Can a student with almost no math truly catch up?

[bibiche]

Not my onions, but I do wonder, so...  A 14 year old self-described "radical unschooler" happened to mention to me that she is thinking of learning some math, because maybe she will one day need more than just basic addition and subtraction.  I confess I was astounded that a 14 year old had not done more than very basic maths. I understand the philosophy behind radical unschooling and the belief that kids will learn when they want to, but is it realistically possible for a kid with almost no math to catch up? I mean, that's a lot of math! She wants to go to college.

 

I like the idea of child-led learning, but crikey! this seems like educational neglect.

[regentrude]

Oh, I think it is possible, if the student is dedicated, and if her not doing any math did not mask a math LD.

It will be hard, and it will likely take longer than four years to become proficient at college prep level math, because long term exposure creates a level of mastery that quick cramming does not accomplish.

But if people manage to learn to play instruments or speak foreign languages as adults, there is no reason a person could not also learn math.

 

I have just never seen this actually happen.

Edited March 27, 2017 by regentrude

[SparklyUnicorn]

I do believe it is possible, but I think the student needs to be highly motivated and willing to put in the work.

 

The fact you brought onions into this discussion is a trigger for me, but ya know, I'm trying to look past and endure.  :lol:

[frugalmamatx]

Following.... I know a kid like this too. 

 

I think if they are motivated they probably could. Maybe using the Saxon Math 1st edition books - they were written to remediate adult learners so would give a nice progression for math skills. 

[Lang Syne Boardie]

1. I agree with you that it sounds like educational neglect.

 

2. In the absence of learning disabilities, yes, she can catch up. I tutored a 15yo homeschooled girl who needed to be taught, on day one, what the word "subtraction" means. We got her through arithmetic and ready for Algebra in just under two calendar years.

 

Edited to add: She was highly motivated, and IMO probably gifted. She was very literate and responsible. I do not think her results were typical. I think average to below average students would never grasp it all so quickly, and would be at tremendous risk of giving up out of frustration and shame.

 

Also, she was able to do this because she had DAILY, one-on one tutoring for two years. That is beyond the reach of most people due to the expense; good luck finding a homeschool mom to do it as a labor of love! It's not like you can enroll a 15yo in an elementary school. You cannot, for several good reasons.

 

I added the above for the benefit of anyone reading who may be neglecting their child's education, assuming he or she will somehow catch up in a year or two, at the last minute...do NOT count on that. That is not how most children learn, and the pressures of looming adulthood can make it VERY hard to concentrate on "introduction to fractions!"

Edited March 27, 2017 by Tibbie Dunbar

[freesia]

I think so, but it would depend on how hard they work and how far in math they want to go. I would say a 14 year old could cover arithmetic in a year. If that is ninth grade then tenth would be algebra, 11th geometry and 12th algebra 2.

[Monica_in_Switzerland]

Yes.  Of course they can catch up.  Many high schoolers graduate with only geometry.  They can take Math A, Math B, alg, geo.  So the 14 year old has 3-4 years to get up to geometry.  I bright high schooler should be able to learn all of arithmetic in less than 6 months.  And if you remove vacations, sick days, teacher service days... I would assume any high school math text could be done in 6 months a piece.  

 

Having said that, having a competent teacher or coach would make a world of difference in keeping the student on track so that minor confusions do not turn into abandoning the goal.  

 

NB:  I do not think this is a "good" way to go about math education.  I just think it's doable.  

[luuknam]

2. In the absence of learning disabilities, yes, she can catch up. I tutored a 15yo homeschooled girl who needed to be taught, on day one, what the word "subtraction" means. We got her through arithmetic and ready for Algebra in just under two calendar years.

 

 

Any idea how many hours/day she worked on this?

[Lang Syne Boardie]

Any idea how many hours/day she worked on this?

 

Two hours per day, five days per week - one hour with me (using online whiteboards and Skype), and about an hour on her own, working additional exercises as homework.

[EKS]

I think that a motivated teen could probably learn enough math to get an average score on college entrance exams.  But I think it would be difficult for her to develop the automaticity needed to go very far with math though, so a math heavy major or occupation may be a stretch.

 

But I'd like to think I'm wrong!

[LucyStoner]

I've seen more adolescents who didn't catch up than kids who did catch up and go on to fluency with math beyond arithmetic.

