kitchen table math, the sequel: John Saxon on the need for speed

## Sunday, July 15, 2007

### John Saxon on the need for speed

Rapid and accurate recall of basic facts and skills dramatically increases students' mathematical sbilities. To that end we have provided the Facts Practice Tests. Begin each lesson with the Facts Practice Test suggested in the WarmUp, limiting the time to five minutes or less. Your student should work independently and rapidly during the Facts Practice Tests, trying to improve on previous performances in both speed and accuracy.

Each Facts Practice Test contains a line for your student to record his or her time. Timing the student is motivating. Striving to improve speed helps students automate skills and offers the additional benefit of an up-tempo atmosphere to start the lesson. Time invested in practicing basic facts is repaid in your student's ability to work faster.

After each Facts Practice Test, quickly read aloud the answers from the Saxon Math 8/7 Homeschool Solutions Manual as your student checks his or her work. If your student made any errors or was unable to finish within the allotted time, he or she should correct the errors or complete the problems as part of the day's assignment. You might wish to have your student track Facts Practice scores and times on Recording Form A, which is found in this workbook.

source:
Facts Practice Tests and Activity Sheets
Saxon Math Homeschool 8/7 Tests and Worksheets
Saxon Math Homeschool 8/7 (\$18.50 at Rainbow Resource)

Yes!

I do wish!

Until I figure out celeration charts, Recording Form A will do nicely.

Facts Practice Tests - Saxon 8/7:

A multiplication
B equations
C 30 improper fractions and mixed numbers
D 40 fractions to reduce
E circles
F lines, angles, polygons
G fractions
H measurement facts
I proportions
J decimals
K powers and roots
L fraction-decimal-percent equivalents
M metric conversions
N mixed numbers
O geometry
P integers
Q percent-decimal-fraction equivalents
R area
S scientific notation
T order of operations
U two-step equations
V algebraic terms
W multiplying and dividing in scientific notation

Anonymous said...

you're taking "celeration" seriously.

to my eyes, it makes the already
formidable disincentives to teach
look almost pleasant.

if these guys actually
get any influence, i'll be

SteveH said...

"Since 1990 the Standard Celeration Society has comprised a collegial organization for all persons who use Standard Celeration Charts to monitor and change human behavior frequencies."

Im all in favor of mastery and speed in the basics of math, but I'm not too keen on schools trying to monitor units of behavior frequency change. I would rather have them monitor units of correctness (grading) on weekly quizzes and tests.

Catherine Johnson said...

if these guys actually
get any influence, i'll be

lol!

THAT WOULD NOT BE GOOD!!!!

Catherine Johnson said...

I'm aiming to become master of the unintended consequence here in my old age.

Catherine Johnson said...

But here's a serious question....addressed to Vlorbik, Steve, Rudbeckia, Barry, Doug (I'm probably leaving people out) --

OK, I'm trying to ask a question of people who are "masters" in math: people who majored in math, are or have been professors of math, work in math-related fields, etc.

Now I have to think what my question is....

At its simplest, my question is: "how fast are you at the fundamentals"?

But it's really more than that.... and I can't quite put my finger on it.

I do take the celeration folks seriously, partly because this is a "return to my roots"; having two autistic kids, I began life with the ABA folks, and this is ABA.

I hadn't quite picked up on that until I was reading a terrific precision teaching site which turned out to be, when I clicked on "Home," an autism site.

Fluency teaching was just coming in when we left our ABA school. I remember being intrigued by it, and instantly thinking it made sense. (I think there's a "timing" problem with autism in some way; I also saw that the ABA teachers ALL, universally, used speed & rhythm ro teach.)

But we left the school then, which means we pretty much left the world of ABA.

number one, I buy the premise, which is that fluency means speed, not just percent correct.

number two, I also buy the finding (and hypothesis) that long-term memory for material you've "learned to an 80 or 90% criterion" (see - I can sling the lingo!) is easily forgotten.

I buy the finding/hypothesis that material learned to a speed-and-accuracy criterion is hard to forget. Maybe even impossible to forget.

I **tentatively** buy the finding/hypothesis that material learned to a speed-and-accuracy criterion is more readily generalized or "transferred" to novel contexts and applications - though this moment, the moment at which some kind of starter expertise happens - still seems pretty mysterious in term of the research both from the behaviorists and from the cognitive scientists.

Catherine Johnson said...

if these guys actually
get any influence, i'll be

This is why, although I'm fascinated by policy, I have ZERO confidence in my thoughts about what policy ought to be.

When I say ZERO confidence, I don't mean I don't have opinions.

I do.

But if you asked me to bet money on whether my favored policy would produce the effects I imagine it would, I wouldn't bet more than 10 bucks.

Catherine Johnson said...

I would rather have them monitor units of correctness (grading) on weekly quizzes and tests.

Why do you say this?

Specifically, I mean.

Catherine Johnson said...

I'm adding Vicky, Linda M., Susan J, and Now Thats Hockey to my "Serious Question" list.

Who else am I missing??

Catherine Johnson said...

I'm missing instructivist!

Catherine Johnson said...

