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Can a student with almost no math truly catch up?

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..They could just pick up a Saxon book (or whatever) and start working on it with their student at an accelerated pace (weekends, longer hours during the week, 12 months a year., etc.)

 

Well, they could, but it's not the most efficient way to proceed.  A good tutor will plan/create lessons specifically for the student, which are designed to build on prior knowledge and push forward as much as possible in one go, making sure that the conceptual part is not left out.  (In fact, I try to make sure that the student understands the "why" at every step of the way.)  So a subtraction lesson might teach borrowing/regrouping, and then if the student gets it, progress rapidly through two, three, four, eight digits in the problem.  This is quite different than traditional texts, which usually increase complexity each year by giving problems with only one more digit than the previous year.  So a student who has to start with the first grade book won't encounter 9000 - 1999 for another two to three textbooks.  Older students can often make that jump pretty easily once they understand the basic idea of regrouping and the "why", and if the goal is "catching up", then better that they practice on the larger numbers if they are capable of it.  Similarly, making use of "multi-tasking" problems, where, say, you have to find the perimeter, but all the lengths involve fractions or decimals, can help the student move more quickly through the material, but lower-level texts made for the needs of a classroom situation don't always provide enough of this kind of challenge.

 

So my point is that yes, you can approach this by just working through a regular textbook and doing more of it than usual in a year, and if this is all you've got, then so be it.  But an experienced tutor can often custom-tailor the curriculum to the specific, ever-changing level of the student's understanding and ability, which can both be more efficient and produce greater understanding in the long run.  

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So my point is that yes, you can approach this by just working through a regular textbook and doing more of it than usual in a year, and if this is all you've got, then so be it.  But an experienced tutor can often custom-tailor the curriculum to the specific, ever-changing level of the student's understanding and ability, which can both be more efficient and produce greater understanding in the long run.  

 

:iagree:

 

When I did this, I was NOT an experienced tutor, but I did loop through four years of elementary (graded) math texts at once. I had used those texts, on the normal schedule, with three other students, so I knew how the concepts were rolled out and enlarged upon, which made it easy to combine and accelerate as suited my 15yo student. If I had it to do a second time, I'd use Lial's BCM, but for the first time through I was more comfortable using very familiar texts with built-in teacher's guides.

 

We would frequently start with the third grade math book, getting the most basic idea and some of the terminology down, and then follow the concept through practice problems (and teaching methods) from the later books. Then I'd circle back around to the third grade book for the next topic. Once we'd hit all the topics from all the elementary arithmetic books, we officially went on to pre-Algebra, for which we did stick to the script.

 

I used to wonder what a real math tutor would think, watching me figure that out as I went...but luckily, no one was watching.

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I see a fair few of these coming through my college. Unfortunately, they usually haven't realized how far behind they are until they actually get admitted (they have been admitted based on their parent-made transcripts).

 

Can they catch up? I'm sure it's possible. One did a few years ago. Do they? Usually not. Often they end up changing majors to something that requires less math, because right now even remedial math classes are not designed for adults who have never been exposed to the material, but rather people who learned it in school, but incompletely. As a result, they proceed (imo) at too rapid a pace to build the needed automaticity for someone who's never been exposed to the material in the first place. Accordingly, people with *extremely* weak backgrounds tend to take multiple attempts at the lowest level of remedial class, and even after passing that struggle with the next class because they just aren't automatic at it -- they need to stop and think about how to solve something like '2x = 6'.

 

This accelerated pace is becoming more and more standard as increased levels of math instruction become the norm for most college students -- there simply isn't the large number of people who never took anything beyond pre-algebra or algebra 1 in school that there used to be, so more and more colleges are eliminating the arithmetic and pre-algebra classes that they used to offer, and some have gone past that and eliminated beginning or even intermediate algebra, and just putting everyone into college algebra. This can actually work if the student had learned the material once and either learned it incompletely or just forgot. An adult in this situation (knowing no math) would be far better off to find a private tutor (if at all possible) or some self-study for adult books (a book such as BCM and Khan Academy drill would be reasonable) rather than hurling themselves at the wall of developmental classes required.

 

I will also point out that even if they do enter and the school still has those classes, and even if they take classes in the summer and pass everything on the first try, a student who places into arithmetic needs two full years to get to calculus, which means that if they're interested in a more quantitative field of study, they're pretty hosed. 

 

A high school student has a bit more time, but tutoring by someone who knows math would be ideal. It might work to be an intensely self-motivated young person who is able to self-teach -- again, I would recommend a book aimed at older students (for a bright student who reads well, BCM might work) over simply starting in 4th grade or so and proceeding through grade-level textbooks -- although something like the topical texts from math mammoth might work as well. 

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I think it's always possible.  I'd start with Saxon 5/4 and go from there.  The problem is, I think, that a lot of people are intimidated by math (often learned from their parents).

 

I thought I read that at the Sudbury Schools when the kids decide to do math, they can go quite quickly because they're older and more engaged. 