As for how much I have seen this, I went to hippie high school which was a democratic school with a decidedly Summerhill ideological bent, and many of my classmates grew up unschooling or attending other free schools. My brother went there for four years after I graduated. The kids who did best at and after high schools all came into the school at ages 14-15 reading fluently and capable of taking algebra. So my anecdote is drawn from knowing more than just a few kids in this situation. I have many very successful high school classmates, but they came to the school with a basic level of math and reading.

Edited March 30, 2017 by LucyStoner

[OneStepAtATime]

1.  If there are no LDs and

2. If the student is highly motivated and

3.  If the student gets targeted one on one tutoring from someone who is really good at remedial teaching to a motivated teen with little background in math and

4. The tutoring was daily, at least 2 hours a day, for an extended period of time then

 

yes it is possible...(but I don't think I would want to learn math that way)...

[marbel]

Agreeing with others that it's doable though not necessarily easy.

 

Also, "wanting to go to college" doesn't necessarily mean going very far in math, depending on the major.  Obviously beyond arithmetic, of course. 

 

Barbara Oakley wrote a book called A Mind for Numbers and taught a Coursera course approximately titled "Learning how to Learn."  She says (in the linked article):

 

I was a wayward kid who grew up on the literary side of life, treating math and science as if they were pustules from the plague. So it’s a little strange how I’ve ended up now—someone who dances daily with triple integrals, Fourier transforms, and that crown jewel of mathematics, Euler’s equation. It’s hard to believe I’ve flipped from a virtually congenital math-phobe to a professor of engineering.

One day, one of my students asked me how I did it—how I changed my brain. I wanted to answer Hell—with lots of difficulty! After all, I’d flunked my way through elementary, middle, and high school math and science. In fact, I didn’t start studying remedial math until I left the Army at age 26. If there were a textbook example of the potential for adult neural plasticity, I’d be Exhibit A.

[bibiche]

Yes.  Of course they can catch up.  Many high schoolers graduate with only geometry.  They can take Math A, Math B, alg, geo.  So the 14 year old has 3-4 years to get up to geometry.  I bright high schooler should be able to learn all of arithmetic in less than 6 months.  And if you remove vacations, sick days, teacher service days... I would assume any high school math text could be done in 6 months a piece.  

 

I agree that getting up to speed on arithmetic would be easy. But my child is a few years younger, and I don't think he would have been able to get through Algebra and Geometry in 6 months each even if he had been older. It took 32 weeks just to get through Algebra, and that was at a clip (and with a strong math background).  I assumed that catching up meant getting beyond geometry as well. Don't most college-bound kids get to at least precalculus?

 

Well, glad to know it can potentially be done anyway.  I hope she is able to succeed. It's funny - we consider ourselves a bit unschooly in that we let DS follow his interests, but I guess really we aren't because there is no way I would let him not do any academic work. Another romantic idea gone.

[JudoMom]

I do think it's doable.  Not easy, but doable.  Also, wanting to go to college doesn't mean she wants to go to a 4 year for a math heavy degree.  She could always start at Community College and take remedial classes.  

I don't know that I'd consider it educational neglect.  It's not how I choose to educate my children, but I'd be more concerned if she couldn't read or wasn't aware of the fact she'll need more math to achieve her goal of reaching college.

[Arcadia]

. But my child is a few years younger, and I don't think he would have been able to get through Algebra and Geometry in 6 months each even if he had been older.

About 4 hours a day, 7 days a week for 6 months would give a child who wants to do it 180 days x 4 hrs/day = 720hrs. That is more than enough to finish typical public school algebra 1 and geometry. I had tutored kids who were willing to put in the hours to catch up due to not understanding their school teachers. Took two months of intensive for a year's worth of public school math, I was tutoring them 2 to 3 times a week.

 

ETA:

These kids are the younger relatives of friends so I was doing it more like volunteer work. It is exhausting and I won't do it for pay.

Edited April 1, 2017 by Arcadia

[LucyStoner]

I would also say that I don't consider the fact that it is possible to catch up later a valid defense for not exposing a child to the richness of math and science

 

I've known very math savvy unschoolers so learning math can happen many ways. Unschooling doesn't need to mean math doesn't happen before 15.

[Farrar]

Sure. Doable. More doable if the family has been doing everyday math type things with them in a purposeful way - playing board games, making the kids manage money and budge things occasionally, etc. Much more doable if there's no learning issues present. Even more doable if they get some help - either from the parents or a tutor.

 

But that kid is obviously at a massive disadvantage. And they might not have the skills or willpower to do it without help. And they might not be able to do it if they have undiagnosed learning issues.

