Unschooling math opinion--how long to catch up--poll (don't have to be an unschooler to vote!)

[OneStepAtATime]

With regards to Khan Academy being sufficient, I think some things need to be considered.

 

1.  Will the parent simply be plopping their child in front of the computer and hoping for the best?  If so, then Khan probably won't be enough.

2.  Khan Academy is a lot more robust than it was even 2-3 years ago so there is definitely more material to work with now but not all kids learn well in this format.

3.  Kids usually also need exposure to paper/pencil learning.  It can still work well, though, if the parent is directly involved and working with the student and incorporating other math rich things into the environment and encouraging working on paper, too, and this format works well for the student.  Khan can absolutely work as a spine.  Jean did it quite successfully with her kiddo.  But she was involved and she provided a math rich environment and the format worked well for her kids.

[Jean in Newcastle]

I haven't read all the posts, and my beliefs about unschooling are dependent upon the family and if it is their cover word for doing nothing, or if it is their approach to schooling. I've met both.

 

I think probably 1-2 years - depending upon the child and their continued level of motivation and ability as well as parental/teacher oversight. Kids don't have a baseline understanding, so they may not realize that they really don't understand this concept - or even a small feature of it that is important. The parent/teacher should have this idea and can try to make sure the kids appreciate the fine points. It is easy to learn how to divide fractions (change / to X, flip second fraction), but if you don't understand why and appreciate that, it may well cause problems with algebra where a basic understanding of that principle is necessary to manipulate your equations to solve.

 

I also don't think Khan is sufficient. Khan is a great introduction, but I think to truly master the concepts, you need more practice. I'm also a fan of paper/pencil math vs. just on the computer. If the foundational concepts are not firmly understood and practiced, then higher level math will be difficult.

There is nothing keeping someone from using paper and pencil while using Khan academy. We certainly used it. The electronic "scratch paper " feature that Khan has is rather clunky. Once Dd figured out the answer on paper, she entered it. Note: I don't think that Khan is best for all or maybe even most people but the paper/pencil thing has zero to do with it.

[Arcadia]

Here's the thing, I managed Bs and even As in High School Algebra and Geometry but I still had a VERY shaky background in basic math concepts such as Fractions and Decimals and Percents and even order of operations, etc. ...

And in the real world I also struggled with not fully grasping those concepts. I had to work really, really hard to get past those deficits to handle the finances for my dad's business when he passed on. Honestly, I resent the huge gaps in understanding that the public school crippled me with.

Our life experiences differ which is probably why my estimates are less than others :)

 

My maternal grand uncle owns a cafe. My mom helps out there as a cashier since she was 6 years old (late 40s). She also helped to check and sign for deliveries. When she was bored, she helped with bookkeeping. She knows about renewing permits and paying business tax. My mom did attended school since 1st grade but she already have most of the 1st-6th grade math curriculum mastered. They use abacus instead of calculators at the cafe but my mom prefer mental math. Of course she won't learn order of operations, exponents and logs from helping to run a cafe but optimization of profits (prealgebra) is indirectly covered.

 

My dad, his siblings, nephews and nieces has all helped in the family business since they were 6. My paternal grandfather and uncles own metalwork shop/factory. In my paternal side, simple trigonometry, machinery and wiring are covered "on the job". It's like attending VoTech since you are 6.

 

I have ex-classmates (all girls school) who grew up on farms. Math is in their everyday life depending on which aspect of farm business they are involved in. All knew bookkeeping and tax forms by the time they were 12. Word problems won't as hard for them because that is their daily life. They were also trained to repair vehicles. I also come from a culture where girls aced their math (the US team that won 1st in European Girls’ Mathematical Olympiad 2017 "tells a story"). So math and languages would be "taught" in daily life whether or not the child Is formally schooled.

[Seasider]

When I stopped unschooling all the kids, and started CM style schooling, it was so much less work. So much less!

 

I'm always puzzled at the automatic association of unschooling with neglect. Not my experience at all.

Unschooling =/= not schooling.

 

Sadly, I've only met two bona fide unschoolers (both hard working, impressive educators!) and a whole bunch of not-schoolers calling themselves unschoolers.

[Jean in Newcastle]

Our life experiences differ which is probably why my estimates are less than others :)

 

My maternal grand uncle owns a cafe. My mom helps out there as a cashier since she was 6 years old (late 40s). She also helped to check and sign for deliveries. When she was bored, she helped with bookkeeping. She knows about renewing permits and paying business tax. My mom did attended school since 1st grade but she already have most of the 1st-6th grade math curriculum mastered. They use abacus instead of calculators at the cafe but my mom prefer mental math. Of course she won't learn order of operations, exponents and logs from helping to run a cafe but optimization of profits (prealgebra) is indirectly covered.

 

My dad, his siblings, nephews and nieces has all helped in the family business since they were 6. My paternal grandfather and uncles own metalwork shop/factory. In my paternal side, simple trigonometry, machinery and wiring are covered "on the job". It's like attending VoTech since you are 6.

 

I have ex-classmates (all girls school) who grew up on farms. Math is in their everyday life depending on which aspect of farm business they are involved in. All knew bookkeeping and tax forms by the time they were 12. Word problems won't as hard for them because that is their daily life. They were also trained to repair vehicles. I also come from a culture where girls aced their math (the US team that won 1st in European Girls’ Mathematical Olympiad 2017 "tells a story"). So math and languages would be "taught" in daily life whether or not the child Is formally schooled.

