The thing is -- it's not about graph theory. It's about ALL of the cool math that is not generally taught to anyone before their 3rd or 4th year of undergrad. It's about the fact that discovering and proving new things in math requires creativity, and yet we run off all the creative minds in the early years by teaching them that math is nothing more than following rote procedures and memorizing mindlessly. It's about graph theory, number theory, modern algebra, set theory, coding theory, cryptology, topology, and every other cool kind of math that is understandable to youth but being denied them in the name of the standard curriculum where they learn nothing but solving equations and factoring polynomials via memorizing complicated procedures that don't mean anything to them and eventually finding rates of change in calculus (if they're actually "good at math") while never *understanding* all the different ways you can interpret a derivative. It's about kids being taught another set of rules to solve problems without understanding that math itself is about problem solving. I'm biased. My degree is in math. I teach math camps. I've taught math teachers at the middle and high school levels. I see teachers who love their kids but are teaching them to robots because they just don't know any better. And I am convinced that folks who go into math at this point do it DESPITE the way we teach mathematics to our youth, rather than BECAUSE of it.

Yeah, I'm trying to get 'em young. :D As an aside, I have noticed there's a real misconception about what it is I actually do in class, because it looks like I'm just sitting and talking with the kids... The co-op is trying to set up a "sub plan" so that sick teachers don't just mean class is cancelled, and so I'm working on my part of that. My "sub plan" is going to be a few bedtime math stories with solutions. But trying to explain why that's my sub plan, instead of a lesson that actually relates to our main content (graph theory) has been tricky. I don't want to make it seem like the other parents are somehow not able to teach it, but so much of what happens in class is me being able to roll with the kids and make math connections on the fly based on whatever random ideas they have, and there's just no way I could make a "sub plan" for these kind of conversations. I've been asked by very well-intentioned folks why I don't just write down what I plan to say... It'd be a good practice for me to get into, they say... And maybe it would? Maybe it's just arrogant to think that I'm the only one there who can do it? But I feel like it just wouldn't work at this point - or at least that it'd kill a lot of good learning that takes place.

So I'm currently teaching a math class at my co-op and I'd say this is spot on. I'd say it's a cross between a math circle and an actual class (I only have half an hour each week! will definitely be getting a full hour next time around) and we're mainly just introducing them to graph theory. It's set for K-5th grade, but I have almost exclusively Kers (who couldn't find another class at that time, mostly, I suspect...). It's been fun because none of the parents know any graph theory of course, and we started very simply just by talking about map colorings and how many colors you need and they got to create their own maps. I'd say that, other than my own kid, every single other child in the class falls into the first category. They're "good at math" and the parents don't really know what to do with that. Since I've started teaching the class, I've actually had a whole slew of parents hunt me down just to talk about their "good at math" kiddo and how they're so bored with their math, and they're surprised when I ask if they've ever considered something other than Saxon... :P When I was in grad school, I taught this math class that was an exit math class for non-stem majors. The only real purpose was to get kids to look back somewhat fondly toward math and to help them see that maybe math was more than they'd previously accepted. So we covered basic graph theory, coding and cryptography, artsy stuff like tilings, and some basic probability/gambling/statistics. Maybe a few other things, but I can't remember now. I vividly remember one girl approaching me after class the first day one term and very kindly and calmly telling me she was going to fail my class and she just wanted me to know ahead of time so I didn't take it personally. She's just not good at math. Has a math learning block and disorder. She just can't do things with numbers and can't pass math classes. I was a little taken aback, but managed to fumble my way through the conversation. Halfway through the term, she had an A (except that she was taking it Pass/Fail instead of graded) and I talked with her about it again. We'd been doing stuff like finding most efficient routes to travel between places, talking about how you know if there are Eulerian circuits (including one direction of the formal proof) and time-processing / bin packing algorithms. She was GREAT at it - especially the graph theory parts of it. And yet, all she could say when I really encouraged her was that this wasn't "real math." I tried so hard to help her see that this was MORE REAL math than all that other stuff that she'd previously failed, but I don't think I ever convinced her. It was such a strange situation to be in -- so encouraging to see her succeed and so sad to see that it didn't matter any more. One of the main reasons I'm teaching this elem class at co-op is not even to nurture the truly gifted kids so much as to show kids (before they've been inundated with drill and kill mentality...) that math is SO MUCH MORE than arithmetic. My husband has told me a few times (like yesterday when we deviated from graph theory to talk about mobius bands because I wanted to do this super cute craft http://www.whatdowedoallday.com/2016/01/mobius-strip-hearts.html)that I'm doing stuff that's over their heads. That I'm just going to confuse them. But I really feel like I'll have accomplished my goal if they come away from my class just saying "That was so cool!" I'm not sure I even care if they can repeat the main point (like I said, lots of K'ers with high energy!), but if they think it's awesome that this little band only has one side (even though it looks like it has two!) and one edge, and if they think it's cool that the inside is the same as the outside on the klein bottle, and if they understand that this is actually still MATH, then I'm gonna call the class a success. :)

Sounds good! I think I'll order the CWP then instead of just charging forward with new content. Thanks!

