This is one of those things that puts me into a teacher rage. Before I rage, take a look at this question from an early elementary test (I believe it’s 1st grade):
Do you know the correct answer?
If you’re my age (32) or older, you know the answer is none of these, because the answer is 8+6=14. This is what we learned in school – to practice and memorize our simple math facts (addition, subtraction, multiplication and division). This was because in the real world when you get older you require immediate recall of these facts to complete other tasks, to say nothing to passing a subject like algebra or calculus in high school.
But now, with the supposed education standards revolution smashing down traditional barriers, the correct answer to this question is actually D. It’s a strategy where you break apart numbers, to make adding larger numbers easier. Only, 8 and 6 aren’t large numbers. Now this particular strategy has kids learning to break apart numbers to equal 10. In this case, you take 2 from the 6 toys and give it to the 8 making it 10. This leaves you 4 left over to add to that ten, giving you 14. Personally, that’s more complicated than just memorizing 8+6=14. Now, I do believe it is important that children learn the numbers that give you 10s (6 and 4, 5 and 5, 8 and 2, 7 and 3, etc), but at the same time they should be learning and memorizing 8 and 6 gives you numbers that ends in 4s (16+8 is 24, 38+6=44, and so on). Just like they should be 9s and 6s giving you 5s, or 8s and 5s giving 3s. This can be applied to any number in any problem with addition. And can be reversed for subtraction.
The problem with the strategy being performed in this question is the students need to know that when they take 2 away from the 6 and give it to the 8, they have 4 left over. So technically they’re required to know subtraction while they’re learning addition. To combat this, they are drawing pictures. Draw 8 circles and 6 circles, grab two circles from the 6 and draw them over with the 8 circles, so visually you can see there are 4 left from the original 6. Ok that’s fine – some kids require visuals to understand what’s going on. I’m totally OK with that because I’ve always believed it’s important to know why the math works, not to just do it. The visual show this, but this is not a strategy that should be taught in place of rote memorization of simple math facts.
Why? Because I taught 5th grade for 5 years, and every. single. year. students (more than half) come into 5th grade still counting on their fingers for addition and subtraction, and are completely clueless about multiplication and haven’t memorized their facts. They also can’t do subtraction because they do it upside down instead of borrowing/regrouping (eg: if the larger number is on the bottom of the problem they just start with that and subtract the number above it, which any adult will know is the wrong, upside down way to do it).
I have a clear memory of starting multiplication in 2nd grade, and having my facts memorized easily by 5th. And because I have them memorized and can look at 9×6 on a piece of paper and have an immediate recall of 54, I can complete 50 multiplication problems in under 50 seconds. Yes, I’ve timed it, because I often did the ‘mad math minutes’ time trials with my class. They marveled at how fast I could blast through writing all the answers, and they said “well you’re the teacher!” To that I said, “no it’s not because I’m the teacher, it’s because I have them memorized and as soon as I see it, I know the answer without thinking. It’s like looking at my shirt and saying ‘that’s blue’ because you’ve memorized that color is blue.”
Now let’s talk about real life. If kids are still coming to 5th grade and higher not knowing their most absolute basic math facts, imagine balancing a checkbook, or counting back change as a cashier. When you’re adding in the tip on your restaurant bill, are you going to pull apart all the numbers and draw a picture on the check to see what you get? Sounds absurd doesn’t it – and you’re probably saying “but Dan, they’ll be much older by then and they’ll be able to do it by then.” Are you sure? When a 10 year old can’t tell me that 12+8 is 20 within 2 seconds, there’s a problem. A big problem.
I’m not saying kids shouldn’t learn to break apart numbers to begin with, to understand why the math works, but it should not be taught as the de-facto way to do addition to small children. Children should begin drilling math facts as early as 1st grade. Pound that stuff into their heads. Drill drill drill drill drill. Flash cards in the car on the way to swim practice. Flash cards between commercials of Sponge Bob. Pop quiz at the dinner table for dessert. Anytime, anywhere.
Parents, get your kids active in memorizing their math facts, early. Don’t rely on the standards and curriculums to do it for you because they won’t. Remember, these standards and curriculums are being written by people who are not teachers, and have little to no experience in education or child development.
The answer is not D.