I’ll give you that it ‘has nothing to do with Common Core’, technically, but I’ll bet you, the teacher didn’t create anything. These lesson plans and and even the homework are all available online. (From CommonCore . Com which I understand has zip to do with Common Core).
My kid is doing the exact same thing and has been marked wrong for making, literally, the exact same mistake.
That’s really at the heart of the issue and it’s why people have a problem with Common Core. Even if Common Core is the wrong target. Call the teachers lazy, call them dumb, call them whatever you want, but it’s what’s going on. They’re getting their lesson plans and worksheets from a website and teaching based on that.
I don’t know why everyone keeps ignoring this point. I guess it’s more fun to be enraged about what we imagine is happening.
This happens to my daughter. She’s in 4th grade doing division but sometimes she has simple addition or subtraction problems where she has to use a certain method. It’s just a reminder, bit if she gets the method wrong, she gets graded wrong, as she should. This doesn’t mean that she doesn’t know the math, that she was taught wrong, that she was penalized for thinking outside the box, or that she is ruined for life because she suddenly can’t do addition to suit the evil Common Core standards.
Not my classroom, but it is my subject, and I’m currently teaching multiplication, and almost exactly this issue came up today: a student modeling some problem like, “Joe has packs of gum, and each pack has six slices of gum,” provided the equation 6 x 5.
My answer was something like,
“So, yeah, 6 x 5, or 5 x 6. Remember how yesterday we saw you’ll get the same answer, you can multiply numbers in either order? When I’m teaching it to you, I’m gonna put the groups first: five packs of gum, with six slices in each, is five groups of six, or 5 x 6. You might find it easier to understand multiplication if you think of it this way. But like I said, same answer either way.”
Now, here’s why it’s important to give a consistent path from story to equation. Most of my students today were able to come up with a simple multiplicative story problem (“Here are four spiders. Each spider has eight legs. There are 32 legs in all. 4 x 8 = 32”), one kid’s problem looked something like this:
He found the correct answer by drawing four fields with 2 goals in each–but he was flummoxed as to how to translate the drawing into either words or numbers. For him, and to a lesser degree for students who aren’t struggling quite as badly, a consistent method for translating a real-world situation (or a story-problem situation) into mathematical symbols is a real help.
But I’d never in a million years take points off for applying the commutative property. Good god.
Certainly! Small-minded teachers who didn’t understand the subject they were purportedly teaching marked correct answers as incorrect with distressing frequency.
It infuriated me then, too. I suspect this is EXACTLY why the response is emotional now.
Exactly. In fact, here’s a great example.
If the homework says (and the lesson plan for the day was about): Break down these addition problems to make them easier to work with (or however it should be worded):
17+3+100
The (most likely) proper answer would be: 10+7+3+100 = 10+10+100=120
If the kid wrote 20+100=120 (or worse, just 120), it would be wrong.
Why? Yes, he can do 17+3 (or just the entire problem) in his head, they were taught that earlier in the year, but it doesn’t teach them how to break down the numbers and build them back up into something easier to work with. It’s a building block to move forward with. Later in the year when some part of a bigger problem includes (probably on purpose) 143+157, they’ll quickly be able to say 200+43+57 and only have to work out the 43+57. The kid that was praised for jumping ahead and thinking outside the box and being super smarter than the rest of the class is going is the one that’s adding 143+157 by hand now.
Math isn’t like reading class. The goal isn’t to be the first one to finish the book or be the furthest ahead. It’s about fully understanding each concept before moving on to the next. Having a rocky grasp or no grasp at all of one lesson will just mean you won’t understand the next one at all.
Right now my kid is learning how to come up with a ‘guess’ as to what an answer should be by rounding all the numbers and then adding. They want her to be able to look at, say, 1233+885+17 and say “well, that’s about 1200+900+20 which means it’s going to be about 1120 (or 1100)”. What if her ‘trick’ was to just find the exact answer and then round to the nearest hundred? Right answer, wrong method. She’d never understand rounding that way. She’d never be able to guestimate that way. She’d never be able to get an idea if her answer is in the right ballpark that way (which is where they’re heading with it). What happens in the next lesson when they’re working on areas of shapes and the teacher say “Can you guess what this should be, it’s 9 x12”. She can’t do that in her head, but she can do 10x10. If she used her ‘trick’, she’d be lost.
