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Ray's Arithmetic users


birchbark
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Bumping in hopes there'll be more responses.

 

We've been using MEP, and I've been really happy with it, but I keep feeling a pull towards Ray's for reasons too thread-derailing to go into right now.

 

Justamouse, thanks so much for that link. The section on math is fascinating! I'm pondering the idea that the first step is to train students to ascertain the number of items in a group without counting each one. It's kind of like C-rods only more concrete. . .

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I found the manual to be a lot like Waldorf and Strayer-Upton and it had a BIG impact on my math teaching philosophy! I have latched heavily onto the need to include whole-to-parts instruction, starting with this manual, and only AFTER reading it, looking further into the other 2 curriculums because they applied the same ideas. Lightbulbs were flashing all over my brain as I read it. It was life changing for me.

Edited by Hunter
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I have used Ray's to pull out " stumped" questions for my math lovers' fun but haven't looked into using the whole curriculum. I just downloaded it.

 

Is there a place to download it for free? I'd like to take a look at it before deciding whether to buy the hard copies. Isn't it in the public domain?

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I'm curious!

 

Um. Gosh, well, you asked. . . .

 

Okay, first of all, the disclaimers: I love MEP. It's taught me more about math than I ever knew before, and it's been for the most part a challenging but good fit for my son, who is bright at math--but in no way highly gifted. I say this all just to put things in context; my thoughts are all based on one somewhat idiosyncratic six year-old.

 

I'm trying really hard not to write an essay here, so let's just say that because of a couple of rabbit trails we followed, my son got, I mean really, really got division. As a result, a whole bunch of those mind-bending puzzles are striking him as just so much busy work. I really want to stress, this is not because he's a math genius and really should be working several years ahead of his current level. It's just that for a variety of reasons, he really mapped his mind around the concept--so we'll be working on a MEP problem and he'll not only pipe right up with the answer, short-circuiting all the work they have you do to get it, but also complain that it's way too easy. I'm tempted to say that MEP drills students on concepts, which can be a really good thing if they're not getting it, but pointless if they are.

 

I'm a little unsure what to do at this point. If I go through the MEP lessons systemically, I think he'll be bored silly, and this is not a kid who handles boredom with great grace. If, on the other hand, I jump ahead, I think we'll be going through the concepts too fast.

 

We did two days of Ray's this past week and if nothing else, it's really highlighted the fact that he needs way more drill than I realized. As I slowly, slowly work through the wealth of material on the CiRCE thread, I think I am finally understanding why drill is so important; he really needs the math facts to become part of him, if you will, and that means he has to just live with them in his head for a while. The danger of racing through MEP, I'm coming to think, is that he'll learn to do fancy concepts and puzzles but not really learn to think in a mathematical way. If that makes a lick of sense :). But Ray's--especially because of the word problems--will offer a wealth of practice but still encourage something greater than just mechanical recitation of the facts.

 

I heard a quotation in one of the CiRCE lectures last night to the effect that with practice, the hard becomes the easy, the easy becomes the natural, and the natural becomes the beautiful. Racing ahead will short-circuit that process. So that (in a nutshell :) ) is why I'm looking at using Ray's.

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phroggies,

 

I took great interest in your thoughts. I have a 5 yo son. I purchased the Rays set several months ago because I was drawn to using an "older" approach and got a good deal on Ebay. I read through the first book, but didn't use it. We just kind of did our own thing for several months. We have since started MEP. I decided to start part way into Year 1, but we're going through it quickly. Much of it is review, but there are some good concepts I don't want to miss.

 

Now, my questions for you. Practically speaking, how do you utilize the Rays books? Are they a supplement to MEP, or are you thinking of just switching over? Do you have your son read the problems in Rays & copy them onto another sheet of paper? Do you work with him on Rays, or can he use it more independently? I know you just started, but I would appreciate any further insight you could provide because I generally agree with your ideas on approaching math.

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Now, my questions for you. Practically speaking, how do you utilize the Rays books? Are they a supplement to MEP, or are you thinking of just switching over? Do you have your son read the problems in Rays & copy them onto another sheet of paper? Do you work with him on Rays, or can he use it more independently? I know you just started, but I would appreciate any further insight you could provide because I generally agree with your ideas on approaching math.