Breach does mean to come up and break the surface of the water. He added in the frog comparison himself (the book talks nothing about frogs!). I see what you're saying about frogs not actually breaching, but I think it's a sufficiently complex point that I may just let it slide for now and not make him re-do it. He gets discouraged when I make him redo too much. On the other hand, figuring these things out helps me help him better in the future, so thanks! :) Lol - Thanks. We're working on splitting things into sentences and adding commas the last few weeks, because sometimes he writes half a page thinking that it's one big sentence. We're not doing formal grammar right now, so we're mainly reading stuff aloud again and thinking about when we "pause" and what makes a "whole thought."

That's why I wasn't sure if I needed to rearrange the entire sentence if we put a period before the "but." I was always drilled that you can't start a sentence that way. But (!!! :D) I also want to edit his work as little as possible, while still teaching him what's right. He loves long sentences and I really wish he'd just write shorter ones... SO much easier for me to correct! :)

My 6 yo is finishing up Singapore PM 3A, but we don't really use any of the extras like CWP or IP. We're supplementing with BA 3A currently, but it goes much slower because his reading lags his math skills. We also supplement with XtraMath just because his multiplication facts aren't memorized yet (The upper left half of the table are pretty quick, but the lower right half take actual thought still). I'm not sure if we should keep plugging away using mostly the textbook and workbook, or if we should start adding in CWP or IP or something like that until he gets the rest of his facts down (or for some other reason). Currently the concepts are straightforward for him: not hard to understand, but time consuming to carry out occasionally. He tries to do most of it in his head still and grumbles when writing down work (especially on 2 step problems involving multi-digit multiplication or long division). I considered doing CWP to address all these issues (practice reading, writing down solutions, continue practicing facts), but also don't want to bore him with stuff he finds really tedious. Thoughts?

My son wrote about dolphins and how they jump out of the water. He compared them to frogs as follows: "Dolphins often breach, or jump out of the water like a frog but dolphins do it in the water frogs do it on land." I'm slightly unsure how to help him fix this sentence. We ended up fixing it to: "Dolphins often breach, or jump out of the water like a frog, but dolphins do in the water, while frogs do it on land." So two questions: 1) Should I have made him put a period after "like a frog"? If so, would we just capitalize the "But" or would we rearrange the beginning of the next sentence? I feel like having two separate sentences would make more sense if the second here wasn't saying "do it" to refer to breaching/jumping from the first sentence. 2) Could/should we have used a semicolon near the end (as in "Dolphins do it in the water; frogs do it on land.")? This was what I wanted to do, but I felt unsure enough that I avoided telling him to. He's young... He's never seen a semicolon before. :) Grammar is my weakness (editing, particularly - I can write ok just by avoiding situations in which I'm unsure what to do!), so I'm sorry if this is a dumb question!

Ok! That makes me feel better. :) I edited my post after thinking on it today and realizing that I definitely let my frustration get the better of me and I definitely wrote too harshly... I skipped curricula alot with my oldest, trying to find a good one, but I wondered the whole while if it was doing more harm than good. I've really been trying to "stick with it" for my second kiddo, and I should know better than to post anything online when I'm frustrated. I always regret it. :) Thanks, all! It makes me feel better to know I'm not the only one that just doesn't really like this book. And it's also good to know that those "errors" aren't errors, and that it's intentional. I find it surprising they don't at least say somewhere that they're gonna start writing it differently, but oh well.

We have been trying 100 EZ lessons. But what is up with this book?? We're halfway through, but I'm not sure we're gonna finish... Teaching "is" as "isss" (rhymes with hiss)? Teaching "cow" as if the "ow" isn't really a phonogram? Why the extra symbols?? Will that actually be helpful by the end? (And I'm not even counting the errors the book contains in the children's stories by missing markings that they've taught the kid to rely on at this point, since some errata is to be expected...) Please, if you think it's great, give me some motivation to continue by reassuring me it's really a good thing! I really wanted to like this! PS. I modified the title because I definitely let my frustration get away with me originally. I really was hoping to get positive stories about this book because I'd like to finish it with my kiddo (I hate stopping things half done). :) So thanks to everyone who's given positive feedback!

He came up with a bunch of these on his own, which is kind of fun. :) He likes to double things and then double again, especially. Silly boy. Thanks!

