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I don't believe in the cream-skimming idea. I've been teaching math for over twenty years and I will tell you this: unless there is some sort of clinical mental deficiency in the person, I can teach algebra to anyone who is willing to pay attention to me, do the work, think about it the way I present it on their own, put in the time, and actually has a desire to learn. I've proven that most anyone can learn algebra over and over again if it's presented to them properly AND they are willing to learn. Over and over and over again, I've taught students who have insisted that they "can't do math" or that they are "no good at math." When they find they CAN, they've pleasantly surprised themselves; but not me. I KNOW anyone without clinical deficiencies can learn this stuff.
And as far as calculus... the calculus concept is doable for most anyone at the typical level taught for science, engineering, and business. It's the algebra that makes the calculus class difficult for many students. Knowing the algebra is the key. And again, anyone can learn it given the time, desire, and thought--preferably with the aid of a good instructor to streamline the process. Folks make it out to be harder than it is. I think typically, they are just not willing to put in the required time and thought. It does take considerable time to learn--something that many people in our Instant Gratification Society have a hard time with. So they convince themselves that they "can't do it." Well, they can. They just don't want to. Nobody is expecting them to come out as Einstein, but they can get this stuff at a functional level. It's not all that unlike the pursuit of any significant skill. You simply have to be willing to invest the time to get good at it. Call it "mindbuilding" which requires mind exercise just as bodybuilding requires physical exercise. The more you think in terms of math the better you get at thinking about it. And that includes most anyone willing to do so.
I don't believe in the cream-skimming idea. I've been teaching math for over twenty years and I will tell you this: unless there is some sort of clinical mental deficiency in the person, I can teach algebra to anyone who is willing to pay attention to me, do the work, think about it the way I present it on their own, put in the time, and actually has a desire to learn. I've proven that most anyone can learn algebra over and over again if it's presented to them properly AND they are willing to learn. Over and over and over again, I've taught students who have insisted that they "can't do math" or that they are "no good at math." When they find they CAN, they've pleasantly surprised themselves; but not me. I KNOW anyone without clinical deficiencies can learn this stuff.
I'll agree with you in general regarding the learning of basic algebra, with the caveat that the student must have minimal deficiencies in basic math (the building blocks necessary for algebra, such as multiplication tables).
That said, cream-skimming can include eliminating students who, for whatever reason, can't or won't put in the effort to learn the material. My point is that the group that Escalante started with was, as far I understand, not insignificantly larger than the group that ended up acing the AP Calculus exam. Call it cream-skimming, tracking, grouping, or whatever you want, the fact is that those willing and capable were separated over time from those that were not. This is a the type of model that many charter schools follow while claiming "miraculous" results. Now of course that's not why Escalante did what he did to help those kids, but it did give outsiders the impression that something was happening that really wasn't. There are some kids that you push and push and push and simply do not respond. Even Escalante left a chunk of them behind.
His biggest complaint was that the movie left the impression that his students, most of whom were struggling with multiplication tables, mastered calculus overnight.
Fact is, Escalante's kids ate, slept and lived mathematics. They arrived an hour before school and stayed two, three hours after school. Escalante drilled them on Saturdays and made summer school mandatory. Some parents hated it, and they let Escalante know it.
I'll agree with you in general regarding the learning of basic algebra, with the caveat that the student must have minimal deficiencies in basic math (the building blocks necessary for algebra, such as multiplication tables).
That said, cream-skimming can include eliminating students who, for whatever reason, can't or won't put in the effort to learn the material. My point is that the group that Escalante started with was, as far I understand, not insignificantly larger than the group that ended up acing the AP Calculus exam. Call it cream-skimming, tracking, grouping, or whatever you want, the fact is that those willing and capable were separated over time from those that were not. This is a the type of model that many charter schools follow while claiming "miraculous" results. Now of course that's not why Escalante did what he did to help those kids, but it did give outsiders the impression that something was happening that really wasn't. There are some kids that you push and push and push and simply do not respond. Even Escalante left a chunk of them behind.
Okay, I can see where you are coming from. Again, from my perspective as a teacher, the key ingredient is willingness. If it's not there, it won't happen. It's the old saying about being able to lead a horse to water, but not being able to force it to drink.