 

I agree.  But there is no information in this case as to what kind of real exposure there has been to math.  I asked up thread about what kind of computer games were used but got no answer.  So perhaps I err more on the side of expecting that it is less rather than more math exposure.  I do this, not because of any knowledge of the OP's situation (because I have none on that) , but because the unschoolers I personally have run into have grossly overestimated the educational benefits of gaming.  And by gaming, what seems to be usually the case in these situations is not the Dragonbox you mentioned, but RPG (role playing games) or FPS (first person shooter) games.  So again, in the face of little information, I am making massive assumptions but I'd rather err on the side of making conservative estimates and advice based on those conservative estimates because it's always easier to find out that things aren't as bad rather than to have it go the other way. 

 

As I said in another thread asking about the transition from unschooling to schooling, it is best in these cases to do some math (and reading) placement tests to see exactly where things lie.  Start at the lowest levels even if it means that the child zooms through the lower grade tests because you want to see where there might be holes when there hasn't been systematic mathematics instruction.  CLE is one company that has placement tests. 

 

[OneStepAtATime]

I agree. But there is no information in this case as to what kind of real exposure there has been to math. I asked up thread about what kind of computer games were used but got no answer. So perhaps I err more on the side of expecting that it is less rather than more math exposure. I do this, not because of any knowledge of the OP's situation (because I have none on that) , but because the unschoolers I personally have run into have grossly overestimated the educational benefits of gaming. And by gaming, what seems to be usually the case in these situations is not the Dragonbox you mentioned, but RPG (role playing games) or FPS (first person shooter) games. So again, in the face of little information, I am making massive assumptions but I'd rather err on the side of making conservative estimates and advice based on those conservative estimates because it's always easier to find out that things aren't as bad rather than to have it go the other way.

 

As I said in another thread asking about the transition from unschooling to schooling, it is best in these cases to do some math (and reading) placement tests to see exactly where things lie. Start at the lowest levels even if it means that the child zooms through the lower grade tests because you want to see where there might be holes when there hasn't been systematic mathematics instruction. CLE is one company that has placement tests.

 

Yes this was my concern as well. There isn't enough detail to know how much exposure to math the child has had or whether they have good solid innate math ability either. I don't. I needed and in fact still need targeted, systematic instruction to really master and internalize a math concept.

[38carrots]

I'm not sure why you split the responses into those sympathetic to unschoolers and those who aren't.  My response has nothing to do with how I feel about unschooling. 

 

I said 12 months--but that would be with having a teacher who is on top of the kid every day making sure things are understood and that time is used efficiently.  With a kid who is left to his own devices and the Khan Academy materials--well, it really depends on the kid.

 

If I were in this situation, I'd run through the basics of arithmetic the first year--addition, subtraction, multiplication, division, fractions, decimals, and percents.  Assuming that went well, the next year I'd do a good prealgebra program that has review of arithmetic built in (Derek Owens is an example, but there are tons of others).  That delayed review will be important to see how much was retained and to reinforce whatever has been or is about to be lost.  I would also do an arithmetic review (3-5 problems each day) for the next two years (so during Algebra I and geometry) to ensure that things are completely retained.

 

I would use a program that is easy to accelerate and that teaches math conceptually.  The stronger a person's conceptual understanding of something is, the less practice he will need to retain it (though he will need to practice to achieve fluency).  I have no idea how conceptual Khan Academy is.  The two programs that I know about that would work well for this sort of remediation are Singapore math and Math U See.

 

I was both interested to hear practical advice and to see whether there would be what I call a respondent bias. Obviously not enough people here to establish this, but I was curious.

 

I think that those with negative attitutudes towards unschooling would think that it would take longer to catch up / progress. I also think that those who started math early and engaged in "memorizing the facts" might feel too invested in this approach to accept that when those things are done at an older age, grades 2-7 (and yes, including pre-algebra) don't take years to cover to a pretty good degree of mastery.

 

Khan Academy is conceptual, I think people are confusing it with IXL with is just drills (or used to be drills when I looked into it, maybe it changed.)

 

I don't have experience with many math students / tutoring (hence asking this question) but in my very limited experience with several unschooled teens (no formal math, motivated, were unschooled but not neglected) catching up and going forward is lightning fast. For most, literally a couple of months. I obviously can't generalize from this. But in my experience those were not "gifted" or particularly math-talented.

 

 

[EKS]

I was both interested to hear practical advice and to see whether there would be what I call a respondent bias. Obviously not enough people here to establish this, but I was curious.

 

I think that those with negative attitutudes towards unschooling would think that it would take longer to catch up / progress. I also think that those who started math early and engaged in "memorizing the facts" might feel too invested in this approach to accept that when those things are done at an older age, grades 2-7 (and yes, including pre-algebra) don't take years to cover to a pretty good degree of mastery.

 

Khan Academy is conceptual, I think people are confusing it with IXL with is just drills (or used to be drills when I looked into it, maybe it changed.)

 

I don't have experience with many math students / tutoring (hence asking this question) but in my very limited experience with several unschooled teens (no formal math, motivated, were unschooled but not neglected) catching up and going forward is lightning fast. For most, literally a couple of months. I obviously can't generalize from this. But in my experience those were not "gifted" or particularly math-talented.

 

I suspect that the difficulty isn't going to be the initial teaching, it's going to be the retention.  Working with a 12yo on basic arithmetic is going to be similar in some ways to working with a gifted 7-9yo--except that the 12yo is going to bring better executive function and stamina to the task.  

