I am looking at the Kahn discussion from the outside since I have been out of the classroom for several years. I admit my first look was one of dissapointment as it does appear to be procedural. It does a good job of procedural, however. They seem to get the math right. Were it riddled with errors, it would deserve severs criticism.
I am once again impressed by P.J.'s take on this and it got me to thinking about print paterials that are similar.
I am willing to bet, if I beleived in betting, that most of you who are over thirty posses(ed) copies of Schaum's outline for something. Calculus was a big seller. There was not much more than worked out examples, but many students found tham very helpful. I suppose they still exist. They served a purpose. I think there was a similar product for novels, Cliff's Notes, I think. Cliff's Notes presented a summary of books like War and Peace in thirty pages. This was certainly not the same as reading War and Peace, but it did help some students wade through the novel and keep track of who was who and what was going on. Scahum's did the same thing for math and science. No one that I know ever used one as a replacement for a textbook, but thousands of students learned important procedures from them.
Am I too far from being accurate to say that Kahn Academy presentations are a digital version of Cliff's Notes/ Schaum's outline, or am I missing something important?
By the way, I found Scham's usefull as a source of worked out examples. I could give my students one of their problems to work without having to create one and work it out to makes sure it "worked out nice".
Wednesday, March 20, 2013
Tuesday, March 19, 2013
What value Khan?
It's almost become a party game among my math educator friends to talk smack about Khan Academy. "The lessons are just procedural!" (not always true--I've seen some conceptual explanations). "There's no effort to build in the Standards for Mathematical Practice!" (Mostly true.) "Some lessons reinforce common underlying misconceptions." (I haven't seen them, but it's plausible.) And so on.
What follows is an open letter to those friends of mine -- and superstar math educators around the country -- who take these positions. I don't think they're wrong. But they are short-sighted. Read on to find out why.
Friends--
At the risk of stating the obvious, you aren't run-of-the-mill math teachers. Of course you can envision--indeed, give daily--lessons that are more in-depth, challenging, authentic, inquiry-based, etc., than Khan Academy. Indeed, I would be shocked if you couldn't.
But that's not the question. Khan Academy wasn't created for yourstudents. It was created for kids whose teachers, in many cases, don't even know the content, much less how to present it clearly or explain it well. Have you been to the elementary schools in my district? Because (as many of you know) something like half the freshmen who come to my school can't use a protractor to measure an obtuse angle --- they tell me it's 61 degrees or something cockamamie like that --- and they TOOK A TEST to get into my school (indeed, the cutoff score for my school is over 800 out of 900 possible points; we rejected more than 2000 kids out of the 2400 who applied). Those kids will get more effective instruction from Khan Academy than they can get in a regular classroom, because right now they aren't getting effective instruction in their regular classrooms, period. (I'm not blaming anyone in particular here, simply making the tautological claim that instruction that doesn't result in kids being able to do the things they are being instructed in how to do is, by definition, not effective.)
It works for other kids too: my daughter was far ahead of her class last year, and for the first half of the year did worksheets in the back of the room. For the second half of the year, she and two friends got to go on Khan Academy and pick their own lesson every day, and she grew more (as measured by NWEA/MAP scores) in that semester than in the previous 1.5 years combined. And she got about a quarter of the way through a standard Algebra I course.
Finally, I'd say this--about flipped classroom stuff generally and KA in particular. Right now, I'm cooking up a pot of Cincinnati Chili (mmm...can you smell it?). It's delicious, nutritious (yay low-fat turkey!), and my kids love it. But there's a diner down the street from my house, and any day I want, I can go there and get a reasonably tasty, reasonably healthy meal at a reasonably low price. And so every week or two--when I'm too tired, or we have nothing in the refrigerator--we go there for dinner. It's not Tru, or Topolobampo, or any of the other great restaurants Chicago is known for--but it's a reasonable way to get fed once in a while. I think KA and other online videos are like that: not as good as the best (although maybe if you watch the first lecture of the Udacity physics series, on Eratosthenes' measure of the circumference of the earth, you'd be surprised). But KA delivers reasonably clear, correct instruction to people who might not otherwise have access to it. Friends who have expressed skepticism about the "All Khan, All the Time" approach: I agree wholeheartedly. Let's give our kids a balanced diet of different kinds of instruction and different ways of thinking about problems. But I don't think that's a reason to trash on Khan altogether.
At the risk of stating the obvious, you aren't run-of-the-mill math teachers. Of course you can envision--indeed, give daily--lessons that are more in-depth, challenging, authentic, inquiry-based, etc., than Khan Academy. Indeed, I would be shocked if you couldn't.