Oh, great! Thanks, All! This is exactly what I was thinking, but wanted some reassurance. I've talked with hubby some about the grit thing because it was something I didn't learn until grad school, honestly, and we want to do better with our kiddos (especially ones who may be bright and skate by easily early on). But I had a hard time verbalizing why I felt like this isn't the the right time or situation for just forcing him to just keep plowing through. When we hit this spot with subtraction, I did just slow it down (maybe he'd do a page or half a page at a time, rather than an entire "exercise" in the workbook) and work on subtraction facts with flashcards, games, or xtramath. I have been adding in BA slowly, but his reading is a little lagging behind his math skills, so it's also very slow going there, too (and with three younger kiddos, I don't quite have as much time as I'd like to sit and just read everything *to* him). He can use a multiplication table easily - does it help them learn those facts to use one, though, or is it a just a stop-gap measure while he learns them other ways? (I honestly have no idea! :) )

My kiddo has always blown through math (occasionally doing 10 lessons in a row just because they were fun). But lately he's really slowed down. He's gone from doing 2 lessons in 15 minutes to doing 1 lesson in an hour. Concepts are fine, but the doing is slow because it's multiplying by larger numbers and long division with remainders, and he just hasn't memorized his upper multiplication facts yet. So we're working on getting those memorized. But I guess I'm not sure what to do in the meantime. Taking an hour to do a single lesson is painful when he's just adding up eights until he gets that 9x8 is 72 (and in the meantime, he's looked around, read the writing on his pencil -- "Look Mom! It says Nebraska Math! I'm doing math!" -- and gotten very distracted multiple times). So I'm tempted to just focusing on the facts and quite the other lessons for a while (Singapore 3A). My husband is concerned that this is allowing him to continue skating by and we're getting ourselves into a situation where he won't learn to work through hard things (e.g., "grit"). He is advanced in math, so there's no harm in slowing down. But I'm not sure it's the right thing to do because it just makes this portion of things take longer. We were in a similar situation when he started subtracting 3 digit numbers with renaming: got the concept, but it took him *forever.* We just plodded through it and were very glad when it was over and we moved on to something else, but I'm just wondering if we should do something different in this instance.

My feeling on this in math is similar to my feelings on history, politics, and religion: it's ok to teach an incomplete concept, but it's not ok to teach an incorrect concept. It's up to the person teaching to simplify a complicated situation in such a way so that their "simplifications" are both understandable for the target audience AND still true. Otherwise, it's an automatic fail in my book.

Ok, so this is probably going to seem like a really dumb question, but can anyone give me some directions on how exactly one uses this Fibel? http://www.amazon.de/Meine-Fibel-Ausgabe-Viererfenstern-Festeinband/dp/3060813817/ref=sr_1_2?s=books&ie=UTF8&qid=1451768979&sr=1-2&keywords=meine+fibel+volk+und+wissen I also have the Arbeitsheft and the Shreiblehrgang. I can read German myself, and I've taught my 6 yo to read in English using the Spalding method, but I just have no idea what I'm supposed to do with these! (They were a very kind gift from someone who knew we were teaching German reading next.) Just go through it, teaching any sounds that differ from English letters, and read whatever reading there is? Do we do other practice on the side? It seems to go from the first letter introduction (M sound) to reading real stories (short, but much more advanced than "Mat sat.") in just just 30 short pages. :)

Yeah, we actually had a talk about this just this morning. It's not so much about spelling, but sometimes he's so focused on READING that he doesn't process what he's reading. I have to stop him every sentence or two and ask him a question about what he read just so that he actually processes. And even then, he often forgets what he read once he's to the end of the paragraph/page. This isn't a writing issue, now, of course, but still one I'm not sure how to fix. Even when I took out the writing altogether, he has a difficult time telling me anything we read -- at least in part, because he wants to tell me EVERYTHING we read, and he has a hard time sorting through everything he heard to pull out just a summary.

Lol. We just talked about the role of thirds and he's so excited. We drew lines with dry erase markers on his view screen and he's running all over taking pictures. :) So glad we have digital given that he's already taken over a hundred pictures since Christmas!!

Yes I will! Thanks to you both!

Thanks! I know I can always google to find things, but I also thought someone here might have experience, and things that are "tried and true" would be better than random experimenting (at least in this area, since it's one I have absolutely no experience with). :) For instance, I didn't know a *single* one of the things it talks about teaching kids 6-10 in the link you sent. How sad is that?!

My Ker has decided he wants to become a photographer. He's relatively serious about it, but I'm not willing to invest a TON into right now, given his age... :) So we bought him a basic camera (only 1.3 megapixels) with digital zoom (we wanted something "tough" enough to get dropped and still survive), and now he really wants to take a photography class, but there isn't anything at our local co-op. Any ideas for something very, very basic that would help him start learning something about photography? I have no idea where to even start, but hubby is taking a photography class at a CC next term, if that might be something we could use to help him?

