LoF Fractions...dealing with lack of information?

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I'm working through LoF Fractions ahead of dd and have found several places where he asks for answers when he hasn't given the complete detail of how to do something. Am I the only one seeing this?

I first noticed it in ch. 12 #1. There is no explanation yet as to why you would make the denominator equal to 12. *I* know this but am a bit frustrated that the question is asked before teaching lowest common multiple. From there my frustration builds when asked to compare other fractions w/o the teaching of how to get them to have common denominators.

Ack! Please tell me I just missed something!

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I sit with my son during LOF, so this has never been a problem. I see what you're saying, though. Since we are doing this after completing Saxon 5/4 which deals with making denominators the same, it is just review for Nathan.

I treat LOF as review, not as instruction.

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Oh... I don't think I like this. :001_huh:

First, it never occurred to me to work through the book first. I looked at chapter 12--what you're talking about-- and I see what you mean. I don't like that.

Now what? I was planning on LoF to teach, not review fractions. Hmmm...

Any suggestions?

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I read somewhere that sometimes he teaches through the answers to the questions. Could that be what he's doing there?

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I first noticed it in ch. 12 #1. There is no explanation yet as to why you would make the denominator equal to 12. *I* know this but am a bit frustrated that the question is asked before teaching lowest common multiple. From there my frustration builds when asked to compare other fractions w/o the teaching of how to get them to have common denominators.
I'm not seeing the problem here. The chapter is called "Common Denominators." An explicit instruction is given to change the 1/4 to 3/12 for the sake of comparison. But would it have really mattered for the purposes of this problem if the student had changed both to 24ths? There are a few more very simple problems of this type before LCM is introduced, and by then the student should seen the need for it. However, this leads to my one beef gap-wise with LoF: The prime factorization technique for finding the LCM is not covered. This isn't really needed for working through the first few books, as the numbers chosen tend to be easy to work with mentally. However, it's a concept that is not addressed later in the series -- unless he'll be picking it up in the as yet unreleased second pre-algebra volume. If you need them, here are some quick lessons from MEP which cover prime factors and LCM.
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I read somewhere that sometimes he teaches through the answers to the questions. Could that be what he's doing there?

No, but he's warming up to it. :)

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I'm not seeing the problem here. The chapter is called "Common Denominators." An explicit instruction is given to change the 1/4 to 3/12 for the sake of comparison. But would it have really mattered for the purposes of this problem if the student had changed both to 24ths? There are a few more very simple problems of this type before LCM is introduced, and by then the student should seen the need for it.

:iagree:

I read somewhere that sometimes he teaches through the answers to the questions. Could that be what he's doing there?

He sort of does this in question 3 â€” after having students compare 1/4 & 3/12, and 2/3 & 7/12 in the first two questions, he asks them to compare 2/5 & 3/8. He does call it a "brain buster" and say the student hasn't "seen a problem quite like this one," so the idea is to see if the student can figure out how to find a common denominator, then he explains in the answer on the next page.

We love Fred here, but I use it for review rather than teaching the concepts because I don't think the concepts are spelled out or taught explicitly enough for DS12. He's a whole-to-parts kid, and not good at inferential learning; I don't think Fred works well for those kind of kids as a "first pass" at the concepts. It's great for review, though, after he's been through the concepts in MM. I'm sure for other kids it would be fine on it's own, it really depends on the individual student's learning style.

Jackie

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I see teaching. It's very clear, but you have to look at everything and maybe have your child really focus; but it's all there! It's great!!

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From there my frustration builds when asked to compare other fractions w/o the teaching of how to get them to have common denominators.
I didn't properly address this part earlier. Several examples are given, and equivalent fractions have already been covered by this point.
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I'm working through LoF Fractions ahead of dd and have found several places where he asks for answers when he hasn't given the complete detail of how to do something. Am I the only one seeing this?

I first noticed it in ch. 12 #1. There is no explanation yet as to why you would make the denominator equal to 12. *I* know this but am a bit frustrated that the question is asked before teaching lowest common multiple. From there my frustration builds when asked to compare other fractions w/o the teaching of how to get them to have common denominators.

