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I haven't read this entire thread, but wanted to offer a perspective based on my experiences.
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My oldest is only turning 10, and always unschooled. Â So I know that doesn't compare to a 19 year old. Â We have never done any formal math, she had a fraction manipulative she rarely played with, I bought a fraction pizza game about 4 years ago, I think we've played it once. Â We do a fair amount of baking as we have food allergies. Â She just had standardized testing done as is a requirement in our state. Â She had the peabody done, which has I think 6 areas. Â It is verbally administered. Â The lowest area she scored in was science/social studies, and she scored right on target. Â Highest was spelling (10 grade equivalent). Â Everything else, including math fell somewhere inbetween (so maybe around 5th or 6th grade math equivalent).
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In high school, my best friend, who had VERY strict parents monitoring her homework, struggled horribly in math, barely making it through algebra
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I grew up in a "fun, fun, fun" home, movies every weekend, arcades, mini golf, you name it. Â My parents literally made fun of me for wanting to go home and get my homework done. Â They NEVER asked me if it was done, if I had homework to do. Â Were not able to ever really help me with any math homework. Â I completed calculus in high school and went on to complete a year of advanced calculus in college.
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I *have* to assume that math skills are somewhat a matter of personal aptitude. Â Many people claim they are good/not good with math, across a variety of life/learning situations. Â Just like some people are incredibly artistic while others (me) can't even draw a basic animal sketch that their preschool can recognize.
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To the OP, I hope your son can achieve his educational goals, and I hope you can be at peace with your decisions.
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:hug  edited because it has been so long since I've posted on mothering that I can't even remember how to do an emoticon...
Tracy
Rockin' mama to Allison (9), Asher (5) and Alethea (3), head over heels in love with my sexy husband, Tony.
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i also just remember something a schoolathome mom told me. Â She is really into math and different ways to learn it and even attended some local math conference. Â She told me something like the following:
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When someone says they don't know algebra it is really that they don't know multiplication/division. Â And when they say they don't know multiplication/division it is really that they don't know addition/subtraction.
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I am not sure if I am remembering that right. Â But at the time it made me remember memorizing my multiplication tables when in 4th grade, and how that is probably the best thing that ever happened to me in all of my schooling years because of just how very often one uses multiplication in daily life.Â
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Anyways, just wondering if not having some of those basic tools readily handy would impede one's ability to do algebra or other higher math later in life, and sort of assuming your son doesn't have those (i know my dd doesn't).
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~Tracy
Rockin' mama to Allison (9), Asher (5) and Alethea (3), head over heels in love with my sexy husband, Tony.
Yes, I agree with this. I think that most of the "I can't do math" issues come from missing foundational skills or concepts. However I disagree with your implication that "knowing" multiplication/division means having the facts memorized. That mayÂ be helpful, especially over the long term, but it's not in and of itself "knowing" multiplication and division. The book "Knowing and Teaching Elementary Mathematics" by Liping Ma helped me see how much the depth of understanding of basic arithmetic can vary  even amongst math teachers!
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Miranda
Mountain mama to one great kid and three great grownups


I want to clarify that I haven't experienced any blasting here at MDC.Â I didn't even consider that anyone would think that's what I meant!Â No, where I've experienced it is in real life, mostly with radical unschooling moms.Â And on unschooling groups (such as Facebook and Yahoo groups).Â I had an email convo with Sandra Dodd the other day, and while I'm grateful for the time she took to write and that she included really helpful links, the overall idea was that the problem is that I have an LD mindset and that it is MY problem.Â I think that might be the case for someand maybe even for me, some of the timebut I also think that sometimes there's an actual stumbling block that needs to be addressed.Â Â I am less attached to a learning philosophy or even a lifestyle philosophy than I am to helping my son in whatever way I can.Â
Wouldn't it be nice if kids could optÂ out of certain subjects in college?Â Like, "I'll take herpetology, world literature, ancient civilizations, and creative writing.Â No classes with quadratic equations, please."Â
Booklovin', relaxed homeschoolin', dog snugglin' mom of the best kid EVER!Â AND...waiting for baby #2, due 5/9/14!Â
Math for our young girls comes easily, and if I didn't know or read about the experiences of any other unschoolers I might conclude that this is the result of unschooling. Â In reading skills and math, my girls so far make the experience of HSing/USing very easy. Â But I know that, while our approach might help, I really think that a good chunk of their aptitude is simply well, I can't say where this kind of readiness springs from, so I won't hazard a guess, but I definitely cannot give the credit to our approach.
