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Mathematics: An Instrument for Living Teaching ??….thoughts/discussion
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I just started reading the SCM Mathematics book and I have a question. I was struck when reading Charlotte’s quote on page 13 (Vol. 1, pp 260, 261) regarding the habit of accuracy. It says…..
“….and quite as bad as these is the habit of allowing that a sum is nearly right, two figures wrong, and so on, and letting the child work it over again. Pronouce a sum wrong, or right – it cannot be something between the two. That which is wrong must remain wrong, the child must not be let run away with the notion that wrong can be mended into right. The fuure is before him: he may get the next sum right, and the wise teacher will make it her business to see that he does, and that he starts with new hope. But the wrong sum must just be let alone.”
Do you interpret this to mean that Charlotte did not recommend allowing the child to correct their mistakes? I usually correct the child’s math with the child and then we discuss and correct wrong answers. However, this passage leads me to believe that I should just allow them to be wrong and move on, possibly reteaching the concept. This might drive my anal self nuts, LOL!
What do you all make of this? I’d love to start a discussion 🙂
Blessings,
Melissa
I would love this, too. I’m reading the handbook as well. But just like anything CM, it takes time to understand what she meant and then how implement it in the lessons/home.
But to help answer your question: I think that is what she means. Maybe the students did some of the work orally/on the blackboard and if they made an error, it was just left wrong (if it was wrong) and then they worked on another problem and the teacher made sure it was right. I’m assuming they did not have worksheets like we do, so they used their blackboards/slates at their desks or in front of the class?? Did the students do independent work, then it was corrected like most of us do?? Or did they learn a new concept, do some practices problems with the teacher watching closely (like copywork/spelling dictation, except in that, we don’t allow them to “see” the misspelled word) and if something was wrong, then they did the next problem together and made sure it was done correctly. Hmmm, not sure how that played out in the classroom (in CM’s day) and how exactly that would play out in our home, especially if we are using a textbook style curriculum at least for now.
I really love this handbook and would like to implement more of her ideas, so thank you for bringing this up again.
I do not know if this is CM or not, but my kids do their math assignment. When they are finished, I take their pencil and give them a pen of any color and have them grade their paper. I call out the answers and watch as they mark them wrong or right. When we have finished grading the paper, then we do the math to see what their grade is and they write it on the top. We then settle in to review the wrong ones and I let them work out what they did wrong (I try not to show them, but let them get it on their own, if they can). Most of the time, it is they reversed a number or added incorrectly etc and not that they didn’t understand the concept. if I see it is a concept issue then I schedule a reteach of that lesson for the next day, but if it is just silly stuff, then they know that those problems are written out onto a sheet of paper so that they can work them again tomorrow. So they learn that sloppy work or not giving their full attentnion to a problem only gets them a less than perfect grade and more work to do later.
We do not have to do too much repeat work here yet and hope to keep it that way. My son is very sensitive when he gets something wrong and I have found that he handles it better when he corrects his own paper rather than me grading it and handing it back to him and he sees three circled etc. So that is why I have them do their own….the other effect is that they get to see how many they got right and so missing just 3 doesn’t seem as harsh and than when they see a grade first.
Oh, if they miss the same problems again the next day, then I reteach the concept and they get a full practice worksheet to complete. Haven’t had this happen yet, but I don’t do it as punishment, but to reinforce the concept and I will make sure they understand that.
I take from Charlotte’s wording that a problem is incorrect anytime it is correct, so all the little things, such as no commas being used, or no labels on word problems, or numbers being tranposed, or written sloppily so that only the writer can cipher are wrong and should be treated as such consistently. It is easy to when you look and they say oh I just forgot to add in the one I carried over. It is important that they know it is wrong, not partly right because they added everything else correct. I catch both my kids trying not to accept that their problems were wrong, but only partly wrong. LOL and I just consistently let them know wrong is wrong.
