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A number line can also teach different ways to solve subtraction in your head.
623-454
454+46 = 500
623-23 = 600
600-100 = 500
46+23+100 = 169
In any kind of written notation, it looks horrible, but it makes solving these problems in your head much easier to think about it in concepts like using the difference from the nearest 100. Do you want to understand how numbers work or do you want dumb robots who just blindly follow rules.
THAT is a problem. Kids need to UNDERSTAND not just follow steps. The only way my geometry kids know to solve problems with ratios is to cross multiply and divide no matter what the problem looks like. They often make a lot more work for themselves because they don't understand the concept of isolating the variable.
If I give them 2/4 = x/8 they cross multiply and divide. If I give them 4 = x/8 they have no clue what to do. This is one of my pet peeves. I refuse to take the extra step. My students often ask me to just do it that way because that's the way they "understand" it. The problem is they don't understand it. They just follow the steps. They hate it when I just multiply by 8 and do the math. They don't get why I can do that.
I've run into that as well. I do tell them that 4 is the same as 4/1. Have them do a few with the whole number turned into a fraction and then that /1 becomes imaginary and they don't need to do it anymore. It's just a matter of showing them and letting them understand.
That is not done enough in the lower grades. That is where I work.
I think that geometry is an excellent example of what I mean. Kids are taught by rote a series of steps to answer a rather artificial question (and by 'kids' I include most college students...it's funny how much more clear calculus was when I had to answer real questions in a work setting rather than just grind through questions in class) plus they never see that the same answer can be achieved via different methods. The methods, really, just provide a different axis through a kind of solution space and are quite related to each other (if different appearing).
I admit that you have to start somewhere, and this is not dissimilar to the arguments you hit on the best methods for teaching foreign languages.
Given a sparseness of intellectual curiosity in your average human, maybe understanding can only be self-taught in any case.
A number line can also teach different ways to solve subtraction in your head.
623-454
454+46 = 500
623-23 = 600
600-100 = 500
46+23+100 = 169
In any kind of written notation, it looks horrible, but it makes solving these problems in your head much easier to think about it in concepts like using the difference from the nearest 100. Do you want to understand how numbers work or do you want dumb robots who just blindly follow rules.
Oh, I see why people hate common core!
You make it sound as if education pre-Common Core was all wrong and that's hardly accurate.
Euler wasn't educated with Common Core and he did alright
You make it sound as if education pre-Common Core was all wrong and that's hardly accurate.
Euler wasn't educated with Common Core and he did alright
I would say that it was all wrong for some students. The same students who excelled with old teaching methods will still probably excel with newer methods.
You shouldn't necessarily use the exceptional genius of one person as the rule.
Leftists want to make everything complicated, even a simple subtraction problem. If you don't think, you will vote for the leftists in both the Democratic Party and the GOP. Democracy exists to inhibit change. Wake up America.
I would say that it was all wrong for some students. The same students who excelled with old teaching methods will still probably excel with newer methods.
You shouldn't necessarily use the exceptional genius of one person as the rule.
Do you do follow up research to see if your projections are correct ?
Our top students did worse then average Asian students in PISA.
600 for our top students, 613 for China's average students.
We pulled a lot of money out of GT programs to funnel to remediation efforts at the bottom scale.
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