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I did notice that, for my oldest who just "got" math with no trouble, that after addition came the understanding of multiplication. Â "Three 5's make 15!!!!" echoed through the house on a regular basis. Â My older sister is a teacher and is just completing her Masters in mathematics, and we talk about stuff like this constantly. Â From her I learned that understanding addition and multiplication can often come before subtraction and division. Â We might assume from our own education that addition and subtraction come before multiplication and division, but I have since learned that it can be otherwise. Â So, the foundation can start in a different place than what we assume, and I definitely know that the reality can be even more individualistic still. Â This reminds me of a game that I heard about and need to find again "Hands on Equations" that uses the concept of algebra without the mathematicshas anyone heard of or tried this game? Â I'm curious. Â But I do know that while you need a mathematical foundation to solve individual algebraic equations, the *concept* of algebra does not necessarily require an understanding or mastery of the numbers. Â In fact, if the understanding is not there, algebra won't make sense even with a perfect understanding of addition, etc. Â (OK, *that* is direct personal experience from my own life! Â I was a straightA math student until the school put me in an algebra class in the 8th grade with other top students. Â Way too early I was so confused!)
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"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."
Only have a second....OP....I was thinking this article might encourage your ds. http://www.psychologytoday.com/blog/creativesynthesis/201112/beyourbestsuckyoumust
Thanks! Very inspiring. I will pass this on to ds.
This reminds me of a game that I heard about and need to find again "Hands on Equations" that uses the concept of algebra without the mathematicshas anyone heard of or tried this game? Â I'm curious. Â But I do know that while you need a mathematical foundation to solve individual algebraic equations, the *concept* of algebra does not necessarily require an understanding or mastery of the numbers. Â
We have! DS and I actually took a couple algebra classes together where this method was used. It was cool, we both enjoyed it. It was several years before he pursued his cc classes and he forgot most of it by then.
This reminds me of a game that I heard about and need to find again "Hands on Equations" that uses the concept of algebra without the mathematicshas anyone heard of or tried this game? Â I'm curious. Â But I do know that while you need a mathematical foundation to solve individual algebraic equations, the *concept* of algebra does not necessarily require an understanding or mastery of the numbers.
We used Handson Equations with my youngest and loved it. I wouldn't characterize it as a "game" as much as math program that uses some boardgamelike "moves" for gaining an understanding of algebra concepts and conventions. You don't play against others. The object is to solve an equation from a worksheet.Â It's suggested for 3rd through 8th graders. We used it with my dd in KG/1st, though she was probably at a 3rd grade level in math. While you don't need to be able to perform operations on fractions and large numbers it is important to have a decent understanding of all four basic operations to about 40. Not full mastery and memorization necessarily, but a good understanding, and strong "number sense." Typically after doing a bunch of moves you'd be left with something like four blue pawns on one side of the balance, and numbercubes totalling 32 on the other side. The child needs to be able to divide the 32 by 4 to arrive at the answer. In another equation one might have to add 5 to 19 and then halve the result. Without enough of a basic arithmetic foundation to handle these computations the program would not work well. But yes, the level of arithmetical fluency required is vastly less than what would be required for a typical algebra course!
