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(I posted this on the K-8 board, but maybe some of you more experienced people can help me think about this, too. )

 

OK, that is a weird question, so hopefully this will explain it.

 

I feel like I have an alright handle on teaching writing skills to my kids, with some knowledge gained from various sources such as WTM/SWB's writing lectures/R&S writing lessons. I feel like I have an alright handle on teaching Latin skills, even though I don't know Latin any more than my oldest child - but I've figured out a few things about the language and was able to set up a study pattern to follow. I know how to teach spelling and reading; I'm doing alright with teaching English grammar (using R&S and applying that knowledge to writing and reading/analysis); I even have a sort of handle on teaching art skills here and there, with the help of some books, when we can get to it.

 

But I've been reading those threads about conceptual vs. rote math, and am nervous. Not really, but just slightly. We have been using R&S and I intend to stick with it til we switch to the old Dolcianis for high school. I *have* found that, like 8FilltheHeart said somewhere in one of those threads, that this traditional program *does* teach concepts - and I know this because I have read explanations in it that helped ME understand elementary things that I never understood before. The TM would tell me to make some little chart or manipulative or something, to illustrate what it was talking about, or it would tell me what to say to the child to help him understand the concept. Sometimes, if my dd10 didn't understand, I was able to figure out a way to explain, that she would understand. Or I was able to figure out how to use something to illustrate it. Even now, when she's going through division flashcards, sometimes I will still say to her: 24 divided by 6? (dd hesitates for too long) OK, 24 cookies divided among 6 people? Oh, 4.

 

BUT. Even before reading those threads, I still usually have this uneasy feeling that *I* don't understand concepts really well, and so I wonder if she does. (ds "gets" math very easily - he is one of those who figures out different ways to solve problems, like I read on another thread) So today I asked her some questions to get her to articulate what she understands so far about numbers, addition, subtraction, mult, and div. - so far so good. (she's in R&S 5)

 

But I find that math is the one subject where I can follow the book to teach my kids, but I never feel like *I* have absorbed and understood the concept well enough. Yet because R&S has so many lessons in it, I always feel this pressure to make sure we get our lesson-a-day in, so we can finish in June. I wish I could take the book, take a step back from it, look at it with a bigger picture, and KNOW which lessons are important, which parts of the lesson are important for them to do, and leave out other parts. I've already dropped doing the tests because the review lessons are way longer than the tests and the tests just repeat what they reviewed the day before.

 

Does anyone else do this? Actually take control of the book and pick out from it what is important? I already do stuff like odds or evens, letting my kids answer many things orally, etc. to make it shorter, but I still feel driven by the book, and I somehow feel like I should be driving the book but I don't know how because math is not my strength and yet I WANT to "see the beauty of math" that Jane in NC is always talking about. I also get math activity books from the library, but even with these I feel like I'm skipping through them in random order. I guess I don't see yet the bigger picture of how to build arithmetic skills - this first, this next, etc.. The only thing I'm sure of is memorizing math facts - yes, that is important to me and I'm glad we did it.

 

I'm not really looking for advice on "how to cut down time in R&S" - more in general, how do I teach math while using R&S and assorted library books? I've looked into buying LoF books, but I don't really want to use another program alongside R&S, but I don't mind creating my own "supplementary games/activities/list of skills" type of thing, as long as I see a pattern and purpose and progression in it, and know what to include and why.

 

So, any thoughts? Who's able to do this, and how do you do it?

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I replied in K-8 before I saw that you x-posted; so I'll copy my reply here as well.

 

It has been my experience that, in order to effectively teach math, a teacher should have knowledge way beyond the material that is being taught. If the math teacher is just one step ahead of the student, she simply can not see the big picture to the extent it is necessary to teach the concepts well and go beyond simply drilling procedures by assigning and grading worksheets.

So in order to "take control" (I like the way you phrased this), you should work ahead and get a thorough understanding of the math material that lies ahead, not just the material you are currently teaching.