 

Sadly, students who have never done formal math are nowhere near ready for Saxon 5/4.  They usually need to start with the algorithms for addition and subtraction (including carrying and regrouping); they can usually do double-digit, small number problems in their head, but not anything more complex.  They often have a basic understanding of "one half", "one fourth", etc., but they may not know anything about fraction notation (that 3/4 is three one-fourths, that the four is how many equal parts you have and the three is how many you are selecting), and they will need to work with equivalent fractions, adding and subtracting fractions, etc.  The fraction work will likely not be very difficult, but it still has to be done. Then there is multiplication - you can start them early on with repeated addition but they're a long way from easily doing stuff like 47x23.  Again, not hard, but the up-front work needs to be done.  And of course there's division.  You can get some basic division ability by teaching division by repeated subtraction.  That gives you the ability to start doing other things, like reducing fractions, that include division, which reinforces the basic fact families.  But again, there is work to be done.  So it could be several months of targeted, daily work to get to something on the level of Saxon 5/4.  

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To understand unschooling requires a very different mindset about education. A key factor is motivation, and if this child wants to learn, then they will. They might not reach their goal within an externally set time, or their goal might change as they progress, but unschoolers can often achieve amazing things simply because of intrinsic motivation, something that is often disregarded in formal/traditional schooling (with damaging consequences).

 

Sometimes people *understand* unschooling's philosophy about education and people and the nature of human flourishing - they still just disagree with it.  I don't think intrinsic motivation flowers best when left alone; rather, most people do better when their intrinsic motivation is externally cultivated - along with self-discipline.  (I also don't think that internal motivation, unconnected to anything larger than our own desires, should be *the* guiding force in human lives.)  Without self-discipline, internal motivation is dependent on our being emotionally motivated - and no matter how much we want to learn something, we don't feel like learning it all the time.  A lot of my "changing goals" was a result of not having the self-discipline to persevere when the going got tough.  I *wanted* to learn them, but that wanting just wasn't enough without the necessary skills. 

 

And that's the point of a lot of the posts in this thread: external factors *do* matter.  External factors *do* affect "intrinsic" motivation.  A kid who wants to catch-up on math faces a lot of difficulties, and motivation alone - while necessary - isn't enough for most kids.  And often kids don't know what they don't know.  I quit a lot of things because I "just wasn't motivated enough".  In hindsight, what that really meant was that I hit more difficulties than I was able to handle on my own.  (And "not achieving their goal in a set time", when that set time is widely accepted, is a much bigger difficulty than many individualist hs'ers give credit for - we don't live in a vacuum.)  This thread lists a lot of potential difficulties inherent to catching up in math - expecting motivation alone to magically trump them is placing a very high burden on motivation, more than it can handle for most people.

Edited by forty-two
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Frankly, I think it's rather presumptuous to assume that anyone who disagrees just doesn't understand the concept. I was unschooled myself for everything but math. I understand the concept. I just disagree with the idea that self-teaching is usually better. Being self-motivated is ALWAYS better, true. But there are times when someone works and works to try to understand, and someone who understands the subject far better can pinpoint precisely WHAT they're missing. There are quite a few things I started learning as a kid, got to a difficult transition and just quit, deciding "well, I didn't really want to do that anyway", because I had no idea how to fix what I was doing wrong or how to persevere through difficulty. 

 

There's also a large difference between "I want to learn this because it is fascinating" and "I want to learn this even though I don't like it very much, because it is necessary for the career I want to pursue". 

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I do not think most typical kids who had no math education at all until they decide to learn as a teen will be able to catch up. I am sure there are some examples of it and it is possible but for most it is insurmountable to have no numeracy skills up to that point. It is not even rare to have a learning disorder. Most people placed in remedial math in college do not end up graduating. Some parts of math you can consolidate but there is not much out there for doing so and math is something that builds up and requires a lot of practice. Even being older does not mean it will happen really quickly. Saxon 5/4 is not easy to just start with and Saxon texts are huge with lots of problems and not much in the way of explanation for concepts. Just because there are examples of people who did it does not mean that most will be able to. To me it is educational neglect to have no exposure to numeracy in childhood and even well into teenhood because they did not want to. I have met very bright adults who had no math education who could not finish college because they were in very remedial math and had so many holes.

Edited by MistyMountain
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I speak as someone with a child who was autonomously educated until early teens, who then chose to study for exams and has a place at university. It's not unusual in the UK for home educators to follow an autonomous education methodology for the early years, and some continue throughout.

I come from a country who use the Cambridge exams as the college entrance exam for locals. Which means that I could have horrible grades for all my years of public school, do very well at the Cambridge A levels exams and get into the engineering faculty of the university that I wanted since admission was solely on exams scores. I did have to have great scores for math and physics for engineering school admission but the university admission couldn't care less about my 9th-12th grade GPA or ECAs or the fact that I failed my PE every year.

 

If my kids choose to apply to a US university instead of applying overseas, their 9th-12th grade transcript would be looked at. That is one reason my kids are looking at universities in Canada, Europe and Australia. There is the community college than transfer route of course. Just saying the direct admission route is different.

Edited by Arcadia

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While this is true, my experience is that you can only get to about 4th grade math with "real world" experience.  Once you get into more complex algorithms, work with multiplying and dividing fractions, and so on  - basically problems where it's not so easy to "see" how it works without targeted practice - then there's no substitute for putting in the work.  So while there is considerable value in hands-on, real-world stuff - working with LEGO and gears and cooking and money and such, as well as problem-solving through puzzles and games - you still need to actually learn and practice the various techniques and algorithms necessary to do higher-level math.  And even for a bright, motivated kid, it's hard to do a decent Algebra I, Geometry, Algebra II, Pre-Calc class in less than a year.