 

Honestly, I'm still trying to wrap my mind around what I want to do. I had a long conversation with my husband last night trying to think through this, and he suggested tacking between them. I'm thinking of something along the lines of a week of Ray's (starting waaaay back in fairly early addition), then a week of MEP (having gone carefully through the lesson plans and picked out the right kind of exercises), and so forth, till we're at division in Ray's--and then I'll re-calibrate. I figure we have the luxury of time; we school five days a week, year round, and I'm not trying to finish anything by any given date. That way he'll get some solid practice but we'll also be able to progress through MEP with a more or less accurate sense of where his conceptual development is.

 

Keeping in mind that we've done a whopping two lessons so far, what I've been doing is simply reading the lesson out to him. My understanding is that one is intended to do the first several years orally, so there's not going to be a lot of independent work (unfortunately). Could you do them by having him read and write the answers? Probably. But here's my two cents on that:

 

One of the things that I'm liking about Ray's is that it is so distilled; problems are presented in the most direct way possible, even the word problems. I'm thinking what my son needs right now is some time building speed and stamina in purely mental terms, and anything that gets in the way of that, like writing, for instance, would just slow him down. When I did Friday's lesson, he was in a loopy mood and so I actually asked him to stand in front of me with his hands behind his back, hold more or less still, and answer in a normal tone of voice. This is not because I'm a big ol' meanie (well, okay, I am sometimes, but that's not the reason) but rather because I wanted to see if it would help him focus, and it did. Going waaaaay out on a limb here, but I've been doing some reading about neuroplasticity (sp?) lately, and although this is a huge generalization, I'm getting the sense that "old-fashioned" educational expectations, both in terms of teacher methodology and in terms of student behavior, were often quite effective and informed (trying. so. hard. not. to write. an. essay. . . ). The idea of oral practice along the lines of what one reads about in one-room schoolhouses seems appealing to me for those reasons.

 

Aren't you sorry you asked :001_smile:? I apologize; I just cannot, cannot seem to answer a question succinctly.

 

Also keep in mind that there's a part of me that is rolling around on the floor laughing at the idea of giving anyone math advice. . .

 

Oh--almost forgot--I found this thread in which some folks are talking about combining MEP and Ray's. It may be of some use to you.

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Please stop apologizing for writing so much! I am seriously hanging on every word :) We are doing MEP and I really like it, but your concerns with it are resonating with me.

 

I've been interested in Ray's ever since I accidentally bought a reprint of the teacher's addition many many years ago (I still have no idea how it ended up in my basket, but I think it was meant to be!) and began reading it. A lot of it just seemed to make sense.

 

Thank you so much for writing out your thoughts (and if you have any more, PLEASE share!). I don't want my math fingers in too many pots, but at the same time I'm not 100% certain about any of the math curricula I've seen, so I have been looking for something to supplement MEP with. I also kind of like the idea of using both a cutting edge curriculum and an extremely old-fashioned one... it seems like two extremes! :D

 

If anyone else is interested, I found links to free online versions through this thread: http://www.welltrainedmind.com/forums/showthread.php?t=44972

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Phroggies you are NOT writing too much!

 

I was reading through some google versions of Ray's again last night. I was struck by how much of what is in the manual is not evident in the 1st couple books. It looks like the part I am so drawn to was taught by the TEACHER not the book. In Strayer-Upton, I can actually see the methods presented in the student text.

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The danger of racing through MEP, I'm coming to think, is that he'll learn to do fancy concepts and puzzles but not really learn to think in a mathematical way. If that makes a lick of sense :). But Ray's--especially because of the word problems--will offer a wealth of practice but still encourage something greater than just mechanical recitation of the facts.

 

I heard a quotation in one of the CiRCE lectures last night to the effect that with practice, the hard becomes the easy, the easy becomes the natural, and the natural becomes the beautiful. Racing ahead will short-circuit that process. So that (in a nutshell :) ) is why I'm looking at using Ray's.

 

What an awesome answer-thank you so much for typing it all out.

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phroggies, thank you so much. And don't apologize for too much explanation -- it's what I was looking for. Your son sounds so much like mine, so all the information is really helpful.

 

I also plan on working through the summer, but our days are still light in workload, so I don't think it would be a big deal. Plus, if we skip a day here and there, I don't worry about it. I'm also not shooting for a particular goal in a certain amount of time - just proceding at whatever rate suits us. And mine gets really antsy as well, and, like you, I find myself being a "meanie" and asking him to be still when he is reciting something to me. But I mix things up - he enjoys throwing a ball back & forth when we do skip counting or when he's answering oral problems.

