Jumping in to state that this grade difference isn’t diagnostic of anything, at least without more background.
Just for starters, it is entirely possible that the essay in question didn’t properly respond to the high school assignment prompt, but did a pretty good job of responding to the (as yet unseen) college assignment prompt.
Of course, being on the lookout for possible issues with study results like these (and the quote is reporting study results, just from a very, very small study) is something I learned in my courses on study design in college—courses that were grounded in a thorough working knowledge of statistics.
Statistics, I stress, that I would have been unable to understand without a thorough grounding in at least basic mathematics (read: algebra).
“Perhaps it would be better to have a very good “household finance” course instead of Alg II for some kids where the teachers would delve into credit card debt, mortgages, etc?” OK, please explain how you can properly teach credit card debt, mortgages, etc, without algebra2? (I can tell you what would happen with this, because it’s done in our school. They never explain interest or exponential growth. Equations are never presented. It’s presented as a mysterious black box that you plug into a calculator, leaving the students with no understanding of what’s really going on.)
How many people do you know who need an accountant to file a simple tax return (one wage earner, a mortgage and a few charitable deductions, plus a thousand dollars or so in interest or capital gains?) How many people do you know who can’t figure out whether to refinance or not? (aah, closing costs. So hard to amortize the 3K over the life of the mortgage assuming you’re going to stay in the house until you pay off the loan). How many people buy their kids renter’s insurance when they go off to college to “protect” against the loss of a $500 laptop- even when they bought the laptop on a credit card which already has a built in “loss, damage or theft” policy?
I’m with Mathyone here. And just ask the carpet folks at Home Depot next time you are there about the number of people who spend hundreds of dollars on “extra carpet” rather than admit they can’t measure a rectangular room and figure out square footage…
One thing I’ve noticed is that folks on both sides of the issue (and I include myself here) seem to be relying on anecdotal evidence rather than data. Since I am off for the summer, maybe I can do some digging.
Also the nature of this forum is decidedly more experience-driven than data-driven, and a lot of this is about sharing stories. I try to offer data where it helps but really, most of the time it’s better to just give more qualitative arguments.
I am with @blossom and @NeoDymium. [Full disclosure: I have a PhD in an applied math field]. Understanding the scientific method is helpful even if you don’t become a scientist. Understanding how studies are designed and statistics are calculated is important to making sense of the modern world. I’d say that interpreting data and making decisions under uncertainty are absolutely among the key tasks people undertake in life. Many people do it badly. My son had a bumper sticker on his door to the effect that lotteries are a tax on the mathematically challenged (though I don’t think it was quite that polite).
More importantly, we have entered an era when most of the returns to education are skewed to people with a certain set of mathematically oriented technical skills. It is not clear when that era will end. Why would we not try to help all of our kids have the technical skills to adapt to a changing job market. Even if you are doing other work, when software arises that can automate what you do, it would be good to be the one setting up the software in companies rather than the displaced former employees whose skills have become superfluous.
To @mstomper, I don’t think the above arguments are anecdotal. But, the anecdotal arguments made by 50+ year olds that either they or their co-workers or friends did well despite not knowing algebra are backward-looking arguments that may no longer be applicable today. In many cases, those folks wouldn’t get in the door today, let alone be promoted to positions of responsibility. Quite a few companies are hitting a stage in which detailed statistical knowledge of customers or of aspects of processes becomes central to the profitability of the business. I’ll defer to @blossom, who hires folks for a living.
When we were shopping for mortgages, the broker was astonished when we worked out which option was a better deal for us. He’d never seen anyone do that before.
In the interest of letting non-STEM majors out of onerous math requirements to study what they enjoy, some colleges use math placement tests consisting of a simple question: “What do you get when you put two and two together?”
The professors always groan when they see how many write down “22” as the answer.
In the interest of having some idea of what I’m talking about, I’ve been reading up on the topic. One common thread that I see is that the big problem is that Algebra isn’t taught very well in our schools. Fixing that is much easier said than done. How many people, regardless of how well they know the material, can teach it in a completely different way than they themselves learned it? Until that’s worked out, I’m afraid little progress will be made. It seems we are basically saying “you need to master this even though we don’t have anyone who can teach it the way you need it to be taught for you to be successful. Also, no excuses.” Can we continue to criticize the way math is taught on one hand while demanding that students who aren’t getting it take it anyway? That seems like backwards thinking to me. Unfortunately, my experience working for a large urban school system tells me that kind of thinking isn’t uncommon in the education world.
As far as my difficulty with math being more of a problem in today’s world, I was constantly told that failure to learn a would cause big problems for me later. I won’t say that it never did, but the warnings of impending doom usually didn’t come to pass. I wish I had been taught better, but it didn’t happen. I’ve always tried to make the most of what I had. Also, my difficulty with algebra wasn’t passed down to our sons. It certainly wasn’t the torture for either of them that it was for me, and the oldest actually likes it.