 

Yeah, I never understand when people claim that you can learn all the math you need from everyday life. Basic addition and subtraction and very simple fractions, sure. But long division? Exponents? Scientific notation? There's really no way for a kid to even be exposed to this stuff, never mind master it, from playing with legos or helping with the shopping. And yes, you can get through life without it, but you can't go to college or do any kind of STEM job.

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Yeah, I never understand when people claim that you can learn all the math you need from everyday life. Basic addition and subtraction and very simple fractions, sure. But long division?

 

 

Not going to go into all of this, but I think it depends on what kind of person you are and what kind of things you do. Like, in a thread on the chat board, somebody said that people on average buy 63 pieces of clothing per year. And then someone else said that the average woman spends $1800 on clothing per year, just for herself (not her family). So, me being me, I did a division. I went simplistic, and just did 1800/60, so just under $30, but, if I was unschooling a kid, we might have fun coming up with the exact answer. 

 

Likewise, when putting money in your bank account, you might end up in a discussion about compound interest, which would likely feature exponents. 

 

But anyhow... I think it really matters on the people involved and the kind of activities they do. I could easily see people not really doing long division and beyond, but on the other hand, if they're into woodworking and carpentry, I can see some unschooled geometry and trig rearing their heads.

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Not going to go into all of this, but I think it depends on what kind of person you are and what kind of things you do. Like, in a thread on the chat board, somebody said that people on average buy 63 pieces of clothing per year. And then someone else said that the average woman spends $1800 on clothing per year, just for herself (not her family). So, me being me, I did a division. I went simplistic, and just did 1800/60, so just under $30, but, if I was unschooling a kid, we might have fun coming up with the exact answer.

 

Likewise, when putting money in your bank account, you might end up in a discussion about compound interest, which would likely feature exponents.

 

But anyhow... I think it really matters on the people involved and the kind of activities they do. I could easily see people not really doing long division and beyond, but on the other hand, if they're into woodworking and carpentry, I can see some unschooled geometry and trig rearing their heads.

I just did a bunch of it for a building project this week. Hadn't seen SOH CAH TOA in forever... Edited by LMD
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Not going to go into all of this, but I think it depends on what kind of person you are and what kind of things you do. Like, in a thread on the chat board, somebody said that people on average buy 63 pieces of clothing per year. And then someone else said that the average woman spends $1800 on clothing per year, just for herself (not her family). So, me being me, I did a division. I went simplistic, and just did 1800/60, so just under $30, but, if I was unschooling a kid, we might have fun coming up with the exact answer. 

 

Likewise, when putting money in your bank account, you might end up in a discussion about compound interest, which would likely feature exponents. 

 

But anyhow... I think it really matters on the people involved and the kind of activities they do. I could easily see people not really doing long division and beyond, but on the other hand, if they're into woodworking and carpentry, I can see some unschooled geometry and trig rearing their heads.

 

Even if it comes up once in a while though, most people don't do enough of this sort of thing for a child to truly master these kinds of problems.

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Not going to go into all of this, but I think it depends on what kind of person you are and what kind of things you do. Like, in a thread on the chat board, somebody said that people on average buy 63 pieces of clothing per year. And then someone else said that the average woman spends $1800 on clothing per year, just for herself (not her family). So, me being me, I did a division. I went simplistic, and just did 1800/60, so just under $30, but, if I was unschooling a kid, we might have fun coming up with the exact answer. 

 

Likewise, when putting money in your bank account, you might end up in a discussion about compound interest, which would likely feature exponents. 

 

But anyhow... I think it really matters on the people involved and the kind of activities they do. I could easily see people not really doing long division and beyond, but on the other hand, if they're into woodworking and carpentry, I can see some unschooled geometry and trig rearing their heads.

Conceptually, perhaps.  But without knowing the basic math algorithms you are tied to a calculator once the numbers get bigger and involve decimals, and even then you need to have enough notation skills to be able to plug and chug through a basic formula, or set up a SOH CAH TOA relationship and solve it.  Kids who have never done formal math are severely limited by their inability to multiply or divide more complicated numbers.  Something fairly straightforward like the Pythagorean Theorem still requires the ability to solve a simple algebraic equation - not difficult, but if you haven't actually done any of it before, you won't have the underlying skills - a notation system, an order of operations system, strategies for how to tackle an equation that needs to be rearranged and manipulated to get the answer.  

 

I guess I just don't see the point.  If a kid is into carpentry, why not help them attain a good foundation in the math involved - not just a bit of mental math and conceptual stuff, but the actual skills that are transferable to other kinds of problems?  And, in a more general sense, if a kid is eventually going to make financial decisions, do basic repairs to their home, and so on - as most of us do - why not, at an age-appropriate level, help them acquire the skills they will need to do this work well?  

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I wasn't saying that I think it's best to do things this way, just that it *is* possible to encounter long division, etc in daily life, if you do a bunch of DIY stuff and run your own lemonade stands or other businesses (that you actually do bookkeeping for etc). 