 

After posting my questions, I read through the arithmetic portion of "Manual of Methods", which was very interesting. After reading that & your post, I'm thinking of going back to near the beginning of Rays as well. I like the concept of being able to recognize groups of numbers without counting. We started out learning to add by counting, and my son will often use his fingers to add, and I'm now rethinking how best to address that situation.

 

If you have any additional thoughts in the future, please share. So many of us here are interested.

 

Thanks again!

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After posting my questions, I read through the arithmetic portion of "Manual of Methods", which was very interesting. After reading that & your post, I'm thinking of going back to near the beginning of Rays as well. I like the concept of being able to recognize groups of numbers without counting. We started out learning to add by counting, and my son will often use his fingers to add, and I'm now rethinking how best to address that situation.

 

 

It's a major light bulb moment reading that, isn't it?

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Y'all are very kind. I'll try tomorrow to post some "footnotes" in hopes that looking at the resources that influenced my thoughts on this might be helpful. I'd also love to hear what others think of them. In the meantime. . .

 

After posting my questions, I read through the arithmetic portion of "Manual of Methods", which was very interesting. After reading that & your post, I'm thinking of going back to near the beginning of Rays as well. I like the concept of being able to recognize groups of numbers without counting. We started out learning to add by counting, and my son will often use his fingers to add, and I'm now rethinking how best to address that situation.

 

My son will still use his fingers every once in a while. I've always thought sufficient drill would "cure" it, but the Manual of Methods is making me think it's a perceptual problem at bottom. So I did a little experiment tonight--I randomly put groups of buttons down on the table and asked my son to tell me the number without counting. He seemed to stop being able to do so at around five. But here's the interesting thing--I tested myself as well, and the best I could do was six, and that was only if they were arranged in a nicely symmetrical way. My husband topped out around five as well. I'm really curious to see whether any of us can train ourselves not to do this (the MoM is not especially encouraging, either: "If the child once forms the habit of counting by ones. . . it will be almost impossible to correct his error).

 

I'm thinking tomorrow we'll start with a game (always a good strategy on Mondays, at least around here), wherein my son and I will compete to see who can establish the number of items in a random group the most quickly--then we'll "check," not by counting, but by splitting the group into smaller groups. Does that make sense?

 

Hunter, do you have any specific experiences or practical advice on how to do this? It's a whole new world for me. And my 2.5 year-old is starting to count, so I'd like to do it differently this time. . .

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You can buy them through Amazon, but I also posted free copies on Googlebooks for you to look at before you made the purchase if you wanted.

 

Thanks. Is it the guide by Ruth Beechick that you all are talking about?

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Hunter, do you have any specific experiences or practical advice on how to do this? It's a whole new world for me. And my 2.5 year-old is starting to count, so I'd like to do it differently this time. . .

 

:bigear:

 

My barely verbal almost 5 year old can only deal with numbers by counting. I'd leave the entire topic alone except she likes to count things. I can't imagine how else we could do this.

 

Rosie

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It's a major light bulb moment reading that, isn't it?

 

It is, but it also has me wondering. How important is it for a child to not count when learning to add? (I mean, if it is almost impossible to fix, as phroggie noted, is my child eternally doomed to fail at math? :001_huh:)

 

Seriously, if he gains a good conceptual understanding (say, via MEP) and masters the drill & memory work suggested in Rays, wouldn't he have a pretty good mastery of math? I'm not sure I see the advantage of being able to recognize a random group of 9 buttons on a table without counting (other than as a really cool bar trick). I would appreciate further enlightenment as to why this is important.

 

Phroggies, you mentioned that your 6 yo also still uses his fingers sometimes. The teaching guide in Rays indicates that children initially need to go through a manipulative phase (and I've seen this in numerous other writings as well). I'm wondering if our sons are just not completely out of this phase, and if further practice & maturity will address the issue.

 

All opinions are welcome.

