There is a dichotomy in math education. Some believe that student learn math best by rote, learning rules and applying the. The other believe in using problem solving for student to develop and create their own understanding of mathematics. Remedial math teachers rely on the first technique but research shows that struggling students learn best by the second method so traditionalist teachers are only going to screw you up.
I have taught arithmetic in college and I have hade many students in 7-12 with trouble in basic arithmetic. I almost every case, the students’ problems were because they really did not have a fundamental understanding of place value. Let me ask you this, if I were to write 231 in base-5do you know why base-5 place values are 125, 25, 1? Do you know why that is equivalent to 326? That is the area I would suggest you start.
As I said once as one of only two people in my special ed program already with a regular ed credential, special ed math is like regular ed math but with fewer students.
Special ed math is much like any special ed classes were you work with individual students using their strengths to help support their weaknesses. Algorithms are difficult because while special ed students may understand each individual step, stringing them together is difficult for them. Another big issue is the direct (traditional) instructional pedagogy vs. exploratory instructional pedagogy contraversy is even bigger in special ed where most people in special ed believe direct instruction is the only method that works with students with disabilities. I happen to disagree which sets me at odds with my co-teacher who “instructs” by having students copy down the answers she tells them.
(b) D’oh you’re right. Shows what I get for posting after a weekend of winter camping with the scouts.
(c) That’s exactly what happens because most students don’t think about how place value works like why do place values go 1, 10, 100, 1000. etc. or how 170 can be thought of as 1 hundred and 7 tens OR 17 tens. Putting them in another place value system (I use base-3 in class) dispenses with their current schema and really focuses them on how place value works.
And by the way I’ve done it with students so I KNOW it works.
It’s not really that bizarre a method. Never bothered with it with any kids I’ve taught, but seen it work. As with anything, some kids respond better/worse to various methods.
Changing bases was the big deal with the “New Math” approach of the 50s and 60s. It can work, but with well-trained teachers and only with certain students. Ya know - like pretty much any other teaching technique. I think we need to throw doctrine out of teaching, make sure that our teachers are well-versed and well-supported in every possible approach, and let them apply whatever technique works for any particular student. IMNAAHO we are wasting time and resources with arguments like “technique x is the best/only way to teach kids topic y”. </soapbox>
That might as well be urdu, I have no clue what you said there. People with dyscalculia don’t just have “trouble with arithmetic”, they don’t get it. It’s a learning disability, like dyslexia. Some symptoms. Which two of my three siblings share. Although when I was in school, learning diabilities were largely unrecognized.
If I see,
72
-29
=…?
written down, I can do it in my head quickly but no matter now often I’ve been taught, can neither understand nor retain the concept of “carrying numbers” or whatever you’re supposed to do.
This makes sense - going to school in the 60s and 70s, I was always taught by rote. So if, at age 55, I should again decide to attempt second grade arithmetic, I need to find some a way to learn that lets me figure out for myself what the “mechanics” are?
The idea with older students with changing bases is for them to get a fresh start and throw out their (mis)conceptions about how numbers work because no matter how many times we move colored disks around in the back of your mind you’re thinking 76 + 48 is
1 1
` 7 6
4 8
1 2 4
with no clue what those 1’s mean other than “You carry them.”
I’m aware what dyscalculia is and in fact your response shows exactly what I was pointing out which was that you have difficulty with place value both conceptually and in practice. That being said, working with dyscalculia is not well-taught in sped programs since most sped professors themselves are not familiar with math pedagogy (hence the insistence by many on traditional instruction). In fact, in my moderate-severe pedagogy class, the professor assigned the one lecture devoted to math instruction on a day she was at a conference so it was purposefully never taught. I went through my entire master’s and credential program at at no time ever taught sped/math pedagogy. Everything I know I had to cobble together from my knowledge of math pedagogy and sped theory. On the other hand, I could probably be a language arts teacher with as much as I learned about literacy and reading/writing/oral language development.
If I were to work you, we would need marbles and bags of various sizes so you could see what “carrying” and “borrowing” are all about.
With at least some older students, I suspect it might work to have them imagine (or even act out) exchanging 10 one dollar bills for 1 ten dollar bill, or 10 tens for a Benjamin. Though as we move to an increasingly cashless society, people may be losing their feel for that sort of thing.
The hard part is that our money system is not a pure base 10 because of nickels, quarters, $20 bills, etc. That is part of what makes it confusing because although many people can look at $20 as 2 x $10 it just doesn’t work like that for someone who sees a $20 bill and not two $10 bills.
This is a great thread. Chiroptera, I’d never heard of dyscalculia, thank you for the education. It would be so cool if Saint Cad could up with something to help you.
