Question about showing work in Math

[holdinon]

For those who have completed or are in upper levels of Math......

'When your kids are getting all correct answers, but don't write down anything but the answers, and can't really even verbalize HOW they got the answer.............do you work with them until they CAN/WILL write it out and/or verbally explain it, or do you just move on?

I know that they do get it, and even when they do get something wrong (not very often), they can just look at it one time and say, "oh, wait...that should have been three-eighths, not four-fifths". But when it comes to explaining how they got there, they have a very difficult time. I can tell that they "know" it, but their explanation will be something like, "well, I take the fourth and move it over there, and then move the 3 over there....." all while drawing/pointing in the air (as if physically moving around the numbers in the sky. Honestly, I can't keep up with what they are saying/doing.

Pre-kids, I was a statistician (an actuary), so I have had a.lot.of.math. I was never a math teacher, but all my classroom experience keeps coming back to me that you are supposed to show your work . I am thrilled that my kids can do this stuff well, and the fact that they can do it well in their heads just amazes me (as, after all my years of math, I still practically have to have a pencil to solve 2+3 ). My oldest is doing another math program (she was too far in when we found Singapore), and she shows every single step that she does. When my Singapore kids were in the lower levels, I was thrilled when they could solve normal addition/subtraction or even multiplication/division in their heads. I think it's just because they are doing more now, and I am realizing that the higher level maths are coming up, and I can't imagine not showing your work in something like that.

Is it OK that they can't write each step down? I am envisioning a college algebra class where they get kicked out for cheating because they turn in a test with what should have 4 pages of written problem solving, with a simple number written across the front Ok, I know I'm being a little dramatic here, but seriously, is this something we need to work on, or will it all work itself out by the time they get to the higher maths? (If it makes any difference, the kiddos that I am referring to are in 5A and 4A.

Ang

[KristinBeth]

I am not an experienced teacher, but my husband is mathy (worked ahead to the end of the math book for fun because math class was too slow ) and he would have trouble with this. He would get right answers, quickly, but didn't know how he got them. It was fast and furious and in his head. When he did write it down, it wasn't the way it was taught, but it was right. I think in class it is (a) to prove you're not copying answers from your neighbor and (b) so the teacher can show you where your mistake was and help you learn. If the answer is right, there is less need for that.

Now I'll let the teachers answer, but I just wanted to let you know that some people just "get it" and don't know how they "got it" necessarily.

[Larissa]

I just had my oldest son tested using the Woodcock Johnson. (an professional administrator tested him and then talked me through it when they were done)

She said that he didn't write anything down on the math portion of his test. He was trying to do all of it in his head. He got some of them right and some of them wrong. She said that the further he gets in math the more that he will need to write the steps down ... especially when we get into long division and so on. So, she suggested that I really start working with him on writing each of the steps down. I love that Singapore is strong with the mental math ... but it is developing bad habits in my children and if I was a better math teacher, I would have caught it and worked on it more. Math overwhelms me. So, we are going to be taking a few steps back and spending the rest of this semester working on things that he hasn't mastered and working more on writing each step down.

Perhaps not writing each step down isn't as important if they are getting everything right ... but that isn't the case with my son, so we are going to be working hard on writing each step down.

[holdinon]

Thank you both for your replies.