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The program teaches negative and positive integers and negative and positive unknowns. Positives and negatives are just two different colours of the same manipulatives.Â The basic moves are very simple ... there are only two, broadly speaking. 1. You can do anything, so long as you do it to both sides of the balance, and 2. "Something and its opposite" counts for nothing, and can be placed or removed from either side without upsetting the balance. Everything has a direct relationship to the symbolic work with linear algebraic equations. My dd is now, three years later, doing real early algebra, and she has a conceptual framework into which to drop the skills she's learning. She doesn't have to memorize and then remind herself that "you can take something to the opposite side and reverse its sign," because that's a concept she understands deeply, having played it out repeatedly with manipulatives using those two basic HandsOn Equations rules.Â
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I feel like I'm talking out of both sides of my mouth on the issue of whether math is necessarily sequential. I said upthread that I agree that difficulty with algebra is likely due to incomplete mastery of arithmetic, but now I'm saying that algebraic concepts can be productively taught long before K7 arithmetic is fully mastered. I think the crux of it is in the mastery of concepts. I don't think one needs to learn every procedure, or memorize every fact, before moving to more "advanced" and potentially more interesting mathematics. But I do think that a deep conceptual understanding of earlier foundational work is essential. Problems tend to arise, in fact, when procedural learning and memorization have masked what is a relatively superficial and gapladen conceptual understanding. For example, the kid who has memorized 7+9=16, but doesn't understand why the answer has to be the same as 8+8. Or who knows that 7x5 and 5x7 and similar pairs of multiplication facts will always yield the same result, but doesn't understand why this is the case. Or who knows that 7x300 is 7x3 with two zeros added on, but has just memorized this as a "rule" ("you do the multiplication without the zeros, and then stick them back on") rather than knowing why it is true.
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Miranda
Mountain mama to one great kid and three great grownups
I feel like I'm talking out of both sides of my mouth on the issue of whether math is necessarily sequential. I said upthread that I agree that difficulty with algebra is likely due to incomplete mastery of arithmetic, but now I'm saying that algebraic concepts can be productively taught long before K7 arithmetic is fully mastered. I think the crux of it is in the mastery of concepts. I don't think one needs to learn every procedure, or memorize every fact, before moving to more "advanced" and potentially more interesting mathematics. But I do think that a deep conceptual understanding of earlier foundational work is essential. Problems tend to arise, in fact, when procedural learning and memorization have masked what is a relatively superficial and gapladen conceptual understanding. For example, the kid who has memorized 7+9=16, but doesn't understand why the answer has to be the same as 8+8. Or who knows that 7x5 and 5x7 and similar pairs of multiplication facts will always yield the same result, but doesn't understand why this is the case. Or who knows that 7x300 is 7x3 with two zeros added on, but has just memorized this as a "rule" ("you do the multiplication without the zeros, and then stick them back on") rather than knowing why it is true.
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Miranda
And I think my own experience is misleading on anything but a superficial level because the fact is that while I did get excellent grades in math (and most definitely understood that 7+9 is the same as 8+8) for the most part I did not internalize math concepts well. Â I was a perfect example of a superficial understanding of basic math functions that temporarily left me hanging when introduced to algebra beyond the basic 8+x=15. Â I did finally get algebra because of those rules. Â Once again, saved by the rules! Â I got good grades because I knew the "tricks". Â So, I did very well by school standards, but not very well really....
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"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."
I've been reading this thread with a lot of interest. My son is only 7 (almost 8) and we unschool in a very relaxed fashion, but lately it seems like he is looking for something 'more', at a bit of a loose end, and the question of introducing academics in a formal way has come up. He's not specifically asking for that (though he did pull out an old Singapore math workbook we have on Christmas Eve to work on) so I don't know that academics are the answer  I just know I've been having one of my unschooling panic attacks lately and this combined with him seeming unsatisfied with life leads me to think academics! workbooks! curriculum! is our answer, heh. We certainly won't be abandoning unschooling in any way, but I do wonder if a bit more guidance from me is what he's looking for. I'm going to have a little 'meeting' with him next week to discuss what things he wants to be spending his time on  see if he'll do some brainstorming, and then we can come up with a plan together to make it happen. I don't know if any formal type of academics will be part of that or not.
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But I do think that a deep conceptual understanding of earlier foundational work is essential. Problems tend to arise, in fact, when procedural learning and memorization have masked what is a relatively superficial and gapladen conceptual understanding. For example, the kid who has memorized 7+9=16, but doesn't understand why the answer has to be the same as 8+8. Or who knows that 7x5 and 5x7 and similar pairs of multiplication facts will always yield the same result, but doesn't understand why this is the case. Or who knows that 7x300 is 7x3 with two zeros added on, but has just memorized this as a "rule" ("you do the multiplication without the zeros, and then stick them back on") rather than knowing why it is true.