 

The problem with going lightning fast is that it doesn't give things enough time to gel.  Some kids don't need that time, but others, when encountering the same material a month or year later, will have absolutely no memory of ever having done anything like it (ask me how I know...).  So you're going to want to watch out for retention problems down the road.  My kids, who had finished arithmetic by age 9, still needed some review several years later.  

[GoodGrief]

I do think a 12-13 year old kid who has led a reasonably enriching unschool existence and without learning disabilities could get up to age-typical grade level fairly quickly, IF the kid was highly motivated to work on it intensely for a period of time. I said 12+ months under the plan you laid out...Khan Academy for an hour a day. But it could be done more quickly for a kid who wished to focus intensely for a time.

 

I wouldn't choose Khan though.

[luuknam]

I don't have experience with many math students / tutoring (hence asking this question) but in my very limited experience with several unschooled teens (no formal math, motivated, were unschooled but not neglected) catching up and going forward is lightning fast. For most, literally a couple of months.

 

 

I suspect that the kids that catch up rapidly spend more than one hour a day though. It's really easy to spend more than an hour a day on math, especially if you gamify it a little with points and badges. When I started Khan again a little over a month ago, I was close to 2M points... so I spent 6 hours one Saturday knocking out a ton of the elementary grade problems they'd added in the past 2.5 years to hit 2M points.

 

Which, btw, I'd recommend doing if you have a real life student like that - have them spend a bunch of hours per day on the math they already understand to get through that and make sure there aren't holes, and only slow down when you reach new material. Though even then I'd suggest spending at least 1.5-2 hours per day, rather than 1 hour/day. 

[idnib]

I don't have experience with many math students / tutoring (hence asking this question) but in my very limited experience with several unschooled teens (no formal math, motivated, were unschooled but not neglected) catching up and going forward is lightning fast. For most, literally a couple of months. I obviously can't generalize from this. But in my experience those were not "gifted" or particularly math-talented.

 

I think this can happen, but I doubt these kids spend an hour/day. That's why I said when teens are motivated to catch up, I would expect them to spend more time and really focus in, no differently than they may have focused in on other topics when those were of interest to them. Catching up years in math (and adding on the math they're missing while catching up) cannot be done by most kids in an hour/day.

 

I do agree there's a sweet spot between doing a small amount each day and a massive amount of catch up at once. We do a some math most days because I don't desire to find that sweet spot and because it's easier. But can someone who jogs every day for an hour be passed by someone who was walking but now runs and sprints in a more focused and intense way for 2 hours/day? Yes.

[Arcadia]

I don't have experience with many math students / tutoring (hence asking this question) but in my very limited experience with several unschooled teens (no formal math, motivated, were unschooled but not neglected) catching up and going forward is lightning fast. For most, literally a couple of months. I obviously can't generalize from this. But in my experience those were not "gifted" or particularly math-talented.

I would have preferred to use the Key to Algebra workbooks to catch up rather than Khan if tutoring because it is easier to revise the workbooks and go over careless mistakes when the tutor is not around than to stay undistracted on the internet.

 

1hr of Math per day is not exactly an hour only of Math per day. A motivated child who wants to catch up on formal math might have whatever math he/she learned that day from a tutor churning in his/her mind all day. I used to do school physics homework in my sleep which was unhealthy as I am already an insomniac even as a kid. My kids can be mentally chewing their schoolwork while eating or walking to the library.

[Bluegoat]

I also agree that an hour a day seems low.  My daughter in grade 6 does an hour and a half a day at school.  I don't know how efficient that is, but it's a good block of time.

 

I would think about two one hour periods, myself.

[Jean in Newcastle]

Not everybody defines unschooling the same way. I have no problem with what I would call the "Colefax Unschooling." Like the Colefax family, an early "pioneer" of the concept. Those parents worked their butts off. They built farm outbuildings to teach geometry. That kind of unschooling - I admire it, but I would not do that, no way! It doesn't mesh with my logical, step-by-step preferences and I don't want to have the kids re-wire the house so they can learn about electricity. (i know someone who did this!) i do think that can be effective, if the parents want to do this and are committed.

 

It's the "Sandra Dodd" unschooling that I am frankly opposed to. I think it's a terrible idea, risks something that isn't the parent's to gamble (their child's future options), and makes a lot of excuses for its shortcomings.

 

Yes.  The first is less "child led" as it is "child collaborated" and "child engaged".  I'm all for that. 

[kiana]

People keep confusing radical unschooling with unschooling.

 

I wish people wouldn't do that.

 

And other people indignantly insist that there is no difference and chastise people for using the term "radical unschooling". Can't win.

[poppy]

I thought unschooling = completely child led.  And therefore "we unschool except for math and language" is not actually unschooling at all.

 

And radical unschooling is = life is completely child led with no imposed limits on food or grooming or sleep or behavior.

 

[Guest]

And other people indignantly insist that there is no difference and chastise people for using the term "radical unschooling". Can't win.

Yes. This is what I have seen. There's a continuum for how "radically" people will unschool and the people on the most radical side often get uppity when they are grouped with unschoolers who strew intentionally, or who limit/ prohibit video games or who still insist that areas have to be covered, however non-didactically.

 

Conversly, I have seen "Colefax unschoolers" who get very irritated when people think they are doing the same thing as those radical unschoolers because they are most definitely NOT. They are going to enormous efforts to strew and expose and facilitate; they buy a ton of subscriptions and materials and books and media so that plentiful opportunities are all around the child.