I'd like to hear what teachers think about this, but I'm putting K-12 teachers in a separate category..... and now can't remember why I wanted to hear separately from teachers as opposed to practitioners.

I guess I'm suspecting instructivist-type teachers are going to tend to think speed is good ---- ??

Doug Sundseth said...

"How fast are you at the fundamentals?"

Quite fast; I normally see the answer to simple questions without consideration.

Possibly related: In the summer between 4th and 5th grade, the summer school I attended did mad-minute multiplication. We were doing 100 single-digit problems in one minute with 95%+ accuracy.

More generally, I've learned other things by extended rote practice and I still know most of those things with no real thought. (German irregular verbs, typing, judo throws.)

Yes, the practice is tedious for both student and teacher. But the student only has to do it once and the teacher is being paid very well. (Note: the work of a teacher is easier and the pay is better than the work and pay on a loading dock -- I've worked on a loading dock.)

SteveH said...

"how fast are you at the fundamentals"?

Fast enough. My wife can multiply 2 two-digit numbers in her head faster than I can, but I am so much better at math. At some point, extra speed isn't a big help. HOWEVER, schools do not come anywhere close to this point!!!!! (If someone quotes me later, I want to make sure there are enough exclamation points. I am all in favor of timed tests of the basics!)

"But it's really more than that.... and I can't quite put my finger on it."

I can "see" things faster. This kind of speed has nothing to do with simple things like how fast you can find a common denominator and add two fractions. [See my post on my favorite identities.] For math problems, like in programming problems, my mind races through all sorts of things that have to do with background knowledge and experience. It's speed, but maybe not what you're talking about. My mind may go very fast(with the basics), but I'm a slow, methodical programmer. When I have to derive or develop some equations, I go very slowly.

"number one, I buy the premise, which is that fluency means speed, not just percent correct."

Speed is an indicator, but it's not the goal. When problems get more difficult, speed is less of an issue. It's better to have enough content knowledge and experience to go in the right direction.

"I buy the finding/hypothesis that material learned to a speed-and-accuracy criterion is hard to forget. Maybe even impossible to forget."

I do a pretty good job of forgetting. I really think you need to make a distinction between the basics and more complex problems. For more complex problems or material, it's better to understand the fundamentals and be able to derive a solution or learn new material quickly.

I remember picking up a book on vector calculus long ago. I sat there and went through the problems very quickly. I set it aside and went back to it six months later. I could still do the problems quickly, but I wasn't any further along than I was before. What I missed were the key fundamental concepts and governing equations that gave me any lasting value. I guess what I'm saying is that after a certain point, there are other understandings that are very important that have little to do with speed.

SteveH said...

I would rather have them monitor units of correctness (grading) on weekly quizzes and tests.

"Why do you say this?"

Because it sounds like they would measure behavior change units instead of right and wrong answers. I wish they wouldn't dress up eveything with fancy talk, but I suppose it doesn't sound scientific enough if they just advocate a link between speed and understanding.

Anonymous said...

what steve said.

i've never been very fast
or tried to be. in fact,
held back and went even slower.
i couldn't compete with the
speed demons and didn't like it.

of course, now that i'm usually
"confused at a much higher level",
i can sometimes impress students
with mental calculations ...
but mostly it's by knowing better tricks.

well, of course, i've done it too.
teaching is indeed easier ...
if you're good at politics.
i quit the docks on my own ...
but was fired from college professing.

vlorbik

SteveH said...

"i couldn't compete with the
speed demons and didn't like it."

I never liked the idea of math as a competition. In the real world, speed is usually never an issue; wasted time is.

Catherine Johnson said...

As I understand fluency, it's speed and accuracy. The element of speed is added to the element of accuracy, not exchanged for it.

Here's the ERIC abstract of Binder's article:

Doesn't Everybody Need Fluency?

Source: Performance Improvement, v42 n3 p14-20 Mar 2003

Discusses fluency, a combination of quality plus speed that characterizes competent performance that is the true definition of mastery. Suggests the need for including a time dimension in measures to show distinctions between levels of performance, and concludes that performance development programs should address fluency to improve learning and performance. (Author/LRW)

Catherine Johnson said...

ok, V, so you say..... but I'm guessing you can add 50 1+5s in under 66 seconds.

I'm guessing you'd add 50 1+5s in under 66 seconds without anyone setting a kitchen timer, either.

Catherine Johnson said...

it's always worse than you think

Anonymous said...

hmm ... my latest comment appears
to have been eaten by blogger.

i've just linked here, so i suppose
i'd better try to restore it.
here goes:

"I'm guessing you'd add 50 1+5s in under 66 seconds without anyone setting a kitchen timer, either."

maybe so. but i didn't get
whatever speed i've got by drill.

consider spelling.
i was very poor at spelling tests
(without even holding back on purpose).
but now i'm probably in the top
few percent of spellers from
the classes i was being matched to
(bright kids with educated parents ...
it wasn't called "university elementary"
for nothing [not back then, anyway]).

i didn't get here by being made
to spell the word correctly 10 times
and then use it in a sentence ...
but rather, by spending the rest
of my life outreading nearly everybody.

without getting all nctm about it,
it seems to me that we should be able
to teach skills while still talking