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Miranda
I'm totally crashing this thread, but I wonder, how does a parent know when a child has this conceptual understanding? DS1 doesn't talk about multiplication, but understands 4+4=8, 40+40=80, 400+400=800 and so on, without being taught that, but if you ask him to explain *why* it works like that he wouldn't be able to (I assume  I haven't actually asked him). He definitely doesn't have all his addition facts memorized  I find it bizarre some of the math stuff he can do but yet he doesn't know offhand that 7+4=11!
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Â Funny thing too is that lots of more formally schooled/homeschooled kids still can get very engaged in experiential math, from what I've seen. Requiring a bit of work each day does not make it meaningless, irrelevant or destroy any possible interest kids could ever develop in it, imo.
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I think it depends on the child, the parents, temperment and dynamics. Â
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I think there are kids for whom "requiring" might backfire. Â
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I think there are kids it will work fine for.
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I think there are parents for whom USing will drive them insane with whatifs (and this is not a judgment call  just reality).
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I'm totally crashing this thread, but I wonder, how does a parent know when a child has this conceptual understanding? DS1 doesn't talk about multiplication, but understands 4+4=8, 40+40=80, 400+400=800 and so on, without being taught that, but if you ask him to explain *why* it works like that he wouldn't be able to (I assume  I haven't actually asked him). He definitely doesn't have all his addition facts memorized  I find it bizarre some of the math stuff he can do but yet he doesn't know offhand that 7+4=11!
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Personally, I don't think memorizing tables are an accurate gauge of understanding. Â I am a perfect example how the memorization of the rules of math does not go hand in hand with understanding the concepts. Â For this reason, I avoid (or, possibly "hold off" would be more accurate) teaching my kids algorithms and mathematical tricks, being content to let them find their way (if you've read my recent posts on this thread you'll know that in my house this is extremely easy, but I also recognize that I *do* have it easy in this area and our experience doesn't necessarily hold true for others, therefore our path doesn't necessarily work for others either. Â Also, my kids are young and there is no pressure to "learn it quickly or else be behind".)
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Unfortunately I don't think that answers your question of how you know that they *do* have it if they don't shout it out as our kids do. Â I do know that conceptual understanding is more random, or at least unpredictable, than the steady, sequential ordering of skills that curriculums lay out. Â I guess the same can be said for reading. Â While laying out fundamental skills to be learned might be a helpful map, far too often it becomes clear that kids will find their own paths and possibly even are better off for it because they are standing on the foundation that they made themselves. Â In my own education, my ability to follow the rules hid the fact that my foundation was far, far beneath my ability to memorize things.
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"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."
heck yeah. Â Off topic, but I memorized answers in science in high school, did Ok on tests, and had no idea what I was talking about. Â
I think it depends on the child, the parents, temperment and dynamics. Â
I think there are kids for whom "requiring" might backfire. Â
I think there are kids it will work fine for.
I think there are parents for whom USing will drive them insane with whatifs (and this is not a judgment call  just reality).
Sorry if I was generalizing, I do agree with you. My point is that kids may actually resist the very things they need and will serve them in the long run. It is up to the parent to decipher when and if that is the case, and trust their own instincts rather than a philosophy that puts the child is completely in charge of their own education. If there are kids that "requiring" will work fine for, then the notion that unschooling, which prohibits requiring anything, provides the most authentic, intrinsically motivated and relevant education is inherently flawed. I feel it will best provide that type of education to those kids who are uniquely suited to it, and also whose parents have the resources and time to provide and support opportunities for these kids.
Yes, he would have preferred to go to college now rather than in a year or two.... but that sort of thing happens all the time in life. Working and waiting for things is frustrating. Rain wanted to go on pointe in ballet when many other kids her age did, but she wasn't strong enough yet. I'm in grad school with people twenty years my junior. It just seems to be that it's more useful to look around every so often and see where things are and where they seem to be going and what your kids might want from you than to look back and second guess those decisions.
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Single mom to Rain (1/93) , grad student, and world traveler
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Just a collection of thoughts......
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In keeping up with homeschooling literature, I have often read about homeschooling parents of kids with diagnosed learning abilities, and how pulling them out of school has helped their child thrive. Â The goal was to make life seem more normal and less centered around the disability. Â That's what I think of when parents start from the other direction having a kid with a learning disability or delay and wondering if homeschooling might be a better choice. Â I have no opinion about this necessarily, just that I know this is an additional motivation for families, the desire for normalcy.