[Closeacademy]

I picked about a year. But I wouldn't do things by grade level but by skill. We use Khanacademy for math and I've found that you can really breeze through things and if you keep doing the mastery checks that you can get a lot of skills checked off really quickly.  One of the things I do too is we start with a skill set & then work our way from easy to hard So that there is always something easy to work on especially after a break. I'm thinking a lot of things will be fairly easy to work through in a short amount of time. 

 

I've read before that they used to didn't teach mathematics until the 7th grade and then took you through things pretty quickly because most people pick up the basics from every day life.

[Garga]

I suspect that the difficulty isn't going to be the initial teaching, it's going to be the retention. Working with a 12yo on basic arithmetic is going to be similar in some ways to working with a gifted 7-9yo--except that the 12yo is going to bring better executive function and stamina to the task.

 

The problem with going lightning fast is that it doesn't give things enough time to gel. Some kids don't need that time, but others, when encountering the same material a month or year later, will have absolutely no memory of ever having done anything like it (ask me how I know...). So you're going to want to watch out for retention problems down the road. My kids, who had finished arithmetic by age 9, still needed some review several years later.

 

I agree with this. I think the student can be "brought up to speed" quickly, but I would fear that it would be shallow and not deep, like a plant planted in ground that isn't deep enough. It'll grow, and then wither and die.

 

That's not true for everyone, but would be a possible pitfall. But...that doesn't help the OP. The child is in this situation and needs to catch up. But I think rushing it is a bad idea.

 

I would start slow now and then when they're older, perhaps they could double up on some math classes? A student could take Geometry and Algebra II in the same year.

Edited April 21, 2017 by Garga

[Guest]

I picked about a year. But I wouldn't do things by grade level but by skill. We use Khanacademy for math and I've found that you can really breeze through things and if you keep doing the mastery checks that you can get a lot of skills checked off really quickly. One of the things I do too is we start with a skill set & then work our way from easy to hard So that there is always something easy to work on especially after a break. I'm thinking a lot of things will be fairly easy to work through in a short amount of time.

 

I've read before that they used to didn't teach mathematics until the 7th grade and then took you through things pretty quickly because most people pick up the basics from every day life.

I don't know when you mean by "used to," but it is also true that it's pretty recent in history that all teens have been expected to do math beyond arithmetic. The percentage of people who studied math beyond consumer-based math was small until the last few decades of the 1900s. When my mother was born, it was still smaller than 50% of students graduated from high school. Most people had no need to do math beyond arithmetic.

 

Also, children in the 20th century had much more practice doing math and, in fact, many "school subjects" in their everyday lives. They had far fewer forms of passive entertainment as present-day kids. Hobbies and games often relied on math skills (playing card games; logic and strategy in checkers and chess; dominoes; keeping statistics in sports.) If mom sent you to the store to get sugar, eggs and oats, you didn't take her debit card. You had cash and you couldn't buy indescriminently; you had to know what you would owe.

 

My point is that you can't idealize what was done "once upon a time" because it seemed to work out fine for Grandpa, KWIM? Our kids have a very different environment from what Grandpa had with different distractions and way different expectations. I wouldn't risk my kids' competancy in math and their suitability to higher learning based on someone somewhere saying Grandpa picked up all the math he needed to know the summer of 8th grade. I really don't see the downside in just chipping away at math in the didactic fashion from Kindergarten or thereabouts.

[luuknam]

Results thus far:  

 

I do not unschool, but I have nothing against unschooling / it is a valid educational option

 

n=53

 

1-3 months:     ---

3-5 months:     1.9%

5-7 months:     9.4%

12 months:    20.8%

>12 months:  67.9%

 

I do not unschool and I think unschooling is neglectful / lower educational option

 

n=28

 

1-3 months:    ---

3-5 months:    3.6%

5-7months:     3.6%

12 months:    10.7%

>12 months:  82.1%

 

I unschool (even if not math)

 

n=6

 

1-3 months:    16.7%

3-5 months:     ---

5-7 months:    16.7%

12 months:      50.0%

>12 months:   16.7%

Edited April 21, 2017 by luuknam

[luuknam]

Oh, and total:

 

n=87

 

1-3 months:     1.1%

3-5 months:     2.3%

5-7 months:     8.0%

12 months:     19.5% 

>12 months:   69.0%

[Bluegoat]

People keep confusing radical unschooling with unschooling.

 

I wish people wouldn't do that.

 

Someone seems to say it's wrong no matter how it's used.

 

I've been told more than once that what you are calling unschooling isn't at all, and also that radical unschooling isn't really unschooling.

 

I say the unschoolers can duke it out themselves, until then I will call them both unschooling and differentiate if required by adding details.

[Bluegoat]

I agree with this. I think the student can be "brought up to speed" quickly, but I would fear that it would be shallow and not deep, like a plant planted in ground that isn't deep enough. It'll grow, and then wither and die.

 

That's not true for everyone, but would be a possible pitfall. But...that doesn't help the OP. The child is in this situation and needs to catch up. But I think rushing it is a bad idea.

 

I would start slow now and then when they're older, perhaps they could double up on some math classes? A student could take Geometry and Algebra II in the same year.

 

I don't know.  Maybe the American approach is different, but around here up through about grade 4 the main thing kids do are the four basic operations, plus money, time, measuring, and so on.

