kitchen table math, the sequel: palisadesk on the math police - & parents teaching math facts

Sunday, March 7, 2010

palisadesk on the math police - & parents teaching math facts

A propos of Kindergarten children being asked to write journals and stories without any instruction in spelling (or even in pencil grip or how to form the letters), and also children being taught -- or not -- number facts and algorithms, this discussion has come up on a couple of other boards I read. One important issue stands out: there is enormous variability in what is required and/or permitted to be taught in these areas.

I advise all parents to get a copy of your district's curriculum documents, if you can (many have them online) and see what teachers are being told to do. It may surprise you. In many places, expectations for teaching the mechanics of writing -- pencil grip, letter formation, manuscript or cursive writing styles, even spelling -- have been *completely* removed from the curriculum. Teachers can of course model them or give instructions en passant, but cannot actually focus on these things as objects of lessons.

Catherine has brought up the use of "instructional coaches." This is becoming more and more common, and one of their (unstated) roles is to act as "literacy police" or "numeracy police." If they see teachers doing spelling, or printing, or teaching math facts systematically, they are to discourage these things and also discuss it with school administration. My district no longer requires math facts to be taught, and teachers have actually been forbidden to practice them in class. They can assign math fact practice for "homework" which is another way of outsourcing to parents, as Catherine has pointed out in the past. This disproportionately penalizes low-SES kids whose parents don't have the time or sometimes the expertise to teach these things to their children.

It's very often not a matter of teachers not wanting to teach "the basics," but of their being prevented from doing so. Many of my colleagues grumble quietly about it, but because it is ordered from on high it can't be openly flouted. It's not clear to me who makes these curriculum decisions higher up the ladder, but sometimes it does seem (as an anonymous person said earlier) that the goal might just be to keep the proles in their place! In my darker moments I am tempted to think this is so.
Outsourcing math facts to parents handicaps all children. I know we've talked about this a lot over the years, but I don't have the patience to go hunting the posts. Easier to write a new post now---

At least two high-SES, highly-educated parents we know told us they were never able to remediate their sons' deficiencies in math facts or in long division. One of these parents went to Harvard. They tried, but they did not get the job done. Even Kumon didn't get the job done for one of the kids. (Not sure why -- possibly because the parents realized what the situation was too late -- ?)

I was lucky because the Saxon Math "Fast Fact" sheets worked for C. after 2 other approaches I tried failed outright: flash cards and flash card software. When I switched to the Saxon worksheets, he learned rapidly.

I had no idea what to make of it. Can't learn his math facts using flash cards? Can learn them practically overnight using worksheets?

Later on, I read a Rafe Esquith passage advising parents that students need to practice material in the format they'll use it on the test. That makes sense. It's consistent with everything I know about animal training and with Dan Willingham's explanation of flexible and inflexible knowledge.

But how many parents know this?

I sure didn't.

At a board meeting recently, our new part-time Interim Director of Curriculum and Instruction made one fantastic observation. She said she'd told teachers that "If we were serving a low-SES population, with parents working two jobs to make ends meet, we wouldn't expect parents to be skilling and drilling the math facts. Our parents have busy lives and many demands on their time, and we shouldn't expect them to do it, either."

Then she added, diplomatically, that in fact parents here, nearly all of whom are high-SES and well-educated, are not getting the job done.

Last year, the 6th grade accelerated math class had to stop dead in its tracks so the teacher could teach math facts & the standard algorithms. The kids were all high-SES and their parents are well-educated.

Teaching math facts isn't simple or obvious. Skilled teachers do it far better than most parents.


Catherine Johnson said...

This will surprise no one who's been reading & writing ktm for a while....I don't know whether my district has official curriculum documents.

Catherine Johnson said...

A dad in town told me that when he was moving his family back to the U.S. from Europe, someone told him to visit the school principal and ask to see the scope and sequence.

He made an appointment with the then-principal in the elementary school here and asked for the scope and sequence.

The principal said, "We don't have a scope and sequence."

That's what he told me.

I believe him. I've never seen a scope and sequence. I've never even heard tell of one.

Obi-Wandreas, The Funky Viking said...

One of the advantages of teaching in a large district, and having a few years of experience, is that it's easy to go unnoticed. So when the district tells everyone that instruction must be explicit, while we must also maintain fidelity to a curriculum which forbids explicitness, Nobody looks to closely at how I make it work.

