Friday, September 30, 2005
Teaching became more mechanical as teachers found that drill and rote repetition produced the “best” results. Both teachers and administrators were tempted to falsify results, and many did.But they don’t bring up the three most important flaws in Romney’s proposal:
- Merit pay destroys collaboration and collegiality. If teachers are in competition with each other, there is little incentive for experienced teachers to share good ideas and improve their colleagues’ success levels. (In some schools, like Weston, such helpfulness is noticed and could well be a component of what’s rewarded in merit pay, but Romney is talking about measuring merit by test scores, not by success as a team player.)
- If standardized tests such as MCAS measure anything, they measure learning that has taken place over a period of years. It makes no sense to reward or punish this year’s teacher for the work of many teachers and parents over a period of years.
- Most important is this related point: Schools aren’t businesses; if the “raw materials” aren’t up to our standards, we can’t reject them and ask for better students. We have to teach whoever shows up. Objective tests aren’t going to measure how well we do this. Who will want to teach the weakest students if we are measured by their test scores?
Thursday, September 29, 2005
You can probably tell that I’m in the camp that finds Back-to-School Night exhilarating.
Wednesday, September 28, 2005
Giving partial credit may be helpful to a student’s grade in school but in real life, people don’t want to know how you did something, they just want the result. The how part gets shuffled into a stack of papers that some poor soul will have to look over later. The answer seems to be more important than how you got it.Artemis is more right than wrong here, so I would give her substantial partial credit. (No, wait — this wasn’t something for me to grade! It was merely a post in a student’s blog.) It’s true that if I go to a doctor or a lawyer or a computer programmer, what I want is a correct diagnosis, correct legal advice, or a working program. I will cerainly not be happy if the doctor notices five of my six symptoms and therefore prescribes the wrong meds, or if the lawyer gets most of the law right and offers the wrong advice, or if the programmer sells me a program that contains a fatal bug.
But of course this is highschool, so partial credit is better for getting into college.
So in that sense Artemis is right. I’m not happy about giving “partial credit” to the adult professional who did most of the work correctly but got the wrong result. But...no adult professional is perfect. Programmers make mistakes — all the time! Lawyers make mistakes and lose cases they should have won. Even doctors make mistakes, and I’m not just referring to malpractice. If we can’t get perfection — and we know we can’t — good work is still better than bad. Otherwise we fall into the well-known trap where the perfect is the enemy of the good. If we refuse to give partial credit — in high school or in real life — we are equating all qualities of work that fall short of perfect.
Anyway, why isn’t high school “real life”? But that’s a question for another day.
Labels: teaching and learning
Tuesday, September 27, 2005
Habits of highly effective teachers?
Each section includes relevant quotations and observations from real teachers. All in all, the catalog shows refreshing self-restraint.
- Use hands-on activities and real data. [In this section, Discovering Algebra is mentioned briefly, but Fathom isn’t, even though it’s chock-full of real data.]
- Try cooperative learning groups.
- Incorporate technology. [Aha! Sketchpad is mentioned twice in this section.]
- Create a curriculum that works for your students.
- Be a little silly. [a surprise]
- Connect math to other subjects.
- Keep learning.
Labels: teaching and learning
Sunday, September 25, 2005
Bullet voting, pro and con
Anyway, the important mathematical issue is this: in both the preliminary and final elections, each voter is entitled to cast four votes for at-large City Councilor, but is it wise to exercise that right or should one cast only one vote, which is known as a bullet vote? (Intermediate positions — casting two or three votes — are also possible of course.) I’ll present both sides with an example from the final election, though the argument holds equally well for the preliminary except that the cut-off point is between the eighth and ninth positions rather than between the fourth and fifth:
- Suppose you and 20 others agree that your first choice is Sam Yoon and your second choice is Matt O’Malley. And suppose, before your 21 ballots are counted, Yoon is in a tight race for fourth place, just 13 votes behind O’Malley. If the 21 of you bullet-vote for Yoon, your votes put him 8 votes ahead of O’Malley for fourth place, letting Yoon squeak in. But if the 21 of you dilute your support by voting for both of these fine candidates, Yoon remains 13 votes behind O’Malley, who then pushes Yoon out of fourth place. Net result: your second choice would be elected and your first choice defeated. Bullet voting is clearly the correct strategy.