Ack! Please tell me I just missed something!

Did you see where he explained this in the lesson?

He said 5/8 was larger than 3/4 and that we could tell this before we reduced 6/8 to 3/4.

He showed that 3/4 and 6/8 are equal on the meters. He says that to compare two fractions, you need to have their bottoms alike. He then goes on to say that earlier we reduced 6/8 to 3/4 by dividing the numerator and denominator by 2- so now we go in the opposite direction and change 3/4 to 6/8 by multiplying top and bottom by 2.

Okay, this just repeats the lesson; but hopefully everyone can see how when he asks the student which is smaller 1/4 or 5/12? And then says, (change the 1/4 to a fraction that has a denominator equal to 12) it’s very clear.

If my dd hasn’t done a concept in LOF before and she doesn’t understand; I have her reread first before I help her with it. Sometimes she just gets it after reading it again.

I don't see the lack of info...like someone said they have already been introduced to equivalent fractions by now..

Edited by lovemykids
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I agree that LoF does not provide enough explicit instruction for some kids. It is excellent for stretching mathematical understanding, thinking outside the box, and real-life application. If your child is math intuitive, LoF might well be enough on it's own. However, my dc are not, and they (and I) need things broken into step by step bits and explicitly explained.

My ds worked through LoF Fractions, and Decimals & Percents with no problems. He loved the story and it really cemented his knowledge and understanding of the concepts. However, this topics had already been covered in other curriculum, so it was a supplement/review.

This year, we used LoF Beginning Algebra for his first and only exposure to Alg. I, and I regret it. I didn't realize how important his prior knowledge of the material was to his success with LoF. About mid-way through the book, things started to become fuzzy, and I am totally lost. Dh is helping him, but I feel ds is barely grasping what he is supposed to do, not truly understanding the concepts fully. My biggest complaint, is that the assumption is made that the student with "figure out" how to apply what has been briefly explained to a complex word problem. The jump from the teaching to the problems is often too great for us, and the idea of including a great amount of "teaching" in the answers, after we have already struggled and agonized over solving the problem with too little info., is very frustrating. I am planning to re-do Alg. I with Kinetic Textbooks.

We still love LoF, but will definitely use it as a supplement in the future, using a very explicit, step-by-step program as a core program.

For the PP who asked what to use to teach fractions, how about "Key to Fractions". You could do this in tandem with LoF, covering the material in Key to before each chapter of LoF.

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I agree that LoF does not provide enough explicit instruction for some kids. It is excellent for stretching mathematical understanding, thinking outside the box, and real-life application. If your child is math intuitive, LoF might well be enough on it's own. However, my dc are not, and they (and I) need things broken into step by step bits and explicitly explained.

My ds worked through LoF Fractions, and Decimals & Percents with no problems. He loved the story and it really cemented his knowledge and understanding of the concepts. However, this topics had already been covered in other curriculum, so it was a supplement/review.

This year, we used LoF Beginning Algebra for his first and only exposure to Alg. I, and I regret it. I didn't realize how important his prior knowledge of the material was to his success with LoF. About mid-way through the book, things started to become fuzzy, and I am totally lost. Dh is helping him, but I feel ds is barely grasping what he is supposed to do, not truly understanding the concepts fully. My biggest complaint, is that the assumption is made that the student with "figure out" how to apply what has been briefly explained to a complex word problem. The jump from the teaching to the problems is often too great for us, and the idea of including a great amount of "teaching" in the answers, after we have already struggled and agonized over solving the problem with too little info., is very frustrating. I am planning to re-do Alg. I with Kinetic Textbooks.

We still love LoF, but will definitely use it as a supplement in the future, using a very explicit, step-by-step program as a core program.

For the PP who asked what to use to teach fractions, how about "Key to Fractions". You could do this in tandem with LoF, covering the material in Key to before each chapter of LoF.

Perhaps it does depend on the child. I have heard that some children thrive in algebra after using Fred as an intro.

Despite being a program for only children who are strong in math, I also find it interesting that Maria Miller of MM recommends using LOF for a child who needs extra help, I guess she means as supplemental; which is the way so many people are using it.