Saint Cad, I’m taking an online class and am having some trouble with financial probability. I’m not going to ask you the answers to my quiz questions, but do you have any familiarity with this if I were to run a scenario past you? It’s pretty basic, but I’ve been hitting my head against the wall for two days.
I think I can help Chiroptera but it would have to be something more than what I can answer in this thread. If not in person then maybe via Skype but that is up to them.
With Chiroptera’s Dyscalculia, the trick would be a constructivism style that has them doing math rather than learning math. The brain would develop its own rules for mathematics but since the brain developed the rules and assuming that the rules are mathematically valid* she would be able to do the math. This is at odds with many special ed teachers that would have her working many problems and explaining the steps slowly to her which will not work. It should be noted that many sped teachers (and many regular ed teachers) are not comfortable or familiar with progressive math pedagogy.
Most sped teachers do not have a good enough grasp of math to know that if a student states a mathematical principle in a non-standard way whether or not it is correct.
This technique strikes me as so unlikely to work that it belongs in the category of things I would have to see to believe.
The many blunders you made in post #21 reduce the credibility of your claim to know what works, and so does this from post #30:
Our monetary system most certainly is a pure base 10, no ifs and or buts about it, and for you to say otherwise is a another indication that you might not be as well-equipped to teach math as you should be.
You say that because you understand how base-10 and decimals and our money system works. If you were to take someone that doesn’t understand base-10 how do you explain nickels and quarters and $20 dollar bills. If you say you don’t then is your student supposed to forget they exist that the next bill after $10 isn’t $100? If you explain that $20 = 2x$10 then considering that is what they’ve been taught their whole life and they still don’t understand place value that you saying it again will make the difference?
Just curious, what is your experience in math pedagogy?
Saint Cad, thank you! Marbles and bags sounds right about my speed, and so does a purely constructivist approach. I’ve been thinking of taking up a “brain training” hobby and once again, trying to find someone who will tutor me in basic arithmetic. Or math classes for adult dummies at a community college.
As a data point, while every single one of the symptoms I linked to above describes me with uncanny accuracy, I can add and subtract in my head quicker, I think, than most people. I was a bartender for five years (through part of high school and uni) back when dinosaurs roamed the earth and cash registers didn’t figure out change. On the busiest, most hecticc nights I was proud of the fact that my till was always dead-on correct. I play games with myself, like mentally adding up all my grocery costs when I’m shopping, or balancing my checkbook in my head, then double-checking with a calculator and am absurdly pleased when I get the total spot on.
For a while I helped teach functionally illiterate adults in a literacy program. I remember being very impressed by all the ingenious coping and compensating strategies most of these people had come up with so they could navigate their lives without knowing how to read or write. I’m sure most people who have a terrible time with numbers generally do the same thing; I certainly do.
Do you feel that it takes a different “breed” of teacher to teach math?
I’ve always sucked at math. My grandmother has always insisted that I simply never had a good math teacher, and if I’d had one, I’d have been able to catch on. Whether she’s right or if I’m just truly dumb when it comes to math (it’s probably both) I don’t know, but I can confidently say that none of my math teachers were particularly good teachers. They just weren’t – I’m not hatin’.
I was discussing recently the schooling of primary school teachers. Sweden does very well as does Singapore, I think. The difference (or one of the differences) is apparently that their primary school teachers are extremely educated. In Singapore apparently they have PhDs! And not in “teaching”, but in their actual subject matter.
My first reaction was that that is ridiculous, that it misrepresents what is required of primary school teachers. I’ve done some work testing students of primary schools that required me to visit many different schools. I saw so many teachers, and huge differences between great teachers and not-so-great teachers. I found it hard to see how having a PhD in a the field of mathematics would make someone a better teacher for young children. But apparently Sweden and Singapore show us this is true.
What do you think? Super-education for teachers to fix the school system? You sound pretty educated yourself, what is your background & training?
I do for one important reason - math is the one subject it is socially acceptable to fail.
Unlike the other subjects (except maybe some of the upper-lever science classes), students are reinforced by home, friend, society and yes non-math teachers that not only is math hard but that it is OK to fail. So math teachers are teaching students that:
Do not want to be there
Have decided that it will be difficult to the point of beyond their capabilities
There is no reason to try because if you fail, so what?
Teachers in most subjects have at worst a small minority with two of these characteristics but few with all 3. A math teacher has most of their students with all 3 characteristics.
Incidently, a Ph.D. in math ed I was listening to at University of Warwick did his dissertation on society’s acceptance of the negative reinforcement of maths.
I need to find some a way to learn that lets me figure out for myself what the “mechanics” are?