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Found 8 results

  1. Much emphasis was made in the "Cheeseburger" thread about the importance of practice, practice, practice when it comes to mastering procedures and math facts. No argument here. But what about the importance of practicing and reviewing the *concepts* to master them? Lots of people said that they had to abandon "conceptual" curricula because there just wasn't enough practice for their kids to master the facts and procedures. But at the same time "traditional" programs were defended as "teaching the concepts" perfectly adequately so long as they explained the why behind a procedure when it was first introduced. And when kids completed the program without retaining the whys, it was because they just aren't mathy, or because they just weren't developmentally ready, not because they just didn't get enough practice. We don't expect that kids will master math facts or the standard algorithms by just seeing them once - why in the world do we think seeing a math concept once is somehow sufficient? A lot of traditional math defenders made a big point that we often learn by doing, that sometimes it takes doing problem after problem before it suddenly clicks. (In college a common joke was that you don't master the material in class 'x' until you are going through class 'x+1' :tongue_smilie:.) True enough. But you learn what you practice. Are you practicing applying the math concepts? Or are you practicing a rote procedure? Bill's descriptions of how he is teaching his son perfectly illustrates what it means to practice thinking through the concepts. For example, with learning math facts, he is having his son think through combining the axioms with his existing fact base to figure out the ones he doesn't know each and *every* time they work on them. The concepts themselves - not just the facts - are reviewed and practiced in every practice session. That is *vastly* different to the standard "show the concepts, but practice the facts/procedure" approach. There a student is shown how to break down numbers using the axioms a few times, maybe even going through the process with each fact. So far, so good. But then all further practice is straight up memorization! So if it takes 100 times of seeing a given fact to learn it, a student will only practice the underlying concept 1 time while learning the fact. They are spending 99% of their time on math practicing surface facts or procedures with no reference to the underlying concepts. No wonder most of the people in this country think math is nothing more than memorizing facts and formulas - that's what the they spent the vast majority of their time in math *doing*! Only naturally mathy people have a chance to learn the concepts, because they just don't need much repetition to achieve mastery. But that doesn't mean that everyone else is incapable of learning the concepts, just that they need more *practice*. We don't expect kids to master anything else without lots and lots of practice. So why do we persist in thinking that mere exposure to math concepts is somehow sufficient, and any failure is due to a defect in the kid (they're just not mathy) instead of a defect in the instruction? If we want kids to learn math concepts, then they need to *practice* the concepts - just like they do to learn grammar and history and science and art and music and sports and anything else.
  2. WE NOW HAVE A WEBSITE UP!!!! It is organized by category, and within each category the videos are organized generally in the order you would teach them. Please refer people to this link and NOT the vimeo page linked in the original thread... http://www.educationunboxed.com If you are just starting, visit the first four categories to start out with. Then you can start at the beginning of any other category, and pick and choose what to do from there! I am still adding videos. I'm sure the pace will dwindle down soon, but there are currently 79 videos up so they should keep you all busy for a while! These videos show you how to teach math CONCEPTUALLY. They will work with any math program. Just look ahead to what you will be teaching next and introduce the concept with C-rods first, then move on to all those worksheets!
  3. This is possibly a dumb question, but is "constructivist" math the same thing as "conceptual" math? I've been reading various rants on the Internet about how awful "constructivist" math is, but many of the descriptions - emphasis on manipulatives, students encouraged to find their own ways of solving problems, focus on building understanding rather than drilling facts and formulas, etc. - seem to apply to much-praised conceptual math curricula like Miquon. Is there a difference? And if so, what is it?
  4. I read this on a teacher's website. It's the teacher's explanation of a subtraction trick taught by Everyday Math. I'm not knocking the teacher for getting the answer wrong - I promise I'm not. My point is that this is just a prime example of why tricks are no match for good conceptual understanding. This one in particular seems extremely cumbersome, and it's really no wonder she got it wrong. I can't really understand why this was considered easier than explaining the concepts behind regrouping. lol Here it is: "The Everyday Math Program has lots of neat ways to teach kids how to subtract, other than the traditional way. They are really good, especially for those students who just can't do the regrouping way without making errors. My favorite method is what I call the Elevator Method. I begin by telling the students my "elevator story." When you go into the hospital to have some surgery, you climb into the elevator and head UP to the surgery floor. You're pretty nervous, so this is a NEGATIVE THING. GOING UP IS NEGATIVE. However, when you get out of the hospital, you climb into the elevator and head DOWN. You're happy that the surgery went well and you are feeling POSITIVE. GOING DOWN IS POSITIVE. Now let's subtract with the problem 807 - 294. Write the problem down with the 294 under the 807. Don't look at individual numbers, but look at place values. We'll start with the hundreds column. We have 8 hundreds and 2 hundreds. 800 - 200 = 600. Write that down under the problem. Put a PLUS in front of it, because we subtracted going DOWN, and GOING DOWN IS POSITIVE. Now look at the tens column. We have 0 tens and 9 tens. 90 - 0 = 90. Write that down under the 600, putting a MINUS in front of it, because we subtracted going UP, and GOING UP IS NEGATIVE. Now look at the ones column. We have 4 ones and 7 ones. 7-4=3. Write that down under the 90, putting a MINUS in front of it, because we subtracted going UP, and GOING UP IS NEGATIVE. Now look at what we wrote down: +600, -90, -3. 600-90=510 (mental math, counting by tens backward if needed). 510-3=507. 507 is the answer. No regrouping necessary, and students can learn to do this really, really quickly! Wow! I hope that helps!" Edit to add that I do think it's a cool trick, but I just don't see how it should be taught in place of good understanding of regrouping. It's a lot to remember, so certainly no easier than just explaining the concept, IMO.
  5. 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?
  6. (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?
  7. I have not used CLE yet , but I am strongly considering it for next year , maybe in combination with Singapore which my son likes --but he needs more review and a spiral program . So I was looking at the samples for grade 2 CLE . For ex. , this is in unit 4 or 2nd grade (still in the beginning) : James read 35 pages in a library book today . Yesterday he read 23 pages .How many more pages did he read today than yesterday? A jack in the pulpit grew to be 89 centimeters tall . A yellow coltsfoot measured 45 centimeters . How much shorter was the coltsfoot than the jack in the pulpit? This seems to be very comparable to Singapore 2 , doesn't it? If you have used CLE math ,please tell me what is wrong with CLE :)
  8. I was attempting to read the thread about conceptual math and frankly, I am just so confused when it comes to types of math programs. I know my children need something different than how I "learned" math, but I really don't know how to give it to them. I've looked at various math programs. I've used Horizons before and was unhappy with the lack of teacher "explanation" given in the teacher manual. I prefered Saxon because it was scripted, but I'm noticing almost NOTHING ever said about it on this board, which leads me to the question, what am I missing? I looked at MEP last night for the first time and it looked good, I'm just confused about how people use it. I've never seen Miquon, but it looks very interesting. I'm just not sure I could pull any of these things off without a LOT of work on my part. I'm willing to put in the work, but I'd like to minimize the trial and error part of it and really have someone just TELL me how/what to do. Does that exist in any of these programs or combo of programs or is anyone willing to tutor me through it? I've had the Right Start games for about 5 months and haven't even opened them because I've been too overwhelmed. I know I sound pitiful. I'm just a language/creative type person, not mathy, so I feel at a loss with all of this.
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