I would like to have my dd work ahead in LOF and see how she handles all the new concepts in pre-algebra, before deciding to use it as review. I think LOF really does work for my oldest. That might not be the case with my youngest dd, weâ€™ll see.

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I read somewhere that sometimes he teaches through the answers to the questions. Could that be what he's doing there?

YES!!! He does that. He wants you to think, to try things and then teaches in the answers. Although this is not common in the States, I've heard of this being done in other countries (just don't remember where right now.) It's a great way of learning, but you need to be there as a guide. It works very well for my two eldest, but my ds needs a lot more hand holding and teaching with this.

For ds LOF definitely has to be a supplement. As for Alglebra, I'm a huge fan of doing Algebra 1 twice, so my middle one is doing LOF first and will do another one second. She's sailing through LOF Beginning Algebra, so evidently her background in math combined with her learning style are lending itself well to LOF. She only had a lot of trouble once with a triangle problem in the quadratic equations chapter.

Edited by Karin
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Oh... I don't think I like this. :001_huh:

First, it never occurred to me to work through the book first. I looked at chapter 12--what you're talking about-- and I see what you mean. I don't like that.

Now what? I was planning on LoF to teach, not review fractions. Hmmm...

Any suggestions?

The Math Mammoth "Blue Series" books on fractions & decimals are inexpensive and extremely thorough. I have looked at a lot of math curricula and I think MM teaches fractions/decimals/percents better than any other program I've seen. It's very conceptual, with the concepts broken down and explained step-by-step, and she really emphasizes the relationships among fractions/decimals/percents, so students can fluidly "translate" between them. Her explanations are more thorough than what I've seen in many Pre-Algebra programs. In fact, I'd say that's true of the MM 5th & 6th grade curricula overall â€” better prep for Algebra than the Pre-Algebra programs I've looked at.

Jackie

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The Math Mammoth "Blue Series" books on fractions & decimals are inexpensive and extremely thorough. I have looked at a lot of math curricula and I think MM teaches fractions/decimals/percents better than any other program I've seen. It's very conceptual, with the concepts broken down and explained step-by-step, and she really emphasizes the relationships among fractions/decimals/percents, so students can fluidly "translate" between them. Her explanations are more thorough than what I've seen in many Pre-Algebra programs. In fact, I'd say that's true of the MM 5th & 6th grade curricula overall â€” better prep for Algebra than the Pre-Algebra programs I've looked at.

Jackie

Jackie, did you ever order the "soft pack"? I am not sure if I should buy it this time around...(I don't even think we are using MM. :lol:)

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Jackie, did you ever order the "soft pack"? I am not sure if I should buy it this time around...(I don't even think we are using MM. :lol:)

No, it's Windows-only (XP, Vista, & 7) and we have all Macs.

Jackie

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No, it's Windows-only (XP, Vista, & 7) and we have all Macs.

Jackie

Okay, thanks. (It looks like it also has LA, interesting. I can't decide.)

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I spoke with Stanley Schmidt (author) this morning. I sent him an e-mail last night. I have to give him a standing ovation! What a guy! He is so accessible! The way he explained it is that he really wants the kids to *think* it through. His opinion was that in most math texts, there is too much explanation, thus not requiring any real thought to the process. He instructed me NOT to teach or step in with my dd as she works through the book. If any other person said that to me, I think I would've slammed the phone down and had some choice words under my breath however I had a real sense of peace about it. He said to give dd his # and allow her to call him if she needs help so at this point, we're going to go for it!

Mr. Schmidt also shared with me his experiences in different math classes, both as the teacher and as the student. What he said about the classes he taught resonated with me. He had a class full of women and maybe one man and all of them would say they hated math. Then they take that attitude to their students and pass that along. I have to :lol: because I know is some part, I have done that to dd.

All in all, he didn't explain much other than the idea that he wants students to use their heads and not have the answers handed to them. I can live with that, especially knowing he is available and willing to answer questions.

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I spoke with Stanley Schmidt (author) this morning. I sent him an e-mail last night. I have to give him a standing ovation! What a guy! He is so accessible! The way he explained it is that he really wants the kids to *think* it through. His opinion was that in most math texts, there is too much explanation, thus not requiring any real thought to the process. He instructed me NOT to teach or step in with my dd as she works through the book.

