Session Title

What Does A Complete, Balanced Curriculum Really Mean?

Better Title

Declaring The Math Wars A Draw

Presenter

Dr. Tom Sallee, Professor, UC Davis, orator first-class

Narrative

I have to admit right away to a total blind spot for this guy. Tom Sallee could read passages from a microwave repair manual and I’d enthuse wildly. He’s dry, sarcastic, though self-effacingly so, and extremely personable, interested in every mundane detail of your life. If I manage to shed some of my more ornery twitches, I imagine I’ll arrive somewhere near his personality. This matters only to me.

“This is a truly gorgeous day,” he said, and gave us all explicit permission to leave if the talk began to not meet our expectations. “If it were blowing a gale out there I might be hurt, but not on a day like today.” I have to believe this kind of confidence is essential to certain really great teachers. He knew no one was leaving.

He discussed California’s math framework for students and teachers. He noted the semantic significance of the teacher goals appearing above the student goals, and along similar lines, he said he thought California prioritized them inadequately.

Currently the student goals read:

1. Conceptual and procedural fluency;
2. Precise communication;
3. Logical thinking.

He thought logical thinking was seeded at least one ranking too low.

He defined the warring math factions as a) those who believe math is about knowing a set of principles from which you should be able to solve something new, and b) those who believe math is about knowing what you have been taught. He said they represent fundamentally opposing world views. At one point he believed that with enough research and enough dialogue those factions would dissolve but “I have given up on that,” he said.

He put these up:

1. Basic Skills
2. Conceptual Understanding
3. Problem Solving
4. Logical Thinking

And asked, how do we test each of these? which of these are cheap and easy to test? which are expensive and hard? which will be tested?

“Let me tell you my answers:”

1. Focus needs to be on long-term learning.
2. There isn’t much point in teaching a topic if students don’t understand it well enough to use it later.
3. A lot of math needs sinking-in time – especially concept development.
4. Practice and thinking needs to be spread out for effective learning.

“Algebra is about four or five concepts. However, if you separate coin, rate, and mixture problems, then there is a lot more there.”

Someone from the crowd asked him to define them.

“You need to understand what a variable is and how you can use it to represent a situation. You need to have a general strategy for solving a series of equations when you have several variables. There is a relationship between equations and graphs. Proportional reasoning. Multiple representations.”

That fifth one was difficult for him.

Special Guest Star

H!, who is half as tall and twice as Norwegian in person.

Visuals

Overhead transparencies. Like last time.

Handouts

A printed Word document.

Homeless

• The Two Lies of Teaching, According to Dr. Tom Sallee: (1) If I say it then they will learn it. (2) If I don’t say it then they won’t learn it.
• “If there was a right way to teach math, we would have found it by now.”
• On precise communication: “I cannot get excited about the distinction between ‘fraction’ and ‘rational number.'”
• On teaching algorithms: “Untrammeled by evidence, unless you understand what an algorithm is going to do, it isn’t going to make sense to you.” “Untrammeled by evidence” is just a fantastic throwaway line.
• On good problems: “A good problem seems natural.” I take this to mean “a good problem reveals its constraints quickly and clearly”. By contrast: “The Schmedley’s speak truth on Tuesday, Wednesday, and Friday,” etc.
• On developing good problems: “Developing problems is not at all an easy task. I have a lot of experience with it and I have failed many times.” He is the President of CPM, incidentally.
• “If there was a right way to teach math, we would have found it by now.”