 

Of course, it's also possible you'd have a kid who wants to learn 100 different foreign languages and who doesn't on their own find a need for long division etc. 

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Not going to go into all of this, but I think it depends on what kind of person you are and what kind of things you do. Like, in a thread on the chat board, somebody said that people on average buy 63 pieces of clothing per year. And then someone else said that the average woman spends $1800 on clothing per year, just for herself (not her family). So, me being me, I did a division. I went simplistic, and just did 1800/60, so just under $30, but, if I was unschooling a kid, we might have fun coming up with the exact answer.

 

Likewise, when putting money in your bank account, you might end up in a discussion about compound interest, which would likely feature exponents.

 

But anyhow... I think it really matters on the people involved and the kind of activities they do. I could easily see people not really doing long division and beyond, but on the other hand, if they're into woodworking and carpentry, I can see some unschooled geometry and trig rearing their heads.

Yes, it's not so much that you learn from doing things in real life, it's that real life throws up problems that you then learn skills to solve. Most of us live in an environment where we can source information. In our case, problem-solving might, for example, involve asking a neighbour with more expertise, researching at the library, buying a textbook, googling the problem or asking on online forums, or simply using "trial and error". Real life problems - building a shed from scrap materials, making a wind-powered generator, travelling to a foreign country, cooking for a vegan friend - provide the incentive/motivation to learn new skills. And yes, trigonometry, rearranging equations and basic algebra have all arisen out of practical real-life practical problems my kids have needed to solve, or simply out of them asking a question to satisfy their curiosity about a subject. (I remember one very clear example when my son (age 7 at the time) and I were talking about the universe. He asked a question that I couldn't answer and we couldn't find an answer to. We looked up the number of a local university, asked to be put through to the physics dept, and my son spoke to a professor there, who was very helpful in answering his question. The physics involved was way beyond anything I've learned!) Edited by stutterfish
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Not going to go into all of this, but I think it depends on what kind of person you are and what kind of things you do. Like, in a thread on the chat board, somebody said that people on average buy 63 pieces of clothing per year. And then someone else said that the average woman spends $1800 on clothing per year, just for herself (not her family). So, me being me, I did a division. I went simplistic, and just did 1800/60, so just under $30, but, if I was unschooling a kid, we might have fun coming up with the exact answer. 

 

Likewise, when putting money in your bank account, you might end up in a discussion about compound interest, which would likely feature exponents. 

 

But anyhow... I think it really matters on the people involved and the kind of activities they do. I could easily see people not really doing long division and beyond, but on the other hand, if they're into woodworking and carpentry, I can see some unschooled geometry and trig rearing their heads.

 

Right, some of those things could come up, but there's quite a large number of kids who don't want to have a discussion about compound interest. So the opportunity is there, but that doesn't mean it will be taken. 

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I guess the question boils down to: catch up to what? Nothing is impossible, but many paths would seem improbable.

 

 

While I don't doubt that the kid caught up, there is no such thing as getting a B on a part of the SAT.

Well my memory is probably faulty on how she worded her post, but I assume she was posting the info in a manner that everyone, including the international posters, could understand. Basically, that while he didn't get a top score, he still did okay. Or perhaps she said 80%, and I remembered it incorrectly.

 

Addressing the other person who doubted my story (I'm on my phone and can't remember who), I'm not making this up, and although I don't know Julie irl, it didn't sound as if she was making it up either. But I realize it doesn't track with the WTM forum mind set, so I shouldn't have mentioned it.

 

Sent from my iPhone using Tapatalk

Edited by Leonana

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Arithmetic is harder than most people admit. It takes so long to learn, using so many tricks, because topics often are presented too early.

 

The volume of topics in basic arithmetic are often about equal to the volume of topics in a basic algebra text. In older arithmetics and algebras, the topics in the arithmetic and algebras were sometimes presented in the exact same sequence and language, with the arithmetic presented as the more concrete version, and the algebra as the abstract version.

 

In my experience, with older average ability learners, both basic arithmetic and basic algebra take about 2 years each to cover. Neither 8 years of arithmetic, taught too early, nor basic algebra squeezed into a single year, seem efficient to me.

 

In the past, in the USA, arithmetic was often delayed and taught quickly to older students. And still is in many developing nations. Young people get a job and pursue education their parents could not afford to provide for them.

 

If the average student can REALLY learn ALL the topics in a basic algebra in 1-2 years, why can't that same student learn an equivalent volume of work that is mostly just a more concrete version of what is in the algebra in the same amount of time?

Edited by Hunter
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In the past, in the USA, arithmetic was often delayed and taught quickly to older students. And still is in many developing nations. Young people get a job and pursue education their parents could not afford to provide for them.

 

 

Can you elaborate on this? I'm not familiar with any time/place in the US when this was common, but we might be using different definitions of older students (and teaching quickly).

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Can you elaborate on this? I'm not familiar with any time/place in the US when this was common, but we might be using different definitions of older students (and teaching quickly).

i

 

The history of the USA is pretty darn short. I was referring mostly to periods of time and places with families with limited means and that needed their children to work. School hours were limited. Reading and catechisms were prioritized and taught earlier than arithmetic. People got around to arithmetic when and if they could.