This is, IMO, one of the factors that contribute to poor math teaching in schools: the teacher's inabilities to do math that is harder than what they teach.

I think for math it is not sufficient to follow the book and be just where the student is - you need to math-educate yourself first, and then you can go back and teach math that is below your highest level of math expertise. That way, you will be comfortable teaching and you will be able to judge materials, procedures, assignments instead of blindly following some prescription.

 

If you feel you are unwilling or unable to do that, I would recommend to "outsource" math by using a curriculum that is designed so the student can work without you as a teacher.

__________________

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ll.

 

It has been my experience that, in order to effectively teach math, a teacher should have knowledge way beyond the material that is being taught. If the math teacher is just one step ahead of the student, she simply can not see the big picture to the extent it is necessary to teach the concepts well and go beyond simply drilling procedures by assigning and grading worksheets.

 

 

I wonder how much it depends on the particular student (and the student's working level and "stage" in terms of development of abstract and logic skills) and the teacher. While there is much in what regentrude says that resonates with me, my experience with dd was practically the opposite, in both math and science. I never taught her formally, lectured, or "presented" material as an authority figure. Rather, we would work through books, problems, ideas, and concepts together; we'd play lots and lots of games; and discuss things constantly.

 

I have gone up through calculus in the (distant) past, but I never felt that I understood ANY of the why's, and could never recreate the steps to solve even the simplest of problems, such as dividing fractions, on my own, before I worked through these things with dd. We didn't use a textbook all the way through elementary school, but drew on a variety of math resources including the magnificent Marilyn Burns books and lesson replacement units, through sixth grade. In 7th grade we used a textbook based on problem-solving strategies, something I'd never been exposed to in all my education.

 

The situation is even worse in science. I had practically zilch science education (was taught by nuns who clearly put science at the bottom of their list of educational priorities, moved schools a lot, and just generally was messed up in terms of science coursework) and considered myself a scientific illiterate. Yet I felt I was at my best with kids (both with dd and with a co-op class) through elementary level and even into junior high when I taught OUTSIDE my own academic speciality. I think this was because I understood the lack of prior knowledge, the lack of understanding, knew what it was like to struggle through, knew what kinds of things presented obstacles to understanding, had just gone through the process of figuring something out or experiencing it myself. I didn't assume too much; I wasn't so comfortable with the material that I forgot their level of understanding or referred to things they didn't grasp or hadn't been exposed to.

 

But I have to stress, I did a lot of this not in conventional "teacher" mode, but as a co-learner, a facilitator, and also as a person who knows how to ask questions and find resources. I was thrilled to figure things out, make new connections, understand a concept I'd read about but never experienced hands-on or in multiple ways; and I think that enthusiasm helped enormously. I was reading outside material as we went along.

 

Now that dd is in high school proper, I'm finding I am at last much happier teaching her in my speciality (history and literature), while handing over science to her chemist father and letting her work through math on her own, which she does quite well. She's fourteen; once she hits fifteen she's at the age for community college in our state.

 

Again, I don't know how much of this is dd, how much is her particular learning style, or what other factors come into play. This has just been our experience.

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I just have a couple of thoughts in response to your interesting conversation.

 

First, I think math is not dissimilar from other subjects in that there are many ways to think about it and many ways to get a right answer. Some programs are better at encouraging this than others (Singapore is supreme, IMHO), but many of the really excellent math students I've seen just get this. My son is on a small "math team" and the coach will tell you that he's taking the kids beyond the textbook-here's-how-you-do-it-and-every-problem-is-doable stage and into the just-try-things-and-know-when-to-give-up-or-get-help stage. All that is just to say that I don't believe you *have* to know how your student gets math or get it in the same way that he or she does.