I love LoF, and I have enormous respect for the author, but I have to say that this does not work for all kids. Some kids really do need to see the big picture first, and understand the concept, before they can do the problems. I agree with Stanley that the problem with many math texts is that they simply teach the procedures, then provide such simple, straightforward problem sets that it's just a matter of plugging in the numbers, with no thought required. One solution to that is to not provide the explanations up front and let students puzzle it out on their own. This is great for mathy kids and intuitive learners â€” this is exactly the approach used in the Art of Problem Solving texts. Another approach is to provide really deep, thorough explanations up front, so the student really understands the underlying mathematical concepts, and then have the student apply the concepts to challenging problems. This is more like Singapore or MM or Foerster's Algebra.

They're both good approaches, but they will generally work for different kids, and I would not follow Stanley's advice if I my child was not a good inferential/intuitive learner. Since DS isn't that kind of learner, we've used MM before Fred, and next year we'll be using Foerster's Alg I followed by LoF Beginning Algebra for a fun review.

Jackie

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My dh does this with our kids all the time. He gives them problems that they have to think to figure out and he doesn't tell them how to do it. Children are amazing, they can do it if given the opportunity.

Fred is awesome. And all the information they need to do the problems is there. It is okay for them to get the wrong answer and then learn from the mistake. In fact, they should be getting wrong answers sometimes and they should have to work at understanding. Knowing that they missed it before, sometimes, makes the information stick when they see how the problem should be done.

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I spoke with Stanley Schmidt (author) this morning. I sent him an e-mail last night. I have to give him a standing ovation! What a guy! He is so accessible! The way he explained it is that he really wants the kids to *think* it through. His opinion was that in most math texts, there is too much explanation, thus not requiring any real thought to the process. He instructed me NOT to teach or step in with my dd as she works through the book. If any other person said that to me, I think I would've slammed the phone down and had some choice words under my breath however I had a real sense of peace about it. He said to give dd his # and allow her to call him if she needs help so at this point, we're going to go for it!

Mr. Schmidt also shared with me his experiences in different math classes, both as the teacher and as the student. What he said about the classes he taught resonated with me. He had a class full of women and maybe one man and all of them would say they hated math. Then they take that attitude to their students and pass that along. I have to :lol: because I know is some part, I have done that to dd.

All in all, he didn't explain much other than the idea that he wants students to use their heads and not have the answers handed to them. I can live with that, especially knowing he is available and willing to answer questions.

Great follow up, thanks for sharing. Be sure and let us know how it goes!

My dh does this with our kids all the time. He gives them problems that they have to think to figure out and he doesn't tell them how to do it. Children are amazing, they can do it if given the opportunity.

Fred is awesome. And all the information they need to do the problems is there. It is okay for them to get the wrong answer and then learn from the mistake. In fact, they should be getting wrong answers sometimes and they should have to work at understanding. Knowing that they missed it before, sometimes, makes the information stick when they see how the problem should be done.

Good point. :)

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The author of Art of Problem Solving said something which shocked me. NOw I have to go back and listen to his talk again, but I *think* he said kids should be getting about half the problems wrong! The kid work through the problems before being given the explanation. This is one thing I liked about RS math, it would throw in problems and DC had just enough prior info, to make that leap...and it was beautiful when it happened. Later, the steps would be given explicitly.

Dr. Cotter says the same thing of RS Geo. It's not meant to be taught and the student should call her with questions.

Must. ponder. this.

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The author of Art of Problem Solving said something which shocked me. NOw I have to go back and listen to his talk again, but I *think* he said kids should be getting about half the problems wrong! The kid work through the problems before being given the explanation. This is one thing I liked about RS math, it would throw in problems and DC had just enough prior info, to make that leap...and it was beautiful when it happened. Later, the steps would be given explicitly.

Dr. Cotter says the same thing of RS Geo. It's not meant to be taught and the student should call her with questions.

Must. ponder. this.

