kitchen table math, the sequel: Mastery Math

Monday, March 19, 2007

Mastery Math

I’m currently in an insomnia-induced state of mental wandering so it would seem unwise to post at this time, but what the heck.

I have been thinking about labels like traditional math, constructivist math, discovery math and fuzzy math. I’ve read discussions about how anti-fuzzy advocates are accused of wanting to go back to “parrot math”. I’ve never totally loved using the term “traditional” to describe what many of us believe to be the best way to teach math. And I can’t remember hearing of a better name.

And I just read this from a March 7 NCTM live chat:

Question fromSalem, Oregon: I am unclear as to how focal points are related to expectations of mastery (understanding) at a grade level. Is mastery (understanding) the goal at the grade level of the focal point?
Skip Fennell:A focal point is a topic or area of emphasis. Teachers will spend time on developing particular curricular focal points at a given grade level. That would then, for many topics, be extended the next year or so, but wouldn’t just be a grade level focus at that or those grades. As teachers know, the variable here is time. Some students need more or less time on a particular topic. Our concern is deep understanding. To get there will just require more time for some students than others.


After considering all this, I came up with a name that I’m going to start using and see if it works to help some people better understand these math wars.

Mastery Math!

Mastery math vs. focal points math.
Mastery math vs. exposure math, fuzzy math, constructivist math, discovery math, group math, spiraling math.

Mastery math, I like the sound of it. I think parents may like the sound of it. (On the other hand, maybe in the morning I’ll think differently. But, as I said, what the heck.)

And now I’ll try to get some sleep.

7 comments:

Barry Garelick said...

Thank you. I will start using the term "Mastery Math".

Catherine Johnson said...

you know, I think that works!!!!

I've been playing around with this forever, trying to come up with the term.

"Traditional math" would be fine if traditional math (which is what C. has in his middle school) hadn't been such a disaster.

I've played around with "direct instruction math" or "cognitive science-based instruction" -- and all of those are way too clunkey.

I'm going to start using "mastery math," too.

Good work!

Thank you!

Barry Garelick said...

"Traditional math" would be fine if traditional math (which is what C. has in his middle school) hadn't been such a disaster.

Traditional math doesn't HAVE to be a disaster; the term is a loaded one. Mastery is much better for that reason. If you don't teach a "traditional" math text to mastery, then it's not going to work, even if the book is excellent.

Catherine Johnson said...

Our concern is deep understanding.

This is a HUGE misconception, and it's ruining my life.

(Hideously enough, that may not be an understatement.)

Our entire math department, top to bottom, is concerned only with "understanding."

That's it.

Period.

EOS.

Then they test the kids on performance: can the kids actually DO the math they supposedly understand.

Answer: no.

They can't.

Remember that end of year assessment Ms. K sent home?

iirc she'd marked down that Christopher "understood" all kinds of stuff, but could do practically nothing.

This goes back to my first brush with constructivist math....Christopher was in the beginning of 4th grade, and had gotten a 77 on a test.

I asked the teacher about it and she said, "Don't worry, he understands the concepts."

I was reassured, but part of me was thinking: hmmm.

He understands?

Shouldn't he be able to do these problems better than a 77%?

Since I didn't know any better I let the whole school year go by before discovering just how wrong "understanding" is as the central goal of education.

Catherine Johnson said...

Barry -- of course you're right; "traditional math" ought to be fine.

The problem is that we have lousy math instruction no matter what.

That's the funny thing about writing ktm: our household is being MULCHED by classically bad, non-conceptual, fragmented "traditional" instruction.

Along with challenge problems from Math League, of course.

When you moosh constructivist "challenge" into really bad traditional teaching, you are in a special kind of misery

KDeRosa said...

Although it was intended for a slightly different topic, Don Crawford just posted this on the DI listserv. How to make sure your traditionally taught course is teaching to mastery:

1. Overall, including new, review and corrected items--are the
students responding at or above 90% correctly (95% when reading)? Less
than that is a problem.

2. Are 100% of student academic errors receiving an error correction from the teacher?

3. Defining engagement as having eyes on the task and answering on
signal--is there an average student engagement (on-task) over 95%?

4. Does the teacher call on non-volunteers and do low-performers get equal or greater than equal proportional distribution of questions?

5. Is ratio of responses to appropriate behavior at least four times as frequent as responses to undesirable behavior?

6. In repetitive (minimal teacher-talk) parts of the lesson, such as word attack, fact practice, spelling practice, etc. are student responses between 10 to 20 responses per minute?

7. In written work are students 85 to 90% correct or better first
time--before workcheck?

8. At the end of each part, does the teacher bring the group to "firm" meaning they do the part at least once through 100% accurately, or without errors?

Liz Ditz said...

It's Liz from I Speak of Dreams.

Mastery Math! Brilliant.

Now we can start talking about Mastery Reading, too.

And K--

Is ratio of responses to appropriate behavior at least four times as frequent as responses to undesirable behavior?--that's a pretty good rule of thumb for effective classroom management, too.