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One method that I associate strongly with unschooling is immersion in reallife activities. Â For families as young as mine this does mean "baking cupcakes" and adding dice and allowance and building birdhouses. Â (It also means counting toys and adding them together "Mama, mama! Â 11 and 6 make SEVENTEEN!!!!! Â And that means..... 12 plus 6 make EIGHTEEN!!!!!!" Â This happened in the car on the way up to grandma's and it cracked me up because I couldn't quite imagine a first grader working on a math worksheet bouncing with the joy of their mathematical discoveries.)
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To me those "real life" activities are one way of learning, but they aren't the only or always superior way. Baking cupcakes is a great experience for many reasons, but for some kids the fact that math happens along the way isn't one of them. While it might be hard for you to imagine that a child would bounce with joy from discoveries from a math worksheet we saw it again and again with Miquon math (and not once with cupcakes).
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As far as disabilities, yes the greater acceptance in the homeschooling world and the flexibility can be helpful for many families but there can be challenges too. Structured intervention is very helpful with some disabilities and if kids are less interested in participating in that at home that can a challenge. Also, I would not assume because we decide kids won't be affected by their differences that this will be the case. Kids still can make comparisons with friends, siblings, neighbors, etc. Sometimes those comparisons lead kids to avoid activities even more as they decide they aren't smart, aren't a reader, don't like to do things that look like school, etc.
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I'm reading this thread with rapt attention, even though I only have an 11 month oldÂ I did attend a semiunschool like school for a bit when I was a kid. But I'm actually posting in response to folks who wrote about wanting a school that doesn't have math requirements (sorry, I'm not sure how to quote from a phone). Anyway, the college I attended is called New College. Its Â philosophy is studentdirected learning. And while there are required classes for specific concentrations, there's no core curriculum requirements like math. Just a little plug for my dear alma mater since I think it would be such a great fit for a lot of unschoolers.Â
To me those "real life" activities are one way of learning, but they aren't the only or always superior way. Baking cupcakes is a great experience for many reasons, but for some kids the fact that math happens along the way isn't one of them. While it might be hard for you to imagine that a child would bounce with joy from discoveries from a math worksheet we saw it again and again with Miquon math (and not once with cupcakes).
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As far as disabilities, yes the greater acceptance in the homeschooling world and the flexibility can be helpful for many families but there can be challenges too. Structured intervention is very helpful with some disabilities and if kids are less interested in participating in that at home that can a challenge. Also, I would not assume because we decide kids won't be affected by their differences that this will be the case. Kids still can make comparisons with friends, siblings, neighbors, etc. Sometimes those comparisons lead kids to avoid activities even more as they decide they aren't smart, aren't a reader, don't like to do things that look like school, etc.
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Agree completely. Part of my son's trouble is LD and part of it stems from lack of confidence due to LD. He got the idea a long time ago that he wasn't as smart as a lot of his peers and instead of working harder to break out of that role, he has embraced it (but not without some dissatisfaction). It doesn't help that he has ended up being one of the oldest kids in class (different schools, different cut off dates) and his 13 yo brother is SUPER smart (99.9 percentile, doesn't study and gets As). He is so motivated about some things, but is hopeless about academics, and though he tries to act nonchalant, I know he wishes it was easier.
Jess, mama to five boysÂ
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To me those "real life" activities are one way of learning, but they aren't the only or always superior way. Baking cupcakes is a great experience for many reasons, but for some kids the fact that math happens along the way isn't one of them. While it might be hard for you to imagine that a child would bounce with joy from discoveries from a math worksheet we saw it again and again with Miquon math (and not once with cupcakes).