 

Secondly, I think the best way for me to assess what my child needs to do/know in the elementary years is to teach the child the lesson -- by looking at the text and exploring it together. In the secondary years, it's key for me to use a program with fully worked out answer keys, to correct the child's lessons myself at least most of the time, and to work back to figure out why any wrong answer went astray (doing a google search online if I need more understanding).

 

Julie

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I think you are on the right track: working systematically through one good basal textbook (R&S) with supplements.

 

We used R&S as well. Every Friday was Fun Math Day at our house: we used mind-benders, Family Math, Singapore's Creative Word Problems booklets, etc. Like you, I didn't want an entire second math program because I believe that R&S does such an excellent job of teaching both how's and why's. However, I also wanted the children exposed to fun elements and seeing "math" as more than just textbook problems to work through....

 

To relieve the pressure of finishing a text within a year, I didn't worry about that. We did, however, finish every R&S textbook. When we started the next one, I would have the children do the chapter review and then take the test for the first 30-40 lessons. There are very few new concepts in those beginning lessons. The chapter review would pinpoint any weaknesses which could easily be addressed without having to wade through an entire chapter of review. By the time the children reached the end of their R&S sequence, they were all caught up, finishing the texts on time, and have been excellent students with excellent math thinking/skills.

 

What you can do to feel "more in control" is to step up your *own* learning. Don't just check out books from the children's section of the library. Get a few reference books, too. I know Rainbow Resource sells several "math overview" books geared for an adult audience that are meant to do just what you are looking for: filling in the gaps between what you learned and why it works.

 

Also, NYT published an interesting little series on math at the start of the year:

 

http://topics.nytimes.com/top/opinion/series/steven_strogatz_on_the_elements_of_math/index.html

 

The nice thing about this method, slightly random though it may seem, is that the more you learn and know, the more you will be able to "add it in" at just the right moment--just like you did with your daughter and long division.

 

HTH,

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KarenAnne,

 

I'd appreciate the title of the book you mentioned above.

 

Regards,

Kareni

 

Crossing the River With Dogs, available from Key Curriculum Press new, but I got a used copy on amazon. The book is suggested for high school, but we had absolutely no problem using it in 7th grade with the exception of the algebra chapter, which we skipped. All the problem sections begin with very easy problems and increase in difficulty; when we got to a point where we couldn't figure any out, we just stopped -- this was usually quite near the end anyway.

 

Having used the book, I'd also get the answer key/solutions manual if I had to go through it again.

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Reading through Professor Wu's online articles and monographs has helped me get a big picture view of school math. I particularly like his chapter drafts on Whole Numbers and Fractions.

 

I understand wanting to feel like you've got a handle on where things are going. (I'm still working on it when it comes to phonics and teaching reading :001_huh: - trying to figure out how to do it "right" has led me to dive headlong into linguistics. I'm learning a lot, though :).) For me I just read, read, read, synthesize my thoughts via posting here or on my blog, and then read, read, read some more. Trying to get a deep understanding of so-called "elementary" subjects has been my main hobby over the past few years.

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Hi all, I am not ignoring this thread - it's just that it's a national holiday here in Canada today, and we have a birthday celebration tomorrow, so I can't do justice with all your great replies tonight. But I will in the next couple of days! I really appreciate it. Always open to hearing more, too, meanwhile.

 

Vicki in MNE - I remember you! So nice to see you here! You gave me a TON of help with R&S a few years ago - I printed out a post that you sent me that was so helpful. Hope you and your family are doing well!

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I replied in K-8 before I saw that you x-posted; so I'll copy my reply here as well.

 

Thanks, I replied to you over there.

 

I wonder how much it depends on the particular student (and the student's working level and "stage" in terms of development of abstract and logic skills) and the teacher.

 

Yet I felt I was at my best with kids (both with dd and with a co-op class) through elementary level and even into junior high when I taught OUTSIDE my own academic speciality. I think this was because I understood the lack of prior knowledge, the lack of understanding, knew what it was like to struggle through, knew what kinds of things presented obstacles to understanding, had just gone through the process of figuring something out or experiencing it myself. I didn't assume too much; I wasn't so comfortable with the material that I forgot their level of understanding or referred to things they didn't grasp or hadn't been exposed to.