- On the other hand, there is also an argument against bullet voting. To understand this argument we have to consider a candidate of medium popularity whom you definitely do not want elected. Let’s call him Steve Murphy, to pick a name at random. Now suppose Murphy is 13 votes ahead of O’Malley for fourth place before the 21 ballots from you and your friends are counted. And suppose that Yoon is way ahead (or way behind, it doesn’t matter which), so your 21 votes for Yoon won’t make any difference in his election. If you bullet-vote for Yoon, what happens? Murphy gets elected by finishing in fourth place! But if you each cast two votes — one for Yoon and one for O’Malley — then O’Malley finishes 8 votes ahead of Murphy and squeaks in for a fourth-place victory! Net result of refusing to bullet-vote: your second choice would be elected and your last choice would be defeated. Bullet voting is clearly not the correct strategy!
Standards-based Education, Part IV
Consider two students. Student A has learned all the material thoroughly and can efficiently solve problems, even when they are unfamiliar and require creative thinking. Student B has done no studying or other preparation and has to reconstruct how to solve every problem, either by guess-and-check or by elaborate work-arounds. What purports to be a 45-minute test is completed by A in 30 minutes and by B in 90. Both students eventually get 88% of the problems right. Do they deserve the same grade?
Perhaps B deserves a higher grade, for having done such a good job of thinking. Or perhaps A does, for having learned the material.
B has demonstrated an important skill, but is that skill the one that’s being tested? B still doesn’t know how to solve quadratic equations.
As John Holt put it, “The true test of intelligence is not how much we know how to do, but how we behave when we don’t know what to do.” This is indeed the true test of intelligence, but we aren’t doing high-school students any service if we leave them unprepared for SATs and for college exams because we let them take as much time as they want in order to make up for what they haven’t learned. There must be a place for timed work and a place for untimed work.
(A separate issue is the one of limited extra time. Certain students, who have demonstrated learning disabilities, are legally allowed 50% or 100% extra time on tests. Their tests are still timed, but an adjustment is made in the amount of time.)
Labels: teaching and learning
Saturday, September 24, 2005
The unreasonable effectiveness of mathematics
But it’s important for us to us to understand why it’s a welcome change. The reason is almost entirely motivational. Some students love math for its own sake and never need to worry about applications. At the other extreme, some students hate math and ask “When will I ever need to use this?” without ever waiting to listen to an answer, because the question is really a complaint rather than a request for information. But the vast majority of students, who are in between these two groups, are more motivated to learn math when they can see that it has authentic applications than when it’s totally abstract (though even they can still be hooked by intriguing puzzles).
The trouble comes when students reverse cause and effect in trying to understand mathematicians’ motivations. Mathematicians practically never start with an application and then develop the theory to support it. Instead, they develop the theory and then eventually it finds an application. This has even happened to prime numbers, long considered one of the most abstract and least applicable ideas in math, being part of number theory, which for millennia was safe from applications. Now number theory in general and prime numbers in particular have become the cornerstone of encrypting messages over the Internet, a practical application if there ever was one.
Eugene Wigner’s famous 1960 article, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” discusses fundamental philosophical justifications for the surprising applicability of math, at least in the area of physics. If you haven’t read the article, do so.
One side-comment on this idea: although science teachers and math teachers have similar sensibilities and overlapping interests, a source of continual dispute between the two groups is the use of units. Science teachers and science textbooks rightly insist on the careful use of units, as their principles and their answers can’t make sense without the correct units. But math teachers and math textbooks usually refer to things like “3-4-5” triangles, with no units attached. Kids are often confused by the mixed messages that this conflict sends, especially since math teachers sometimes do insist on units. Students want to know who’s right, the math teacher or the science teacher. After I say that of course the math teacher is right (at least if the student has a sense of humor), I point out that both of the teachers are right, becasuse they’re engaged in different endeavors. Science almost always requires correct units in order for statements to make sense, but math is more abstract, and part of its unreasonable effectiveness is that mathematical theorems are general and do not depend on particular units. When we’re doing an applied problem, we do use units and make sure that they are correct.
Friday, September 23, 2005
Standards-based Education, Part III
Let’s call our topic X. We’re supposed to believe in the following conclusions:
- All students can learn X.
- Since some students will learn X faster than others, we need to grade them on their final achievements, not on their progress as of a specific date.
- In order to be able to schedule a summative assessment for X (final test or whatever) on a particular date, we have to provide extra hours of learning time for any student who needs them.
- If X is deemed important, it’s important for all students, since we don’t want to close the doors on any particular future for any student.