Thanks. :)

I think this is mostly the case for me, as well. OTOH, my *current* strengths and my heart don't necessarily line up. My heart has always been in music and languages. In high school, I wanted nothing more than to learn more languages and be more involved in music. Unfortunately, the demands of PS really didn't leave me much opportunity to pursue those interests in any real depth. I was in the IB program (I knew my parents couldn't pay for college and was doing all I could to get as much college credits ahead of time), had a relatively full time job outside of school (35-38 hrs/wk), and could manage to get all A's without too much extra strain, but that left nothing left for music and languages. I was good at them, for the time I was able to give them (passed fluency tests in both German and Spanish very early on, landed leads in musicals, etc.), but I just couldn't pursue those without giving up on what I thought (at the time) I "needed" to do (i.e., accrue college credit and get a college degree without much in terms of money or resources). In hindsight (and something I've been pondering in light of the conversation on the blue collar/working class thread), I so wish I could've been homeschooled or self-taught during that period. I was good at learning, but being so driven by the PS system meant that I settled for an A, rather than actually learning the material. Had I had the option to learn things at my own pace, and to my own interest, I believe I would've learned much MORE of the school subjects I had to (and much more quickly, because my motivation would have been different) AND I also would've had time to pursue my love of music and languages. Here I am in my 30's with a phd in math (people are just waiting to throw money and scholarships at people who excel in hard sciences, huh? that is without a doubt the *main* reason I went into math when I realized I couldn't afford to study whatever I wanted) and my heart is really still lost in languages and music. Granted, I think math is cool and fun, too. But it doesn't hold the place in my heart that music and languages do, and it never will. But despite any wishful thinking to the contrary, I think my music & languages boat has just sailed. This isn't a woe-is-me sort of post, because I feel very blessed to be where I am right now in life, but this reflection comes with the understanding that not only are those things far more difficult to learn once you're older, but they're also far more difficult to do when you have 4 children you're caring for and schooling. :)

I wouldn't normally post this thought I had, but it seems extremely relevant to the conversation, so here goes: When I read stuff like this, it often just makes me shake my head in disbelief. Not because there's anything wrong with it, but just because the idea of $6700 for a 12 week program (so just under $600/wk) being relatively inexpensive - even with financial aid available - is beyond my comprehension. I get that it's cheaper than college and all, but...

So I also wanted to add to the discussion that none of my real-life homeschooling friends are on boards like these to my knowledge (none of them have ever heard of them when I bring them up, at least). I live in an area where homeschooling is very popular/prevalent for personal and religious reasons. I think almost all of the homeschoolers near me would be considered lower middle class, with jobs that don't require a high level or specialized education or training but are more about hard work, loyalty, and picking things up as you go. For these families, the most important reason to homeschool is usually a combination of avoiding the evils of PS (and private, for that matter...) and wanting to be the main influence in their children's lives (even beyond the preschool years). Most of them don't have advanced degrees, and many have little beyond high school or some basic college. Most of them qualify for state assistance of some sort, regardless of whether or not they take it. They don't break their heads over getting the best curriculum or the best for their kid, and they're perfectly content with a "good enough" academic education that still allows them to be with their kids most of the time and more carefully control their children's exposure to undesirable content/environment. I'm not sure why most of them aren't on boards like these, honestly. I don't know if they just never heard of it or if there's no desire or both. They're content to have a real life community of homeschoolers to connect with (think: co-ops and such). Now that I'm thinking about this, I wonder how much flack they've gotten regarding their own education and experiences, as it pertains to being an effective and qualified teacher to their children. I'm interested in talking with them some about this once the coop starts back up, if I can find a tactful way of doing so, because it relates to a question I posted on these boards a while back when I was sort of dumb-struck that people were just using curriculum a friend recommended without actually doing any research into what type of curriculum it was, pros, cons, etc. I just couldn't understand that people were (seemingly) putting so little thought into the education they gave their children, but I've since just really come to realize that the academic side of things just isn't as much of a priority for them and they're actually quite content with "only" a "decent" academic situation. So I wonder if this type of board, just by its nature, excludes some of the "blue collar" "working class" folks that this sort of thread is gearing towards. I don't know. I just wonder. ETA except for my advanced degree, there are no huge differences between myself and my friends here who I described above I don't think. I may have grown up poorer than them and I may have been blessed with more intellect by lucky fate than them, but I certainly didn't have an easier or richer life or childhood than most of them.

I totally get this too. I feel like people are *either* critical od us for having me stay home to homeschool (bc I have far more education and earning power than dh) OR the "approve" because I'm so educated and "can actually teach".