Ah ha ha! I totally meant renaming! I always called it "carrying", but the Singapore books call it renaming, which I'd never heard of. I was talking to my dh and kept saying remaining instead of renaming and I guess the mixup followed me into my post LOL oops!
Discrete means separate, individual, distinct. 'Discrete Mathematics' deals with the study discrete mathematical structures. In short it's used extensively in the sciences especially computer science. It's used in making decisions, forming algorithms, graph theory, sets, matrix algebra, and more. If you have kids that want to do anything with electronics or computer science related fields like programming or building websites, mathematics essential to those fields and should learn as much math as possible including discrete mathematics. The term is very broad so it includes a lot of directions you could possible go.
Couple of thoughts: - As a math nerd, I side with Steve. I ticked my step father off when he was taking classes at the community college because I used to "sneak" his mathbook for fun, LOL. (It says a lot about my step father that I actually got spanked for that, but that's another story.) - As a homeschooling mom, I also tend to think it unnecessary because it is obviously not needed by your son. It's stuff like that that I'm skipping from the public schools. - As a math nerd who frequently worked so fast in high school that I would occasionally add 3-2 or come up with the wrong answer, OR as someone who has done extensively huge problems with multivariable calc and advanced physics, OR as someone who watched the Mars Orbiter mission get lost because the wrong units were used, which could have been caught on double-checking the steps...I say show the work, at least in higher math. I think a mesh of earlier poster hit on the best of both worlds: work through the first few by showing the work so you know how it's done, do the rest forever and ever in your head, and do the work for the ones you got wrong. I think that's the way we're gonna go over here.
Hey, know what really is confusing to teaching maths? When you know the terms as one thing and they change it on you, so you go to explain it to he kids and they have all these crazy new names like renaming? instead of borrowing, now when I tell my kids they go and borrow an egg from the neighbors they understand it, when I tell them to rename it they say " why? why shoudl it be renamed?" so I chose to explain the two at the same time, I have dont this all the way up to geometry now, taught them the books says this but what it REALLY MEANS is... Once you figure out the concept they are reteaching in some crazy way, you just recall the trick or easy way to teach them that one too!
Thank you, Jackie for the kind words above. *blush* If I have any wisdom at all it is just from having been there, done that, made all the mistakes. Thanks to the Lord, he's taught me through them. WEll, OK.....sometimes.... ROFL!!!!
I actually am finding the diagrams more interesting the more I 'get it' in teaching it but still not sure why we have to learn it ( as the kids ask me , especially my ds12 "and when will I use this in the real world?" lol
I think I'd find a balance. I was a natural too when I was young and showing my work only frustrated me. However, when I was doing questions in my head I wasn't always sure how I got to the answer and wasn't always using correct reasoning to get there. That only gets you so far in math and my little house of cards tumbled in high school. So encourage him but maybe have him show his work 1 out of every five questions or something so you can understand his reasoning. Or talk the concepts out with him.
I knew what you meant, but I had no idea how you got there! LOL When I was a kid, we carried and borrowed. When my dd was in grade school, she had to "regroup". When my ds was in grade school, they "traded". When I worked in public school, they taught "renaming"..... When dd was in second grade, they had to make "ten sticks" and "one sticks" and physically regroup and trade and whatever. Like lay out a problem using these popsicle sticks, some of which had ten crayon dots on them, and some of which had one each. So to lay out a problem like 37 + 29, they had to put down 3 ten sticks and 7 one sticks, then put down 2 ten sticks and 9 one sticks, then grab a bundle of the ones and physically trade that for a ten and put it in the tens place, then write down the numbers these piles of sticks represented. DD, a very bright girl, was totally flummoxed. So I told her, 7+9 is 16, puy down the 6 and carry the 1, and 1 and 3 and 2 is 6, the answer is 66. OH! she said, Why didn't they SAY SO???? She worked out her math homework quite cheerfully and correctly, and never used those stupid sticks again!!!
We did Singapore Math. It taught mental math before it taught how to do it on paper. That drove me nuts. In the end, I decided to have them write it out a couple times to show they can, but then to move on and let them do it as they please.
Oh, my children always had to redo wrong problems so if they missed something, I made them show their work on the redone problems too.
