The other week I had to sub in special education for a few days. The children had been learning borrowing and regrouping for months but hadn't been able to catch on to how to do it. Two of the children had been in life skills until just this past year so that may have been part of their difficulty. They would either just randomly write another number on top or would reverse the problem (5-7=2) Because of schedule changes, I ended up only have two of the students most of the time. I showed those two how I borrowed and regrouped, by having them just write a 1 next to the number on the right side instead of trying to convince them to add 10. And they got it. After they had done that a few times, they were able to cross out the number and write the correct number to add on top. Those two continued to borrow and regroup correctly throughout the week so there is a good chance they will continue to do so this week too. The real interesting thing is that their teacher would have never shown them this because she wanted them to always cross out the number so she could be sure of which number they were working with.

But do they understand the concept? They are doing it but it's the understanding part that needs to addressed. It sounds like the teacher should have been working with base ten blocks.

I think it's very beneficial for kids to see different ways of doing things. Some ways "click" while others do not. I think the ten blocks is a great idea. The visual and kinesthetic part of it really helps the kids.

Base ten blocks had already been used - they didn't work. The teacher had already tried every strategy she could think of (and she's a special education veteran teacher). She never had kids that were so low they had been in life skills before. I agree that the knowing is more important than the understanding at this point - at least one of the two boys I was working with had been in a class last year with goals such as "be able to recognize your address when you see it written down." The others in the class, who haven't been in life skills, are still very low academically. The teacher said this was the lowest group she's ever worked with.

I think the "how" is just about always much easier once you understand the "why"-- especially in math. Once you understand place value and why changing a "1" in one column equates to a "10" in the next, the whole "how" question ceases to exist.

I can think of a few areas where a little 'how' is needed before you can get to the why, but as far as math goes I agree with this completely.

Sure-- the alphabet comes to mind. But as a math teacher, I ALWAYS explain the "why" first. It tends to make things so very much easier for my kids.

That presumes they are capable of understanding the why though. Its possible that they can't, due to their disability I asked today, and the two kids are still doing the math right. Sometimes knowing the why just creates hopeless confusion - look at higher level math and some things they never teach the "why" for because its too complicated to get into

I agree. In my experience teaching special needs children, many times they could understand the "how", but they just couldn't grasp the "why". For those children, the "how" is all they can muster.

I'm sorry, but if they can't understand 'why' what use is it to them? It's just a parlor trick, not math. A dollar-store calculator would be cheaper, more reliable and easier to carry around if you just want something that gets results without understanding them.

I'm another one for sometimes (not nearly always but definitely sometimes) skipping some of the why for special needs kids. I think in this case, the important part of the why is for them to understand that subtracting means taking away and this is how you do it. If they don't get how borrowing works but they know when to do it then they have what they need for real life.

And what would you expect them to do when the batteries in their calculator ran out? Just randomly guess and end up trying to pay $.75 for something that cost $300 and vice-versa. And what job would you expect them to be able to hold as an adult if they needed to carry a WORKING calculator with them at all times? *A calculator would be far more reliable for all students. But I don't see you advocating removing math from schools entirely and just handing out calculators to everyone to carry everywhere instead

No I didn't. I just proved how ridiculous what she was saying is. There is a ton of math you do without ever knowing the why (any math teacher can give you a ton of examples on the spot). And there are times you know the why, but not the how. And in cases like this, the How is far more important than the why. And i've just shown why that's the case. Read my post again if you didn't see it.

It is quite obvious that you don't have any experience with teaching very low special education students...

As someone who is very anti-calculator, I think we have to discuss the level of diability of the child. I teach in a Catholic, college prep school. No one who can qualify for admission for my school should need a calculator until they hit Trig. None of my 3 kids is disabled. As long as I have anything to say about it, they won't be using calculators for quite some time to come. They, and the kids I teach, need to know the "WHY" so the "HOW" has some sort of a context. But for kids who are very low special ed, I can see that it would be different. My kids aspire to college, to jobs that require higher order thinking. I can certainly see that a kid whose disabilities limit their aspirations, knowing the "HOW" is sufficient. I think we're comparing apples and oranges. And, for the record, I liked this forum a whole lot better when we weren't comfortable flinging around words like "ridiculous" and insulting each other.

I'd suggest that if you don't know why a piece of math works that a calculator isn't going to keep you from making bad decisions. and neither is knowing any particular math procedure. Teaching students a procedure without a concept is like teaching them to push a series of buttons on a calculator- neither one is teaching them math. I'm disturbed that this seems 'okay' in the context of special ed students.

Today I worked with several students who know how to brush their teeth but will never know WHY they brush their teeth. Does that mean that the fact that they know how to brush their teeth and can remember to brush them on their own twice a day is just a meaningless parlor trick rather than an accomplishment. Or is the fact that they've learned how to do a skill they will need to know how to do for the rest of their life what is important. I believe it is - from your previous comments about math, you see teaching these students to brush their teeth as being completely worthless, for no other reason than they can never understand why. And one of the boys in this thread, could have easily been grouped in with these teeth brushers just one year ago, so you can't say that's comparing apples to oranges either. What you seem to be overlooking is that these aren't just special education students, they are LOW special education - they are students who were life skills last year. Do you know what life skills is? Goals in life skills involve things like being able to recognize your address when its written down. Most kids grasp that one around 12 years of age, if the teacher has been reinforcing every day since kindergarten. That's the level of these children even with their "improved" special education status. They are the kids you only have in your classroom for homeroom, lunch and recess.

(I'm really going to get it for this comment, but oh, well...I'm bored and have nothing else to do...) Might there be a reason for these kids (who are likely to not retain this information once practice has stopped, and certainly not over the summer) needing to know the HOW only? I'm thinking state testing...sometimes you do what you have to do, then once that is over, teach the kids what they REALLY need to know to live... Deny it if you will, but I challenge any teacher to say they have NEVER jumped through a hoop to satisfy someone (or some entity) in order to get to the real work of a classroom...

Maybe I missed something here. If the students are so low learning disabled that they do not understand why they brush their teeth, then it kind of seems like apples and oranges (or maybe apples and soccer balls). If basic life skills are the most they will accomplish, I don't see how putting a 1 instead of regrouping tens would even matter. Personally, I have rarely seen cases in math where the Why doesn't matter. We do How math works, Why math works, and Where math works, so they have a full understanding. I realize this is for mainstream kids, but I'm just throwing in my