 

I would actually be quite surprised to get a 12 year old, even with no formal math, who could not add and subtract pretty easily, and who could not do time, or make change.  And probably a lot of measuring type things a s well.  All those things come up in daily life for most people, even kids.

 

I don't think it would take long to learn multiplication and division, with a drill period every day which could be ongoing.

 

The big new things in grade 5 and six here are fractions and decimals, but again, those are fairly straightforward.  It's a good thing to practice, but when I think about it, the kids in school actually aren't practicing those things endlessly either.  My dd did multiplying and dividing with decimals for the first time this year, and it was a unit of about a month and they won't touch it again this year. 

 

I think the key would really be that the tutor would have to step outside the box as far as progression of skills.  You can start to think about algebra, for example, while you still could use dome more practice with fractions.  And you can also practice some skills you've learned together with new things.

 

My experience is that for elementary school, most kids are developing number sense without a lot of artificial opportunities created to that end.

 

But I agree - I wouldn't rush.  I think starting at grade 7 the student could be caught up and also doing well, certainly by the end of high school, and probably much sooner, like the end of jr high.  But as long as the former is true, I can't see why there would be a need to rush too much.

[poppy]

Results thus far:  

 

I do not unschool, but I have nothing against unschooling / it is a valid educational option

 

n=53

 

1-3 months:     ---

3-5 months:     1.9%

5-7 months:     9.4%

12 months:    20.8%

>12 months:  67.9%

 

I do not unschool and I think unschooling is neglectful / lower educational option

 

n=28

 

1-3 months:    ---

3-5 months:    3.6%

5-7months:     3.6%

12 months:    10.7%

>12 months:  82.1%

 

I unschool (even if not math)

 

n=6

 

1-3 months:    16.7%

3-5 months:     ---

5-7 months:    16.7%

12 months:      50.0%

>12 months:   16.7%

 

So the question, how long would it take a 12 year old catch up with 1 hour a day of instruction?  

And almost all unschoolers think less than a year, while almost all non-unschoolers think more than a year.

And obviously at the end of the year the child is 13.

My question is , what level of math is a 13 year old supposed to be competent at?   (My kids are younger).

[Bluegoat]

So the question, how long would it take a 12 year old catch up with 1 hour a day of instruction?  

And almost all unschoolers think less than a year, while almost all non-unschoolers think more than a year.

And obviously at the end of the year the child is 13.

My question is , what level of math is a 13 year old supposed to be competent at?   (My kids are younger).

 

Here are the outcomes for my province.

[luuknam]

Interesting correlations between attitudes towards unschooling and time estimated.  Even if n=not enough to say anything really :)

 

 

Right, especially for the "I'm an unschooler" results. It's not even my poll though - I just wanted to make the results easier to read, not draw any real conclusions from it.

[mellifera33]

I'm surprised that so few unschoolers answered the poll. Maybe I'm just conflating the WTM boards with my local homeschool groups, where I feel like the odd one out because we have required subjects each day. 

 

We don't unschool. I love the idea, and my kids follow their interests for some subjects, but with the mix of LDs we're dealing with here I can't imagine how proficiency in core subjects would ever happen if we unschooled. I would like to do more unit studies focusing on the kids' interests in the future, but I will need to have a few serious blocks of planning time to make them encompass all subjects. 

[Arcadia]

I'm surprised that so few unschoolers answered the poll. Maybe I'm just conflating the WTM boards with my local homeschool groups, where I feel like the odd one out because we have required subjects each day.

Only 87 people voted so not many boardies voted. I didn't vote.

My family is child led so neither an unschooler nor do we have required subjects. My oldest is only in 7th though so no high school credits to worry about yet.

 

Also what is included in parenting in my family culture might fall under homeschooling in someone else's definition. For example basic reading, handwriting, addition, subtraction, simple fractions (division) and multiplication, reading an analog clock, using cash to buy food are all verbally taught before formal school.

 

For example a birthday party at home. One of my relatives would prompt the young birthday child or children (twins) to count how many people are around and cut the cake into as equal a slice as possible. To us that is a "lesson" in party etiquette but it can also be counted as math.

 

My extended family also let young relatives buy food at fast food places with dollar notes and coins for the family. So the young kid would have to figure out how much a few burgers, milkshakes and sundaes cost either by simple addition or multiplication of decimals. Then they have to figure out the amount of change to expect which would cover subtraction of decimals since we give a twenty dollar bill usually to the child. To us, it is a life skill that kids need to have before formal school age (1st grade) as our school cafeteria did not have stored value card in my days. Now I can give a young relative a gift card instead of cash.

 

ETA:

All my relatives know how to play poker, blackjack, gin rummy since young. That is how my extended family ring in the new year. So gaming probability is covered.

Edited April 21, 2017 by Arcadia

[kiana]

I agree with this. I think the student can be "brought up to speed" quickly, but I would fear that it would be shallow and not deep, like a plant planted in ground that isn't deep enough. It'll grow, and then wither and die.

 

That's not true for everyone, but would be a possible pitfall. But...that doesn't help the OP. The child is in this situation and needs to catch up. But I think rushing it is a bad idea.

 

This is what we run into with the remedial classes at our college. We're able to get them to where they can do algebra, but because we've learned it all in one rushed semester, they haven't really done the amount of practice necessary to internalize it. People who start in remedial math often tend to flounder in precalculus or calculus, where they need to have not only learned the algebra rules but internalized them.

 

It doesn't mean it's fruitless, but it means that someone who's going further than just gen ed math really needs to put in out of class practice time to get the depth of knowledge that others who had done it all along would have. 