Math mistakes in the real world have caused shopping malls to fall, bridges to collapse, and airplanes to make emergency landings. Wrong is wrong.
We do corrections just as you all have described. Perhaps she is saying that we grade to be sure a concept is learned to know if mastery is reached so we know if they should move on to a new lesson. If the concept has not been learned, we need to repeat the lesson. And that silly mistakes are pointed out so the student is aware of it so they can be more careful next time to not receive any such undesirable marks. That if it is marked wrong to let the child know, but leave it wrong. Next time, they should be motivated to get it right.
Thank you for sharing this passage with us. It is very interesting. I wonder if we should change. It would make lessons go a little quicker.
I know one mom that uses a math program with a fair number of problems – the child does half the problems. If there are any wrong, they have to do more of the problems (with her watching so she can correct any problems with the process….) so the child has motivation to do it right the first time – and if there are problems, they get more practice…
This is really thought provoking, and different from how I thought of teaching math.
I think Charlotte was thinking that when a child is allowed to end the lesson with all problems correct, that they did not figure correctly at first, they would not have the motivation to truly learn the material for the next lesson, because they could always correct. To have to move on with errors remaining might motivate the student to ponder the lesson and perhaps come to understanding on his own, or to seek further teaching and help.
I think the significant part of the quote is ‘he may get the next sum right, and the wise teacher will make it her business to see that he does, and that he starts with new hope.’
As the teacher, we should be striving to ensure that the lesson is taught well and understood, and the next problem will be solved correctly. If we correct each problem with the child, then at the end of the lesson we have a page of correct problems and all seems well, but if we don’t correct and allow wrong to remain wrong we can know how we are succeeding in teaching our child. Several incorrect answers may indicate where we are not teaching to our child’s understanding.
How important it is to see that our children are hopeful of doing better in the next lesson!
I’m sure there are great character lessons here too. Not every wrong is easily corrected. We must learn how to put the past behind us and focus on the now. To grow from our mistakes.
What a great discussion and I hope it continues! From the context of the passage as well as Charlotte’s overall philosophy, I take it to mean that we would be fostering a habit of carelessness in our children if we allowed a correction or a “do-over” due to work done hastily. There is a big difference in getting a wrong answer because they don’t understand a concept and getting a wrong answer because their work was done haphazardly or without care.
Link this with CM’s methods of reading and narration and it makes even more sense.
Warmly,
Richele
I am really struggling with Math. I am reading/using the above mentioned book but feel like I’m not doing enough. We also do math read alouds and Family Math games. I have dd7 (delayed) and ds5.5. I know they are young but when I look at MUS and RS, etc I feel like maybe we would be better with a guide like that. I was planning on using Ray’s and/or Life of Fred but I keep going all over the place. I am on the LivingMath forum and they suggest that you don’t have to wait until a child has mastered a concept prior to introducing another. CM seems to say otherwise according to this book. And then I know that parents seem to flip flop between programs and then the kids are either behind or hate math. I know I’m looking for that magic program but I think in the end I need more direction. Does anyone else feel like this with using this book? Am I even making sense? Thanks for your help.
Richele and others, I find this interesting. Now, I don’t have the SCM book yet (it’s one I want to buy soon). Here is my question about this topic. Is there value in working through missed problems with a child but allowing their original grade (with wrong problems) to stand? This is what we do. If a child missed two problems that’s the grade they get. We usually work through the missed problems together (me watching while they work and orally explain the steps) so I can correct a misunderstanding if there was one. So while the incorrect answer still counts in the grading scheme, we also work on improving their knowledge. Reworking the problems also is a natural (to me) consequence that takes more of their time if they were rushing through in the first place and being careless.
THoughts? Agree? Disagree? I really want to know!!