 

Of course at that same time in USA coastal cities and other more developed countries, advanced work was pursued earlier, but we did have pockets of farm and factory kids that didn't get to arithmetic until the other subjects were tackled and sometimes not until they could pursue education with their own money or until apprenticed.

 

I love to read old textbooks and teacher manuals. I no longer am much interested in what modern writers say happened. I'd rather read the writings of the people themselves, as they often do not match at all what I have been told.

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Apologies that you read my reply as such. Perhaps it is me misunderstanding the concept, then? I understood that unschooling was the same as what we in the UK call autonomous education. Autonomous education is non-coercive and child-led. It does not preclude the use of textbooks or tutors, rather it is a path determined by the child (not anyone else), which may-or may not - involve conventional or non-conventional resources and tutors. Autonomous education is not neglect, it is not "not learning", it is simply a child following the educational path he or she chooses. Some autonomously educated children choose to learn something because it is necessary for the career they want to do, and some do not. Autonomous education does not preclude taking exams or going to college, although many choose alternative routes to having a fulfilling life. They key words are *choice* and *non-coercive*. If a child is made to learn something, then they are not autonmously educated. I speak as someone with a child who was autonomously educated until early teens, who then chose to study for exams and has a place at university. It's not unusual in the UK for home educators to follow an autonomous education methodology for the early years, and some continue throughout. In a country that thinks it's normal to put 4 year olds in classrooms, John Holt's books are popular :)

 

Sorry, I missed your replies -- I'm not on general board much.

 

Yep. This is exactly what I'm talking about when I say unschooling. 

 

You and I are in complete agreement about how unsuited to children's learning the push towards early, formal classroom education is. It's terrible, and it turns kids off learning before they can even get started. But I've seen some significant issues w/students for whom unschooling apparently meant "play world of warcraft all day every day" until they got to be 18-20, at which point they wanted to start university and had little background to do it. I think that a lot of parents interpret "they'll learn when they need to know" as "No matter how little they know at 18, they can start university and they'll do just fine in whatever they want to study because they're self-directed learners" which just isn't so. 

 

Here, in the UK, we also have grade restrictions for entry into education and the past few years have seen higher entry requirements into all levels of higher education. Hence the reason why my child chose to start studying for exams at age 13, despite little prior formal education. It's near impossible to enter a college (high school) course at age 16-19 to do A levels without certain grades at GCSE/IGCSE. If a student misses the 16-19 age window to enter college (high school) many courses at this level are then closed to them, due to funding. Even most courses offering a practical version of A levels (BTECs) require certain grades at English and Maths GCSE to progress. Yes, it would be possible to enter some (not all) universities simply with A levels and no prior accreditation, but it is very expensive to take A levels at home and, for some subjects, impossible to do so outside of recognised educational establishments.

 

We used to have the option of evening community classes to take exams, so that "late starters" could catch up - no longer available. We used to have the option of a heavily discounted 'open university' for people to study a degree at home - now it's very expensive. Options for those not following the conventional route or timing into higher education are becoming increasingly limited.

 

This is the reason why many home educated children here, including autonmously educated ones, choose the conventional route into education when they get to their teens. Obviously, there are also many home educated children who never enter formal education: they get a job, start up businesses, or choose a very different path. Personally, I think the less conventional route is a more difficult option than it used to be here.

 

I still believe it is possible to "catch up" maths, having done no prior formal maths. However, as I said, it might not be do-able within an external time scale, or the outcome/goal might change along the way, and, obviously, it requires a certain amount of hard work and dedication!

 

Your second post is exactly in line with my thinking. I am sad to see that the UK is also moving towards making it more challenging for students who have simply never been taught or never cared to learn and so forgot everything to "come back" from it. 

 

It is also becoming far more challenging here to become anything other than an entrepreneur without formal educational credentials, because so many employers are using a bachelor's degree as a proxy for a certain degree of literacy, numeracy, and critical thinking, and so there are many jobs which really don't require more than a high school diploma and some ability to learn that are closed without either an "in" or a bachelor's degree. 

 

This is not directed at you, but it is really, really unfortunate when advice is given based on what could be done 30+ years ago (when there were still a lot of remedial options available in community colleges, or night high school that granted a full diploma, and there were a lot more entry-level jobs open without a degree) when these options are increasingly scarce. 

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This is not directed at you, but it is really, really unfortunate when advice is given based on what could be done 30+ years ago (when there were still a lot of remedial options available in community colleges, or night high school that granted a full diploma, and there were a lot more entry-level jobs open without a degree) when these options are increasingly scarce. 

 

Our state's graduation rate is so low, all these options are still readily available.

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Our state's graduation rate is so low, all these options are still readily available.

 

That is a good point -- I should have added "in some areas". 

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The history of the USA is pretty darn short. I was referring mostly to periods of time and places with families with limited means and that needed their children to work. School hours were limited. Reading and catechisms were prioritized and taught earlier than arithmetic. People got around to arithmetic when and if they could.

 

Of course at that same time in USA coastal cities and other more developed countries, advanced work was pursued earlier, but we did have pockets of farm and factory kids that didn't get to arithmetic until the other subjects were tackled and sometimes not until they could pursue education with their own money or until apprenticed.