I've seen many math success stories with those who were "no good at math." But in every case, they were willing to put in the time and learn even if they may not have always been so happy in doing so. On the other hand (and I know most all teachers see this over and over), a closed mind on the part of the student is a brick wall (unless it is "opened" somehow). Sadly, it comes down to the idea that if they do not care about their education, I don't have the time to care about their education, either. If they don't care, I don't care. I'll put the time into those who do. I think that's more along the lines of what you meant with the cream-skimming idea. A certain percentage will never learn it--not because they can't, but because the refuse to.
Correct me if I'm wrong, but wasn't there quite a bit of attrition from this "program"? If so, that tells me that there was a significant buy-in necessary from the students, as well. In fact, this seems very similar to the cream-skimming that goes on in some charter and private schools that then turn around and claim to be performing miracles. Makes for a great story, but if looked at only superficially it will present an inaccurate portrayal of reality.
There is ALWAYS a significant buy-in necessary from the students, in order for success to be tenable.
I don't believe in the cream-skimming idea. I've been teaching math for over twenty years and I will tell you this: unless there is some sort of clinical mental deficiency in the person, I can teach algebra to anyone who is willing to pay attention to me, do the work, think about it the way I present it on their own, put in the time, and actually has a desire to learn. I've proven that most anyone can learn algebra over and over again if it's presented to them properly AND they are willing to learn. Over and over and over again, I've taught students who have insisted that they "can't do math" or that they are "no good at math." When they find they CAN, they've pleasantly surprised themselves; but not me. I KNOW anyone without clinical deficiencies can learn this stuff.
I was a kid who thought I "couldn't do math."
I was an honors student who, unprecendentedly, flunked freshman algebra. I failed because I was intimidated, behind from day one, and often spent class in the nurse's office with an upset stomach from nerves. The teacher agreed that if I would attend class regularly, come in after school for help, and show good faith effort in that way, he would not fail me. He failed me anyway. I never did catch back up. I took a summer course to make up the failed course. When I was working one on one with my very patient summer school teacher, I realized that, yeah, I COULD "do math," if presented in a particular way, and being given sufficient practice opportunity - the way I was initially taught it was done in such a way that I was never given sufficient time to grasp and practice a concept until I was solid on it before moving on to the next (as a teacher myself, now, I know that I need to monitor my students for individual mastery before barreling forward...nobody did that for me, and algebra was the only class where it ever mattered). I learned I COULD do it. But I never liked it. Never loved it. Never was interested in it. Never preferred it. I'm functional, but it will never be a big part of my life, outside of what is needed for basic functionality. It's akin to a person who only reads as much as they need to get by. I do think that I was very, very poorly taught math, almost from day one.
When I was working one on one with my very patient summer school teacher, I realized that, yeah, I COULD "do math," if presented in a particular way, and being given sufficient practice opportunity - the way I was initially taught it was done in such a way that I was never given sufficient time to grasp and practice a concept until I was solid on it before moving on to the next (as a teacher myself, now, I know that I need to monitor my students for individual mastery before barreling forward...nobody did that for me, and algebra was the only class where it ever mattered).
Absolutely--and I think this is a key concept that our educational system, in general, doesn't accommodate very well at all. I've had students that literally take 4 hours on a test that most other students finished in 20 minutes. And that is fine by me. I don't believe in timed tests at all and learned from my own experience (as a student and a teacher) that they are counterproductive in many cases. It doesn't matter to me if it takes a student 20 hours to get a concept that takes a "math whiz" 10 minutes. In the end, they both have the concept. I was much that way as a math student. Math wasn't really my strong subject. But I put in the time to understand it. By the time I was nearing graduation, I was literally studying math all of my waking hours. I was "slow," but when I got it, I got it. And I generally did just as well on tests (that weren't timed) as any of the math gods in the classroom.
Speed of learning should not be an issue as much as it is in our system. As you say, folks get rifled through, and no time is taken to let those who can learn it learn it, if they simply need more time to absorb it. It's not any "less learned" if it takes Student A ten times more time to learn than it does Student B. AND, I would conjecture that it has nothing to do with either student's intelligence. I'm reviewing some math right now. I've read the text 3 times now. Eventually, I'll absorb it at my own pace. We don't all learn alike or at the same speed.
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