- In fact, not all students can learn X. Some are severely brain-damaged. Some don’t have the prerequisite knowledge. Some have such severe emotional problems or disrupted home lives that they are not prepared to learn. Even if for some reason you exclude all those students from consideration, the reality is that June 21 is going to come around right on schedule — right after June 20 — and not everyone can learn everything by that date! The only way to believe that all students can learn the material of every course by the end of that course is to dumb down the demands and thereby penalize the kids who are most capable and most interested in learning. That’s one of the effects of the No Child Too Far Ahead Act, or whatever it’s called.
- In an ideal world, it would be great to grade students on their final achievements, not on their progress as of a specific date. But in the real world, any teacher who does that is inviting students to procrastinate and procrastinate. I would love to think that grades aren’t important, but if I don’t grade tomorrow’s quiz, there will be too many kids who will just slough it off.
- Sure, we should provide extra hours of learning time for any student who needs them. We should also have class sizes limited to 18 (the average in Switzerland). But the number of hours in the school week and the realities of school budgets make both of these dreams impossible. High school class sizes average 23 in the U.S. (29 in California!), and they’re not likely to drop any time soon. Weston does provide 50% extra classtime for Algebra 2 students who have been identified as needing it, but even in Weston you can’t get that for geometry or precalculus. (And if we had the budget to offer it, how many students could fit it into their schedule? And what if they also need extra time in history and science and Latin?)
- Item 4 is particularly well-intentioned. Indeed we don’t want to close the doors on any particular future for any student. That’s why Weston requires Algebra II for all students. But that’s a baseline, not a general conclusion about all topics. There’s simply too much material that’s important, and what’s essential for the student who’s going to take AP Physics simply isn’t the same as what’s essential for the student who’s going to take AP European History, no matter how much we might like to pretend that everything’s that one student needs is also needed by another student.
Wednesday, September 21, 2005
No bad puns
Remember, there are no “bad” puns — all plays on words are good, and the louder the groans they elicit, the better. And never forget, do not insult your audience by calling attention to the coming wordplay.
Tuesday, September 20, 2005
Labels: teaching and learning
Sunday, September 18, 2005
Constitution Day unconstitutional?
There is an interesting article on the subject in Inside Higher Ed:
Edward Rubin, the law dean at Vanderbilt [University], is anything but muted on the topic. “I’m surprised that the Congress and the president would choose to honor the Constitution by violating it,” Rubin said. “Nothing could be further from the meaning of the Constitution than compelling speech about a particular topic at a particular time.”
Labels: teaching and learning
Saturday, September 17, 2005
More on the miraculous iPod
First, Keith got himself interviewed by Fox News the other day and showed the iPod on camera; I didn’t get to see that, since for some reason I don’t watch Fox News. Then he was interviewed yesterday by Channel 7, and I did get to see the segment on their evening news show. (As soon as my wife caught the promo, she woke me up out of a sound sleep at 11:15 last night so I could see the broadcast.) I have it on good authority that the segment also aired several times this morning during Channel 7’s Today in New England show.
What will Keith do for an encore? Can he use this as the basis for the computer game he’ll be writing later this semester as his final project in Computer Science?
Friday, September 16, 2005
Standards-based Education, Part II
We all know that testing has four purposes:
- To provide feedback, both to the teacher and to the student, giving a snapshot of how the student is doing and how much s/he has learned. (For those who like euphemisms, we say that a test provides an opportunity for the student to demonstrate competence.)
- To create a learning experience that supplements classwork and homework.
- To furnish data that the teacher will use to calculate a grade.
- To satisfy requirements of colleges, the state of Massachusetts, and the No Child Left Behind act.
But in our Department meeting this week we all read an article by Paul Black and Dylan Wiliam, who argued for a fascinating variation on purpose #2:
...formative assessment produces significant student learning gains and...helps to narrow the achievement gap between low and high achievers.Although a good editor could reducing the length of this article by about 50% and thereby greatly improve it, its research offers a potentially critical conclusion. Perhaps we finally have an answer here to the vexing question of how to narrow the achievement gap. (See my post of July 1.)
Labels: teaching and learning
Wednesday, September 14, 2005
A miraculous iPod
Tuesday, September 13, 2005
Standards-based Education, Part I
But approximately another 30% consisted of ideas that I disagreed with and considered wrongheaded. I will discuss these in later posts.
So that left 10% that was actually useful to me.
This is the first of a series of posts reflecting on SBE with the perspective of six more years of teaching since the original workshops.
