A friend of mine is a special ed teacher at a highly selective science-oriented magnet school. She has observed a number of incoming freshman who are unable to handle beginning (9th grade) algebra. I'm guessing that some (most? all?) of them have no inherent math disability, but have merely been poorly instructed (most come from elementary schools that use Everyday Math/Investigations and from middle schools that use Connected Math).
Anyway, when she asked me what I knew about math remediation programs that might help prepare these kids for algebra, I realized I had absolutely no ideas and should turn to ktm for help. Any suggestions?
She should contact the math department at the local community college. They generally have a lot of experience with math remediation—they may even have a number of teachers who do nothing else.
ReplyDeleteThe book Basic College Mathematics by Margaret Lial is used by community colleges for arithmetic remediation. It also contains some introductory geometry and algebra. It is an excellent text, and wonderful to use with older kids as it is targeted at adults and does not seem babyish.
ReplyDeleteI've heard good things about the new-ish DI program, Essentials for Algebra -- it appears to be designed for exactly this population. I looked into it for a student I was considering tutoring and it also comes highly recommended by a couple of math tutors I know.
ReplyDeleteHere's a link to the
placement test which tells you whether the student is at the appropriate instructional level to benefit from the program.
You can often get this (and other DI programs) used on sites like Ebay; as long as you don't write in the books you can sell them for about what you paid for them (I use plastic page protectors and have the student write with whiteboard markers).
. The materials you need are the 2 Teacher Presentation Books, the student textbook, and the student workbook (the teachers' guide is not essential).
Here's how one website describes the program:
The typical student who qualifies for this program is greatly behind in understanding math...is completely confused about fractions, does not understand the relationship between fractions and whole numbers,the operations of combining,multiplying and simplifying fractions, or the relationship between fracions and division..
I've used some of the other DI remedial math programs (such as the ones on ratios, percents, basic fractions) aimed at this age group and found them clear, well-laid-out and effective. I probably have some more information on this program saved on my computer at home if needed.
The problem is "merely been poorly instructed" very likely means "has been taught false things for many, many years, and understands not one whit of what it is supposed to mean."
ReplyDeleteThey need to unlearn and relearn arithmetic and fractions and decimals to remediate successfully.
These are the bulk of the kids at the schools where the kids can't pass proficiency on state exams in grades 6, 7, and 8. I have seen these kids in class after class and heard of even more of them. They can be quite gifted, even. But they don't understand
any principles. They think the right answer is whatever the teacher says it is.They can't even get the procedures right because they can't remember them correctly, and that's because none of them mean anything to them.
These are kids who don't know they can't just randomly drop the zeroes in .0308 because that's what they think their teacher told them. They are kids who think that if you have 5/8, then 5^3/8^3 is an equivalent fraction because you "do the same to top and bottom." They don't know what it means if you told them (x,y)=(2,3) and them asked for (y, x) and just come to a full stop. they are the kids who think 9/8 can't exist.
I know of no good remediation programs, because they all require teaching the same material that almost no one understands in the first place. And the books are so wretched.
MSMI has been asked repeatedly now to teach such material to kids or to write such a curriculum for teachers to use remedially. But it isn't as if you can just do that over night and do it well.
MN requires algebra in 8th grade, so this remediation takes place here in elementary or middle school. With the schools doing such intervention with MSMI, I teach the teachers using Wu's book predominantly, though simplified. Then I have them reteach their students fractions, decimals, number lines for positive and negative numbers the way they were taught, but using Singapore math problems from 3B forward.
while GSW/OP is right that community college instructors do remediate this material, it's probably with a very different goal than a science-oriented magnet school goal.
the CC is not preparing kids to take more math on a STEM track, they are just trying to got their students able to pass the math needed to work some bookkeeping, compute the interest on a bank account, do the basic stats class required for a Lib arts or soc Sci major. and likely, their teachers aren't trying to fix major misconceptions and undo fallacies.
the kids you are talking about cannot just be taught "do it this way, here's the formula." They MUST see taught why it works, because they cannot possibly make sense of calculus just by doing procedurally with no comprehension.
I know nothing of Essentials for Algebra, but the other DI math materials would not possibly prepare kids for a stem oriented magnet school, so i'm skeptical.
At this point, I would advise a school to roll their own curriculum after having their teachers read Wu.