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It is, but it also has me wondering. How important is it for a child to not count when learning to add? (I mean, if it is almost impossible to fix, as phroggie noted, is my child eternally doomed to fail at math? :001_huh:)

 

I logged on here to see if anyone had any ideas before I got started on our homeschooling day, so I haven't had a chance to look at all of Hunter's links (THANK YOU!) but I did glance at the Waldorf one and it says kids should recognize quanitities at least to five--so I'm wondering if that's a natural limit that could be overcome with training but doesn't absolutely have to. Also, I joined the Ray's Yahoo group last night and did a quick search on this--several people who have used it said they had success teaching it remedially and/or that while helpful, it wasn't "essential." So that gives me hope.

 

Seriously, if he gains a good conceptual understanding (say, via MEP) and masters the drill & memory work suggested in Rays, wouldn't he have a pretty good mastery of math? I'm not sure I see the advantage of being able to recognize a random group of 9 buttons on a table without counting (other than as a really cool bar trick). I would appreciate further enlightenment as to why this is important.

 

Phroggies, you mentioned that your 6 yo also still uses his fingers sometimes. The teaching guide in Rays indicates that children initially need to go through a manipulative phase (and I've seen this in numerous other writings as well). I'm wondering if our sons are just not completely out of this phase, and if further practice & maturity will address the issue.

 

Couple of quick thoughts here--yes, I think you're right about this being to a certain extent a phase. My son does this less and less. I'm thinking about number recognition (this is the phrase Hunter's Waldorf link used) more in terms of tightening up his skills than covering up a huge, awful gap. I'm also thinking that programs like MEP have some of this built in--for instance, in Y1, whenever a new number is introduced one of the first things is to look around the room and find collections of objects which, when added up, equal the new number. There's also a lot of work with rods, which I would think would accomplish similar goals. So I think our sons have been beneficially exposed to this; I'd just like to draw it out and strengthen it.

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I think it can be remediated in the home, much easier than in the school. The author of the eclectic manual was writing to young teachers with the purpose of indoctrinating them about the importance of teaching with the most efficient method possible. We are not the author's audience. I'm learning to read an author's words in context of who he is talking to, knowing that his word choices, emphasis and warnings are aimed at his target audience.

 

When we see the numbers, we see them grouped. 6 LOOKS like 1 and 5, 2 and 4, 3 and 3. Later on rearranging the numbers for mental math will be easier, when we have SEEN what 6 IS. Even as adults many of us, only know of numbers as small as 5-10 as THEORY. If THEORY starts at understanding what 5 is, then everything after that is theory and not totally applicable. That is a scary thought :-(

 

We are first generation homeschoolers. Few of us will reach the promised land. We do our best and then pass the baton to our kids and grandkids. When you graduate your children, you will probably have some gap time--as I am having now-- to study educational theory and new methods, that you will be able to offer your children to educate the grand babies.

 

Don't panic and obsess over everything your learn about the "best" way to teach. If you have time and desire, apply what you are learning. If you are getting overwhelmed, pull back and teach with the methods that are more familiar for NOW. We know how pitiful our educations were, but we are okay. I think everyone here is housed, has adequate nutrition and at least substandard but present medical care. Yes we WANT better for the next generations...but panicking and overstudying instead of BEING with that generation isn't going to benefit as much as a calm mommy and home.

 

So we read during our down time. We add little bits here and there as we are able. We think ahead to the next few generations. We work on their character and mental health FIRST. We LIVE, because none of us are promised a tomorrow.

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Hunter, thanks for your wise words. My math education, especially at the elementary and middle-school level, was pretty sub-par, and it's the subject I feel the most nervous about.

 

Just a few footnotes, as I said. Birchbark, I read through the other thread you linked to. My reading on the subject doesn't give me much of a sense as to whether to focus on mental math as opposed to other forms--but it does suggest that some formal math, and lots of drill, would have some definite advantage. The approach I'm seeing in the first several years of Ray's, which seems to combine thorough understanding of the concepts with LOTS of drill (the MoM suggests additional drill to even what Ray's provides) makes a lot of sense, regardless of whether you're talking about written or oral practice.