 

I'm on the fence about educational neglect. I hope the parents are supportive of her desire to learn - willing to invest time and resources to help her achieve that goal. IME, some unschoolers are just waiting for that moment - even "radical" unschoolers. But others seem determined to keep backing off and not providing that help - if the child "really" wants to learn, they must do it alone. And that, IMO, is absolutely educational neglect.

[fralala]

Oh, I think it is possible, if the student is dedicated, and if her not doing any math did not mask a math LD.

It will be hard, and it will likely take longer than four years to become proficient at college prep level math, because long term exposure creates a level of mastery that quick cramming does not accomplish.

But if people manage to learn to play instruments or speak foreign languages as adults, there is no reason a person could not also learn math.

 

I have just never seen this actually happen.

 

Agree with this, and wanted to add the anecdote of my mother, who, in her sixties, decided her math education had been very poor and has been studying math ever since. Just for pleasure.

 

I would also add the opposite, which is that a remarkable number of homeschoolers I talk to seem to (and public schoolers-- I live in a competitive, Kumon-lovin' part of the country) have children who are accelerated by two years or more in math. This suggests, to me, that math learning-- especially elementary math-- can be compressed into a shorter time frame than usually allotted it in schools. There is a LOT of repetition of concepts built into most math curricula (to account for summer slump)-- I don't mean the practice that makes operations automatic, but conceptual repetition that is unnecessary if you're not taking big breaks from math.

 

Now, my view is that getting into the Math Habit is as much a part of becoming math-y as anything else, so even though you could catch up at a later age, you might not necessarily catch up on the Math Habit (unless your family was unusually good at incorporating mathematical thinking and computing into daily life). If I don't do something regularly, I might be under the impression that I'm not "good" at it or that it's not my strength, when it reality, I just haven't flexed that muscle enough. I'm not an unschooler and think kids have to be forced into strengthening some muscles so that they can one day enjoy using them. But I also don't think that catching up in impossible, for the motivated and confident kid (or retiree) who doesn't mistake a flabby muscle for being "bad" at something, or it being a weakness.

[letsplaymath]

A 14 year old self-described "radical unschooler" happened to mention to me that she is thinking of learning some math, because maybe she will one day need more than just basic addition and subtraction...

 

First, I would not take a casual comment as truly representative of her knowledge. She may not have done much schooly math, but life itself forces humans to develop many informal math skills. 

 

Second, if she really is interested in learning, then she needs a curriculum that builds on those informal skills. I would suggest Herb Gross's Adjective Noun Math.

[justasque]

I do this kind of tutoring.  It helps a lot if:

1) The student has had some kinds of mathematical experiences - board games, building with LEGO, handling money.

2) The student has access to a one-on-one tutor who is willing and able to create a custom curriculum for the student designed to get them up to speed.

3) The student is fairly bright without LDs.

4) The student is interested in learning the material and putting in the work to do so.

5) The student is willing to work at least an hour a day on homework, and to be tutored for 90+ minutes at least twice a week.

6) The student has a supportive family situation - time and space to do the work, transportation to tutoring, family who takes the endeavor seriously.

7) The parent understands that the student's peers have been working for 200-300 hours a year for many years, and while some things will take less time for an older student to master, "catching up" with peers will not happen overnight.  

 

The difficult part is usually finding (and paying) the tutor.  You need someone experienced with this kind of work, who is willing to gently push the child to achieve up to their potential, and yet not be judgmental about the situation.  You need someone with the know-how and resources to pull together a custom curriculum.  You need someone local enough that the student can go to tutoring regularly.  And you need to be able to compensate the tutor - and this is usually the sticking point.  It takes at least two hours of prep time per hour of class to work out what the student will be capable of during the next class, and how far/deep you are likely to be able to go, to find materials that specifically target the concepts being taught, at the correct level, and move at the ideal pace, and to prep Plans B & C & D in case the student goes faster or slower than expected.  You need to be experienced enough to be able to present the same material multiple ways, to be sure you can find the way that best fits the student - this is not the "open the book, read the lesson" kind of teaching.  And you need to be able to create those "aha" moments that build a complex understanding of the subject, as the foundation must be very, very firm to support the rapid pace that will be needed if "catching up" is the goal.   Point being, this kind of tutoring can be very expensive - as it should be.  (Or, you can find someone like me, who is sometimes willing to barter for tutoring nice, motivated kids.  But that's very rare, because it takes a LOT of time.)