That’s either a trick question or a badly phrased one. If somebody asked, “What do you get when you ADD two and two together?”, sure, four is the answer. But the phrase “PUT two and two together” makes it sound like you’re “putting” two digits next to each other.
Definitely an issue. I can’t really give you an obvious solution since even the experts haven’t really been able to solve that one. The issue of US grade schools being ineffective at teaching math (among other subjects, to be fair) is a large issue with many causes and no easy solution. Lack of parental support is one of the big issues, and one of the hardest to overcome…
I would say yes, we should require students to pass subjects even if they don’t really agree with how it was taught. It doesn’t diminish the importance of the skill they have to learn. Though perhaps, those who have no interest in pursuing any form of advanced education in the first place should be able to receive a high school degree as a terminal degree (in the sense that, if they wish to go further then they will need to take remedial classes in community college) without taking algebra 2. For the college-bound, they really should not be able to go without algebra 2, even if they want to pursue a definitively non-mathematical path.
It’s like not knowing how to spell, or being a bad writer. Sure, you’ll be able to get by without it and perhaps have a good career outcome. But it’s always going to be a gradual, persistent limit that diminishes what you are capable of accomplishing. It gives you a very notable blind spot in your abilities that, over the years, becomes increasingly difficult to correct, because very few people really take to elementary education in their later years unless they absolutely have to. Being a student is tough.
I hope the day comes when every student will be taught what they need to know in a way they can actually learn it. That is, of course, a tall order. I speak from experience when I say that unsuccessfully trying to learn a subject can be excruciating. It goes beyond unpleasant for some of us. Many times I flung my algebra textbook across the room in frustration. In an earlier era I probably would have dropped out, since I never liked school anyway. As it was, my ability to skim and summarize helped me graduate from college cum laude and my ability to quickly locate and evaluate information (and teach students to do the same) has made me an effective librarian. Obviously the thought of someone with similar issues being held back today is a sore spot for me. If they can succeed despite a substandard math background more power to them.
I mentioned this sorta in passing upthread. However, reacting to math not being taught well by claiming that this means math simply shouldn’t be taught is simply an absurd leap of (il)logic.
I’m not saying it shouldn’t be required. If we’re going to make Algebra 2 a graduation requirement ( I think it is in our county, but tha that hasn’t been an issue for us) we need to be able to make sure everyone has the opporunity to learn it. If that isn’t accompished, it seems to me that the options are to have a lot of students fail to graduate or dumb the class down beyond recognition. Honestly, how many students are going to gravitate toward careers requiring mastery of subjects that drive them to tears? While I’m sure it can and does happen, I would wager that it’s just as common for someone to succeed despite not mastering subject matter everyone “knows” they will need. Even in elementary school I tended to tune out when I heard the words “everyone needs” used together. While it would sometimes be accurate, it was often a sweeping generalization. Not as often as “no one needs”, but often neverthleless. I also don’t mean to imply that students shouldn’t have to take any classes they find difficult. But classes that are almost unbearable because no one can figure out a way to teach the material to that particular student? Many students already hate school enough as it is. There’s got to be a way to find a balance. We’re not talking “no one needs anything harder than elementary arthmetic” vs. “everyone needs precalculus”, after all.
FWIW, my state requires 3 years of math for graduation, with at least most of the urban school districts in my state requiring Algebra 1; several of the rural districts do not mandate any particular level, however.
I’m absolutely fine with Algebra 2 not being required for graduation. I could have graduated with just “General Math”, but I didn’t consider doing that. I actually did ok in Geometry. I learned during some of the reading I did today that having trouble with either Algebra or Geometry but not both is actually pretty common. Our younger son struggled a bit with Geometry but made A’s in Algebra 2 this year. Algebra was my mom’s best subject (she was valedictorian, so she actually did well in everything). My siblings also had few problems with math.
I found it interesting that lack of success in Algebra doesn’t necessarily stem from not learning basic arithmetic well enough. One of Hacker’s critics wrote that being good at basic calculations can actually make it harder to learn algebra. I can certainly calculate in my head, so that resonated with me. Someone also compared not learning algebra to trying to play music without learning to read it. I do that too, although I do have a rudimentary knowledge of musical notation. When I played with my wife, who is classically trained, looking at the music was actually and impediment. When I just trusted my ear I did fine.
I’m sure I won’t convince anyone that I know what I’m talking about here, but I’ve learned some things I didn’t know before searching for background information.
@mstomper , my sister was similar to you when she studied music, she pretended to know how to sight read, but in reality she was playing by ear. She did much better (and sounded much better) that way. But I suppose that if she had continued to the highest levels that her deficit in sight reading would have become a big problem.