Today’s topic is the idea of writing the unit test (“summative assessment” in educationese jargon) ahead of time. The theory is that you should “begin with the end in mind” rather than go day by day and see where you end up. That’s a fine theory, reminding me of a poster I had in my college dorm room back in the sixties: “If you don’t know where you’re going, you’ll probably end up somewhere else.”
So of course I want to begin by thinking through what I’m going to want my students to know and to be able to do at the end of the current unit. I have no problem with that.
But I have a very big problem — two big problems, in fact — with the notion that all the teachers who teach sections of a course should actually agree on and write the final unit test ahead of time:
- Teaching to the test. In this time of federally mandated standardized testing and so-called “no child left behind,” it’s supposed to be OK to teach to the test. But let’s look at what really happens if the teacher knows the final test when beginning the unit. We always run short of time. We can’t possibly teach everything we want to teach on a topic, and a 60- or 75-minute test can’t possibly test everything that should be tested on a topic. Both teaching and assessment are necessarily selective. If I know the final test ahead of time, I will inevitably (even if only subconsciously) make decisions based on what’s on the test rather than on what’s most important for students to know. Worse yet, many teachers will become competitive and want their students to do better than other teachers’ students, so they may inadvertently become corrupt and actually teach problems nearly identical to ones on the test, perhaps only changing the numbers. There’s a reason why standardized tests are never revealed to teachers.
- Cheating. Unless all the sections of a course meet at the same time, some students will find out the test questions from others. That’s the main reason why Weston High School’s Math Department gives all final exams at the same time. But that’s impossible with a regular unit test. In fact, there’s never even a single day when all sections meet. It’s just inviting kids to cheat when the same test is given over a period of two days. (I know, you’re shocked, shocked to hear that there might be cheating in Weston, and I hate to disillusion you...)
Monday, September 12, 2005
FEMA and Internet Explorer
Hurricane Katrina victims seeking to file claims with the Federal Emergency Management Agency (FEMA) may only do so with Internet Explorer 6.0 or above.
...the use of Windows PCs and Explorer have also caused some consternation among relief workers who have reportedly complained of the time it takes to set up and secure a Windows machine versus other operating systems, which rely on other browsers.
...many of the IT professionals who have rushed into the relief effort carry Apple PowerBooks...
Saturday, September 10, 2005
Showing a calculator to a group
Wednesday, September 07, 2005
The Kutztown 13
...a group of high schoolers charged with felonies for bypassing security with school-issued laptops, downloading forbidden internet goodies and using monitoring software to spy on district administrators.That’s high security for you.
The students, their families, and outraged supporters say authorities are overreacting, punishing the kids not for any heinous behavior — no malicious acts are alleged — but rather because they outsmarted the district’s technology workers....
The...district issued some 600 Apple iBook laptops to every student at the high school about 50 miles northwest of Philadelphia. The computers were loaded with a filtering program that limited Internet access...
But those barriers proved easily surmountable: The administrative password that allowed students to reconfigure computers and obtain unrestricted Internet access was easy to obtain: ...the password was taped to the backs of the computers.
Labels: teaching and learning
Sunday, September 04, 2005
Hopkinton High School teacher Rachel Bartlett appeared before the School Committee this week to complain about being asked to bump up grades for a mediocre group of 11th-grade students. She refused, but the grades were raised anyway, lifting the overall class average from 70 to 77...Yes, of course we have to meet the students where they are. That’s in September. But then we take them somewhere else, and we should grade them according to what they know and what they’ve learned along the way. It doesn’t do students a service to give them high grades when they don’t know anything.
Bartlett, a 25-year veteran of the Hopkinton schools, told the School Committee Thursday that she tries to maintain high standards for all her students and wasn’t pleased with what this year’s group achieved. But, she said, “This past year I had two sections of students with particularly weak skills and poor work habits. The grades reflected that level of skill and effort.” She added that few students took advantage of extra help when it was offered...
Bartlett told the committee that Gould asked her to change the grades and “meet the students where they were.”...
The problem is exacerbated when students don’t take advantage of opportunities for extra help. But even when they do, effort can only take you so far. If you haven’t demonstrated competence in what you’re supposed to be learning, what message is being sent when you are given a high grade?
Labels: teaching and learning
Saturday, September 03, 2005
It’s extremely frustrating trying to make a single stylesheet work in all three browsers. Why do we have so much trouble with padding and width?
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