 

Schools are usually not equipped to provide this level of support, both financially (one on one) and academically (custom curriculum), thus students who enter school this far behind are usually put into lower-track classes in which expectations are very low but because the topic is still more advanced than appropriate, the student still does not have the foundation for success.  And, in turn, without the math, otherwise-bright students cannot do higher-level science, and thus will be put into lower track classes for that too.  

And yet, when a bright student gets the appropriate support and teaching, they can do honors-level work, albeit a few years behind their peers.

 

I am not a fan of parents knowingly putting their child in this position; however it is sometimes unavoidable as other, more important issues (health, life) must be made a priority.  I am concerned when homeschoolers tell each other "kids can catch up if and when they want/need to" without adding that this catching up will take significant time and effort, and potentially be very expensive if a tutor must be hired.  For most younger kids, a gentle, fun math worksheet or activity every other day after breakfast can create a solid foundation for later, more formal work.  This isn't always possible - sometimes other things must come first - but when it is, the effort can pay off in the long run.

[J-rap]

I believe absolutely that one can catch up.  I've read enough war-time biographies about people whose childhood education was pretty much completely stalled, for years, and yet they ended up going on to become doctors, scientists, and such.  Of course it depends on the person and their motivation, if any learn disorders exist, etc. 

[Jean in Newcastle]

I took a woman in her 40's who didn't even know simple arithmetic up to algebra in six months.  She came from a country where, in her words, she passed math by bribing the school officials.  She was very strongly motivated to learn the math because her job was instituting a basic math test and her job depended on it.  Granted, we did not go beyond that level but I assume that while she might have slowed down her pace with higher math concepts and skills, she could have still learned it. 

[SparklyUnicorn]

I essentially did this.  I mean yes sure I've been going over the basics with my kids for years.  BUT, when I was motivated to learn what I needed to get to where I am now, I had to knuckle down.  I basically studied 2 pre reqs in about 4 months.  I put in a lot of hours. 

 

 

[Renai]

I assumed that catching up meant getting beyond geometry as well. Don't most college-bound kids get to at least precalculus?

 

Well, glad to know it can potentially be done anyway.  I hope she is able to succeed. It's funny - we consider ourselves a bit unschooly in that we let DS follow his interests, but I guess really we aren't because there is no way I would let him not do any academic work. Another romantic idea gone.

 

Not where we live. But, our state isn't within the top 40 for education either, so there's that.

 

Nah, I think you should keep your romantic idea AND your academics. It balances. :D

[stutterfish]

nm 

 

Edited June 10, 2017 by stutterfish

[MotherGoose]

Sure it's possible. But my fear is that the child gets really mad at mama for not preparing her for college in a timely manner. What if kiddo wants to go to college etc and graduate high school but just never actually realized the amount of math necessary to do this until she was 14 or 15 when she was going to have to spend quite a lot of time doing other academic coursework?

[Ellie]

Not my onions, but I do wonder, so...  A 14 year old self-described "radical unschooler" happened to mention to me that she is thinking of learning some math, because maybe she will one day need more than just basic addition and subtraction.  I confess I was astounded that a 14 year old had not done more than very basic maths. I understand the philosophy behind radical unschooling and the belief that kids will learn when they want to, but is it realistically possible for a kid with almost no math to catch up? I mean, that's a lot of math! She wants to go to college.

 

I like the idea of child-led learning, but crikey! this seems like educational neglect.

 

Yes, of course it's possible.

 

Depending on where she lives, she can take a basic math class at her local community college. Or she can self-study, knowing what her end goals are.

 

I don't feel the need to modify the term "unschooling" by calling her parents "radical unschoolers," and I would be very hesitant to accuse them of educational neglect.

[LMD]

Agreeing with others that it's doable though not necessarily easy.

 

Also, "wanting to go to college" doesn't necessarily mean going very far in math, depending on the major. Obviously beyond arithmetic, of course.

 

Barbara Oakley wrote a book called A Mind for Numbers and taught a Coursera course approximately titled "Learning how to Learn." She says (in the linked article):

I was a wayward kid who grew up on the literary side of life, treating math and science as if they were pustules from the plague. So it’s a little strange how I’ve ended up now—someone who dances daily with triple integrals, Fourier transforms, and that crown jewel of mathematics, Euler’s equation. It’s hard to believe I’ve flipped from a virtually congenital math-phobe to a professor of engineering.

One day, one of my students asked me how I did it—how I changed my brain. I wanted to answer Hell—with lots of difficulty! After all, I’d flunked my way through elementary, middle, and high school math and science. In fact, I didn’t start studying remedial math until I left the Army at age 26. If there were a textbook example of the potential for adult neural plasticity, I’d be Exhibit A.

