kitchen table math, the sequel: The Revolt Against Lousy Math Instruction May Just Go Viral

Friday, November 13, 2009

The Revolt Against Lousy Math Instruction May Just Go Viral

This example was just posted at BoingBoing, a large group blog, at this post.

Do You Understand My First-Grade Child's Homework?

The blogger asks
My six-year-old told me she doesn't understand her homework. After studying it for 15 minutes, I *think* I understand what she's supposed to do, but I'd like a second opinion.
Is it from Everyday Math?

Go add to the BoingBoing comment fun, if you like.

(I have another question -- homework for six-year-olds? I'm ok with requesting reading at home, but that's it. Period. The end.)


Kai said...

Actually, "making ten" is a powerful approach borrowed from Asian math programs and is a staple of Singapore math in the early grades.

Anonymous said...

I did Singapore Math as well and went to the bank and got rolls of pennies, dimes, and dollar bills.

I sat in the middle of the floor and we worked with pennies for a while and discovered how cumbersome they grew to be.

We swapped out for dimes and then later for dollar bills.

Nobody failed to get that base 10 is an efficient way to deal with all those ones.

"Counters" ?

Niels Henrik Abel said...

To add to Kai's comment:

Making ten is a necessary skill for abacus manipulation, and hence makes sense in Asian contexts.

Don't know of too many American kids that are being taught the abacus, and would thus derive maximum benefit from it.

Liz Ditz said...

I guess I wan't clear enough

1. Adding 1-digit numbers for a 2 digit solution appropriate for 1st grade?

2. Is this a good example of homework for first grade

3. Is math homework ever appropriate for first grade?

4. Why is this child (a product of a highly-educated household) struggling?

Liz Ditz said...

Plus, people, please go to and read the comments.

Amy P said...

I think the concept (making tens) is important to Singapore Math, however, it's very interesting to compare the execution. The question here is conceptually simple, but the directions are impenetrable. It's almost better to just ignore the verbal instructions. "Draw counters to solve." Huh? I can only imagine what a low-income, uneducated or non-English speaking parent makes of that (both "draw" and "counters" are ambiguous). This is confusing stuff and it feels machine-translated. As the Boing Boing people point out, giving an example would help a lot. I think it would be an interesting exercise for education students to give this to them and ask them to make it easier to understand.

I think clarity may be one of the great unsung virtues of Singapore Math. My daughter is in her third year of Singapore Math at her private school (she's in 2nd grade) and I don't think she has ever asked for help with a workbook assignment. I feel like she could probably use a bit more practice on showing work when carrying and borrowing, but her homework assignments never evoke a panicked "huh???!!! She's been sick and out of school for three days. I got the math assignment from the teacher for yesterday. They were starting division. I'm not sure she had ever seen the division sign before, but she took to it like a duck to water. It's very visual and initially, all you have to do to solve the division problems is to count up how many apples or flowers or whatever are in each group, but I still think that it's a tribute to the Singapore approach that the initial introduction to division is so painless, especially considering the kids had only about 10 pages of multiplication this year before jumping in to division.

Kai said...


Everyday Math, TERC Investigations... all of the "reform" math programs are actually modeled after Asian math programs. Unforthuantly, the execution is horrible. When they developed the programs, they didn't get the essence of it. They took the superficial stuff and didn't get to the core.

This Everyday Math exercise makes me feel queasy. It takes a wonderful idea, an idea that makes memorizing addition/subtraction facts easier and convolutes it into something weird.

Crimson Wife said...

I don't get the pennies bit, but the 8 + 3 = 10 + 1 is the way my DD's math program (Right Start Mathematics) teaches.

Allison said...

Arithmetic is based on understanding place value. Place value matters whether you've seen an abacus or not. The standard algorithms for arithmetic rely on the understanding of place value, and aid the understanding of it.

The idea that you have some number of 100s, some number of 10s, some number of 1s, that's place value.

So of course children MUST learn that 8 + 3 is 11 is 10 + 1, because otherwise you cannot learn to write 11, and know which columns those 1s are going into.

The point of the exercise you've posted is correct. The problem is with the way they've written the assignment, and with whatever has come before.

In Singapore Math, for example, before they start figuring out that 8+3 is 10+1, they figure out that 11 is 8 + 3 and 11 is 10 + 1. That might seem like a trivial intermediate step in one's knowledge, but it isn't to a child.

The worksheet as shown is confusing. Too many empty boxes. the sideways arrows don't mean anything. No example is worked out to show how you're supposed to do it. "Draw counters" is not a clear sentence in the English language. That the right column is trying to show you how to group by tens, and that you're supposed to draw in the second number and then notice the grouping by tens, and that's the same as the arrow trying to show you what the middle column is doing, is not clear if you don't already understand.