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I do not think worksheets are anti USing at all; I do think requiring worksheets is. Â Â
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I wish parents were easier on themselves, in general. Â No one has a cystal ball, children grow up so fast  it can be hard to stay ahead of the curve and realise you need to change tactics before they are grown. Â That being said  adults are well, adults. Â I don't think there is a magic window for learning math or any other subject  if a young adult decides they need to learn math  they can. Â It may make everything take a little longer, but in the span of a lifetime, I don't think it is overly relevant. Â This is a message we can convey  flexibility and nonrigidity (and forgiving ourselves for any perceived lacks). Â I am not saying this to negate anyones experience  but because I know moms are often too hard on themselves. Â
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I'm reading this thread with rapt attention, even though I only have an 11 month oldÂ I did attend a semiunschool like school for a bit when I was a kid. But I'm actually posting in response to folks who wrote about wanting a school that doesn't have math requirements (sorry, I'm not sure how to quote from a phone). Anyway, the college I attended is called New College. Its Â philosophy is studentdirected learning. And while there are required classes for specific concentrations, there's no core curriculum requirements like math. Just a little plug for my dear alma mater since I think it would be such a great fit for a lot of unschoolers.Â
I agree New College is a great school and it can be wonderful for kids who are out of the box thinkers. It is worth nothing though that as a public college that is part of the Florida University system, it does expect applicants to have four years of college prep math during high school. Four years of college prep math in high school would at an absolute minimum include algebra 2 and geometry, but more typically for competitive schools include precalc and calc.Â http://ncf.edu/c/document_library/get_file?uuid=37eb56ed41e04eabbf135fc47e263212&groupId=48902Â Also, as a public liberal arts college admissions have gotten quite competitive. They accepted around half of the students who applied last year (and of course most students primarily apply to schools where they believe they will be accepted). http://collegesearch.collegeboard.com/search/CollegeDetail.jsp?collegeId=621Â Â Â For me this is a good example of why it may make sense to make sure a student doesn't close too many doors by skipping math. Even if what the kid wants to do is study philosophy at a hippie college, they likely are still going to need math to get in there.
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My sister is an extreme but great example for rethinking the notion that there are "windows" where math is learned more easily. Â She had only a GED and was terrible, terrible at math and insisted that it was because she would just never "get" it. Â 4 grown kids later (she started her family at 19) she went back to school, first for her education degree and then for her Masters in math education. Â I was surprised 6 years ago that she intended to teach math. Â But she set her mind to it, saying "if I can learn this stuff, then anyone can." Â One quarter left, she "gets it" and she's acing her exams and evaluations.
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I don't bring that up to say, "Hey, just wait until you are 40something!" Â No, no. Â I merely use it as an example that math is something that, with effort, can be picked up along the way. Â
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The important thing is that the learning has meaning. Â It could be for the sake of the work itself, like adding up toys or the Miquon math example from Roar (seen especially in younger kids). Â Or it can be less about the immediate work and more about the long term goal (more a trait of older kids and especially adults). Â
"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."
I agree New College is a great school and it can be wonderful for kids who are out of the box thinkers. It is worth nothing though that as a public college that is part of the Florida University system, it does expect applicants to have four years of college prep math during high school. Four years of college prep math in high school would at an absolute minimum include algebra 2 and geometry, but more typically for competitive schools include precalc and calc.Â http://ncf.edu/c/document_library/get_file?uuid=37eb56ed41e04eabbf135fc47e263212&groupId=48902Â Also, as a public liberal arts college admissions have gotten quite competitive. They accepted around half of the students who applied last year (and of course most students primarily apply to schools where they believe they will be accepted). http://collegesearch.collegeboard.com/search/CollegeDetail.jsp?collegeId=621Â Â Â For me this is a good example of why it may make sense to make sure a student doesn't close too many doors by skipping math. Even if what the kid wants to do is study philosophy at a hippie college, they likely are still going to need math to get in there.
Yes, exactly. And math is not the only way to close doors. Ds has told me that just integrating into the lifestyle required for formal education has been extremely challenging. This is despite the fact that he began his cc experience at 15, beginning with one class. For a few years before that, he was on campus attending informal homeschool classes. He has said that time management, learning to answer to others, to balance classwork, his job, and social time have been very difficult.
And again, my purpose with this thread is to share this experience so that unschooling is not just viewed through rose colored glasses. A lot of good things have come from our experience, but a thorough education is not one of them. However, we are dealing with our situation, and I'm confident ds will be just fine in the long run.