Thanks for this link! Looks very interesting!

[SparklyUnicorn]

Don't most college-bound kids get to at least precalculus?

 

 

 

Don't know the answer, but I'd be surprised if this was true.

[Garga]

Yes, of course it's possible.

 

Depending on where she lives, she can take a basic math class at her local community college. Or she can self-study, knowing what her end goals are.

.

Maybe. My friend's daughter clearly has dyscalculia. They've tried for years to help her. The daughter insisted all through homeschooled highschool that she wanted to be a hairdresser.

 

And now suddenly, the daughter wants to go to college. She took placement tests and scored so low that the college will not grant her admittance into even their remedial math classes. She'll have to find somewhere else to learn the basics so she can get into the remedial class. Not the remedial algebra class...just the lowest math class they even offer is too high for her.

 

This is not a fancy community college--just a run of the mill community college.

 

So, the family might not be able to have her take a remedial college course if she's too far behind.

[forty-two]

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 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.

I wonder the same.

 

I delayed formal math with my oldest until she was eight. I had bought into the win-win unschooling-inspired reasons for delaying math: that kids learn it faster when they are older and with all their informal math experience, they will actually end up *ahead* of their peers, even though they started later. But she turned out to be 2e, which I didn't properly grasp until we had started formal lessons, and we are not magically starting late and ending ahead. We are working hard and thoroughly (aiming for depth over speed) and a result we are not really making up the time - we make a little over a year's progress in a year's time. And I'm feeling it as I'm staring 7th grade pre-algebra in the face - outside timetables matter more to me now then they did when I so blithely delayed math in the firm belief that there were no trade-offs, that of course my smart girl would catch up and surpass her ps peers effortlessly. She *is* smart, but learning math is effort-ful, and my naive belief in hs delaying-magic trumping steady work over time has (shockingly ;)) proven false. I'm just thankful it was only to age 8 - with tweaking and careful effort, we can be on target for 8th grade algebra.

 

Also, wrt delaying masking learning issues (and how sometimes early difficulties that prompted delaying could be a sign of learning issues): I delayed in part because steady, disciplined work over time was hard for *me*. And I conflated delaying *formal* math with delaying *steady, planned, disciplined* work on math. "Informal math" meant "when I feel like it math" - which happened, but happened inconstantly. In the younger grades, steady effort over time working on informal, experiential math might well be better than steady effort over time working on formal math. But the message I heard and embraced was that *incidental* math that happened "naturally" through living life - no intentionality required other than intentionally avoiding formal math :rolleyes: - was inherently superior to steady effort over time on formal math. Obviously avoiding learning to work steadily over time didn't magically help my ability to work steadily over time; rather, it was just going ahead and making a steady effort to do daily math, working though the difficulties on both our parts, that helped us both to get better at teaching/learning math.

[Garga]

A lot of replies have talked about tutors, but she might not need a tutor. If the parent was just waiting for the student to want to do math, the parent might be quite happy and content to work hard to get her up to speed for themselves with some sort of curric that they choose. It doesn't have to be a tutor. 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.)

[Leonana]

I used to be part of the Living Math Yahoo Group. The owner of the group and website, Julie Brennan, posted about tutoring a young man to catch up. He was 20 years old, and was unschooled, but with no math knowledge other than making change. He wanted to go to college. He was able to speak Chinese fluently, so he had some benefits to his schooling.

 

She said she tutored him once a week, and he did Kahn Academy the rest of the week. I can't remember how long they did this, perhaps six months. He took the SAT and got a B on the math portion.

 

 

Sent from my iPhone using Tapatalk

[wapiti]

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

 

He took the SAT and got a B on the math portion.

 

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.

[mellifera33]

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.

 

B for bombed, perhaps?

[wapiti]

B for bombed, perhaps?

 

Perhaps there was a miscommunication, e.g. maybe the kid got 80th percentile.

 

 

Back to the OP, it's hard for me to fathom such a mindset that would so disadvantage the child.

[katilac]

Oh, I think it is possible <snip>

 

I have just never seen this actually happen.

 

This is where I stand - I don't doubt that it's possible for some people, but I have never seen it happen in my 13+ years of homeschooling while being involved with various groups. 

 

First, I would not take a casual comment as truly representative of her knowledge.  

 

This is true. 

 

I took a woman in her 40's who didn't even know simple arithmetic up to algebra in six months.  She came from a country where, in her words, she passed math by bribing the school officials.  She was very strongly motivated to learn the math because her job was instituting a basic math test and her job depended on it.  Granted, we did not go beyond that level but I assume that while she might have slowed down her pace with higher math concepts and skills, she could have still learned it. 