 

  • First, the CiRCE quotation I mentioned was in Andrew Pudewa's talk, "Reflections on Redeeming Repetition: Rut, Routine, and Rituals," found here. I botched the quotation a bit--I googled it and it's "The hard must become habit. The habit must become easy. The easy must become beautiful"--but this is a nice talk about the virtues of repetition, with some discussion of the neurological effects (be forewarned; it also has a great deal of Christian content if that's an issue).
  • Second, Malcom Gladwell's book, Outliers, has a great deal to say about drill, especially the idea that it takes about 10 years of practice to achieve expertise. Mind you, I had some problems with Gladwell's book, and am not comfy with his suggestion that Chinese students are good at math because their ancestors worked in rice paddies. But it contains a number of fascinating cases of practice really making perfect.
  • Norman Doidge's book, The Brain that Heals Itself had a tidbit about Victorian methods of teaching in relation to language arts. I have to quote from this online source as I neglected to write down the quotation while I was reading the book (head smack):

    "Some teaching techniques abandoned in the sixties as too rigid may be worth bringing back.

     

    Rote memorization probably strengthened visual and auditory memory (and hence thinking in language and pictures), just as an almost fanatical attention to handwriting probably helped to strengthen motor-symbol-sequencing capacities — and thus not only helped handwriting but also added speed, automaticity, and fluency to reading and speaking.

     

    Timing is important. Neuroplasticity is at its maximum in children up to 11 years old, though fortunately teenagers and adults can still benefit after that age ."

    Now, I know he's talking about language here, but I'm going to risk a generalization and say that perhaps pre-1960s classroom methods for math might have the same effect on mathematical reasoning.

  • I haven't read these articles yet, but I found this quotation here whilst poking around:

    "Research shows rather convincingly that real competence comes only with extensive practice [bjork & Druckman, 1994]. Yet practice is certainly not sufficient to ensure understanding. Both the evidence of research and the wisdom of experience suggest that students who can draw on both recalled and deduced mathematical facts make more progress than those who rely on one without the other [Askew & Dylan, 1995]."


 

There's more, but that's all I can recall solid references for. I should perhaps emphasize that I have absolutely zero expertise in this field; I just read pop science books about brains for fun :). I'd be happy to hear other info if anyone wants to share.

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My eldest son used the first three Ray's books, and all of my boys used the Primary book before going on to any other formal math lessons.

 

Some of my best homeschool memories have to do with lisping four-year-olds, Ray's Primary math in my hand, and chalkboard, blocks, buttons, and muffin tins scattered across the rug.

 

And any kid who learns fractions with Ray's has learned fractions forevermore, amen.

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My eldest son used the first three Ray's books, and all of my boys used the Primary book before going on to any other formal math lessons.

 

Some of my best homeschool memories have to do with lisping four-year-olds, Ray's Primary math in my hand, and chalkboard, blocks, buttons, and muffin tins scattered across the rug.

 

And any kid who learns fractions with Ray's has learned fractions forevermore, amen.

 

That is very comforting to hear. I've still not implemented anything. We're going to finish up our curriculum for this year in a few weeks and I'm going to try Ray's Math over the summer.

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Those are some interesting articles. I am always interested in neuroplasticity. I have suffered some significant brain damage because of frequent uncontrolled seizures and malnutrition. The seizures have eased up a bit in the past couple months and for the first time in years, I'm healing and remediating, faster than I'm sustaining new damage. My writing abilities are almost normal now and my speech has improved. I still can't divide, but believe that will come back with work, and I'm honestly thankful to have lost the ability as it lead to my current fascination with primary maths.

 

All of this math theory is important and GOOD, and worth devoting time to as long as we are not neglecting the GREAT to do so. I have to constantly check myself and establish priorities, because it can be so hard not to obsess and jump on bandwagons and catastrophize, and lose perspective on what is really important.

 

It does take drill, lots of drill to master anything, so we need to be very wise about what we set out to master. Sometimes we teach our kids tricks. Those tricks can keep people off our backs and give us more room to teach in peace, so...I don't warn against them, as long as we are aware of what we are doing. Math and classical languages are the easiest place to prove to the world our child is getting a superior education. I too had a lousy education, but managed to somehow get my youngest and I through the first few chapters of a calculus book and most of the way through an ancient Greek grammar before the PTSD and poverty and just mess halted me in my tracks. I don't know if I would focus on the tricks again or not. It had it's pros and cons.

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  • 3 months later...
Y'all are very kind. I'll try tomorrow to post some "footnotes" in hopes that looking at the resources that influenced my thoughts on this might be helpful. I'd also love to hear what others think of them. In the meantime. . .