[amy g.]

This is a different situation, but I had a kid who was behind in math due to learning disabilities.

 

She spent a couple of summers working 6 hours a day with the tutors at her college and was able to make a B in college algebra which ruined her 4.0 GPA.

 

What is interesting to me is that when she was tested again, she no longer qualifies as LD. They said that all of that intensive work forged new neural pathways. She isn't particuarly good or efficient in math now, but she has worked her way up to the low average range.

 

This summer, she is taking Trig and I imagine she will be back working on it 6 hours a day. Hopefully she will get an A and it won't ruin her new GPA at her transfer school.

 

So I think kids can make up for lost ground if they are motivated. Maturity helps too, but if it were my kid, I'd ask for more than 1 hour a day if I really wanted the new skills to stick.

[Arcadia]

It doesn't mean it's fruitless, but it means that someone who's going further than just gen ed math really needs to put in out of class practice time to get the depth of knowledge that others who had done it all along would have.

The OP's example is a motivated unschooled 7th grader. I took the 1hr a day in the OP to mean an hour of instruction a day. So if OP tutors the child for the equivalent of an hour a day, the motivated child can consolidate and master the skills in his/her free time which includes the entire summer.

 

7th grade math isn't prealgebra yet. There is so much spiral in math from prealgebra to calculus, and I am assuming this unschooled kid has not been taught anything wrong yet like order of operations taught wrongly. So he/she has nothing wrong to unlearn unlike someone who failed maths in school. I find clean slates are much easier to tutor than remedial.

 

My oldest is a 7th grader and while not motivated, he does have plenty of free time. If he needs to bring his weakest subject up to level, an hour a day of direct instruction would be sufficient because he can put in the extra hours and effort in his own time. Someone who is in remedial math in college would have lots more time commitments than my DS12.

[Jean in Newcastle]

The OP's example is a motivated unschooled 7th grader. I took the 1hr a day in the OP to mean an hour of instruction a day. So if OP tutors the child for the equivalent of an hour a day, the motivated child can consolidate and master the skills in his/her free time which includes the entire summer.

 

7th grade math isn't prealgebra yet. There is so much spiral in math from prealgebra to calculus, and I am assuming this unschooled kid has not been taught anything wrong yet like order of operations taught wrongly. So he/she has nothing wrong to unlearn unlike someone who failed maths in school. I find clean slates are much easier to tutor than remedial.

 

My oldest is a 7th grader and while not motivated, he does have plenty of free time. If he needs to bring his weakest subject up to level, an hour a day of direct instruction would be sufficient because he can put in the extra hours and effort in his own time. Someone who is in remedial math in college would have lots more time commitments than my DS12.

 

But the program suggested was Khan Academy.  And while I did make it work very well for us, it was because I was there giving instruction alongside Khan.  Many people who use Khan, use it as a program because they think that they can get away without interacting with the student.  I used Khan as a "spine" for tutoring, not as a substitute for tutoring. 

 

7th grade math does include prealgebra in this current era.  One problem taken directly from 7th grade math on Khan academy:  solve   3x + 2 > 5

[rainbowmama]

It really depends on the kid. Not the same, but I took very little formal math in high school: I didn't finish past geometry. I tested into calculus for college, skipping algebra II and pre-calc, and aced my year of college calculus with little trouble. My oldest is very math. She rips through Beast Academy books in a couple of weeks and then doesn't do any formal math for months while waiting for the next one to be published. Erratic, short bursts have not hurt her ability to internalize the content, so I leave her alone, though I'm relieved that we finally finished Beast Academy and will no longer have to wait on a publishing schedule.

 

My second child is not me or my daughter. Unlike my oldest, he couldn't informally learn how to read an analog clock or estimate the tax on things before formal schooling: it took a lot of repetition for him to internalize it, as did borrowing, as did understanding fractions (not working with them, just understanding them), as did remembering geometric terms. He doesn't have any learning disorders: math just isn't as intuitive to him. 

 

I think some twelve year olds could catch up in a matter of months. I think some could take years. I personally wouldn't want to take that gamble, but I've never had a really resistant kid who might benefit from more maturity, either. 

[38carrots]

But the program suggested was Khan Academy.  And while I did make it work very well for us, it was because I was there giving instruction alongside Khan.  Many people who use Khan, use it as a program because they think that they can get away without interacting with the student.  I used Khan as a "spine" for tutoring, not as a substitute for tutoring. 

 

7th grade math does include prealgebra in this current era.  One problem taken directly from 7th grade math on Khan academy:  solve   3x + 2 > 5

 

Hm...Never actually thought of the bolded part. When I said "using Khan" I meant using their curriculum and computer layout. I wouldn't want a child to start a subject on their own, though I love Sal's explanations--much better than mine. He really instills a deep conceptual understanding.

 

Are people in general afraid of prealgebra?

[Jean in Newcastle]

Hm...Never actually thought of the bolded part. When I said "using Khan" I meant using their curriculum and computer layout. I wouldn't want a child to start a subject on their own, though I love Sal's explanations--much better than mine. He really instills a deep conceptual understanding.

 

Are people in general afraid of prealgebra?

 

I have seen thread after thread start with someone saying "I don't want to have to sit with my child for math so how can I set up Khan Academy?"  or "I set up Khan Academy for Junior but found out after a month that he's been skipping all the explanation and just winging the answers."  I realize that some kids are not only motivated but have stellar self control and study skills but I think that method sets a lot of kids up for failure. 

