My ds 11 is doing problem solving in his math. The question is, Do you really have to go through all the steps to figure out the answer? He reads the question and figures it out in his head and gets the (right) answers very quickly. I told my dh that ds should probably do the steps, because later he might really need to know them. So I am making him do them. But right now it is just slowing him down and frustrating him.
I would let them work the problems any way they want, but be clear that if you can't follow the steps on paper they don't get partial credit when they come up with the wrong answers. In most higher math classes, partial credit is given for those who work the problem correctly but make a stupid arithmatic mistake causing them a wrong answer.
My kiddo does this but it makes it really hard if she makes a mistake & you go looking for where she made it. That, & as CM says, you get marks for correct working out in exams even if your actual answer is wrong. That is the only real reason for insisting on showing working imo.
I make my dd show me that she understands how to do it on paper, but after that she can do it anyway she wants. I always got in trouble in school for not showing my work. My dd is a lot like me. It's faster & easier for her to do it in her head. She knows how to do it on paper, but that takes more time & concentration.
my dd's are doing this all the time, what we have decided to do with them is let them do half where they say the answer out loud and the other half they have to work out on paper for us, now the one they do on paper if they are wrong then they have to do them all on paper.. I hope this make sense..
My dd is like that. My dh who is the same way insists taking all the steps is worth its weight in gold. lol. I think that you should do a mix. Allow him to do part of the problems showing you the steps and part in his head. Afterall, aren't the steps there for those of us who can't do it in our heads? lol.
My dh always likes to make sure they know the steps. He says it's great they can do it in their head! But if they don't know all the steps and learn how to use them correctly, that when they get to the higher math they'll tend to get lost.
Okay,k I had one really good math teacher in life, I will always remember MR RIGHT< he got up extra early to drive into school an hour early on the early day to teach me math, personally I hated it at the time but later realised it was great! ANYWAY< He told me that it is great that I can do it in my head, but I need to write it down just the same because someday the problem may be too big to keep track of in my head and it would come in handy then. I have two kids who love to do it in their head, it works out to be correct answers too so I make them write out so many of the problems to prove to me that they can do it correctly on paper , just for the sake of writing it out. I know in thier heads they are figuring it, because thats hwo I do it, I see it in my mind first then on paper later. So we work it together that way, and with a little and a lot of fuss over the paper work they still do it.
I'll be the rebellious one. . . Nope. . .I don't think it's important to have to show the steps until you actually have to work it out that way. This to me, is really a cultural question. In other countries where math is supposedly so much stronger these 'steps' are not emphasized as much as practical thinking skills. Being able to do Math in one's head is an invaluable skill and being able to 'see' the math is worth honing IMO. I could be wrong, but I'm assuming at 11 we're not talking about theorums or several stepped calculous problems but rather fractions, decimals, percentages, complex operations etc. All of which can be done in the head and having to write out something you clearly understand slows you down so that you don't get as much 'meat'. Hope that made sense. . .there's some kind of screaming going on here So go ahead. . .call me rebellious and wild. I can take it. ;-) But my short answer is if they get it wrong. . .it has to be written out. . .but there is more value to being able to do it in one's head. ;-) Oh and as a teacher in a classroom--I totally made my kids write it out bc that was the only way I could grade it. Don't have that problem in hs.
I agree that it's an invaluable skill. The only reason I have Joslyn prove that she can do it on paper, is so that I have it on paper. That way, if someone comes knocking at the door someday & I have to prove that she's really learning, I can pull out some of her work to show.
same with John, he has to show me he really does know how to do it and dd too! not all of them, because I love that we can do it in our eads here, I just want to know that if its wrong, how did they get it wrong, so doing it out on paper shows me that they know the method, and then when they DO get a wrong one we work that out on paper to find the problem area.
I agree 100%. My son is notorious for doing it in his head and at first I used the argument that he wasn't good enough to do it that way and that was why he was producing the wrong answer. Now he's much better at math, so I can't use that argument anymore.:lol: So I starting asking myself why I was insisting that he do it in steps when he didn't need to right now. I think it was because I was programmed that way. Whenver I realize that I'm schooling a certain way because that's how I was programmed, I tend to do the opposite. Homeschooling is about being in charge of making the decision of how you do it, not which method you decide to use. My additional 2 cents!
I would say, even with higher math functions, that you allow them to work the problems mentally. If/when they get wrong answers, ask them to redo the problem on paper. This will accomplish several things. 1. allowing them to keep the love/like of math alive without bogging them down with busy work. 2. nurturing the mental math processes that other countries foster routinely. 3. showing them that many times wrong answers can be avoided by working the problems on paper. 4. you can see where they are going wrong... and if it's an understanding issue or if they just got lost doing it in their head. If you make them write down at least the answers, then staple the paper with the work for the incorrect ones to that page, you will still have a paper trail for any gov't agent to follow.
I totaly agree that it is important to learn to do it in your head, but there will come a time in life when they will HAVE to write down for proof, and they will need to show thier work in that setting, which is why we randomly make sure they show me they know what to do
Yeah, that's what we do---randomly, not EVERY time, just to keep the steps clear in their heads, so that when they NEED the steps for proofs, they will remember how to do them.
On this note.... My mom is a math genius! She can do complex Calc equations in her head. When she was in school, she took summer school classes in math... for fun... every summer (now you know why I'm so screwed up ). By the time she was a sophomore in hs, she had taken every class the school offered and used to have one on one class with the math nun (Catholic school). She even named my sister after the women. Fast forward many many years. When I was in highschool, she went back to college. She wanted to be a math teacher. The problem was that math was so second nature to her that she had no idea what the steps were. Only that when she looked at a problem she knew the answer. She did great in class, but couldn't teach to save her life.
