Math Mondays: Bad at Math? It’s not you–it’s your English.

There’s a lot of hubbub and headscratching about the repeated performance of Asian countries on the TIMSS tests (Trends in International Math and Science Study) in comparison with the results from the US. The top 4 performing countries in the Math section are Singapore, Korea, Japan, Hong Kong, for every year of their included results. And the US? Well, I won’t sugarcoat it.

In short, the tests showed U.S. fourth-graders performing poorly, middle school students worse. and high school students are unable to compete. By grade 4, American students only score in the middle of 26 countries reported. By grade 8 they are in the bottom third, and at the finish line, where it really counts, we’re near dead last. Its even worse when you notice that some of the superior countries in grade 8 (especially the Asians) were not included in published 12th grade results.

Different people have their theories–up till now, I’ve believed that I am so bad at Math that I, alone, have depressed the scores on the TIMSS for our entire country since 1972. I still think there’s something to that.

However, I just read a fascinating chapter in the book Outliers: The Story of Success (an excerpt of it here) and it brought so much together for me in my quest to understand why I can’t do math, why Naturalist struggles with it as well, and how to take a different look at numbers.

First, he starts off the chapter talking about digit span, and memory, things I brought up last week. Basically, digit span memory (or, how many numbers you can remember consecutively) affects a persons ability to perform math easily. Gladwell takes it a step further, in a direction I hadn’t thought about:

Take a look at the following list of numbers: 4,8,5,3,9,7,6. Read them out loud to yourself. Now look away, and spend twenty seconds memorizing that sequence before saying them out loud again.

If you speak English, you have about a 50 percent chance of remembering that sequence perfectly If you’re Chinese, though, you’re almost certain to get it right every time. Why is that? Because as human beings we store digits in a memory loop that runs for about two seconds. We most easily memorize whatever we can say or read within that two second span. And Chinese speakers get that list of numbers—4,8,5,3,9,7,6—right every time because—unlike English speakers—their language allows them to fit all those seven numbers into two seconds.

It has a lot to do with the sounds the numbers make in Chinese vs. English. In Chinese, the numbers are pronounced faster, which leads to a digit span of about 10 numbers vs. our 6. Fascinating…but it gets better…

It turns out that there is also a big difference in how number-naming systems in Western and Asian languages are constructed. In English, we say fourteen, sixteen, seventeen, eighteen and nineteen, so one would think that we would also say one-teen, two-teen, and three-teen. But we don’t. We make up a different form: eleven, twelve, thirteen, and fifteen. Similarly, we have forty, and sixty, which sound like what they are. But we also say fifty and thirty and twenty, which sort of sound what they are but not really. And, for that matter, for numbers above twenty, we put the “decade” first and the unit number second: twenty-one, twenty-two. For the teens, though, we do it the other way around. We put the decade second and the unit number first: fourteen, seventeen, eighteen. The number system in English is highly irregular. Not so in China, Japan and Korea. They have a logical counting system. Eleven is ten one. Twelve is ten two. Twenty-four is two ten four, and so on.

That difference means that Asian children learn to count much faster. Four year old Chinese children can count, on average, up to forty. American children, at that age, can only count to fifteen, and don’t reach forty until they’re five: by the age of five, in other words, American children are already a year behind their Asian counterparts in the most fundamental of math skills.

I’ve always felt like math was like speaking a different language…I hear “48 plus 87”, have to decode the words to make numbers, then take those numbers and make them do stuff. I don’t do this very well, or very quickly. But to think of them as “four tens 8 plus eight tens 7” just clicks faster. Why didn’t I think of that before? There is a math curriculum, Math U See, that encourages the younger kids to call the teen numbers “one-ty (11), two-ty (12), three-ty (13), etc.” which, while we didn’t use the curriculum we did use that method to help Naturalist with her mental blocks with those numbers.

He continues:

The much-storied disenchantment with mathematics among western children starts in the third and fourth grade, and Fuson argues that perhaps a part of that disenchantment is due to the fact that math doesn’t seem to make sense; its linguistic structure is clumsy; its basic rules seem arbitrary and complicated.

Or, more to the point…that’s when math made me cry. Every time I had to do math in 3rd grade and up, I would end up crying. Every time I had to take a timed test while trying to translate the foreign language of math into something I understood, I cried. I just thought that everyone felt that way…I know very little people who sing the praises of math, so I assumed everyone struggled with it like I did. Then I met Hubby, who can do math as easily as breathing…and felt even worse about my own ineptitude. MATH! Why do you scorn me?!

“The Asian system is transparent,” says Karen Fuson, a Northwestern University psychologist, who has done much of the research on Asian-Western differences. “I think that it makes the whole attitude toward math different. Instead of being a rote learning thing, there’s a pattern I can figure out. There is an expectation that I can do this. There is an expectation that it’s sensible. For fractions, we say three fifths. The Chinese is literally, ‘out of five parts, take three.’ That’s telling you conceptually what a fraction is.