 

 

 

My son will still use his fingers every once in a while. I've always thought sufficient drill would "cure" it, but the Manual of Methods is making me think it's a perceptual problem at bottom. So I did a little experiment tonight--I randomly put groups of buttons down on the table and asked my son to tell me the number without counting. He seemed to stop being able to do so at around five. But here's the interesting thing--I tested myself as well, and the best I could do was six, and that was only if they were arranged in a nicely symmetrical way. My husband topped out around five as well. I'm really curious to see whether any of us can train ourselves not to do this (the MoM is not especially encouraging, either: "If the child once forms the habit of counting by ones. . . it will be almost impossible to correct his error).

 

I'm thinking tomorrow we'll start with a game (always a good strategy on Mondays, at least around here), wherein my son and I will compete to see who can establish the number of items in a random group the most quickly--then we'll "check," not by counting, but by splitting the group into smaller groups. Does that make sense?

 

Hunter, do you have any specific experiences or practical advice on how to do this? It's a whole new world for me. And my 2.5 year-old is starting to count, so I'd like to do it differently this time. . .

 

 

I have found that RS math is the best resource for teaching kids NOT to count by ones. I was having that same problem with my oldest (and my middle was starting as well). RS A is focused on teaching kids to count by 5's and 10's. Miquon also does this to a certain extent. That was the main reason I stopped using SM. It was instilling in him a need to count by ones.

 

I am so intrigued by Ray's Math. I saw it at the CiRCE conference last weekend. I love RS math, but would it be possible to switch to Ray's when I am done with RS or should we be supplementing with it now? (1st grade) I am supplementing with Miquon now.

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I just wanted to say that I have started to use Ray's and MUS, with my son. One week Ray's, one week MUS. I like the rote and relaxed way of Ray's and the visual, how and why of MUS. MUS is another curr. that really focuses on getting your child to see the number without counting. Their blocks help tremendously to do this. They also want your child to really know their facts before moving on to the next concept.

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Don't panic and obsess over everything your learn about the "best" way to teach. If you have time and desire, apply what you are learning. If you are getting overwhelmed, pull back and teach with the methods that are more familiar for NOW. We know how pitiful our educations were, but we are okay. I think everyone here is housed, has adequate nutrition and at least substandard but present medical care. Yes we WANT better for the next generations...but panicking and overstudying instead of BEING with that generation isn't going to benefit as much as a calm mommy and home.

 

So we read during our down time. We add little bits here and there as we are able. We think ahead to the next few generations. We work on their character and mental health FIRST. We LIVE, because none of us are promised a tomorrow.

 

This is a precious gem of wisdom I should be wearing around my neck.

 

I've been following links and reading a string of threads while reading the manual linked to from one of them (was it this one? see .. that's how lost I am).

 

This thread has been a wonderful read .. along with whatever else along the same lines I have been reading this afternoon. :lol:

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I'm finding it interesting to reread this old thread, and am actually being helped by my own "notes". As I mentioned in this thread I have some brain damage and memory loss, so it's really funny to read my old posts. Amazingly I'm pretty consistent...considering :-0 I love, love, love this stuff; but find it hard to keep up with. Sometimes I get so overwhelmed and lost in it all, and just walk away for a bit. Last week I was so overwhelmed with it all. This week I'm entranced with it all, but I'm noticing I'm doing a huge amount of odd word substitutions, so I know my brain isn't functioning so well, and my time might be better spent on open-and-go, but...this is what I'm doing for better or worse.

 

There are recent threads here about the Grube method and the books written more directly off of it, than Ray's.

 

I think I'm going to use Ray's starting with the Practical Arithmetic, but Franklin and others before that. I need the Grube's in the STUDENT book, not just the teacher's manual.

 

For those using Ray's Practical Arithmetic, there is Dubbs supplementary problems as well as the Test Examples. Answers are included. I didn't find out about Dubbs until very recently :-0

 

With all the Ray's talk, how have we never heard of Dubbs and Grube? :-0

Edited by Hunter
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Because the name Ray inspires a lot more confidence than the other two?:tongue_smilie:

 

Yeh, but I remember when Ray's was kinda new by Mott Media. There were no free internet versions. I guess whichever versions were put into hardcopy by the oldschool homeschoolers are considered the ONES.

 

It makes you wonder which one of our curriculums will be reprinted 100 years from now and WHY.

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