I don't have a problem with 30 minutes of homework for 6 year olds. How else will a child learn their math facts?

I do have a problem with homework that's not clear.

Allison said...

The comments on Boing Boing are worse, though.

That adults can't figure this piece of paper out means the ed school EM supporters have a LOT of evidence on their side that prior education in arithmetic led to no critical thinking skills. This only lends more weight to their side of the argument: the standard way of teaching was a disaster! We are right!

It just isn't that difficult to figure out that 8 + 3 is 10 + 1 is 11 pennies is 1 dime and 1 penny. If the adults can't do that, what CAN they do?


Allison said...

--Adding 1-digit numbers for a 2 digit solution appropriate for 1st grade?

Yes, absolutely.

2. Is this a good example of homework for first grade

The LEVEL is appropriate. The presentation and instructions are not.

3. Is math homework ever appropriate for first grade?

I'm sticking with yes.

4. Why is this child (a product of a highly-educated household) struggling?

Because it's been several decades of garbage in and garbage out. The highly educated know almost nothing, apparently, about the most basic forms of arithmetic. There is really no excuse for the parents not being able to figure out what this homework assignment was intending. (It is a confusing assignment FOR A CHILD. It is an UNFAIR assignment FOR A CHILD. It is appalling that college educated adults can't figure out what this page was asking for, as it speaks to great ignorance on their part.)

Anonymous said...

What Allison said!

Anonymous said...

I had a student once that had the use of an Abacus written into her ed plan. I'd never seen this before so I went looking for one. Big mistake!

People looked at me like I had three heads. I never did get one but it made me go learn all about the Abacus since I figured I'd have to teach it. It's a fantastic place value tool.

Did you know there are competitions in Taiwan where kids go through huge calculations like 9 digit multiplications at blazing speed, beating calculators?
The really good ones no longer use an actual Abacus, preferring a virtual one where they simply go through all of the hand and finger motions.

But I digress. One of the things I 'discovered' is called Chisan Bop. It's a Korean inovation that uses the fingers of both hands as a mini Abacus with thumbs being worth 5 and digits being worth 1.

I loved this and adopted it as my solution for the unavailable Abacus. It was so cool I decided to take four third graders who were struggling with math facts and teach them Chisan Bop. I went to the fourth grade math teacher and said "Give me your four worst adders."

I arranged special sessions and began my experiment. Epic fail! Two of them could not distinguish their left and right hands and one had a birth defect that left her with missing fingers. It was disastrous.

I learned from this the danger of jumping into things you don't know anything about, blinded by your enthusiasm and novice skill set.

I still think the Abacus and Chisan Bop are great tools but they're not panaceas. You need a whole different set of skills to operate them, than are commonly taught in the U.S. so you can't just air drop them into a foreign setting expecting magic.

SteveH said...

What Allison said!

SteveH said...

This reminds me of Everyday Math's "What is the One?" unit. It seemed to me that they were making it more difficult by trying to make it easier.

I see this with place value. It's almost as if curricula are afraid to dive right in and get to work. They want "understanding". They over-think everything. Then they don't give enough practice to make sure that real understanding takes place.

Just do it. There is no one technique that will avoid the need for practice. Too many times I've had what seemed like perfectly clear explanations fall apart when I got to the homework set. Once again, they don't see the linkage.

Anonymous said...

I am going to disagree with Allison about first learning 8+3=11 and then 10+1=11, in Singapore math. I think the way it is presented is as a method of figuring out what 8+3 is, assuming you first know the teens; 10+1=11, 10+2=12 and so on.

Also, when I taught this to my kids using Singapore, we start with bona fide actual physical pennies. Put 8 here, 3 over here. How many does 8 need to make 10? (You have to know some arithmetic to be able to do some more arithmetic.) So slide two over. Now there are 10 here and 1 there. Eleven! Then after awhile just do it with numbers rather than using manipulatives. My 6-year old very regularly adds numbers this way, going into the "numbers to 40" section of Singapore 1B.

I agree that the presentation on the worksheet shown is bad. Rather than being arcana that only math teachers know, "making ten" can be a method of calculation that little bitty kids can master.

CassyT said...

I'm not sure I would be exchanging pennies for dimes this early in first grade, but I certainly would be working with a 10 board and manipulatives of some sort.

Having worked with teachers, I can think of a couple reasons that this student is struggling:

#1. The teacher was behind in the lesson and just handed out the home enjoyment assignment scheduled for that day, whether it applied to what had been taught or not.

#2 Yesterday the students learned to make 10, they haven't actually mastered it yet. Tomorrow, maybe they'll be skip counting by 2's.

Amy P said...