This only underscores my belief that sometimes we need to get outside the box to find things that work for us, rather than continue to try to work a curriculum that isn’t working. It’s harder to do that with our huge gorilla of a public school system, but since I don’t have that problem anymore I’ve been able to look high and low for a better math way for both Naturalist and myself. Interestingly, I’ve found that the more Eastern I go for ways to do math, the better Naturalist and I get at it, and the more we enjoy it. Specifically, Vedic Math has been amazing at showing us both the beauty and pattern of numbers. We discovered this on a whim, when a Math Monkey opened up close by and she took some classes there.

Anyway, I know this isn’t exactly a fun math game this week, but I found this chapter so fascinating that I had to share it!

(another article about the differences between Western and Eastern math:
English words may hinder math skills development)

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Happy Valentine’s Day!

it takes a village worth of crafts to make valentines cards.

May yours be filled with lots of glitter, chocolate, and people you love!

Happy Flare Friday!

soarin' towards the sun

I loves me some flare!

I should have been more specific…

when I asked her to go upstairs and ‘get ready’ to go grocery shopping.

I should have been more specific...

2e Tuesday: What was I writing about?

Memory. Sweet, constant memory. We remember lots of things…smells, tastes, sounds, feelings, words. We use memory to help us in mundane tasks..the memory of letter shapes that we use to write words, the memory of what we just heard to help us carry out a job, the memory of number order to help us make computations in the grocery store. If you can’t remember things, it’s hard to do them properly or function without extreme frustration.

At 10, Naturalist tested in the 2% for working memory. This is most often found by using a ‘Digit Span’ test…how many numbers can you remember and recall.

It can be seen as a measure of working memory (or short-term memory, depending on the psychological framework used), although other factors such as attention and comprehension also contribute to the performance on this test.
In a typical test of memory span, a list of random numbers is read out at about the rate of one per second. The test begins with two to three numbers, increasing until the person commits errors. Recognisable patterns (for example 2, 4, 6, 8) should be avoided. At the end of a sequence, the person being tested is asked to recall the items in order.

Individuals with larger memory spans can keep in mind more different stimuli, and this seems to give them an advantage for a wide variety of cognitive tasks. Memory span has been linked to performance on intelligence tests, reading skills, problem solving, and a variety of other cognitive tasks.

While her short term memory was at 1%, her long term memory was somewhere at 93%, meaning she has a powerful memory for things if they make it into her long term memory. To clarify the difference:

long term memory is memory that can last as little as a few days or as long as decades. It differs structurally and functionally from working memory or short-term memory, which ostensibly stores items for only around 20 seconds. Biologically, short-term memory is a temporary potentiation of neural connections that can become long-term memory through the process of rehearsal and meaningful association.

Practically speaking, before I knew about digit span tests, working memory, or percentiles, I thought either I or Naturalist was stark raving mad. I knew all about her crisp mind for detailing things that had happened long ago. She would tell me, in detail, all about her room when she was 9 months old, and how one night she was reaching up to play with her mobile when she saw a big bright light outside her window (the moon) and it was so pretty she looked up even higher and then tumbled over because she wasn’t good at sitting yet. She can draw photographically accurate pictures of her 3rd birthday party…the bouganvilla climbing the trellis, the colors of the flowers, the donut cake and differently shaped pools. Her recall of the places we visited while living in Europe when she was 4 oftentimes out details my memories.

But when I ask her why she isn’t doing [x, y, z] like I just asked her 2 minutes ago, she goes, “Huh? What? I don’t remember you asking that!”. When she used to sit at the table with homework, she’d look up at me with tears and say, “I don’t remember how to do this. I don’t remember doing anything like this in school!” There are few things as frustrating as looking at someone who is so good at remembering minute details and having them say, “Wha??? I don’t remember that…” I tried to keep an even tone, but this always got the best of me. My anger would go from 0-60 because obviously she was 1) lying, and she thought I was 2) an idiot. And obviously she was blowing off school and not applying herself and omg, she was doomed to the life of a slacker because where do you go but DOWN when you already have such a bad attitude about school in 3rd grade! And secretly, I was worried that she was as dumb as a stump. I know, NOT the kind of thing a mom should think, and most of the time I didn’t, but sometimes she’d get this vacant look in her eye and say…”I don’t remember” to something that happened not a day before. What was I to think?!

I’m not alone. If you google “working memory problems” you will get bunches of amazing articles that talk about this.

However, the researchers identified that poor working memory is rarely identified by teachers, who often describe children with this problem as inattentive or as having lower levels of intelligence.