 

I love to read old textbooks and teacher manuals. I no longer am much interested in what modern writers say happened. I'd rather read the writings of the people themselves, as they often do not match at all what I have been told.

 

I've never forgotten the Mathematics of Child Street Vendors article I read back in anthropology class; it is my personal reference when I think about the amazing mathematical human brain and formal schooling. For many students, it is not so much "catching up" with basic arithmetic as it is learning the formal language of mathematics, right? A lot of the long, drawn-out elementary math curriculum is steeping children in this language; however, in terms of arithmetic  skills, they may not be ahead of children without formal math training. (Not to mention intuitive geometric knowledge.)

 

(And some little part of my brain is telling me that you have already said all this much better on another thread, Hunter...the importance of being able to communicate mathematical ideas and translate the firing of one's neurons into the language of math.)

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Lots of people have added this caveat of "unless there's a learning disorder." I find myself wondering how a learning disorder would be discovered before it was too late in a circumstance like this. I have a 2e child who reads well. If not for the formal schoolwork we've done, I don't think I would know at all about her difficulties. They just don't appear in the course of life outside school. Yet they have had a major impact on her progress in learning math. She's a gifted kid, born to two parents identified as gifted in their own school years, one of whom is an engineer, so it would seem we would have had every reason to expect she could learn whatever she wanted to fairly quickly, whenever she decided.

 

I wonder this as I know someone in my own life who has chosen not to teach any formal math to her kids, with the reasoning that they will learn it quickly if/when they decide they want to, with the rationale that since she and her husband are very smart, the kids obviously won't have any issues. It didn't play out this way for us, even given the fact that my child has a very high IQ.

Exactly this! I had no reason to expect two children with learning disabilities given my history and my husband's. Maybe it's my anxiety or just a bad experience, but going forward I hope for the best and plan for the worst just so I'm prepared. I'd hate to be blindsided by a learning disability with so little time to remediate it. I'm ticked enough that I didn't figure out I had one dyslexic and one dysgraphic until they were each in third grade!

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I knew an unschooled kid who got through grade 1-6 math in a couple of months before successfully doing 7th grade at school.

Also, people who start things later do tend to progress faster. For example, while we've all heard of amazing musical prodigies, most kids who start learning violin at age 2 or 3 practice less than 15 minutes a day and take simply forever to get through their first book, whereas keen adults can start one year and be playing Vivaldi Am concerto the next year, because they have a more mature understanding and better concentration, and practice a couple of hours a day. 

I think that math, even in the higher grades, contains a lot of repetition, and could be gotten through in much less time than schools typically spend. If the kid has no relevant learning disabilities, has access to suitable materials, is highly motivated and is able to spend several hours per day, I'd be willing to bet that her goal is quite achievable.

Edited by IsabelC
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This is purely anecdotal, but among all my homeschool IRL aquataintances (about 100) about 15 have been unschoolers...

 

Of all those unschoolers ALL were from generations of Americans on both sides-

 

It makes me think the unschooling mindset can only be developed in people who do not fear and are not at all concerned about poverty or job competition.

 

Just my silly observation

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Another thought- seeing the hour and hours of study necessary to truly master Algebra 2 and Geometry, I can't imagine doing it much faster.

 

And I question the long term retention for kids who are working to catch up and have to move so fast in order to do so.

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And I question the long term retention for kids who are working to catch up and have to move so fast in order to do so.

 

Good point, but then I would suspect that long term retention may be questionable for *everyone* who isn't required to use that learning regularly as part of their work or further education.  I mean seriously, how many of us who haven't yet home educated "all the way through" would be able to sit down tomorrow and pass the exams we did in our final year of school? I know I'd struggle with some of them!

Edited by IsabelC
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Didn't read comments. To the op, the answer is yes, of course. Why would you think she couldn't?

There are adult refugees that had zero schooling and "caught up", plus graduated college, including math, in only a few years.

Edited by Tohru

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Didn't read comments. To the op, the answer is yes, of course. Why would you think she couldn't?

There are adult refugees that had zero schooling and "caught up", plus graduated college, including math, in only a few years.

With what kind of degree? Can someone really become an engineer having zero math And then catching up in a few years? Ans did these refugees have basic math and then just were missing high school math?

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Another thought- seeing the hour and hours of study necessary to truly master Algebra 2 and Geometry, I can't imagine doing it much faster.

And I question the long term retention for kids who are working to catch up and have to move so fast in order to do so.

 

That depends on why they are catching up. Are they not taught or have a school teacher who couldn't teach, those people tend to catch up fast with one to one tutoring. If their motivation for catching up is because it is a prerequisite for what they want to do, then long term retention is likely to be okay compare to a high school kid who is just checking the 4 years of math box.

 

 

With what kind of degree? Can someone really become an engineer having zero math And then catching up in a few years?

No idea about recent refugees but my husband has an ex-colleague who is a Vietnam war refugee and didn't know any English when he came over just before middle school age. He went on to an associate degree in engineering after graduating public high school in San Jose. He is in his 50s.

 

Considering that quite a few people on the high school board mentioned that precalculus and no physics is required to enter engineering, someone who is just unschooled and not a refugee or ESL could reach precalculus starting formal math at 14.

 

E.g.