But that's not the question. Khan Academy wasn't created for yourstudents. It was created for kids whose teachers, in many cases, don't even know the content, much less how to present it clearly or explain it well. Have you been to the elementary schools in my district? Because (as many of you know) something like half the freshmen who come to my school can't use a protractor to measure an obtuse angle --- they tell me it's 61 degrees or something cockamamie like that --- and they TOOK A TEST to get into my school (indeed, the cutoff score for my school is over 800 out of 900 possible points; we rejected more than 2000 kids out of the 2400 who applied). Those kids will get more effective instruction from Khan Academy than they can get in a regular classroom, because right now they aren't getting effective instruction in their regular classrooms, period. (I'm not blaming anyone in particular here, simply making the tautological claim that instruction that doesn't result in kids being able to do the things they are being instructed in how to do is, by definition, not effective.)
It works for other kids too: my daughter was far ahead of her class last year, and for the first half of the year did worksheets in the back of the room. For the second half of the year, she and two friends got to go on Khan Academy and pick their own lesson every day, and she grew more (as measured by NWEA/MAP scores) in that semester than in the previous 1.5 years combined. And she got about a quarter of the way through a standard Algebra I course.
Finally, I'd say this--about flipped classroom stuff generally and KA in particular. Right now, I'm cooking up a pot of Cincinnati Chili (mmm...can you smell it?). It's delicious, nutritious (yay low-fat turkey!), and my kids love it. But there's a diner down the street from my house, and any day I want, I can go there and get a reasonably tasty, reasonably healthy meal at a reasonably low price. And so every week or two--when I'm too tired, or we have nothing in the refrigerator--we go there for dinner. It's not Tru, or Topolobampo, or any of the other great restaurants Chicago is known for--but it's a reasonable way to get fed once in a while. I think KA and other online videos are like that: not as good as the best (although maybe if you watch the first lecture of the Udacity physics series, on Eratosthenes' measure of the circumference of the earth, you'd be surprised). But KA delivers reasonably clear, correct instruction to people who might not otherwise have access to it. Friends who have expressed skepticism about the "All Khan, All the Time" approach: I agree wholeheartedly. Let's give our kids a balanced diet of different kinds of instruction and different ways of thinking about problems. But I don't think that's a reason to trash on Khan altogether.
Sunday, March 3, 2013
What's Wrong With Grade "Inflation"?
At dinner last night, I was talking to a friend involved in education, and she was pressing me hard on what she perceived to be grade inflation at my school. I could have argued the facts more vigorously: the kids she meets are applicants for an ultra-elite college (she's an interviewer), so when they say "I'm getting A's and so are my friends," that's hardly a representative sample of the class. But I admitted that our bell curve is centered on a B--probably a high B--rather than on a C. And then we started talking past each other: her interpretation seemed to be that, because our kids are really smart and do their work, our attitude was something like "They probably deserve A's, so why not just give them A's?" Her response to this hypothetical motive was to ask me "What do you do to differentiate students?"
In fact, it's more complicated than that, and at 24 hours remove, I feel more clearly the need to challenge the entire premise of her argument. (And, to be fair to my friend, this is a common argument. So even if I've misattributed it to her, it's an argument worth discussing.) You see, my goal isn't primarily, or even partially, to differentiate students. I understand that that's something colleges wish I would do, that the entire college admissions system depends on using grades (and test scores) as differentiators. But I'm a teacher, and so my goal is, primarily, to teach. And at some level, that's the opposite goal.
At the beginning of my course, I have to figure out two essential questions. The first--really the a pair--looks at the present and immediate past: what do my students know and what can they do? The second pair looks towards the future: at the end of my course, what do I want my students to know, and what should they be able to do? If I'm waxing philosophical, I add a third essential question: ten years from now, what do I want them to retain of the experience of having been in my class?
Once I've articulated my standards, students who meet those standards get good grades: A's and B's. In fact, when my students get mostly A's, I generally feel like I've done a good job: it means that I've gotten most of my students to master all or almost all of my standards. When my students get C's, D's, or F's, that's supposed to tell them that there's room for improvement. And it tells me that there's room for me to improve, too: because especially when you're working with children, you can't take their attitudes and behaviors as a given. If a kid struggles and doesn't do homework, I wonder what I could do to convince him or her that the homework is worthwhile, that time spent doing these problems will be fruitful in some crucial way.