What is the typical profile of a child with working memory impairments?
In a classroom, common characteristics of working memory impairment include:
*Low abilities in literacy and numeracy
*Frequently failure to complete learning activities
*Frequently failure to remember instructions
*Normal social integration with peers
*Very reserved in group settings, rarely volunteer information

On the one hand, working memory allows us to identify those with unrecognised potential, and on the other hand, to aid those who were previously considered ‘unmotivated’ or ‘daydreamers’.

Those words, plus inattentive, ADD, and not focused were all ways that I and her teachers used to describe her. I’d shake my head and because she wasn’t being disruptive or destructive in the classroom, we’d usually have a good natured laugh about it before I’d go home and bang my head against the wall.

“It could be that working-memory problems give rise to observable behavioral symptoms of ADHD: distractibility and also poor academic achievement,” she says. Working-memory deficits might also underpin some reading disabilities, as it controls the ability to recall words read earlier in a sentence, says Tannock.

Many children and adults with attention deficits report that they have trouble remembering events that took place within the past 24 hours. Students also often have “gaps” in their knowledge of basic skills because they tune in and out in the classroom. They are often reluctant to engage in tasks, such as schoolwork and homework, which require sustained mental effort. Even when children with attention deficits attend to the appropriate information, they may only attend at a very superficial level. Therefore, they fail to elaborate on the incoming information. They do not activate prior knowledge and relate it to the to-be-learned information. For example, if a student is reading about the Battle of New Orleans, he may fail to retrieve information he already knows about war, New Orleans or Andrew Jackson from his long-term memory store. This failure to sufficiently elaborate on incoming information often results in deficits in long-term memory storage and retrieval.

Students who have deficits in encoding information in memory may have trouble remembering directions or what they have just read. They may also have trouble remembering what their teachers said during class lectures. Further, they may have trouble remembering what others said during conversations. Their deficits may be more pronounced in certain sensory systems or modalities, such as visual, auditory or kinesthetic. Most of the children I see in the clinic who are having school problems have relative weaknesses in their auditory short-term memory, and because much of the information that is presented in the classroom is presented in an auditory/verbal format, this weakness leads to significant functional problems for them.

Deficits in working memory may be manifested in a number of ways in the school setting. Students may have trouble with following through on directions even if they understood them. They may have trouble with solving math calculation problems that involve multiple steps, such as long division or problems in algebra, because in order to solve these problems they need to access information about math facts from long-term memory while remembering what they have just done and what they need to do next. They often have tremendous trouble with word problems in math because they are unable to keep all the information on their mental “plate” while they are deciding what information is most relevant and what process they need to use to solve the problem. They may have functional problems with reading comprehension because they fail to remember the sentences they just read while reading the sentence they are reading. Writing composition is often an arduous task for them. It requires them to retrieve their ideas from long-term memory while simultaneously recalling rules about capitalization, punctuation and grammar and writing their ideas down. In class, they must remember what their teacher has said while taking notes. They must remember the teacher’s questions while searching long-term memory for the answer. If they are looking up a word in the dictionary, they must remember the word while looking it up. Similarly, when they are answering questions in the back of their textbook chapters, they must remember the question while searching the chapter for the answer.

Uh, yeah. Once, someone asked Naturalist if she’d been outside the US. And this girl with vivid memories of pigeons in Venezia and glaciers in Switzerland got a puzzled look on her face and said, “No.” Later, when I reminded her of our trips she looked at me, shrugged her shoulders, and said, “Yeah, I forgot about all that right then”.

When I ask her what happened on a certain day, and it is still that day, she’ll look at me and say, “Ask me in two days, that’s when I’ll remember it better.”

Sometimes she’ll come out with some facts and when I ask her where she learned it, she’ll say, “A year ago. But sometimes my memories take the fast way into my brain, and sometimes they take the slow way in. That one went in last year but only came out right now!”

And this, my friends, is the delight and the agony of some 2e kids. Briliantly detailed minds that may or may not remember what just happened, or what they just read, or where they just went. And if they do remember, it will be in a few days or weeks or months time.

I think the most significant roadblock with Naturalist is her low working memory. Sometimes she just can’t access the quick and gifted side of herself. Luckily there are ways to improve working memory, and things that can be done about it. But this post is already long enough, so I’ll save that for another day. I will leave you with some other great reads about working memory to tide you over…

About Working Memory.com

Working Memory in the Classroom

If you recognize yourself or your child in these descriptions, come on over and join us at the Out of the Box Thinkers group on Yahoo. You can ask me more detailed questions about it, and I may (or may not) remember what you’re talking about.

Math Monday: Magic Multiples!