Catherine Johnson said...

We have a tiny little district & the administration is intent upon hiring **lots** of instructional coaches.

They want consistency across the classrooms.

Also, they want SMART Board Equity. I kid you not. That is a focus. There are children in the K-3 school who can go through all 4 years and **never** be taught in a classroom with a SMART Board!

Of course, there are quite a few kids who can go though all 4 years without ever learning to decode proficiently, but nobody's talking about Reading Equity.

Hainish said...

Many of my colleagues grumble quietly about it, but because it is ordered from on high it can't be openly flouted. It's not clear to me who makes these curriculum decisions higher up the ladder

Usually a superintendent or assistant superintendent in charge of Curriculum and Instruction (or Curriculum and Technology, or what-have-you).

The incentive structure behind it is interesting. For many of them, forcing an "improvement" on one district is a steeping-stone to a job in a better-paying district.

MiaZagora said...

I'm not convinced that these highly-educated, Harvard parents *can't* teach their kids math facts. My sister did it - mostly as a single parent, and she only went to community college. Just 15to 20 minutes or so a night with flashcards or some pencil and paper thing she did. She also played math-intensive games with them - like UNO, Yahtzee, and other games like that. There is a plethora of help for learning math facts on the web (I like's approach)- I'm sure these Harvard grads know how to Google? :0)

Michelle said...
This comment has been removed by the author.
Michelle said...

The part about not teaching handwriting is absolutely true for us this year. My son has received no handwriting instruction in kindergarten. Thankfully I've worked with him so he's got decent writing, it could be better though. We'll be doing Handwriting Without Tears over the summer to correct some problems.

He has received no spelling instruction either. We're doing spelling at home along with phonics.

Anonymous said...

As I was looking through some math fact "drill" sheets, the district math coach came in and proclaimed, (with nose in air) "oh, drill and kill, I see."

I really wanted to spout off and tell her that our highly-touted conceptual Everyday Math program was leaving some first graders behind with no skills to speak of, but lots of confusion. I had to bite my lip and tell myself "hold tongue, hold tongue."

Anonymous said...


You are so, so wise. Jumping on this early is key.

I was so distracted by the math stuff, that I ignored the writing debacle that was occurring right before my eyes. Since my first son has a severe writing disability, I just chalked it up to it all being very hard for him. Of course, I was baffled when he would come home in early grade school with sheet after sheet of unlined paper.

But when the second one, who has no learning problems, started coming home with the same mess, I knew I had to do something. Unfortunately, I just kept trying to fill gaps here and there instead of having a writing plan parallel to what the school was doing. I knew it worked for math, but I just didn't get it together early enough.

By the time my second son was in middle school, I
realized his grades (and self esteem) were plummeting, so I had to have him write ad nauseam until he gained some fluency and confidence. Thank god for all the homeschooling curriculums out there.


I had the same comment come at me a couple of times. I finally came back with something I picked up here a few years ago. I just said, "We like to think of it as 'drill and skill.'


farmwifetwo said...

Most children will learn math facts with repetition. Over and over and over again. What's a few addition facts, subtraction facts/day. Show them using counters etc. These children should easily be taught if they are given the resources to learn, not some windy...

5+5 = 10, 6+6 = 12, therefore 6+5+11 when they are in Gr 3.

Then comes the rest. We have worked our way through numerous ideas to teach little boy math facts (he's in Gr 3, reads at Gr level, language is mid Gr 1 - all tested this year). And I finally found a solution that works. Not flash cards, not fingers, not counters, not a calculator but repetition.

Eldest son has poor short term recall. He takes his spelling words and writes them out 3x's/day all week for the test on Fri and usually gets perfect. I don't quiz him, his book is open to make certain he's spelling them correctly.

So, I used the same theory and we're doing math facts the same way. Over and over and over every night, there's another 20 math Q's... with the answers beside us... We have mastered the 0+, 1+ and 2+ in the last 2mths (never said it was quick)....

Problem is, most parents have never been taught math, most teachers have never been taught math... Those like myself that majored in engineering, accounting... got A's in Calculus and barely studied.. get math. We get the in's and out's, the tricks, the rules and how to bend them or twist them. How "if in doubt make it zero" applies.

