Good gosh |
Or you say that 76 + 52 = 78 + 50. Which is a lot easier for me, when I'm doing mental math. And it uses one of those first-grade strategies that the "math expert" calls 'training wheels". |
Also -- what exactly is wrong with teaching kids to add and subtract using "properties of operations"? Here's are some examples of when it would be quite smart to do so. (a) 49 + 27 + 1 In the above case, a student could very easily solve the problem mentally, without needing to line the numbers up and use the algorithm, blindly working from left to right or top to bottom. "9 ones plus 7 ones is 16 ones, plus one one is 17 ones. Write the 7, carry the 1. 1 and 4 and 2 is 7 in the tens column....." So much easier to use property of operations, and add 49 and 1 to get 50, then easily add the 20 to get 70, and add the 7. (b) 33 + 59 – 9 Stupid to add from left to right first, then subtract 9. Smart to subtract the 9 from 59 first. (c) 58 + 27 - 58 Smartest to subtract the 58 from the 58. Does your "math expert" think the above problems should be better solved using the traditional algorithm, at all times, or would he agree that using knowledge of property of operations could make life (and arithmetic) easier? |
Well, I am a teacher, and I'd be upset if my employer told me not to comment on Common Core State Standards, publicly. I do it all the time, but I do it by posting links directly to the Common Core State Standards. They are there for all people to see. |
If so, then let's not throw the baby out with the bathwater. Poor implementation can be addressed. |
I just watched the video. The teacher is complaining about the curriculum GA came up with and made her and all the other teachers, teach. It was so bad, they had to drop it, and started to use a curriculum NYS developed. They sound bad. But she doesn't say that the standards themselves were bad -- the scripted lessons she was forced to follow were bad. It would be good for GA to write a GOOD curriculum. Or for GA to allow school districts or teachers to decide what they need to teach to allow their students to reach the standards set. |
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"The Problem With Common Core Math Standards" http://www.huffingtonpost.com/nicholas-tampio/common-core-math-standards_b_4180854.html In a recent policy paper, two professors on the Common Core Validation Committee, R. James Milgram and Sandra Stotsky, observe that the math progression does not reach precalculus. College students who did not take a precalculus course in high school rarely go on to earn a bachelor's degree in a STEM area. In point of fact, the Common Core does not prepare students for careers in science, mathematics, engineering, finance, or economics. "At this time, we can only conclude that a gigantic fraud has been perpetrated on this country, in particular on parents in this country, by those developing, promoting, or endorsing Common Core's standards." |
Here is what is wrong with CC (or if you wish, how it is being implemented): Any math problem can be solved many ways. Any reasonably motivated student, even if "only" taught the standard algorithms, will naturally and gradually came up with his/her own mental shortcuts and intuitive visualizations that are useful/meaningful to him/her. Doing so will be driven by the student's own urge to save time and reduce errors. And each student will probably come up with somewhat different shortcuts and visualizations, and that is fine. It is important to keep the lessons centered on the the standard algorithms because: 1) Those standard algorithms always work. Yes there is a nice shortcut for 300-201 or $20-$4.99, but you need a more general method for $21.27-$8.69 2) There needs to be a universal method that all students can use to communicate and "prove" the correctness of a result to others. The standard algorithms are best suited for this. I see teachers giving questions that require the student to make sense of some wacky visual or verbal interpretation for solving some particular math problem. If that interpretation doesn't happen to "click" for a particular student, then the whole exercise is counterproductive. Kids are smart and creative. They will develop their own innate ability to understand/visualize. |
Because it's more efficient for "reasonably motivated" students to "naturally and gradually" come up with their own methods, instead of being taught them? Do you expect them to "naturally and gradually" come up with their own algorithms, too? Because kids are smart and creative?
Now me, I expect math teachers to teach math. I don't expect kids to invent math all over again for themselves. |
The Common Core does not call for a pre-calculus course. That doesn't mean that, under the Common Core, nobody should take pre-calculus. That just means that there aren't Common Core standards for pre-calculus. There aren't Common Core standards for science, either. Do we conclude from this that henceforth schools will no longer teach science? |
Why hasn't Virginia adopted the Common Core Standards? |
First of all, understand that these different ways to perform computations are only being talked about in the early years -- 1st, 2st, some 3rd -- as kids develop number sense. The number sense should be solid by 4th grade, and students should continue to use that bedrock of number sense to be able to do mental math efficiently, and use algorithms when necessary. Secondly, I completely disagree with you, that students will naturally and gradually come up with mental shortcuts. Once you have a method that works, and you know it works, it is very likely that you will just stick with that method. I know for me, that is exactly what I did. I learned very early on to add and subtract by counting on, or counting down, and to this day, to subtract 9 from 17, I count down from 17 nine times. Sometimes I even use my fingers. I do it more so when I am under stress, which makes mental math hard for me; even though I know, and have taught my children, that subtracting 9 is almost like subtracting 10, you just take one fewer so your answer will be one more than 7. There are in fact accepted, efficient ways of performing mental calculations, and kids should be explicitly taught these. Otherwise you end up with kids just trying to memorize number facts with flashcards, kind of like kids who aren't taught how to sound out words, but who have to try to memorize whole words by sight. It isn't efficient and it uses up working memory.
No one is saying don't teach the standard algorithms. However in the early years, it is also important to teach other methods that develop number sense.
Yes, there is a big problem in early elementary math today, in that the vast majority of teachers aren't prepared or trained for teaching anything but the standard algorithms, and the curriculum designers aren't much better.
Dear God, no, this would be the worst possible outcome. Math, like decoding, should be explicitly taught, and kids should be given plenty of opportunity for practice. You do NOT want a generation of children growing up inventing their own way to add and subtract. |
They have spent many years developing the SOLs, which they think are superior to the Common Core. The SOLs are pretty good. |
http://blog.al.com/wire/2013/11/unlike_alabama_these_five_stat.html |