kitchen table math, the sequel: Kai on teachers writing curriculum

Monday, January 19, 2015

Kai on teachers writing curriculum

Kai writes:
Wasn't Englemann the same one who said (paraphrased), "Making curriculum and teaching it at the same time is like building the airplane as you try to fly it...".

Curriculum is hard. At one of my schools I spent 30 hours over the summer just making a scope and sequence with four other people. "Making your own curriculum" is just shorthand for non-systematic throw it against the wall and see what sticks.
Building the airplane while you try to fly it---I love that!

I don't remember reading that before.

Let me tell you: 30 hours to write a scope and sequence with four other people sounds fast to me.

That reminds me!

Daniel Kahneman has a fabulous curriculum-writing story in Thinking, Fast and Slow:
A few years after my collaboration with Amos began, I convinced some officials in the Israeli Ministry of Education of the need for a curriculum to teach judgment and decision making in  high schools. The team that I assembled to design the curriculum and write a textbook for it included several experienced teachers, some of my psychology students, and Seymour Fox, then dean of the Hebrew University's School of Education, who was an expert in curriculum development.

After meeting every Friday afternoon for about a year, we had constructed a detailed outline of the syllabus, had written a couple of chapters, and had run a few sample lessons in the classroom. We all felt that we had made good progress. One day, as we were discussing procedures for estimating uncertain quantities, the idea of conducting an exercise occurred to me. I asked everyone to write down an estimate of how long it would take us to submit a finished draft of the textbook to the Ministry of Education. I was following a procedure that we already panned to incorporate into our curriculum: the proper way to elicit information from a group is not by starting with a public discussion but by confidentially collecting each person's judgment. ... I collected the estimates and jotted the results on the blackboard. They were narrowly centered around two years; the low end was one and a half, the high end two and a half years.

Then I had another idea. I turned to Seymour, our curriculum expert, and asked whether he could think of other teams similar to ours that had developed a curriculum from scratch. This was a time when several pedagogical innovations like "new math" ha been introduced, and Seymour said he could think of quite a few.


He fell silent. When he finally spoke, it seemed to me that he was blushing, embarrassed by his own answer: "You know, I never realized this before, but in fact not all the teams at a stage comparable to ours ever did complete their task...."

This was worrisome; we had never considered the possibility that we mint fail. My anxiety rising, I asked how large he estimated that fraction was. "About 40%," he answered. By now, a pall of gloom was falling over the room. The next question was obvious: "Those who finished," I asked. "How long did it take them?" "I cannot think of any grow that finished in less than seven years," he replied, "nor any that took more than ten."


Our state of mind when we heard Seymour is not well described by stating what we "knew." Surely all of us "knew" that a minimum of seven years and a 40% chance of failure was a more plausible forecast of the fate of our project than the numbers we had written on our slips of paper a few minutes earlier. But we did not acknowledge what we knew. The new forecast still seemed unreal, because we could not imagine how it could take so long to finish a project that looked so manageable. ... All we could see was a reasonable plan that should produce a book in about two years....


We should have quit that day. None of us was willing to invest six more years of work in a project with a 40% chance of failure. Although we must have ended that persevering was not reasonable, the warning did not provide an immediately compelling reason to quit. After a few minutes of desultory debate, we gathered ourselves together and carried on as if nothing had happened. The book was eventually completed eight(!) years later. By that time I was no longer living in Israel and had long since ceased to be part of the tam, which completed the task after many unpredictable vicissitudes. The initial enthusiasm for the idea in the Ministry of Education had waned by the time the text was delivered and it was never used.

This embarrassing episode remains one of the most instructive experiences of my professional life.
Planning fallacy


SteveH said...

A curriculum (usually) means a sequence of courses that lead to a desired coverage of content and skills. I've put together a number of college courses in math and computer science. It's not bad if you can find a decent textbook. I've done some classes where I've added a lot of my own new material, but never one where I created everything from scratch. Our math department did, however, lay out the number and sequence of classes required for various degree programs. These generally evolved over time so that nobody ever created a curriculum ab inito.