I don't have the workbook on me, but I think the way that Singapore handles this is to have two groups of bunnies or books or whatever. The instructions will say something like "circle ten", and it's really easy to understand and follow those directions, just like it's easy to follow the division instructions I mentioned upthread. Concrete goes to abstract. The reform math people probably think that that's what they're doing too, it's just that in reality, the child gets gummed up in their abstractions at the point when they think they are being concrete.

It's really amusing (or sad) to think about the fact that Singapore is presumably put together by non-native English speakers, while Everyday Math is presumably put together by native English speakers. The foreignness of Singapore Math does pop up in the workbooks from time to time (durians and rain trees), but the directions that I've seen so far are really intuitive.

Cranberry said...

We're using Singapore Math to supplement our school's use of Everyday Math. The early SM addition and subtraction pages do side-by-side exercises, both numerical and pictorial. So, the child would write 10 + 1 = 11, following the guide of ten bunnies plus one bunny off to the side.

This may sound trivial, but when I look at this example, it isn't: in Singapore Math, children never have to find counters, or draw bunnies. They count printed pictures, and draw circles around them to group them. The first exercise is always worked, so the student follows the example.

My son has spent huge amounts of time drawing 10, 15, 20, whatever, objects for Everyday Math exercises. That time is wasted, from a math standpoint. The possibility for error is introduced, as the child could draw 9 bunnies instead of 10, and not realize it.

It sounds funny, but maybe it's cultural? The Asian art I've seen seems to aim for simplicity and elegance. The Singapore Math books focus on the math. The American Everyday Math exercises add unnecessary steps, which slow everything down, and are a distraction.

My child can whip through several Singapore Math exercises, without tiring himself out. With Everyday Math, there's the riddle of "what the heck are they asking for this time," as things aren't arranged logically, then there's the artsy-crafty aspect, then there's the thematic dropping of anything learned or reinforced on that page, as the next page, or homework assignment, does something completely different.

Anonymous said...

What Cranberry said.

And it isn't just EM that does this. My son brought home worksheets like this in middle school. Lots of drawing (one sheet had him draw 15 calculators) instead of just getting to the point.

Once I was helping out in a kindergarten class and when I looked over at the worksheet one group was doing I was amazed at how complicated they made simple counting.

Something like a number picture is frowned upon when all a sheet like that does is make sure the child knows what number is next. Get it right and voila, a picture. It's simple without needing any real explanation.

The new sheets had steps and drawing involved to reach the same result. And like the sheet posted, there were missing instructions so most kids just stared at it until the teacher came over and explained (a couple of times) what was being asked for.

Little kids only have so much attention span in them, and slower ones have even less. By the time the teacher had finished with the explanations, the kids looked drugged, and they still weren't sure what they were supposed to be doing. Many of them still struggled with counting up to 20.

My only guess is that they were trying to add "critical thinking" to the sheet, so they weren't just the bad old rote sheets from the old days. It would have been funny if it weren't tragic, especially for the strugglers.


lgm said...

Wow, a real colored worksheet. Must be a very rich district...ours would have taken the sample workbook and photocopied a photocopy and given that to the children. The circles wouldn't have been recognizable as pennies on the childrens' copies.

>>Liz asked
1. Adding 1-digit numbers for a 2 digit solution appropriate for 1st grade?

Speaking as someone who has helped in gr. 1, this ws is appropriate for this time of year. Learning goals will be different for different students. The primary goal as others noted is learning the concept of 'make a ten', or regrouping into groups of 10s and 1s. In my experience, children with good number sense will be chuckling as they recognize other number bonds and they mentally move the pennies around in their mind. The class has likely been grouping all year as the count the number of days since school began...our district uses popsicle sticks(1 per day) and they make a big deal on the days that they can regroup a collection into ten and then of course the "100th Day of School" where they count ten bundles of 10. Only well above grade level children will be expected to read the instructions - all others were expected to understand from the teacher's verbal instructions or her visual example done in class.

>>2. Is this a good example of homework for first grade

H.W. varies by district. Ours doesn't send math home in Gr. 1.

>>3. Is math homework ever appropriate for first grade?

Yes. Children need practice. My district asks the parents to play board games, cook, and do everyday math activities.

>>4. Why is this child (a product of a highly-educated household) struggling?

Barring an LD or a chaotic classroom, usually children struggle when missing mastery of a pre-requisite skill needed for the current lesson and/or the lesson was poorly delivered or the child didn't attend to the lesson & there wasn't a helper to reteach in small group. Note some children cannot recall or process instructions well. They should be referred for testing.

Why this particular child is struggling can't be determined from the info given. It should be a 3 minute homework for a child who understood either the concept or the procedure and has the fine motor skills to draw numerous circles in the boxes.

SteveH said...

"With Everyday Math, there's the riddle of 'what the heck are they asking for this time,'"

I had many thoughts like that.