 

I don't know. ime, getting "up to" algebra is far different from algebra and beyond. My "up to" algebra teachers would have told you I was a great student, my algebra and beyond teachers, not so much! 

 

I essentially did this.  I mean yes sure I've been going over the basics with my kids for years.   

 

That's really very different from never having gone beyond subtraction, imo. The basics go far beyond subtraction. 

 

 

I don't feel the need to modify the term "unschooling" by calling her parents "radical unschoolers,"  

 

That's how the girl described herself, not how the OP described her parents. 

[bibiche]

First, I would not take a casual comment as truly representative of her knowledge. She may not have done much schooly math, but life itself forces humans to develop many informal math skills.

 

Second, if she really is interested in learning, then she needs a curriculum that builds on those informal skills. I would suggest Herb Gross's Adjective Noun Math.

Apparently they don't do any living math either (DS was talking to her), so I guess we can take her at her word.

 

Thanks for the suggestion. If the subject ever comes up I will certainly suggest it to her. Obviously I am not going to otherwise because, again: not my onions.

[Enajaliehs]

Yes, it is possible. But, as many others have said, it takes a lot of hard work and dedication from the student.

 

My brother's girlfriend's family (8 kids, she's the oldest) for various unfortunate reasons were/are inadvertent unschoolers. The girlfriend (now late teens) decided when she was about 15 that she wanted to know more about maths. My siblings and I were homeschooled, and used Saxon maths. We offered her tutoring and the use of our textbooks. She started Saxon 54 in Feb, skipped to 65 after about 50 lessons, just over a year later she finished Algebra 1/2. She was doing up to 20 lessons and up to 6hrs tutoring each week. She worked very hard, and has reaped the benefits. (As an aside, she doesn't enjoy maths, and only learnt because her lack of maths skills was adversely affecting her life.)

So, yes it is possible. She did have a general idea of addition and subtraction, but that was it. It has taken time, and while she probably won't ever go to university, she is now competent at maths and shouldn't have too many issues with it in life.

 

If at all possible, help the girl learn, provide her with resources, and direct her towards possible learning avenues.

[Ellie]

A lot of replies have talked about tutors, but she might not need a tutor. If the parent was just waiting for the student to want to do math, the parent might be quite happy and content to work hard to get her up to speed for themselves with some sort of curric that they choose. It doesn't have to be a tutor. 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.)

 

:iagree: :iagree: :iagree:

[Ellie]

That's how the girl described herself, not how the OP described her parents. 

 

I stand corrected.

 

I still am not ready to accuse the parents of educational neglect.

[Dmmetler]

I know an unschooled teen who is doing this now. Having said that, he was a STEM, hands-on kid. He hated anything on paper with a passion (he has vision issues, making reading physically hard, especially in the early years where his prescription was changing rapidly, so what was good a couple of months prior would lead to headaches if he tried to focus too hard on print or anything too small. Once he was old enough to get contacts, that stabilized things quite a bit and the correction was better, making books much less scary) . For him, the desire to do Math came at about age 13 when he started to look to the future and realize what was required to get into college. He caught up to Algebra in about a year, and going year round should be able to finish calculus before starting college, with the plan being to move to DE math at age 16 when he's eligible for the state grant.

 

Having said that, this is a kid who had internalized a lot of math (things like gear ratios) and was able to do really good mental computations before ever picking up a math book, because his interests led him into math-intense disciplines. So, getting caught up to Algebra in a year was more a case of putting together all the puzzle pieces already there. And, his desire to formalize it happened to coincide with it just plain becoming easier.

[Farrar]

I know an unschooled teen who is doing this now. Having said that, he was a STEM, hands-on kid. He hated anything on paper with a passion (he has vision issues, making reading physically hard, especially in the early years where his prescription was changing rapidly, so what was good a couple of months prior would lead to headaches if he tried to focus too hard on print or anything too small. Once he was old enough to get contacts, that stabilized things quite a bit and the correction was better, making books much less scary) . For him, the desire to do Math came at about age 13 when he started to look to the future and realize what was required to get into college. He caught up to Algebra in about a year, and going year round should be able to finish calculus before starting college, with the plan being to move to DE math at age 16 when he's eligible for the state grant.