 

Re. prealgebra.  I was just responding to the statement that "7th grade isn't prealgebra yet". 

[Arcadia]

Many people who use Khan, use it as a program because they think that they can get away without interacting with the student. 

That is happening in some schools though (but I don't know the full details) as a each public school kid proceed at their own level trial. I do agree that Khan Academy as an independent curriculum with no oversight has a high chance of failure though for most kids. My reference to 7th grade not being prealgebra yet was in reference to how my public middle schools call the math course offerings in their class catalogs.

 

"With support from the Bill & Melinda Gates Foundation, in fall 2011 Khan Academy began a two-year formal pilot program in a number of California school districts, charter schools, and independent schools serving diverse student populations. At the same time, the foundation contracted SRI Education’s Center for Technology in Learning to study the implementation of Khan Academy resources and tools in those schools during the 2011-12 and 2012-13 school years. The study involved the participation of 20 public, charter, and independent schools; more than 70 teachers; and approximately 2000 students in each study year." https://www.sri.com/work/projects/research-use-khan-academy-schools

 

Hm...Never actually thought of the bolded part. When I said "using Khan" I meant using their curriculum and computer layout. I wouldn't want a child to start a subject on their own, though I love Sal's explanations--much better than mine.

My kids loathe Sal Khan's videos. They literally run away. Even my computer loving kid prefers to do SAT prep on paper and color the bubbles than use the Khan SAT prep where he can just click on the answer instead.

 

I come from a country with intergrated math and no such thing as prealgebra and most of the parents in my social circles are not educated in the states.

[Jean in Newcastle]

That is happening in some schools though (but I don't know the full details) as a each public school kid proceed at their own level trial. I do agree that Khan Academy as an independent curriculum with no oversight has a high chance of failure though for most kids. My reference to 7th grade not being prealgebra yet was in reference to how my public middle schools call the math course offerings in their class catalogs.

 

"With support from the Bill & Melinda Gates Foundation, in fall 2011 Khan Academy began a two-year formal pilot program in a number of California school districts, charter schools, and independent schools serving diverse student populations. At the same time, the foundation contracted SRI Education’s Center for Technology in Learning to study the implementation of Khan Academy resources and tools in those schools during the 2011-12 and 2012-13 school years. The study involved the participation of 20 public, charter, and independent schools; more than 70 teachers; and approximately 2000 students in each study year." https://www.sri.com/work/projects/research-use-khan-academy-schools

 

My kids loathe Sal Khan's videos. They literally run away. Even my computer loving kid prefers to do SAT prep on paper and color the bubbles than use the Khan SAT prep where he can just click on the answer instead.

 

I come from a country with intergrated math and no such thing as prealgebra and most of the parents in my social circles are not educated in the states.

OK - now I understand on the prealgebra comment.  But in reality, there are pre-algebra concepts being taught even back in grade school.  Because the US also integrates to some degree in the younger years, it isn't labeled as such outside of the teacher's manuals or on a state learning standards chart.

 

My kids loathe Sal Khan's videos as well.  I took the place of the video.  ;) 

[Shellydon]

So the question, how long would it take a 12 year old catch up with 1 hour a day of instruction?  

And almost all unschoolers think less than a year, while almost all non-unschoolers think more than a year.

And obviously at the end of the year the child is 13.

My question is , what level of math is a 13 year old supposed to be competent at?   (My kids are younger).

 

My kids complete Algebra 1 at age 13. 

[Closeacademy]

I don't know when you mean by "used to," but it is also true that it's pretty recent in history that all teens have been expected to do math beyond arithmetic. The percentage of people who studied math beyond consumer-based math was small until the last few decades of the 1900s. When my mother was born, it was still smaller than 50% of students graduated from high school. Most people had no need to do math beyond arithmetic.

 

Also, children in the 20th century had much more practice doing math and, in fact, many "school subjects" in their everyday lives. They had far fewer forms of passive entertainment as present-day kids. Hobbies and games often relied on math skills (playing card games; logic and strategy in checkers and chess; dominoes; keeping statistics in sports.) If mom sent you to the store to get sugar, eggs and oats, you didn't take her debit card. You had cash and you couldn't buy indescriminently; you had to know what you would owe.

 

My point is that you can't idealize what was done "once upon a time" because it seemed to work out fine for Grandpa, KWIM? Our kids have a very different environment from what Grandpa had with different distractions and way different expectations. I wouldn't risk my kids' competancy in math and their suitability to higher learning based on someone somewhere saying Grandpa picked up all the math he needed to know the summer of 8th grade. I really don't see the downside in just chipping away at math in the didactic fashion from Kindergarten or thereabouts.

Really wish we had reply buttons on here instead of quotes.

 

I read something in a book by the Bluedorns years ago about this. And yes, it was before modern times. And I am not idolizing anything just stating something that I had read about in the past.

 

Math is not something that is child-led in my home. But I do think that someone can be caught up quickly on the basics.

[Guest]

Really wish we had reply buttons on here instead of quotes.

 

I read something in a book by the Bluedorns years ago about this. And yes, it was before modern times. And I am not idolizing anything just stating something that I had read about in the past.

 

Math is not something that is child-led in my home. But I do think that someone can be caught up quickly on the basics.

It seems to me though - why risk it? It's kind of like a Pascal's Wager in my mind. Consider:

 

Possibility #1: teach the child math systematically from Kindergarten. If the child is math-intuitive, motivated or gifted, you have not lost anything. If the child is not motivated, intuitive or gifted, they will need all the time they can get and you're better off because you know this earlier.