"My only guess is that they were trying to add 'critical thinking' to the sheet, so they weren't just the bad old rote sheets from the old days."

Yup, and notice how many of the sheets have so few problems to do. I remember getting angry at my son for not doing his EM homwork sheet after I told him to sit and get to work 5 minutes before. He did them already. They are trying to disconnect understanding from mastery. They don't like the idea that mastery proves understanding, not the other way around.

TerriW said...

This may sound trivial, but when I look at this example, it isn't: in Singapore Math, children never have to find counters, or draw bunnies.

We run into this one a lot -- I suppose the workbook folks are trying to make things more, ah, "fun" for the kids, but my girl just wants to do math, you know?

Audrey gets to something like that, and I tell her she can just draw a line or dot per item. Or if it tells her to color the right answer, she asks if she can just circle or X it. Why not, as long as the right answer is marked.

This is one of those "Thank God we're homeschooling" times, because I see my otherwise very math oriented kids getting points nicked off for not wanting to follow the irrelevant directions.

Catherine Johnson said...

My son has spent huge amounts of time drawing 10, 15, 20, whatever, objects for Everyday Math exercises. That time is wasted, from a math standpoint. The possibility for error is introduced, as the child could draw 9 bunnies instead of 10, and not realize it.

One of my longstanding furies at the public schools.

And not only because it's a waste of time in terms of math. It's also a waste of time in terms of drawing.

fyi: When I finally took 3/5 of a Betty Edwards drawing course, I discovered that drawing is math. (We started out with grids & learned pencil sighting soon after.)

That was a revelation!


Representational drawing is math.

I think all kids should be taught grid drawing if they're going to have art classes.

I remember when we were doing the 'sighting' lesson (that's the term, right?) we had a couple of older ladies who were just totally flummoxed. They couldn't do ratios & proportions in their heads... and they didn't seem to know what the principle was in any case.

Catherine Johnson said...

That lesson was a revelation to Ed, too. He wrote about the Madame Caillaux trial, which was so famous at the time that newspapers produced accurate courtroom drawings overnight for next day's paper. He'd never understood how they could do it.

Once I showed him the grid technique, he got it. He thinks they may have had a bunch of artists working, each one producing one part of the grid.

Drawing With a Grid

Catherine Johnson said...

I haven't read all the comments yet, so somebody may already have said this, but why exactly can't there be directions for the parents who are going to be tasked with reteaching this concept and overseeing the homework?

Catherine Johnson said...

That was a chronic source of annoyance and anti-budget despair around here: if I'm going to reteach math at home, I need the Teacher Edition.

I always thought of that great line about Ginger Rogers: she did everything Fred Astaire did, only she did it backwards and wearing heels.

That's parents reteaching public school math at home.

Catherine Johnson said...

"This looks like the same lessons my 9-year-old brother is forced to do. Whatever workbook they're from, it's honestly chock full of ambiguous nonsense that's far worse than this, where the largest challenge is deciphering what the heck is being requested of the student.

I'm not sure about this one myself, though.

Whoever wrote this damned workbook is a mountebank and a fool."

Wish I'd written that.

Anonymous said...

This is stupid. I knew what it was instantly, and it's a VERY sound teaching strategy, MUCH better than "counting up." It is, in fact, the way Asian math programs visualize bundling (or "grouping").


The blanks are, of course, 11, 1, 11 for one. And three more coins should be colored to show how you make a 10 and have 1 left over.

2 is 12, 2, 12, same procedure on coloring.

3 is 11, 1, 11. Same procedure again.

This is how you add, folks! This is the phonics of addition! The ONLY problem is the lack of directions to aid parents who are, themselves, very poor with the fundamentals of arithmetic.

EM isn't bad because it's bad. It's bad because it requires good teachers (and most elementary math teachers have a VERY shaky grip on basic math) and because it is really appropriate only for gifted students, as it moves far too fast, it spirals, and it covers too many topics for the vast majority of kids.

Anonymous said...

>1. Adding 1-digit numbers for a 2 digit solution appropriate for 1st grade?

My DS's curriculum had him adding two digit numbers in his head and 4-digit numbers on paper before the end of the year. This is WELL within the ability of the average 1st grader.

>2. Is this a good example of homework for first grade

The instructions are at fault here--they are impenetrable.

>3. Is math homework ever appropriate for first grade?

Math fact drills, yes--2 minutes per day. Nothing that isn't fact drilling until 3rd grade at the earliest.

>4. Why is this child (a product of a highly-educated household) struggling?

Poor teacher, not that bright, not paying attention, or all three. With a bright kid and a good teacher, EM works well. That's why schools embrace it. Miss one of those, and it's a disaster for most kids, though.

From what I've seen and heard, the average math teacher is as prepared to teach EM as she is to fly to the moon.