After re-reading my original post, I am afraid it may come across in a way that I did not intend. So.....
Please let me assure you that I am in no way considering Singapore Math may not be so great. Entirely the opposite. I have had many, many days when I kick myself for not using Singapore with my oldest (who is now in pre-algebra). I had seen singapore when she was in K, and came very close to using it. But since she was my first child, and I was not a teacher, and yada-yada (all that stuff new homeschool moms think ), I was afraid to use it because it was so non-traditional. But over the years, of course, I developed more confidence, and then decided I didn't care much about what was traditional, and just wanted what was best for my kiddos .
Oldest was too far in to math at that time to make a change, but my others have all started out with Singapore (well, they didn't actually start with it, but when we switched over to it, they were going into 2nd and 3rd grades, and we began with 1A to fill in the gaps). I have seen a tremendous difference in the way my younger kids understand math. My oldest can "do all the steps", because that's what she's been taught. But the difference is, that when my oldest comes to something new, she needs to learn a new set of steps, because she doesn't have the understanding that my youngers do. The youngers can look at things they have never seen before (within reason of course ), and solve it a good portion of the time because if they understand A and B, then C is not that great of a leap. And this is with All of my Singapore kids (not just the two I am asking about now), so I don't think it has to do with whether they are mathy or not (one of them I would consider "mathy", the others are mostly average ). Singapore, in my opinion, produces a much better grasp of the way math "works".

Ok, sorry to get so off track....I just wouldn't want anyone to read negativity towards Singapore in my original post. Now, back to topic...

I know that they understand. I believe they even know the procedure. I think the problem comes in the area of communication. Does that make sense? They could communicate the procedures they use when we were doing most everything until recently. I think I just started noticing it when they were doing fractions. And the main reason I noticed, is because they were showing off by "helping" their big sister . They corrected her, but couldn't explain to her how they knew the answer. So then I started paying a little more attention and asking them, "how did you get your answer?" more often. They just have a very difficult time communicating that to me. So now after typing that out, I am wondering if this is similar to when kids are beginning oral narrations. You know they know they material, but they just can't seem to form their thoughts very well. Could that maybe be the same case here? If so, maybe if I just ask a few leading questions, and work up to a full explanation, by the time they get to algebra and up, they will have developed the art of "narrating" their math procedure. Am I way off here? Would love some thoughts on this
Ang

[Larissa]

I didn't think you portrayed Singapore negatively at all! I LOVE Singapore and am not considering a move to another curriculum. There are strengths and weaknesses to any curriculum and I am very happy with Singapore and the results that it is producing!
I have just seen with my oldest son that because of how much mental math is involved ... that he is not writing the steps down ... and in his case, he absolutely does need to write the steps down. He is weak in the area of math and would be able to see his mistakes if he would write all the steps down. Every child is different!

[holdinon]

Larissa,
I did not think you were saying that. I hope you didn't think my last post was directed at you! . I totally got what you were saying.
When I saw my original post on the main board, it just looked....I don't know....can't really say....But the title I chose didn't really reflect my question well. It looked more like I was questioning the Math itself. I had briefly proof-read the post itself, but didn't notice how "bold" the title appeared until I saw it on the board index. I didn't realize I could edit the title or I would have just done that (which I have now done). It was the title that was just sounding a little "off". That was why I wrote the second post. I'm sorry if you thought I was responding to you personally .

[Larissa]

OH no, I didn't think that at all!

[my3sons]

For those who have completed or are in upper levels of Math......do you work with them until they CAN/WILL write it out and/or verbally explain it, or do you just move on?

We just move on. In fact, during our standardized Iowa Basic Skills testing, the dc didn't even want any scratch paper - which frightened me enough to set it out for them anyway. But - they didn't need it, and they did terrific on their tests. Singapore really does hone dc's mental math skills. Many times all of the steps dc in another math program may use are not even needed by Singapore math students - many of the steps are simply cut out by a solid understanding of number sense in general. If dc are continually missing problems however, then this is an indication that mental math skills are not in place enough for doing the math "in their head", and at this point, writing out or orally discussing answers is helpful. HTH!

In Christ,
Julie

[netpea]

It has been my experience that if you don't write down the work, it will get to a point where you just can't keep up with the math. Not in the lower grades, but eventually it will bite you in the butt. It's a fine line to walk. you want them to be able to do mental math well but eventually, they will need to be able to do their work on paper for higher level math. There is no way to solve complex alebraic equations without writing it down, and if they get to calculus / differential equations that is also true. I do not always require the work to be written out but I do require it at least part of the time to make sure they know how.