 

But I have to stress, I did a lot of this not in conventional "teacher" mode, but as a co-learner, a facilitator, and also as a person who knows how to ask questions and find resources. I was thrilled to figure things out, make new connections, understand a concept I'd read about but never experienced hands-on or in multiple ways; and I think that enthusiasm helped enormously. I was reading outside material as we went along.

 

You know, I am SO glad you posted your experience. I really do understand when people say, "study ahead so you can understand," and I've done that in spurts with Latin, math, and English grammar. But I waffle back and forth between doing that and "just" learning with my oldest. I think it's because when I think to myself, "Colleen, you simply MUST finish this year's grammar book months ahead of ds, so that you will completely understand what is coming up" and repeat the same for Latin, math, now logic, and his science/history/literature reading, I completely overwhelm myself and give up and revert back to "study alongside him."

 

I think what might be bothering me is that even though this is working in the sense that ds gets pretty much everything so far, and dd does, too, with sometimes some different type of teaching from me, I am the one who has a hard time absorbing everything, probably because of my age and because I feel the weight of responsibility to educate them to the best of my ability. I sometimes wish I could just concentrate on one thing at a time, but I can't or else they will miss out. And so far with elementary and jr. high school, it seems pointless to farm that out, besides the fact that we just can't practically do that.

 

I guess with the math part of our lives, I should just sit down one night and go through the overall concepts and just think about (or ask my kids some good questions) how I've seen my kids understand concepts or how they've been able to use what they've learned so far.

 

First, I think math is not dissimilar from other subjects in that there are many ways to think about it and many ways to get a right answer. Some programs are better at encouraging this than others (Singapore is supreme, IMHO), but many of the really excellent math students I've seen just get this. My son is on a small "math team" and the coach will tell you that he's taking the kids beyond the textbook-here's-how-you-do-it-and-every-problem-is-doable stage and into the just-try-things-and-know-when-to-give-up-or-get-help stage. All that is just to say that I don't believe you *have* to know how your student gets math or get it in the same way that he or she does.

 

Secondly, I think the best way for me to assess what my child needs to do/know in the elementary years is to teach the child the lesson -- by looking at the text and exploring it together. In the secondary years, it's key for me to use a program with fully worked out answer keys, to correct the child's lessons myself at least most of the time, and to work back to figure out why any wrong answer went astray (doing a google search online if I need more understanding).

 

Julie

 

Thanks, Julie, this is very encouraging. I liked what you wrote about the math coach, too. Also, we do look at the math texts together and explore the lessons.

 

I think you are on the right track: working systematically through one good basal textbook (R&S) with supplements.

 

We used R&S as well. Every Friday was Fun Math Day at our house: we used mind-benders, Family Math, Singapore's Creative Word Problems booklets, etc. Like you, I didn't want an entire second math program because I believe that R&S does such an excellent job of teaching both how's and why's. However, I also wanted the children exposed to fun elements and seeing "math" as more than just textbook problems to work through....

 

To relieve the pressure of finishing a text within a year, I didn't worry about that. We did, however, finish every R&S textbook. When we started the next one, I would have the children do the chapter review and then take the test for the first 30-40 lessons. There are very few new concepts in those beginning lessons. The chapter review would pinpoint any weaknesses which could easily be addressed without having to wade through an entire chapter of review. By the time the children reached the end of their R&S sequence, they were all caught up, finishing the texts on time, and have been excellent students with excellent math thinking/skills.

 

What you can do to feel "more in control" is to step up your *own* learning. Don't just check out books from the children's section of the library. Get a few reference books, too. I know Rainbow Resource sells several "math overview" books geared for an adult audience that are meant to do just what you are looking for: filling in the gaps between what you learned and why it works.