I am not a home or unschooler here, but I wanted to share my story. I was raised in a religion where girls had little need of schooling. As a result I never mastered math, but more than that I never had motivation or tools to learn to work through a problem, to break it down into more manageable pieces. Whatever the subject is, a child needs to be taught how to conquer and think through a problem, and to not give up. Take a break yes, but not give up completely.Â
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When I went to college after getting out of the culture of my birth I had to take remedial math. It wasnt the math that was important, it was the discipline involved with learning it, as well as skilled tutors. I now have both a BA in English and a degree in nursing. Lots of math involved in the second one. I wish I had been pushed earlier in math. I do think there is a critical window. Just like language, learning math and other things is often easier when younare younger. But its never too late, it just isnt as easy.
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I have my kids in piano for the disclipline and the brain skills. My little one had to know how to approach the new piece one measure, even one note at a time. This skill will serve her well in life. I also teach them that no matter what is is, they need to do it the best they can, learn to follow instructions, and know how to organize their tasks such as pet care and other responsibilities. These are life skills, ones that will help them hold a job amd be productive members of society.
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What I get from the OP is that her child maybe did not learn some of these life skills that translate into the math issue. I agree that r an evaluation may be needed, or maybe if thats not the issue a life coach may be of great help.
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bad typos sorry typing on ipad
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I can't believe I didn't think of this before. Your anecdote reminded me of John Mighton. He's was a complete and utter math failure in school who went on to become a successful playwright. As an adult he not only became fascinated by math education, going back to university, almost failing firstyear calculus in the process, eventually earning a PhD in mathematics and doing postdoc research in knot and graph theory, but founded a charitable organization called JUMP (Junior Undiscovered Math Prodigies). This is a tutoring organization which was originally developed to rescue students from math failure at the earlymiddleschool level, kids who were considered so behind as to be considered essentially unteachable. He wrote a book called "The Myth of Ability" about the backstory and execution of JUMP, which is part storytelling, part philosophy and part practicality. It is very compelling stuff and it might be useful and inspiring for Tigresse and her ds.
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My takehome message was that anyone can learn almost anything, but that when there's "baggage" from failure or from being many years behind, anxiety and fear that the subject is inherently nonsensical to oneself are often the main obstacles to learning. The key to overcoming that obstacle is engendering a feeling of succes. Whatever learning tasks were the original "gap" ages ago are now easily within the learner's abilities, but the anxiety around the whole deal is now the block. Mighton uses somewhat counterintuitive strategies to help students shed that baggage. He often goes back as far as fingercounting, building a sense of success from execution of steps and procedures so simple that the learner could not fail with them, and then applied those rote procedures to more advanced skills in a similarly rote fashion, in absolutely tiny progressive steps, building confidence, until lo' and behold, a particular skill which is more advanced than the learner's purported math gradelevel has been built up and fully mastered. The confidence engendered by this then helps quell the defeatism. The other thing which I found somewhat counterintuitive is that he goes after a deep conceptual understanding of math initially using a very rote and procedureoriented approach. But his point is that one can't think deeply, ponderingly and creatively with fear of "not getting it" floating around in the forefront. So you must prepare the mind for deep conceptual thinking by sticking to rotelearned procedures for computation that are reliable and allow students to shed their fear of confusion.Â
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Anyway, Tigresse, at 18 your ds is probably selfaware enough to get a lot out of the book at a personal level. I highly recommend it. You would probably enjoy it too.
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Miranda
Mountain mama to one great kid and three great grownups
I hear your message, Tigresse, and I am thankful for reading your story. Â I imagine parents of top public school students thinking that this type of success is available to all within the public school system "if only". Â Same for the unschooling successes.
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I've had the thought briefly before, but this thread has reminded me to ask myself, "What exactly do I expect from unschooling? Â What outcome? Â Why are my goals for my kids?" Â Also, I need to mull over the question, "What will happen if one or both of my girls start really struggling with something? Â What options will I have? Â Which will I pursue? Â And what do I expect will be the result of each possibility?" Â
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It's not so easy just to insert oneself into something and find success these days. Â Even our area organic farmers are looking for interns fresh from Evergreen, not someone like me looking for change of lifestyle. Â Backcountry trail work requires a specialty because every member needs to have skills to offer the group outside of the immediate trail work. Â National Park Service Rangers need degrees, and sometimes law enforcement training. Â Even volunteering with the local gardening organization teaching the kids classes requires that the candidate be pursuing a degree related to the field. Â I use these examples because these are the challenges that I have personally faced in my adult lifetime (not that these were insurmountable, just that more was required than I ever expected. Â I chose the Road over higher education and eventually found the challenges I sought in the gardening business.)