Keys to algebra full set - do over summer, might not need a tutor. Starts from basics

Prealgebra- fall term

Algebra 1 - spring term

Geometry- summer term

Precalculus- fall term

 

Some high schools here go on block schedule so that's what I based on.

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Didn't read comments. To the op, the answer is yes, of course. Why would you think she couldn't?

There are adult refugees that had zero schooling and "caught up", plus graduated college, including math, in only a few years.

 

I guess based on what she has said about her math knowledge (addition and subtraction and nothing else) as well as the amount of time I see my child putting into math. He spends a fair amount of time (his choice) working on math at a slightly accelerated pace.  It just seems that with only three years remaining before college admission, a child with virtually no math would have to work at a very accelerated pace to reach an advanced level of math and thus have to commit an enormous amount of time to the endeavor.  

 

I also tend to think of math as a language to be immersed in. Sure, you can become fluent in a language without immersion, but with a lot less facility than if you are using it all the time.

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I wonder if the speed at which some people can catch up on math threatens some people? It doesn't invalidate the usual practice of doing math for 12 years to admit that there can be a faster streamlined approach for older students who are motivated and/or ready for math instruction. It's already been pointed out that purposefully waiting can lead to LDs being missed. And waiting for someone who is ready early can be demoralizing and boring. But conversely, some late bloomers like me bash their heads against the math wall for years and might even give up. I'm thankful that I didn't give up because all these math skills got easier for me in my late teens and up.

 

 

Sent from my iPhone using Tapatalk

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I just came across this article today.  I really think this is a dangerous article while I think this can work for some families the bolded bite sized quotes  set false expectations of how easy it is to learn maths. â€œDid you know that all of K-12 math can be learned in 8 weeks? † https://projectinspireplanner.com/blogs/project-inspire-1/how-to-inspire-a-love-of-math.

Edited by rebcoola

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I wonder if the speed at which some people can catch up on math threatens some people? It doesn't invalidate the usual practice of doing math for 12 years to admit that there can be a faster streamlined approach for older students who are motivated and/or ready for math instruction. It's already been pointed out that purposefully waiting can lead to LDs being missed. And waiting for someone who is ready early can be demoralizing and boring. But conversely, some late bloomers like me bash their heads against the math wall for years and might even give up. I'm thankful that I didn't give up because all these math skills got easier for me in my late teens and up.

 

 

Sent from my iPhone using Tapatalk

 

I think anyone should try if they are motivated, and never give up on a dream or idea that they are into.

 

BUT you being a "late bloomer" doesn't equate to your parents purposefully deciding to make things hard for you by waiting till your teens to even learn multiplication tables, fractions etc. etc.  THat sucks!  I feel angry when I think about it.

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I think anyone should try if they are motivated, and never give up on a dream or idea that they are into.

 

BUT you being a "late bloomer" doesn't equate to your parents purposefully deciding to make things hard for you by waiting till your teens to even learn multiplication tables, fractions etc. etc.  THat sucks!  I feel angry when I think about it.

 

I agree.  But it also meant that I did not push my own late bloomers when they started to struggle.  We still did math - but at their pace even if it meant cementing skills for longer or just exploring some more math rabbit trails at a lower level.  One of my late bloomers is doing just fine in his STEM classes in college and is going to be going into a STEM field.  The other one rabbited ahead last year and is now at grade level but without being pushed and is also planning on going into a STEM field when the time comes.  But I was able to do that because I homeschool.  In a B & M school, the late bloomers get labeled and the early bloomers (often) get to spin their wheels while those who are "on target" have everything at their pace.  I do understand however, that this is not at all what the OP described happening in this family who just did not do math for years. 

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I think anyone should try if they are motivated, and never give up on a dream or idea that they are into.

 

BUT you being a "late bloomer" doesn't equate to your parents purposefully deciding to make things hard for you by waiting till your teens to even learn multiplication tables, fractions etc. etc. THat sucks! I feel angry when I think about it.

Unschooled children can still choose to learn their times tables and fractions. Being unschooled doesn't preclude learning these things - or learning anything - at any time. Parents with unschooled children don't stop their children from learning: on the contrary, many are extremely involved in and proactive about their children's education. I don't think anyone here should be making judgements or assumptions about other folks' parenting or educational methods. Edited by stutterfish

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I wonder if the speed at which some people can catch up on math threatens some people?

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That is not the case here. In fact, we did precious little math that looked like typical school math until age 9 or so and I myself heard a lot of concern from relatives that DS was "behind." There were no rote worksheets here, but there was an engaging math circle, lots of fun logic games, reading, building, exploring, etc.

 

My worry was that a child not exposed to a math rich environment would have a difficult time achieving her goals. I also find it a little sad that she has missed out on a lot of fun stuff, much in the same way I would be sad if a child weren't introduced to music or art or poetry, but that is a different point (or perhaps not...).

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That is not the case here. In fact, we did precious little math that looked like typical school math until age 9 or so and I myself heard a lot of concern from relatives that DS was "behind." There were no rote worksheets here, but there was an engaging math circle, lots of fun logic games, reading, building, exploring, etc.

 

My worry was that a child not exposed to a math rich environment would have a difficult time achieving her goals. I also find it a little sad that she has missed out on a lot of fun stuff, much in the same way I would be sad if a child weren't introduced to music or art or poetry, but that is a different point (or perhaps not...).