 

Also, NYT published an interesting little series on math at the start of the year:

 

http://topics.nytimes.com/top/opinion/series/steven_strogatz_on_the_elements_of_math/index.html

 

The nice thing about this method, slightly random though it may seem, is that the more you learn and know, the more you will be able to "add it in" at just the right moment--just like you did with your daughter and long division.

 

HTH,

 

Thanks, Vicki. Your explanation of how you did R&S is exactly what you told me years ago, that I had printed out. I didn't quite dare to mostly skip 30-40 lessons or just do the review lessons in those early chapters, but it gave me the confidence to skim quickly over some of the early lessons and rest in my children's comments of, "Yes, Mom, I do remember doing this last year - I get it; I know how to do it."

 

I did put an adult math reference book on hold at my library.

 

And thanks for the link to the NYT articles - it seems to me that Jane in NC mentioned those at some point here recently, too. I'll have fun reading through those.

 

Thanks for the reassurance about my method of R&S plus supplements and sort-of-random-but-useful learning that I can incorporate into life.

 

Reading through Professor Wu's online articles and monographs has helped me get a big picture view of school math. I particularly like his chapter drafts on Whole Numbers and Fractions.

 

 

Thanks for this link - he does have some interesting articles!

 

I also had a look at your blog - very interesting! Interesting reading a the CLAA (is that correct?) website about classical math learning. I couldn't see if they had actual books to sell, though? Or samples of lessons?

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I also had a look at your blog - very interesting! Interesting reading a the CLAA (is that correct?) website about classical math learning. I couldn't see if they had actual books to sell, though? Or samples of lessons?

CLAA is a self-paced online academy - classes are, iirc, $125 each. You can sign up as a full student or just take classes a la carte. It does look very interesting - it is truly classical in a historically meaningful sense. I keep tossing around the idea of taking the arithmetic or grammar course.

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We have been using R&S and I intend to stick with it til we switch to the old Dolcianis for high school. I *have* found that, like 8FilltheHeart said somewhere in one of those threads, that this traditional program *does* teach concepts - and I know this because I have read explanations in it that helped ME understand elementary things that I never understood before. The TM would tell me to make some little chart or manipulative or something, to illustrate what it was talking about, or it would tell me what to say to the child to help him understand the concept. Sometimes, if my dd10 didn't understand, I was able to figure out a way to explain, that she would understand.

 

I think I figured out something. I looked closely at my R&S book 8 that ds is going through, and found that the "introduction" section in some of the lessons actually has questions/discussion that either reinforce previous concept learning, or introduces the current lesson's concept. You see, because ds has taken to math so easily, I would sometimes tend to gloss over that part and get right to the lesson. He understood, we'd talk a bit about it, and I'd assign him his written work. But this is the section where concepts are talked about from different angles, and where questions are asked (similar to how R&S grammar has oral review questions in the TM, that I do religiously go over each day with both kids) that get kids thinking about the ideas from different angles. I checked my other TMs, and this "introduction" section starts in book 6. Good thing dd is not up to that yet, or we'd have had more trouble. It made me resolve to be more faithful even with her oral drills in book 5, even if she complains. Even these will drill things from past lessons, that might not be included in the current lesson. Anyway, I'm going to have a closer look at the intro sections in book 7, to compare to the intro sections in book 8, to make sure I know what ds understands for concepts. I'm pretty sure he's up to snuff in them, but I need to reassure myself. I did go through most of the intro. sections with him today in book 8, up to his current lesson. He understood most things, but I did find a little snag which we untangled, in BOTH of our understandings of the commutative, associative, and distributive laws. Nice!

 

I feel a bit better about all this, and resolved to just stick with the TM a little more closely now. I guess if I do this for my oldest, even though he "gets" math more easily, I will have more confidence myself and be able to teach my younger more easily.

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