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Even with all this in mind, I still believe in my heart that unschooling is the right path for me and my kids. Â But, never having been one to be rigid* or follow along on anything that wasn't my own idea as well, I doubt that I would hesitate much to choose a path outside the traditional view of unschooling. Â
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*(OK, I've been known in my youth to be extremely rigid! Â Hopefully those who know me will forgive me, because they, too, were also idealistic at that time in their life. Â I'm in my 40's and I still have so much to learn!)
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"She is a mermaid, but approach her with caution. Her mind swims at a depth most would drown in."
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I haven't read this entire thread, but wanted to offer a perspective based on my experiences.
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My oldest is only turning 10, and always unschooled. Â So I know that doesn't compare to a 19 year old. Â We have never done any formal math, she had a fraction manipulative she rarely played with, I bought a fraction pizza game about 4 years ago, I think we've played it once. Â We do a fair amount of baking as we have food allergies. Â She just had standardized testing done as is a requirement in our state. Â She had the peabody done, which has I think 6 areas. Â It is verbally administered. Â The lowest area she scored in was science/social studies, and she scored right on target. Â Highest was spelling (10 grade equivalent). Â Everything else, including math fell somewhere inbetween (so maybe around 5th or 6th grade math equivalent).
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Personally, I don't think memorizing tables are an accurate gauge of understanding. Â I am a perfect example how the memorization of the rules of math does not go hand in hand with understanding the concepts. Â For this reason, I avoid (or, possibly "hold off" would be more accurate) teaching my kids algorithms and mathematical tricks, being content to let them find their way (if you've read my recent posts on this thread you'll know that in my house this is extremely easy, but I also recognize that I *do* have it easy in this area and our experience doesn't necessarily hold true for others, therefore our path doesn't necessarily work for others either. Â Also, my kids are young and there is no pressure to "learn it quickly or else be behind".)
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Unfortunately I don't think that answers your question of how you know that they *do* have it if they don't shout it out as our kids do. Â I do know that conceptual understanding is more random, or at least unpredictable, than the steady, sequential ordering of skills that curriculums lay out. Â I guess the same can be said for reading. Â While laying out fundamental skills to be learned might be a helpful map, far too often it becomes clear that kids will find their own paths and possibly even are better off for it because they are standing on the foundation that they made themselves. Â In my own education, my ability to follow the rules hid the fact that my foundation was far, far beneath my ability to memorize things.
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I'm struggling with this. I did well in math at school but never really understood it or liked it. My husband, on the other hand, did his PhD in maths and sees math as beautiful and elegant and fun. When people say things about kids having a conceptual understanding of math and not memorizing, I really (sounding stupid here!) don't know what they mean! Can't you have both? I'm trying to find the words here... ah struggling... someone mentioned earlier the difference between a child memorizing an addition fact, say 5 and 3 are 8, but not knowing why the answer has to be the same as 4 and 4. I don't know either! They just are the same because they are the same! :) I asked my dh why and he looked at me like I had two heads, "I don't understand the question". So I am baffled. And so is my mathematician dh. ;)
Ds1 hasn't really been taught any math and hasn't made a point of memorizing math facts but does seem to understand a fair amount  is that just what people mean, that math comes to the person naturally? Can't you teach a conceptual understanding?
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I'm totally sleep deprived here so I don't know if I am making any sense. And sorry for getting so offtopic!!
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I can take a crack at it.....
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I think when people talk about a Â conceptual understanding of math they really mean number sense. Â To me that means an abililty to manipulate numbers to get the answer you are looking for.
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Ex: Â My 9 yr old has not memorised what 8x4 is. Â She knows (can add in her head) that 8+8=16...so two groups of 8 is 16. Â If you double it (4 groups) you will get 32. Â They are all sorts of other way to work out 8x4 (including times it by 5 then subtracting 8, as it is 4 groups and not 5).
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Now I don't think there is necessarily wrong with memorising multiplication if that floats your boat (as long as kids have a strong number sense  I think that is way more important than memorising "facts"). Â Some argue it is faster to learn tables, but I am not so sure. Â My 9 yr old can come up with 8x4 pretty darn quickly.Â
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