Tag: unschooling

  • How to Teach Subitizing: 1 – 4

    How to Teach Subitizing: 1 – 4

    The comparison of numeracy to literacy is curious.

    Learning math is the opposite of learning to read. When you read, usually simultaneous to learning a language, you sound out words and then put meaning to them. When you learn to count and do math, you know the meaning inherently and then put a language to it.

    At some point we learn to recognize words without sounding them out. And at some point we learn to recognize quantities without counting them out. This is called subitizing.

    The Your Baby Can Read program uses the concept of subitizing to teach reading – you show your baby the word alongside the object. So the shape of the word car is as recognizable as a car itself.

    The children using Your Baby Can Read don’t learn to sound out words. They don’t understand the concept of letters any more than babies not using the program. But they instantly recognize the shapes of the words – giving them an (assumed) advantage.

    Aside: We didn’t use the “Your Baby Can Read” program, not because it was gimmicky (I love anything that looks gimmicky), but because there is a huge DVD element to it. We decided not to put Daughter in front of the TV for her first 2 years. A decision we stuck with, but sometimes was a struggle!

    This article contains a “your baby can count” type program. (And it’s a free download!)

    How did we learn subitizing?

    I don’t recall having been taught it directly. Although I could be wrong. The research on it has been happening since the early 1900s, so it might have been taught without being labeled “subitzing.”

    In a previous article about why learning to subitize is important, Christine Guest commented that she learned it out of frustration for counting with chanting.

    I wonder how many of us do that. Are grownups so adept at subitizing that they forget that’s how we assess quantity? Maybe we’re taught to chant-count because that’s the way we think counting is.

    But it isn’t!

    How do you teach subitizing?

    Images are accompanied by the written numeral as well as the number spoken aloud. The images would be printed on cards, done via video or “live” with 3D objects.

    I’m still working on the numbers 5-10 and up, but for the numbers 1-4, the following 8 styles of image sets would be done twice. Once using the same objects for each image set, and once using different objects for each image set.

    1. Organized in a row vertically.
    2. Organized in a row horizontally.
    3. Organized in a row diagonally.
    4. Organized in a row other way diagonally.
    5. Organized in a regular shape (triangle, square).
    6. Organized in a differently oriented regular shape.
    7. Organized in an irregular shape.
    8. Organized in a different irregular shape. (There will be more of these for 4 than 3, etc.)

    The objects could be blocks, cars, little dolls, just about anything. I created the set below from blocks I found left in Daughter’s block set.

    Each zip file contains a few .jpg files with 4″ x 6″ pictures. You can print them at home or ship them to Walmart, Target, CVS, etc. for printing. I left off the MathFour.com logo so the kiddos wouldn’t get distracted. Please share them along with links back here.

    What do you think? Can you use these? Did you?

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  • Toddlers Begin Counting at the Number 2 (not 1)

    Toddlers Begin Counting at the Number 2 (not 1)

    I had this grand idea when we got married and were hoping for kids – I would teach our children to count starting at 0.

    When Daughter was 15 months old, I decided we should start teaching to count with negatives.

    But I was wrong on both.

    And so is everyone else.

    Why do we teach toddlers to count?

    We practice counting 1-10 with our kids. We know (somehow) that before they’re official school age, they should know how to count to 10. And how proud we are as parents if they can count to 20!

    But these are just words.

    I can teach Daughter to memorize the Fibonacci sequence, but she’d no more know what that means than what counting to 10 means.

    In fact, I know this first hand because I used to count to 10 in Spanish. And I’d leave out ocho everytime!

    I saw a guy made fun of in Germany because he told a waitress he had fünf people in his party and held up four fingers. (She did it behind his back to another waitress – she wasn’t so rude to say it to his face. (Thank goodness; I would’ve had to go Texan on her.))

    We teach toddlers to count for the same reason that we teach them to say please, thank you, yes ma’am and no ma’am – because someday they’ll understand what it means. And in the meantime they can establish good habits.

    So where do they start understanding?

    Regardless if we teach a toddler to start counting with -5, 0 or 1, they start with 2.

    -5 to a toddler makes no sense. Teaching -5 to a toddler can only be dreamed up by a math teacher with no kids (i.e. me three years ago).

    0 is useless. Why would you even mention that you have zero? Maybe saying that there are zero cookies after she ate them all might work. But generally zero things can’t be seen and by the time you’re down to 0 cookies, there’s probably a meltdown in the works. And we all know there’s no learning during a meltdown.

    1 is just as useless. Why count things that are only one? They started with one mom, one dad, one dog, one couch, one bed, one bear,… Almost everything in their world is a single. The number “one” is just as useless to them as the words “the” or “a.”

    But 2 is interesting!

    Daughter was so amazed at the discovery that she had two SnackTraps. Not just the ordinary situation of a bowl of snacks but “TWO BOWLS!”

    As soon as multiple copies of things are in her world, she takes note. If you’re an identical twin, the first time your child sees you with your twin might be traumatic. My best friend is the daughter of a twin and she tells horrors stories of this discovery.

    This is an extreme, but consider all the pairs of things that kids can notice – two shoes (vs. only one that you can find when you’re freaking out and you’re late), two forks (when you’re begging for yours back from her because you’ve not eaten since breakfast), two cars (when you need to get in one and she insists on going in the other).

    And, toddlers really don’t start counting at 2. They don’t start their mathematical careers with counting at all! They start by recognizing multiples. And 2 is the first and fastest multiple.

    So what can you do?

    Keep teaching your kids to count – they still need this skill, just like they need to memorize math facts. But also teach them to subitize (recognize amounts without counting them out). Hold up two of the same items and exclaim “TWO ORANGES!” Then go to another two items and exclaim, “TWO RAISINS!” Stick with one number at a time.

    Daughter is on “two,” so we’ll stick with that for a few months. We’ve got plenty of time.

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