Thanks for all your feedback, which I will pass along. I'm not sure to what degree the school thinks of itself as preparing its kids to take more math on a STEM track. While it is a science-oriented school, it calls itself a "science leadership" school. Apparently the teachers do create their own curricula...but the school is highly project-based and I'm not sure what the reigning philosophy is there as far as math instruction goes. In other words, my sped friend may be somewhat on her own re math remediation.
ReplyDelete"I'm guessing that some (most? all?) of them have no inherent math disability, but have merely been poorly instructed (most come from elementary schools that use Everyday Math/Investigations and from middle schools that use Connected Math). "
ReplyDeleteYou guess wrong. It may not be an "inherent math disability", but the delusion that kids who start algebra without a basic knowledge of math were poorly taught is utterly unfounded. I teach algebra remediation, and rest assured, the kids learn it and forget it, learn it and forget it, over and over again. It doesn't matter what method you use.
Nothing is as foolish as promoting educational policy based on the belief that kids who don't learn just haven't been taught. No, they just don't have the cognitive ability to master the material. It's hardly complicated.
Cal,
ReplyDeleteI agree with you that delusions are generally unfounded.
At the same time I think it deluded to insist that kids who start algebra with insufficient preparation couldn't possibly have been poorly taught. We're talking about a highly selective magnet school, remember (one that selects its students from those in the top percentiles on statewide standardized tests). We're talking about a city that uses Investigations, Everyday Math and Connected Math, and elementary school teachers who need little preparation in math in order to become certified.
Which is more likely: that kids scoring in the top quartile on state tests are incapable of mastering pre-algebra, or that a combination of Reform Math programs and ill-prepared teachers failed to give them the opportunity?
Perhaps your students are different. But from what you're saying about them, it sounds like you, and more importantly they, would be much better off if you stopped teaching them algebra remediation. Why do you bother?
The best math instruction is not going to be enough for a child who lacks the cognitive ability to do algebra 1. However, poor math instruction can absolutely prevent students from reaching their maximum potential. We can't change innate ability, but we have a responsibility to make sure everyone get the opportunity to make the most of their potential. The "fuzzy" math programs in vogue today aren't doing that.
ReplyDeleteCal,
ReplyDeleteI have met kids who IQ test as highly gifted with the errors I describe in this post and others. They get placement in gifted schools, and they have no learning disabilities. These kids aren't failing to manage algebra 1 because I'm deluded. They are failing to manage because they have been taught false things. This is not delusion. these kids can learn and do after they are taught true things.
no doubt there are some students who can't manage the material of algebra. i don't know what percentage, but i'm talking of fractions and arithmetic. since i now have evidence of kids whose only reason for not managing the material was bad instruction, i know bad instruction can prevent learning.
in a school that had a class of students with proficiency of, say 80% on a state test and now has a proficiency the next year of 40% for the same students, it's not that we suddenly hit the cognitive limit on half of the priorly proficient 11 yr olds. and when a different school of the same demographic population has proficiencies doubling the rates, it's unlikely it's just the students' cognitive limitations.
--based on the belief that kids who don't learn just haven't been taught.
i'm saying kids who aren't taught don't learn. not the same thing.
Cal says, as usual:
ReplyDelete"Nothing is as foolish as promoting educational policy based on the belief that kids who don't learn just haven't been taught. No, they just don't have the cognitive ability to master the material. It's hardly complicated."
It's one thing to quibble with a comment that says:
"(most? all?)"
but quite another to claim that it's all IQ. You are guilty of the same thing you are complaining about. You've never shown any interest in trying to separate the variables. Apparently, the world is defined by what walks into your classroom.
Why don't you carefully explain how IQ should drive educational policy. Is this your "hardly complicated" solution? Do you assume that Everyday Math's "trust the spiral" is a workable substitute? How do you propose to separate good math curricula from bad ones?
Thomas Jefferson High School for Science and Technology in northern Virginia has been experiencing a similar problem.
ReplyDeletehttp://www.washingtonpost.com/local/education/math-and-science-gaps-found-at-elite-fairfax-school/2012/05/30/gJQAmT2s2U_story.html
Any indication this is a problem at more than one science magnet school?
If you'd like a technology approach, I've found having students complete www.Buzzmath.com the best way to be Algebra ready. First 30 licenses are free! It's my pick for a summer school before Algebra or a remediation program for weak students starting Algebra 1
ReplyDelete