I have no doubt, very few can teach their children, if they have the slightest learning disability, math. How can they... they never learned it themselves.

Ari-free said...

"Teaching math facts isn't simple or obvious. Skilled teachers do it far better than most parents. "

You can do it by showing the pattern to make up each number (for example, 5):
0 + 5 =
1 + 4 =
2 + 3 =
3 + 2 =
4 + 1 =
5 + 0 =
Each pattern is easy to remember since the left side goes up from 0 and the right side goes down to 0 and the answer is the same for each group.

and then for subtraction we take each addition pattern that we already know and show that subtraction is the inverse:
0 + 5 = 5
5 - 0 = 5

1 + 4 = 5
5 - 1 = 4

2 + 3 = 5
5 - 2 = 3

3 + 2 = 5
5 - 3 = 2

4 + 1 = 5
5 - 4 = 1

5 + 0 = 5
5 - 5 = 0
Things stick better in the mind when they are related to other facts.

Crimson Wife said...

We're pretty much treading water in our homeschool until my DD finishes memorizing her times tables. What drives me nuts is that she'll seemingly have them down pat in a straight drill context but then when she's actually called upon to *USE* the facts as part of a word problem, she'll make a dumb mistake like today when she was claiming 3 X 9 = 21. Argh!

Catherine Johnson said...

Ari is right!!

Remember that great post Exo wrote one time about the Russian system for teaching math facts? As I recall, there was a schedule - by April the kids would know 'X.'

Parker & Baldridge explain how to teach the math facts logically (probably exactly as Ari describes).

As to whether Harvard grads can teach math facts to their kids --- well, sure.

BUT you have to know you need to do it & if you find out late you're going to be trying to figure out how to do it and overcome the resistance you're going to get.

Like Susan, I needed to do a lot of remediating in ***everything*** --- handwriting first and foremost. But all of my focus was math.

Could I have remediated handwriting?

Yes, I probably could have, and I tried. I researched programs and picked what was probably a decent one for us.

But I didn't get the job done.

Catherine Johnson said...

Crimson Wife - Wayne Wickelgren's take on the math facts is that the reason they're so difficult to memorize is that they're way too similar. You're using just the 10 digits for all the math facts. Too much 'interference.'

Catherine Johnson said...

I spent a quarter of a century believing that 6 x 7 is 43.

Which just goes to show.

Catherine Johnson said...

C. has boycotted Megawords this school year.

He's gonna be finishing the textbook over spring break & summer.

Then we'll have... two books left, I think.

SteveH said...

"...when she was claiming 3 X 9 = 21. Argh!"

I remember those things with my son. It took a while. He is still not as good at figuring in his head as my wife and I. Then again, we grew up pre-calculators and had to do things like interpolating in our heads. I remember races to see who could first calculate something like 2/3 of the distance between two numbers from a table in the back of the book.

Ari-free said...

For multiplication, everyone should know x1, x10 and the x9 has a fun pattern. 2's are doubled, 4's double the double and 5's halve the 10's. There's another pattern that should be taught: The off diagonal. If you know the square (which makes the diagonal) you can figure what's off and vice versa.








I couldn't find a mathy trick for the others but you just can't beat 5678: 56 equals 7x8!

Ari-free said...

"I spent a quarter of a century believing that 6 x 7 is 43."

It also goes to show that you didn't know the rule that an even number times anything is always even. :)
And you couldn't would say 3 X 9 = 21 if you knew those 2 digits had to add up to 9. These extra tricks provide an extra check on your intuition even if you think you know your facts cold.
Zig Engelmann's method (from Give Your Child A Superior Mind)relies on skip counts but he also lists checkpoints. For example, for 3 he points out: you always hit 21, you always hit 24 and you always end up with 30.


bky said...

The situation Crimson Wife mentions, where the child does well on isolated tests but makes arithmetic mistakes in the course of large problems, tends to show up in spelling lessons too. My kids can spell very well on spelling tests, but will tend to misspell the same words when writing a paragraph on an assigned topic. With practice this smooths out.

It helps to go up a level. One level up from spelling tests is writing dictated sentences. With my first grader, I will give him 3-4 sentences a day, short simple sentence that each use as many of his spelling words as possible, going back to previous lists. Learning words from a list is one level; learning to use them in the context of writing a sentence is another level. This helps.