I like this! I am climbing a personal mountain here as we go through these steps. I was always the kind of person that most things came easily to so when it wasn't easy I would give up. That sits in the back of my mind and eats away at me as I raise/teach my kids. I have made a commitment though to conquer those things which I find difficult. This math thing is just a tiny part of the bigger picture!

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The author of Art of Problem Solving said something which shocked me. NOw I have to go back and listen to his talk again, but I *think* he said kids should be getting about half the problems wrong!
I love this. Something similar jumped out at me when I was reading Mindset: An example was given as to how a teacher (or parent?) should reasonably respond to a perfect math test, and the answer was essentially to apologize for wasting the student's time by not allowing them to stretch and learn more. I took this to heart.

:D

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I'm working through LoF Fractions ahead of dd and have found several places where he asks for answers when he hasn't given the complete detail of how to do something. Am I the only one seeing this?

I first noticed it in ch. 12 #1. There is no explanation yet as to why you would make the denominator equal to 12. *I* know this but am a bit frustrated that the question is asked before teaching lowest common multiple. From there my frustration builds when asked to compare other fractions w/o the teaching of how to get them to have common denominators.

Ack! Please tell me I just missed something!

This is why we only use LOF as a fun supplement. I know that some use it as a standalone but I personally don't think it has near enough information for me to be comfortable using it as our only math curriculum.

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This is why we only use LOF as a fun supplement. I know that some use it as a standalone but I personally don't think it has near enough information for me to be comfortable using it as our only math curriculum.
To be fair, few here recommend using the first two books as a standalone curriculum. :001_smile:
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The author of Art of Problem Solving said something which shocked me. NOw I have to go back and listen to his talk again, but I *think* he said kids should be getting about half the problems wrong! The kid work through the problems before being given the explanation. This is one thing I liked about RS math, it would throw in problems and DC had just enough prior info, to make that leap...and it was beautiful when it happened. Later, the steps would be given explicitly.

AoPS was designed specifically for kids who are gifted in math and who intuitively "get" the connections and patterns and underlying concepts. I think it's a fantastic program for those types of kids, but for kids who don't think that way, the throw-them-in-the-deep-end-and-let-them-figure-out-how-to-swim approach will just leave them half-drowned and convinced that they're stupid and will never understand math.

IME, whole-to-part learners â€” regardless of IQ â€” do not do well with programs that require them to infer underlying rules and concepts based on seeing/learning individual parts (this goes for language, grammar, science, etc., as well as math). DS12 is highly gifted, but he is a V/S, whole-to-parts kid who is not intuitively mathy, and AoPS would never work for him. I bought AoPS and Foerster's Algebra, both rigorous programs but opposite in approach, and I can see that DS will "get" Foerster's with no problem, but he'd be lost in AoPS â€” unless he did Foerster's first, so he already understood the concepts before tackling AoPS. If he tried to do AoPS first, the frustration of constantly being wrong because he was just randomly guessing at things he didn't intuitively "get," would make him hate math forever.

If your child does learn "the AoPS way," then by all means go for it, but I'd hate for people think that the AoPS/LoF approach is ideal for everyone â€” or that their child "isn't good at math" just because they don't learn that way.

Jackie

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I spoke with Stanley Schmidt (author) this morning. I sent him an e-mail last night. I have to give him a standing ovation! What a guy! He is so accessible! The way he explained it is that he really wants the kids to *think* it through. His opinion was that in most math texts, there is too much explanation, thus not requiring any real thought to the process. He instructed me NOT to teach or step in with my dd as she works through the book. If any other person said that to me, I think I would've slammed the phone down and had some choice words under my breath however I had a real sense of peace about it. He said to give dd his # and allow her to call him if she needs help so at this point, we're going to go for it!

Mr. Schmidt also shared with me his experiences in different math classes, both as the teacher and as the student. What he said about the classes he taught resonated with me. He had a class full of women and maybe one man and all of them would say they hated math. Then they take that attitude to their students and pass that along. I have to :lol: because I know is some part, I have done that to dd.

All in all, he didn't explain much other than the idea that he wants students to use their heads and not have the answers handed to them. I can live with that, especially knowing he is available and willing to answer questions.