Out of curiosity, what grade and public or private?
I think what you’re doing is great. The difference is that you explained, at least to some degree WHY they could do it either way.
I know a lot of pubic school teachers (and not their fault, it’s the way the system works, at least around here) that end up teaching classes they don’t want to teach…or even understand.
I have a feeling many of them would mark it wrong because the lesson book (that they buy online) says to mark it wrong and they don’t know any better, not until they get to the lesson on commutative property and they themselves learn it the night before.
Imagine tomorrow the school decides you’re teaching a new subject that you have very little knowledge of, here’s the text book, here’s your lesson plan, here’s the homework worksheets. When a kid writes something up a bit differently than the answer key says and you don’t realize it’s technically correct, you might still mark it wrong.
So the teachers were never instructed how to teach according to the standards of the real Common Core. The school district simply told them to teach according to its standards. Some of the teachers didn’t understand what they were supposed to teach, and they were given the idea that they would be fired if they couldn’t do it without any instruction. So they found this website commoncore.com which has no relationship with the group that actually created the Common Core. It claims that it can show these poorly instructed teachers what to teach.
The problem then is school districts that can’t be bothered to instruct their teachers on new ideas that they are supposed to teach, teachers who are too lazy to learn by themselves (or are lost about what’s going on), and a website that’s probably set up by some scam artists.
The convention is not universal for multiplication. It is universal for matrices. A 2x3 matrix is not the same as a 3x2 matrix. I believe that’s what this teacher was trying to get across. The idea that in the future, it will be important to know that when you have matrices of the form YxZ, the Y is the number of rows, and the Z is the number of columns. Not the other way around.
Sometimes teachers want to expose you to an idea now, so that when you encounter it later in your studies, you aren’t as confused. Like I said, I’m not sure this is the best time to plant seeds for matrices. What grade was this kid in? 2nd grade-ish? That’s when I learned my times tables. On the other hand, maybe times tables are old hat to these kids and the whole point of the lesson was learning to distinguish between rows and columns? All the sudden, the teacher doesn’t seem so stupid.
Almost certainly it’s third grade–the grade I’m currently teaching, fwiw. It’s far more important for children learning multiplication to understand the commutative property than it is for them to understand a principle of matrix theory, and the common core math objectives for third grade bear this out: the commutative property, unlike matrix theory, is explicitly mentioned.
There’s a good point to be made here. We’ve seen countless complaints that parents can’t help the kiddies with their arithmetic any more since it’s all done different, and the terminology is all different, and the processes are all different, and just getting the right answer isn’t good enough.
And we’ve also seen the complaints that the educational materials are crapola – no textbooks, or only very poor cut-rate books hastily written by third-rate textbook houses, or cheesy handouts downloaded and printed from [noparse]shit4brains.com[/noparse] – compounded by possibly poorly trained teachers who might not have made the desired points very clearly in their classes.
At the very least, there should be textbooks or handouts that describe what students and parents need to know, in simplified language that even old fogeys can understand.
We see these handouts with problems like “Draw the boxes to illustrate 5x3” or “Show 5x3 as repeated addition” – but are there instructional handouts to go with them that explain “5 x 3 means five groups of three things each” and “3 x 5 means three groups of five things each” ?
I was tough not to say 3 times 5, but to say 3 multiplies by 5 ie 3,3,3,3,3 or 3+3+3+3+3
Then it was pointed out to us ( if we didn’t see it already that 3 multiplied by 5 = 5 multiplied by 3.
I matriculated with maths 1&2, physics, chem and economics, then did 2 years of engineering. never did I hear most of these terms used by others in this thread.
If the teacher is trying to prepare them for future maths classes by falsely implying that 5x3 =/= 3x5, she needs to be fired.
Numbers are not matrices. Marking number multiplication wrong because it does not follow the same rules as matrix multiplication is as stupid as marking it wrong because number division does not follow the same rules.