For K-12 math, much of the curriculum is already mapped, backwards, from calculus. Schools can select the traditional calculus, pre-calc, algebra II, geometry, algebra I and pre-algebra, or buy into some sort of existing "integrated" math package (curriculum).

When you get into K-6, schools usually buy into some existing package like Everyday Math. However, many do seem to claim the vanity of creating their own math curriculum ... or at least it's a claim just to keep parents off their back. I can't imagine that uncertified (in math) K-6 teachers would have the temerity to even attempt to create math content let alone a curriculum.

educationrealist said...

All teachers develop their own curriculum, particularly in math, particularly in high school. Even the ones that say they don't, do.

The minute you skip a chapter in a book, or a section of a book, or skip a bunch of questions, you're moving from the intended curriculum to the teacher's designed curriculum. Teachers skip chapters all the time.

Then there are teachers who basically ignore the book (raises hand). One thing mathematicians and math teachers agree on--math text books aren't much use. The only real difference is whether the teachers *want* a book or not.

There is just no earthly way you're ever going to get more than a small fraction of high school teachers to actually use textbooks.

Catherine Johnson said...

Ed has tried teaching history without a textbook (to undergraduates).

Students hated it.

Anonymous said...

In high school, the quality of the teachers is sometimes iffy. And you might miss a week of school with the flu. A textbook, even if the teacher doesn't rely on it for explanations, at least gives the student an independent platform for scoping out the material. Plus, it's a lot easier to manage than a blizzard of handouts and in-class notes. I still treasure a few of my HS textbooks, especially math and science. Hegner & Stiles, anyone?

SteveH said...

"There is just no earthly way you're ever going to get more than a small fraction of high school teachers to actually use textbooks."

Do you have any data on this?

My son's math teachers (7th grade onwards) all used textbooks and followed them closely. His K-6 teachers followed Everyday Math workbooks closely.

Education Realist said...

I described very clearly what I meant by that sentence in the paragraphs before.

Logically, the idea that a textbook is some sort of sacrosanct curriculum makes no sense. And the minute teachers go off book, they are building their own curriculum. So the only real question is to what degree teachers use textbooks. I imagine the numbers go from 0 to 70 or 80%.

"Students hated it."

Students hate all sorts of things; their hatred is orthogonal to whether or not it's effective. Besides, I'm talking K-12. College students are obsessed about grades; college profs about their ratings. Not the same animal.

SteveH said...

"I described very clearly what I meant by that sentence in the paragraphs before."

I didn't ask what you meant. I asked for data on your claim.

"I imagine .."

I see. "... a small fraction..." means 0 to 80 percent, and it's based on your imagination.

".. the idea that a textbook is some sort of sacrosanct curriculum makes no sense."

This is a straw man.

".. their hatred is orthogonal to whether or not it's effective."

Always? Catherine was talking about "it", a specific case.

froggiemama said...

My son's honors geometry teacher is not using a textbook. But he is doing a good job. The course is very rigorous, much different from the 9th grade geometry I remember from the old days. My husband, who is a PhD quant, says he is amazed they are getting 9th graders through this.

In my college courses, I increasingly do not use a textbook because the students won't buy them anyway, and there are rarely books that correspond closely to what I need to teach. We do use a textbook for CS1/CS2, which is a fairly standardized course, but as I said, only a minority of students buy it.

Anonymous said...

One reason for schools to insist that teachers follow a (hopefully good) textbook is that it protects students from bad teaching. Meaning that if they don't get it in class, they have another chance to get it from the book. There are lots of reasons kids might not get it in class besides bad teaching too, all of them legitimate reasons to follow a good textbook.

That said, most high school textbooks contain more information than can be reasonably covered in a year. This is intentional--they expect teachers to choose which chapters are appropriate for their particular class. Frequently you'll see in math textbooks a few "throwaway" chapters at the end--topics that are nice to have but not necessary to move to the next level.