Interesting you write this... I just came to the conclusion (we're only part way through Fractions) that I really like Fred. Mostly because it is so different from MUS and challenges my ds by NOT giving him all the answers. My ds was complaining a chapter ago saying, "But he didn't say "how" to do this problem!" I looked at it and pointed out to ds that he KNEW all the little steps, now put them together. My ds LOVES the story line of Fred, but balks a bit at the math. That is actually what is making me continue with it! He actually has to **think** about how to use the math he knows. MUS does not really make him do that.

We use Fred as a supplement, rather than the primary program. I let MUS introduce the topics, then we work in Fred.... it's a great pairing in my estimation!

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The Math Mammoth "Blue Series" books on fractions & decimals are inexpensive and extremely thorough. I have looked at a lot of math curricula and I think MM teaches fractions/decimals/percents better than any other program I've seen. It's very conceptual, with the concepts broken down and explained step-by-step, and she really emphasizes the relationships among fractions/decimals/percents, so students can fluidly "translate" between them. Her explanations are more thorough than what I've seen in many Pre-Algebra programs. In fact, I'd say that's true of the MM 5th & 6th grade curricula overall â€” better prep for Algebra than the Pre-Algebra programs I've looked at.

Jackie

Jackie,

Thank you for telling me of this program. I will certainly look into it.

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I spoke with Stanley Schmidt (author) this morning. I sent him an e-mail last night. I have to give him a standing ovation! What a guy! He is so accessible! The way he explained it is that he really wants the kids to *think* it through. His opinion was that in most math texts, there is too much explanation, thus not requiring any real thought to the process. He instructed me NOT to teach or step in with my dd as she works through the book. .

I agree with this approach. Kids retain more when they discover things, but leading along, as he does, helps a lot. In a society where mathematical innumeracy abounds, I think we could use a lot more of this :).

What I do is wait until my dc have trouble with something in LOF and then step in to help them.

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I love LoF, and I have enormous respect for the author, but I have to say that this does not work for all kids. Some kids really do need to see the big picture first, and understand the concept, before they can do the problems.

Jackie

:iagree: I also think sometimes you can do this thinking and discovery process along with whole to parts learners at times, but with something different than LOF. Or they could simply read the book through once or twice without doing the problems and then go back and do it with the problems with the big picture in mind. I think this is why my middle dd is going through the book so quickly; she is very vs and has always been a whole to parts learner. However, in her case, we took a year to help her develop the linguistic aspects of math, which she was weak in before.

As for my ds, he's already done some fractions in SM, but the problem he had is he wasn't reading the answers to the Your Turn to Play sections and it eventually caught up to him. There is a lot of learning there, too.

In the books after Fractions & Decimals, there is also learning in the answers to the cities that are given in the text.

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The author of Art of Problem Solving said something which shocked me. NOw I have to go back and listen to his talk again, but I *think* he said kids should be getting about half the problems wrong! The kid work through the problems before being given the explanation. This is one thing I liked about RS math, it would throw in problems and DC had just enough prior info, to make that leap...and it was beautiful when it happened. Later, the steps would be given explicitly.

Dr. Cotter says the same thing of RS Geo. It's not meant to be taught and the student should call her with questions.

Must. ponder. this.

I love this. Something similar jumped out at me when I was reading Mindset: An example was given as to how a teacher (or parent?) should reasonably respond to a perfect math test, and the answer was essentially to apologize for wasting the student's time by not allowing them to stretch and learn more. I took this to heart.

:D

Wow. I really needed this. I need to put this somewhere I can always see it.

Last year was the first year we really 'graded' math. I graded the MEP tests and diagnostics in the academic route. At the end of the diagnostics it has a chart that tells you to stay on track, or assigns you a different route. I think it was around the 3rd diagnostic that I actually read it. We finished the rest of year doing the express route and I've had to completely change the way I see progress.

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This is good to know. My dd is not reading the answers in Your Turn to Play either. I will make sure that she know to do that.

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I have really enjoyed this thread. I guess you all just put into words why my ds loves this program and is acing Algebra: he's an intuitive learner and all that plugging in just confuses him. He actually needs the application, to understand the process. I love this place.

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