Now I'm not saying that every time a class gets all A's, everything's hunky-dory. Sometimes it's a sign that the time has come to raise standards, to demand more of students. If you have kids who are currently scoring at the 40th percentile, then when they get all A's, you have external evidence that they have room to grow (that 40th percentile score), and internal evidence that they have the capacity to do it (they're doing everything you ask and are being successful). So then you raise standards. The same might be true if your kids are scoring at the 80th percentile, or even at the 90th--it depends on what your overall goals are. You might change your standards: spend less class time on the stuff they're clearly mastering, and add in projects or more exploratory work. (Some of these changes might decrease test scores but reflect important long-term goals that standardized tests rarely assess.) Partly it depends, too, on what it takes for your students to meet those standards: are they getting A's easily, or are they doing multiple retakes, asking lots of good questions, etc.?
Where do classroom standards come from? In many cases, the common core, or state directives. In the case of the class I'm teaching, they come from my reading of comparable classes taught at the University of Chicago and the University of Illinois. I have external validation--from those schools--that the things I want my kids to be able to do are reasonable goals for honors first-year math majors. I have internal validation that few, if any, of my students find the coursework easy; they all make some mistakes, and many come back for multiple retakes of my quizzes and tests. So yeah, if at the end of the semester almost all of my kids can do those things, then almost all of my kids will get A's. I'm not going to run around trying to ratchet up standards and lower the number of A's. I'm going to be glad that they, and I, have done our jobs. And if colleges can't tell the difference between them without actually reading the two-page single-spaced recommendations I write for the majority of my students--well, that's their problem.
In fact, it's more complicated than that, and at 24 hours remove, I feel more clearly the need to challenge the entire premise of her argument. (And, to be fair to my friend, this is a common argument. So even if I've misattributed it to her, it's an argument worth discussing.) You see, my goal isn't primarily, or even partially, to differentiate students. I understand that that's something colleges wish I would do, that the entire college admissions system depends on using grades (and test scores) as differentiators. But I'm a teacher, and so my goal is, primarily, to teach. And at some level, that's the opposite goal.
At the beginning of my course, I have to figure out two essential questions. The first--really the a pair--looks at the present and immediate past: what do my students know and what can they do? The second pair looks towards the future: at the end of my course, what do I want my students to know, and what should they be able to do? If I'm waxing philosophical, I add a third essential question: ten years from now, what do I want them to retain of the experience of having been in my class?
Once I've articulated my standards, students who meet those standards get good grades: A's and B's. In fact, when my students get mostly A's, I generally feel like I've done a good job: it means that I've gotten most of my students to master all or almost all of my standards. When my students get C's, D's, or F's, that's supposed to tell them that there's room for improvement. And it tells me that there's room for me to improve, too: because especially when you're working with children, you can't take their attitudes and behaviors as a given. If a kid struggles and doesn't do homework, I wonder what I could do to convince him or her that the homework is worthwhile, that time spent doing these problems will be fruitful in some crucial way.
Now I'm not saying that every time a class gets all A's, everything's hunky-dory. Sometimes it's a sign that the time has come to raise standards, to demand more of students. If you have kids who are currently scoring at the 40th percentile, then when they get all A's, you have external evidence that they have room to grow (that 40th percentile score), and internal evidence that they have the capacity to do it (they're doing everything you ask and are being successful). So then you raise standards. The same might be true if your kids are scoring at the 80th percentile, or even at the 90th--it depends on what your overall goals are. You might change your standards: spend less class time on the stuff they're clearly mastering, and add in projects or more exploratory work. (Some of these changes might decrease test scores but reflect important long-term goals that standardized tests rarely assess.) Partly it depends, too, on what it takes for your students to meet those standards: are they getting A's easily, or are they doing multiple retakes, asking lots of good questions, etc.?
Where do classroom standards come from? In many cases, the common core, or state directives. In the case of the class I'm teaching, they come from my reading of comparable classes taught at the University of Chicago and the University of Illinois. I have external validation--from those schools--that the things I want my kids to be able to do are reasonable goals for honors first-year math majors. I have internal validation that few, if any, of my students find the coursework easy; they all make some mistakes, and many come back for multiple retakes of my quizzes and tests. So yeah, if at the end of the semester almost all of my kids can do those things, then almost all of my kids will get A's. I'm not going to run around trying to ratchet up standards and lower the number of A's. I'm going to be glad that they, and I, have done our jobs. And if colleges can't tell the difference between them without actually reading the two-page single-spaced recommendations I write for the majority of my students--well, that's their problem.
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