the diploma, you have to be able to do 9th grade English, math and civics. You first take it in 8th grade, and your scores can count if you pass. You take it again in fall of 10th, when everyone in theory should be able to pass it. If not, you get a final chance the start of your junior year. If you still haven't passed, you are on track to get a certificate of attendance, not a diploma. UNLESS, you pay to take the exam elsewhere.

Not surprisingly, the vast majority of kids can pass in 10th grade, even the math (considering it's basic math, algebra and geometry).

Interestingly, though, there is a class for those on the attendance track, called Consumer Math, that they must pass. It teaches you how to get a loan, how to invest in basics like CDs, money markets and a 401K and how to properly budget your income. Sadly, I think *this* is the class every kid needs.

[moiread]

God, yes. In my first year of high school, I was saddled with a math teacher who taught mostly by talking. I can't imagine how that would be helpful to almost anyone trying to learn math, because WHAT ABOUT THE COMPUTATIONS, WE HAVE TO SEE THEM, but especially so in my case because I have a severe auditory learning disability. I really, really struggle to retain anything I have to process from that medium. I just can't keep it in my head at all. It's like water in a sieve, and it drives me insane. I was a middling to above-average but not brilliant math student previously, and then I got that teacher, and suddenly I was failing miserably. When I approached him for extra help, with the specific request that he find another method of teaching it to me, he refused. When I went to the guidance office to be transferred to another class, it turns out the only other class available to me (and that was already going to require switching some other classes I was not happy about having to change) was... also taught by the same math teacher. Because there were only two. So instead I opted to be dropped down from the pre-university stream to the no-intentions-of-post-secondary stream, because that's where they had room, and to re-take the unversity-bound class over the summer at another school.

It turns out that I really, really loved the lower math class, and not because I aced anything put in front of me. I loved it because everything was a practical example, everything had a use case I could relate to, and it was all incredibly useful things I never got out of the more advanced class. Like oh, gosh, so this is how interest rates work! Not only did I find it infinitely more useful, but it put me in a much better stead to take the advanced class over again during the summer. I got along much better when things were presented as real-world scenarios (and it proved to me that there is no doubt about the real-world applications of math) instead of lofty abstracts with strange names and lots of funny symbols.

I am a Canadian from Ontario, not an American from Minnesota, but I still wish they could reverse that particular tendency. We should start with the practical stuff for everyone, and then add onto it from there.

[rmnilsson.livejournal.com]

After spending a lot of time in Educational Psych classes, I have come to the following personal conclusions... Math is a toolset.
Arithmetic is a lever - basic, but very useful to everyone on a daily basis.
Calculus is the big floor-mounted bandsaw - most people don't need to use it in their lives outside of class, but it makes short work of problems that are very difficult to solve in other ways.

So learning math has is not only about learning to operate the tool, it is also about learning when to use which tool.

Part of the difficulty in teaching math is that education classes(at least as of about 6 years ago, when I left grad school) tend not to focus on how to teach students to identify what tool to use when. For example, a sample of American primary math teachers had great difficulty coming up with a non-classroom example of when one would use division of fractions (e.g. 1/3 divided by 3/4). And college math courses aren't going to cover that material.

This is also part of the difficulty of testing students' math learning - there are two parts, and it's difficult to test them both, because the wording of the test can lead different students to attempt to apply different tools to the problem, particularly when dealing with subcultures within the same general culture. This is, in my opinion, part of the reason why the performance of black students on standardized tests underpredicts their ability to use math. And part of the reason why people fear having standardized tests to determine whether students can graduate.

Personally, I have found that I can do very well in math as long as I can see how to use it. I don't do so well at math when I don't see the application. Either way, I can pass the test just fine. But if I don't see the application, then I won't remember it 6 months later.

[mrissa.livejournal.com]

They couldn't come up with a non-classroom example of division of fractions? Seriously?

What Is Wrong With Things, right there.

I think you're absolutely right, though, about math as a tool kit, and how it's not well-taught in that context.

[careswen.livejournal.com]

I used basic algebra today while modifying a crochet pattern. I thought of your post.