 

Having said that, this is a kid who had internalized a lot of math (things like gear ratios) and was able to do really good mental computations before ever picking up a math book, because his interests led him into math-intense disciplines. So, getting caught up to Algebra in a year was more a case of putting together all the puzzle pieces already there. And, his desire to formalize it happened to coincide with it just plain becoming easier.

 

This reminds me more of the kids in the Benezet study (the most misunderstood, misapplied justification for "not teaching math"). In that study, the kids were given lots of number games, lots of living math exposure, lots of logic problems, just no formal instruction. And then they were able to "catch up" by synthesizing all of elementary math very quickly. Well, with all that good preparation, that's no wonder. Same in that kid's case.

[justasque]

This. I've known many unschooled children and, whilst they might be unfamiliar with formal mathematical vocabulary, their 'real world' experience exposes them to many mathematical principles. Often they've developed quite original mathematical processes to solve real-world problems and this can be a real strength. Ime, if an unschooler wants to learn, they will, just not necessarily to an externally-determined time frame. :)

 

The exception to this might be if the child has a learning disorder, or has had a very restricted, neglectful/harmful environment.

 

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.

 

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.

 

Quite true.  While it's theoretically possible to "catch up" with a lot of hard work, there are all kinds of things that will make it difficult for specific students.  That includes LDs, time issues, access to instruction and materials, access to mentoring, and finances (both in terms of affording materials and instruction, and in terms of the luxury of not having to work full-time-plus at a minimum wage job to support oneself).

 

Yes, of course it's possible.

 

Depending on where she lives, she can take a basic math class at her local community college. Or she can self-study, knowing what her end goals are.

 

I don't feel the need to modify the term "unschooling" by calling her parents "radical unschoolers," and I would be very hesitant to accuse them of educational neglect.

 

Not all CCs will have a class low enough for a student who has done no formal math whatsoever.  Which should be no surprise, because, since we have compulsory attendance laws, most teens and young adults have at least covered the basics somewhere along the way.  To offer a class, you have to have enough paying customers to make it worthwhile.  Both in CC and in public high schools, there are rarely enough kids who are this far behind to constitute an entire class.  And, when there are lower-level high school classes, they are designed for kids with serious learning difficulties, not for bright kids who want to move quickly and go into some depth with the material because they are aiming for college-level work.  Kids who are in this position generally have complex reasons for it - war refugees, very sickly children, non-English speakers who also have math delays, and so on.  They are thus not easy to group together because their needs are complicated and unique.

 

I agree that getting up to speed on arithmetic would be easy. But my child is a few years younger, and I don't think he would have been able to get through Algebra and Geometry in 6 months each even if he had been older. It took 32 weeks just to get through Algebra, and that was at a clip (and with a strong math background).  I assumed that catching up meant getting beyond geometry as well. Don't most college-bound kids get to at least precalculus?

...

 

There are many different colleges, offering many different majors, at many different academic levels.  Some of them will be quite happy to take your money regardless of your background.  If by "college-bound" you mean "aiming at being accepted at a decent school, in an academic major", then yes, most kids around here do Alg I, Geom, Alg II, at minimum, then usually Pre-Calc or AP Statistics.  The ones aiming at STEM careers and/or merit scholarships also do Calc, sometimes AP Calc, by doing Alg I in 7th or 8th grade and doubling up on their math classes in junior or senior year.  

 

Many majors require a decent amount of math both before and during college, because it's so integral to so many subjects.  Business, nursing, and even trades like electrician or carpenter require a solid understanding of math. 

 

A lot of replies have talked about tutors, but she might not need a tutor. If the parent was just waiting for the student to want to do math, the parent might be quite happy and content to work hard to get her up to speed for themselves with some sort of curric that they choose. It doesn't have to be a tutor. 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.)

 

This clearly assumes a parent who is themselves pretty solid with math beyond the fourth grade level.  And not just able to DO the material themselves, but to actually TEACH it, perhaps to a child who learns differently than the parent.  That's not every parent's strong point.  And it's not just a matter of doing it year-round, etc.  An honors level high school math class will take a solid investment of time for a well-prepared regular student - they are likely to be doing homework nights and weekends, September through mid-June.  Adding in an extra two-three months in the summer only gets you one extra course over the four years of high school.  And don't forget - this kind of student CAN'T be on a normal schedule for science either, as they simply do not have the math skills required for Physics or Chem, even at the middle school level.  You can't calculate density given mass and volume unless you can divide - which takes a bit of time to work up to if you're starting with subtraction.  So as well as catching up on math, these students often have to catch up on science courses as well if their goal is to be a good candidate for a decent college in a fairly academic major.