It’s time for Math Monday again! Can you stand it? This time, I’ll show you our favorite way to find multiples. All you need is some markers (we use old, stale gumdrops leftover from our Christmas Gingerbread house making…), a pair of dice, and a 99 number board.

rainbow of gumdrops.

With Fun Factors, the point was to role a number on the dice, and cover that number plus all the factors (numbers that go evenly into the number rolled) of that number on the 24 board. For this game, we roll a number and then find the multiples of that number on the 99 board. We started out playing this on the 24 board from Fun Factors, but that quickly became not as challenging so we kicked it up a notch.

multiple magic game

So, to illustrate, the day we played this game, Golfer started out rolling a 2. This meant that he covered up 2, and then 4,6,8,10, etc. etc. until he covered all the numbers when counting by 2’s. “I just covered up half the board with one roll!” he shouted. Math excitement is very contagious. Good to know when dealing with two mathphobes like Naturalist and me.

multiples of 2

From here, you just keep rolling the dice until you fill in every number. Which actually isn’t possible, because of prime numbers, so you’re left with prime numbers uncovered, which is also fun to see.

spot the prime number(s)

I love playing this game because it serves to highlight so many math concepts that get lost in the world of worksheets and memorizations. In fact, looking back, I wish I would have done this with Naturalist back when she was in 3rd grade, instead of all those worksheets she brought home for homework. With dyscalculia, number concepts are harder for her to connect to, especially when learning them out of a textbook. Counting by anything other than one leaves her in tears, so asking her to multiply or count by 3 or 7 or 8 completely shuts her down cold. Anxiety, panic and frustration, which is nothing new to an old mathphobe like me but it’s sad to see in such a little girl! But when she can actually see and create patterns, something clicks and it’s smiles and fun.

Interestingly, while Golfer is a math whiz at computation, when he fills in his chart, he counts methodically up by the number. He can answer math questions faster than either Naturalist or I can, but he fills his chart in much slower because Naturalist and I can spot the pattern the numbers create and just fill it in much faster. For instance, Naturalist figured out right away there was a pattern for 8:

multiples of 8

and 11 (it’s going diagonal, can you see it?)

finding 11 pattern

And actually, she pointed out that the multiples are exactly like the moves in chess. The 1’s are the pawns, the 2’s, 5’s and 10’s move like the castles (going back and forth), The 11’s and 9’s move like the Bishops, going diagonal, and most astounding to me was that 7 & 8’s move like the Knights in that down-1-over-3 move. Trace it out on her card to see for yourself:

Behold, the patterns!

When we finish this game, it’s one of the few times Naturalist wants to stay and do MORE math. Finding those patterns is addictive!


Click through the link for a printable pdf 99 chart with a short paragraph on how to use it to help form solid number sense.

Stress Relief 101–Peanut Butter, Chocolate, & Puppies.

This week has been a doozy Chez Child’s Play. Tantrums, mental breakdowns, whining, emotional overloads, sleeplessness followed by extreme crankiness…and that’s just me! I won’t even get started on the kids issues.

During times like this, in which I am the rock on which everyone crashes, there is only one thing to do. It happens to be the first step to stress relief, and it involves chocolate and peanut butter.

Please, if you ever find yourself with an overwhelmed child or you yourself are heading in that direction, take a step back and move into the kitchen. Put everything on the backburner and make it your life’s work to find powdered sugar, chocolate chips, and peanut butter so that you may construct the Almighty Bringer of Peace:

chocolate peanut butter ball.

The Chocolate Peanut Butter Ball.

Recipe:

Melt a cup or so of chocolate chips in the microwave. Start at 30 seconds, mix, put in for another 30 seconds, mix, etc., etc., until melted.

Have child stir peanut butter and powdered sugar together. I don’t have precise measurements because this is usually done under the gun, but I’d say about a cup of each? You can add more of either ingredient as needed. It should reach the consistency of play doh.

Form round type objects with a spoon, and then dump peanut butter mixture into melted chocolate mixture. Roll it around until covered.

Place gooey chocolate ball on paper plate.

Repeat until you have a plate full of chocolatey peanut butter balls.

Place in freezer for 10 minutes or so.

While the balls chill out, take a moment to chill yourself and your child out. Lick the rest of the melted chocolate out of the bowl or something.

Pretty soon you’ll have these:

chocolate peanut butter ball.

But don’t ask your daughter to hold one up for the camera like this:

chocolate peanut butter ball.

Because she’ll just hold it up for a second and then take off to eat it in peace somewhere else.

she's getting away with the Chocolate Peanut Butter Ball!

Bye bye Chocolate Peanut Butter Ball. Hellloooo smile!

This little recipe has gotten me out of many an escalating crisis.

If that doesn’t seem to be working, grab a puppy and get some puppy kisses. I happen to have one here that’s ready to start lickin’…

Frito Bandito