For multiplication and other arithmetic, you have to figure out what the next level is. If you are working on the multiplication table, the next level up could be multiplying 2-digit numbers by 2-digit numbers, not as a timed tests, but as a worksheet with a reasonable, not stressful, number of products. Maybe just 5 to 10 problems.

For every level there is a level up that provides in-the-of-combat practice for the previous level. As another example, when kids know the basic operations of arithmetic with fractions, you can go to solving linear equations with integers and fraction coefficients, such as

(2/3)*T - 5/8 = 3/4 + (5/4)*T

Solve for T. Just give them a few on a worksheet. Each equation requires several arithmetic operations. They will make all kinds of mistakes that they don't make when you just give them fractions to add/subtract/multiply/divide.

Just don't make the next-level-up practice too hard. A small handful of problems at a time every day.

bky said...

Oh yeah, about going to the next level, you have to introduce the next level while still working on the current level. That would mean that you show the child how to multiply 2-digit numbers while they are learning but have not mastered the times tables, or learn about capitalization and periods when they are still learning to spell "first grade words". The timing might be the hard part: how firmly does you child need to have the times table or part of it before going on to the next level. That is an implementation detail left to the user.

lgm said...

7x8 , well you already know 7x4
it's the same as 4x7 and that's 28

so 7x8 is easy as it's 7x4x2
...just double 28 to get 56.

This needs to be shown pictorially and the child given time to process. If he hasn't mastered addition, go back and master addition.

If the child is allowed to use the properties (associative, communitive, identity, zero, distributive) life is easy and practice is smooth.

The 8s can be done this way (use commutative property aka order property when teaching child):
8X0=0x8=0 zero property & already known
as part of the 0s
8X1 identity, already known as part of the 1s
8X2 double
8X3 double 8 and add another 8
8X4 double 8 and double again
8X5 multiply 8 by 10 and halve
8X6 already know 6X6, so double 8 and add it to the product of 6X6 i.e. you recognize that 8X6 is (6x6)+(2x6) distributive property
8x9 use distributive property any way you like, but also master

Elementary students that learn to know the properties intimately have an easy time in math.

Check out Denise at Let's Play Math if you haven't already. Her thoughts on Number Bonds and "The Game that is worth 1,000 Worksheets" are something that everyone parent of a little one should know. The Brits have some nice materials for those that don't have access to a math methods book: The level one assessment makes me realize why so many have difficulty - their environment doesn't give them opportunity to develop the concepts through play and family activities and school just doesn't have the time to make up the gap for all.

Crimson Wife said...

Yeah, I'm trying to have my DD work on applied multiplication problems as we continue to work on getting the times tables memorized.

Today's frustration was hearing her correctly answer drill problems for ten minutes and then turn around & claim that 51 x 700 = 45,700.

rocky said...

(2/3)*T - 5/8 = 3/4 + (5/4)*T
-(5/4)*T + 5/8 + 5/8 - (5/4)*T
(2/3)*T - (5/4)*T = 3/4 + 5/8

8 - 15          6 + 5
-------- * T = -------
   12              8

(-7/12) * T = 11/8

(-12/7)(-7/12) * T = 11/8 * (-12/7)

      11    -12
T = ----*-----
       8      7

      11    -3
T = ----*-----
       2      7

T = (-33/14)

This is probably not what you meant.

bky said...

Rocky , yeah, that's what I meant. The point is for students who can do a worksheet of many individual problems in arithmetic with fractions, if you go to the next level of, say, solving linear equations, they will have to do several instances of arithmetic in the course of doing the algebra, and low and behold, at first they will make many arithmetic mistakes that they were not making when they only saw one thing at a time, e.g. 3/4 + 4/5 = ? and things like that. The analog to spelling is kids know their word lists and do well on spelling tests; then when they write dictation sentences using those same words, they start to misspell them. Going to the next level, i.e. writing dictation sentences, not only teaches them about capitalization, punctuation, and so on, but re-teaches them the spelling everyone thought they already knew. Solving the linear equations not only gets them doing some algebra, it makes them relearn all that arithmetic that they thought they had down pat from worksheets.

It seem unrealistic, in general, to think that you're going to really nail level n and then go to level n+1; when you get there, some of that level n stuff will seem slippery all of a sudden. This has been my experience learning and homeschooling my own kids. Isn't that common?