 

I used to be part of the Living Math Yahoo Group. The owner of the group and website, Julie Brennan, posted about tutoring a young man to catch up. He was 20 years old, and was unschooled, but with no math knowledge other than making change. He wanted to go to college. He was able to speak Chinese fluently, so he had some benefits to his schooling.

 

She said she tutored him once a week, and he did Kahn Academy the rest of the week. I can't remember how long they did this, perhaps six months. He took the SAT and got a B on the math portion.

...

 

Even putting aside the issue that the SAT does not result in letter grades, I am very skeptical of this story.  Going from, what, about 4th grade level? to doing well on the SAT (which requires algebra and geometry), in six months is very, very unlikely.  Even if one student was able to do it, we should not extrapolate from that one case to assume that it is within the capability of every student.  

My experience is that students who are behind can catch up from 4th grade to just before pre-Algebra in a year of very targeted, guided work, but that after that, they will take roughly the same amount of time as anyone else to work through pre-Algebra, Algebra, Geometry, and beyond.

[bibiche]

I still am not ready to accuse the parents of educational neglect.

 

Well, I am not accusing them of anything. I was pondering the situation and trying to determine if it fit my definition of educational neglect or not. Most of the responses from people who clearly know more about math education than I do have confirmed what I suspected, that IMO it is indeed educational neglect.

 

I know lots of people who unschool (and as I mentioned earlier, I consider our family to be unschooly). Some of the people do it remarkably well, following and/or anticipating their children's interest and making sure to provide all sorts of educational opportunities to capitalize on that interest.  I know others who seem to do it less well, but I am not concerned about their children's future.  In this case, I am concerned about the girl's educational prospects.  IMO not teaching any maths beyond second grade level is not adequately preparing a person for the future and is not consistent with basic educational standards.

 

What would constitute educational neglect for you?

[Jean in Newcastle]

My personal opinion is that it is neglect if math isn't being taught even in nontraditional ways.  And to answer someone's question upthread about LDs - I think that it is playing Russian Roulette of sorts because it could mean that LDs are not caught early and that makes things even harder.  I do not think that it is neglect if math is being taught in nontraditional ways that still cover a broad spectrum of mathematical knowledge. 

 

That said, I think that we can always learn.  The issue is the words "catch up".  If you mean, can someone with no LDs and the interest to do so, learn math up to a pre-calculus (since I believe that was the level mentioned), then I think that the answer is unequivocally yes.  If you mean, can someone with no LDs and interest learn the material within a specific time frame, then I think that the answer is "perhaps yes but perhaps not".  They might have to take some extra time to learn the material. 

 

My anecdote about the woman I taught who was in her 40's was more an illustration of how age does not keep people from learning.  Obviously I know that teaching her through pre-algebra was not the same as teaching someone up to pre-calculus.  I think that our rate of learning does slow as material gets more complex but we can still learn. 

[OneStepAtATime]

My personal opinion is that it is neglect if math isn't being taught even in nontraditional ways.  And to answer someone's question upthread about LDs - I think that it is playing Russian Roulette of sorts because it could mean that LDs are not caught early and that makes things even harder.  I do not think that it is neglect if math is being taught in nontraditional ways that still cover a broad spectrum of mathematical knowledge. 

 

That said, I think that we can always learn.  The issue is the words "catch up".  If you mean, can someone with no LDs and the interest to do so, learn math up to a pre-calculus (since I believe that was the level mentioned), then I think that the answer is unequivocally yes.  If you mean, can someone with no LDs and interest learn the material within a specific time frame, then I think that the answer is "perhaps yes but perhaps not".  They might have to take some extra time to learn the material. 

 

My anecdote about the woman I taught who was in her 40's was more an illustration of how age does not keep people from learning.  Obviously I know that teaching her through pre-algebra was not the same as teaching someone up to pre-calculus.  I think that our rate of learning does slow as material gets more complex but we can still learn. 

This is an important point.  I am learning more math teaching my own kids than I learned in ps.  The vast majority of us are capable of learning at nearly any age and do, quite often.  If there is no specific time frame then this is really not an issue, IMO, in a general sense.

 

But trying to learn math with no real math exposure in a traditional or nontraditional way within a very specific time frame, such as a person at 15 years old just starting out and trying to learn all the math necessary and expected through High School level and to pass the SAT and get into a desirable college within the standard time frame expected of a neurotypical public schooled High Schooler might be considerably more challenging.  It can be done.  It would not be an easy path to take.

[umsami]

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. 

[justasque]

..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.