Hi Tristan and mrsmccardell, I just wanted you to know that I saw your questions and will respond as soon as I am able. We have company on their way over, followed by a puppy training class and a business phone conference at 9pm so, barring insomnia, it will be tomorrow. I wish I had a math emoticon 🙂
So I am better able to understand your question, mrsmccardell, when you say you are “going all over the place,” do you mean the sequence in which you are teaching things or in your debate on the method for teaching math you will be using?
Until then,
Richele
Richele, “Both” is my answer to your questions! We’ve dabbled with money before we got to the official starting point per cm math book and dabbled in other things. I was just planting seeds for later in depth learning once curr is chosen. And then my debate on which curr. to really follow. We have 4 dc and am I crazy to think that there may be one size fits all…otherwise, how do you keep that many different math programs going? I’m seeing too many friends with high school students and they are on their 4th math program. Thanks for any help. Enjoy your company and take your time getting back to me.
mrsmccardell, I feel your pain 🙂 I have a 12th grader who hates math so much, and it is a very difficult subject for her, so we opted to scrap it this year knowing she’s met her basic math requirements of algebra and geometry, is not going into a math field, and is attending a technical program vs. university. It has been a huge relief!
I have a 4th grader with math anxiety. She’s used A Beka, Horizons, and MUS. I thought MUS was the cat’s meow until Gamma struck with multiple digit multiplication and place value over 1000. I’ve tried a billion different ways and games to teach these concepts and she still isn’t able to get it. We’ve since scrapped the MUS and have been in math limbo ever since.
I also have a dyslexic 3rd grader using RS Level B for the second year. It’s going VERY SSLLOOOOWWW!! He does seem to have a general knack for math, aside from calendar math, which I think is totally screwed up because of his dyslexia.
I’m assisting my sister in getting her homeschool off the ground with my 2nd grade niece that was just pulled from a parochial school. They’re using Scott Foresman Mathematics…just finishing the workbook that was sent home with her. It’s over 540 pages!!!….can you imagine for 2nd grade!!
I also have two one year olds in the mix. I am realtively good at math and didn’t have any struggles in school. However, doing math yourself and teaching math are two totally different things. I know what I want to teach, I just have no idea how to go about it.
I currently own or have owned at one point nearly every math program you can imagine. We have boxes of math manipulatives and resources. This does absolutely no good if you don’t know what to do with them. I want something that says today you do “X”, tomorrow you do “Y”, and the next day you do “z”. At least until I get a feel for it and then can branch out on my own.
I recently started reading the SCM Mathematics books, hence the reason I started this discussion, but still can’t wrap my brain around it. It’s all fuzzy in this 40 year old mind…LOL!!
I have jumped programs. I have instilled math anxiety. I have created a monster and now want to run the other way….someone please save me…..
Blessings,
Melissahttp://reflectionsfromdrywoodcreek.blogspot.com/
Much of your solution depends on patience…you have to observe readiness. Formal, abstract math is quite difficult to understand without concrete understanding. You can push through the pages, as you’ve seen, without it making sense. That’s where you “instill math phobia.”
Hands on, real life practice will probably suit you well for quite a while, giving you plenty time to choose a curriculum.
I have stacks of math curricula, too. It had to wait until later to be used. But, we do employ facts practice even while they are working on hands on problem solving. It’s a resource for later use. I’ve no clue where I line up as far as CM approach to math. It’s been a trial and error approach with each child.
@TailorMade you said “But, we do employ facts practice even while they are working on hands on problem solving”
Can you give me an example of what this looks like in your day?
I know Ruth Beechick(sp?) says that you shouldn’t rush through the manipulative stage and I undersand and agree with it. I just feel like I should have done that when they were younger and not starting at 6 & 7. How else are other year 1 students starting with other curr. that starts with abstract numbers on a worksheet? I am still doing manipulatives b/c it’s a necessary stage…I just feel late in the game.
I think Math Mammoth looks good. I may try that in a few months…even if I just do it orally and use it as a guide.
I’m a little grumpy right now so I don’t know if I’m making sense.
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