 

I agree 100%

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I just came across this article today.  I really think this is a dangerous article while I think this can work for some families the bolded bite sized quotes  set false expectations of how easy it is to learn maths. â€œDid you know that all of K-12 math can be learned in 8 weeks? † https://projectinspireplanner.com/blogs/project-inspire-1/how-to-inspire-a-love-of-math.

 

So the one kid who learned it all super fast apparently spent 7 hours + per day, 7 days a week. That doesn't sound like the optimum way to do it!

 

 

Also, here is the other linked article, explaining how the 8 weeks figure was arrived at. He makes a ton of assumptions, eg kids only listen to their teacher 2/3 of the time, half the teaching provided isn't relevant to a given student, students do no homework...

http://www.besthomeschooling.org/articles/math_david_albert.html

Edited by IsabelC
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I just came across this article today. I really think this is a dangerous article while I think this can work for some families the bolded bite sized quotes set false expectations of how easy it is to learn maths.“Did you know that all of K-12 math can be learned in 8 weeks? †https://projectinspireplanner.com/blogs/project-inspire-1/how-to-inspire-a-love-of-math.

Quoted from the article you link, not everyone has natural learners like her daughter and son though. Her whole post sound like a brag/advertisement.

 

"My daughter hasn’t had a formal math lesson given by me since she was 9. Is she math illiterate at 15? Absolutely not! At 11 she was taking Danika McKellar Algebra books to her room for before bed reading. She has claimed the entire set of four books as her own and they now live in her room. She has read so many books about math and numbers, watched and copied Vi Hart videos, and she notices math concepts and ideas everywhere! Math is natural for her."

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Quoted from the article you link, not everyone has natural learners like her daughter and son though. Her whole post sound like a brag/advertisement.

 

"My daughter hasn’t had a formal math lesson given by me since she was 9. Is she math illiterate at 15? Absolutely not! At 11 she was taking Danika McKellar Algebra books to her room for before bed reading. She has claimed the entire set of four books as her own and they now live in her room. She has read so many books about math and numbers, watched and copied Vi Hart videos, and she notices math concepts and ideas everywhere! Math is natural for her."

Well yes, that's the thing about unschooling: if a student is keen to learn about something, they will learn a lot. But many kids don't have any particular interest in math and will not choose to learn it unless/until they need it. Hence the teens having to power through nearly everything in a few weeks. My 13yo doesn't like math much, but he has agreed to keep studying it since I explained that many of the sorts of jobs he may be interested in later (jobs that don't need brilliant people skills) will require some level of math achievement/ability. He likes the idea of staying 'on grade' so that he isn't limiting the possibilities, or having to catch up with an excessive amount of math in a short space of time.

Edited by IsabelC

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So the one kid who learned it all super fast apparently spent 7 hours + per day, 7 days a week. That doesn't sound like the optimum way to do it!

 

 

Also, here is the other linked article, explaining how the 8 weeks figure was arrived at. He makes a ton of assumptions, eg kids only listen to their teacher 2/3 of the time, half the teaching provided isn't relevant to a given student, students do no homework...

http://www.besthomeschooling.org/articles/math_david_albert.html

 

Cramming like this will never develop the number sense and mathematical intuition that a continuous study of math over many years can. This student would not have time to THINK through hard problems - he might be able to get trained to crank out formulaic problems, but he will not become proficient in mathematical problem solving, because he won't have any time to spend time working on hard problems. Heck, I have sat for two hours over one single geometry problem; my DS's works on one complex problem for half the week.

The claim is absolutely ludicrous.

I don't doubt that the student managed to get into college calculus - but whether he understands math and can apply it outside a scripted course environment is highly doubtful.

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Cramming like this will never develop the number sense and mathematical intuition that a continuous study of math over many years can. This student would not have time to THINK through hard problems - he might be able to get trained to crank out formulaic problems, but he will not become proficient in mathematical problem solving, because he won't have any time to spend time working on hard problems. Heck, I have sat for two hours over one single geometry problem; my DS's works on one complex problem for half the week.

The claim is absolutely ludicrous.

I don't doubt that the student managed to get into college calculus - but whether he understands math and can apply it outside a scripted course environment is highly doubtful.

It is possible if he has a brain with particular strength in mathematical understanding and problem solving.

 

I agree with you for a student with average mathematical ability.

 

I'm actually thinking of myself here--I had limited formal math for a variety of reasons (too many language changes being one of them) and arrived at high school math with some gaps that did limit my ability to keep up in class--but did not particularly limit my problem solving ability. I achieved perfect or near perfect scores on tests like the SAT (I was good at figuring out ways to solve a problem even if I hadn't done similar problems before) and one of the highest scores in the school on the AHSME (predecessor to the AMC12)--high enough to qualify for the next exam level--in spite of basically failing math class. With zero prep or any idea of what the exam would be like.

 

Which makes me think that extensive math background isn't always an pre-requisite for conceptual problem solving ability.

 

Obviously ability was no help in cases where I hadn't had the exposure to know what the problem was asking for or what principles might apply...

 

I know you are talking about much harder problems but it was definitely problem solving not rote learning that was my strength in math.

Edited by maize
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