 

Possibility #2: don't teach the child systematically from Kindergarten. "Trust" the child to learn what they need to know when they need to know it. If the child is math-intuitive, motivated or gifted, it will probably work out. If the child is not motivated, intuitive or gifted, you may not know the full extent of this until it is too late to remediate effectively. If this is compounded because your life circumstances have changed and the child must go to b&m school, now there are a lot of difficulties.

 

So, it seems to me that the most logical wager is to teach the child systematically from Kindergarten. There is nothing to lose by doing it this way. There is much potential loss by not doing it this way unless all the stars align and everything plays out ideally.

[luuknam]

My kids complete Algebra 1 at age 13. 

 

 

And at least one person is planning on doing AOPS Calculus for 7th grade, according to the planning thread.

 

I don't think there really is an answer to "what level of math should a 13yo be competent at". I do think that it'd be mighty hard to catch up (before, say, the end of high school) to the 7th graders who are doing AOPS Calculus if starting formal math in 7th grade. OTOH, there are special needs kids who are never going to get to 1+1=2. But anyway, assuming we're talking about an average kid, I'm not sure there's a compelling reason to be more advanced than finishing pre-algebra by the end of 8th grade. 

Edited April 22, 2017 by luuknam

[38carrots]

It seems to me though - why risk it? It's kind of like a Pascal's Wager in my mind. Consider:

 

Possibility #1: teach the child math systematically from Kindergarten. If the child is math-intuitive, motivated or gifted, you have not lost anything. If the child is not motivated, intuitive or gifted, they will need all the time they can get and you're better off because you know this earlier.

 

Possibility #2: don't teach the child systematically from Kindergarten. "Trust" the child to learn what they need to know when they need to know it. If the child is math-intuitive, motivated or gifted, it will probably work out. If the child is not motivated, intuitive or gifted, you may not know the full extent of this until it is too late to remediate effectively. If this is compounded because your life circumstances have changed and the child must go to b&m school, now there are a lot of difficulties.

 

So, it seems to me that the most logical wager is to teach the child systematically from Kindergarten. There is nothing to lose by doing it this way. There is much potential loss by not doing it this way unless all the stars align and everything plays out ideally.

 

Possiblity #1: Teach the child math systematically from Kindergarten. If the child is math-intuitive, motivated or gifted, he might start resenting math because the early years of arithmetics and "math facts" can be absolutely soul sucking, especially to gifted children. If the child is not intuitive, motivated or gifted, he might resent math even more and might start feeling like he "can't do math."

 

Possibility #2": Don't teach the child systematically from Kindergarten. If the child is math intuitive, motivated or gifted he'll be picking up math anyway, he has a chance to grow up loving math when he is ready to study it beyond arithmetics. Meanwhile, the child might have enjoyed other things and developed other passions without being burdened by "math facts" and mindless worksheets. If the child is not motivated, intuitive or gifted, he still has an opportunity to grow up without hating math and his confidence intact--which is one of the biggest precursors to being successful in math later on.

 

Obviously, in my opinion there's much to lose in teaching a child who is not intersted or not ready too early.

 

I do agree that there are risks involved in both approaches. Some are easier to digest than others, especially in our culture of achievement. Different people take different risks.

 

[Arcadia]

And at least one person is planning on doing AOPS Calculus for 7th grade, according to the planning thread.

Completed :lol:

ETA:

If you are looking at the 2016/17 thread. Else I am not the "guilty" one :)

Edited April 22, 2017 by Arcadia

[luuknam]

Completed :lol:

ETA:

If you are looking at the 2016/17 thread. Else I am not the "guilty" one :)

 

 

Oops. I just search the boards for 7th grade planning thread and didn't notice it was last year's (it was only on page 2 or 3 of the Logic Stage board). Not that it matters for the point I was making.

[Jean in Newcastle]

It seems to me though - why risk it? It's kind of like a Pascal's Wager in my mind. Consider:

 

Possibility #1: teach the child math systematically from Kindergarten. If the child is math-intuitive, motivated or gifted, you have not lost anything. If the child is not motivated, intuitive or gifted, they will need all the time they can get and you're better off because you know this earlier.

 

Possibility #2: don't teach the child systematically from Kindergarten. "Trust" the child to learn what they need to know when they need to know it. If the child is math-intuitive, motivated or gifted, it will probably work out. If the child is not motivated, intuitive or gifted, you may not know the full extent of this until it is too late to remediate effectively. If this is compounded because your life circumstances have changed and the child must go to b&m school, now there are a lot of difficulties.

 

So, it seems to me that the most logical wager is to teach the child systematically from Kindergarten. There is nothing to lose by doing it this way. There is much potential loss by not doing it this way unless all the stars align and everything plays out ideally.

 

 

Possiblity #1: Teach the child math systematically from Kindergarten. If the child is math-intuitive, motivated or gifted, he might start resenting math because the early years of arithmetics and "math facts" can be absolutely soul sucking, especially to gifted children. If the child is not intuitive, motivated or gifted, he might resent math even more and might start feeling like he "can't do math."

 

Possibility #2": Don't teach the child systematically from Kindergarten. If the child is math intuitive, motivated or gifted he'll be picking up math anyway, he has a chance to grow up loving math when he is ready to study it beyond arithmetics. Meanwhile, the child might have enjoyed other things and developed other passions without being burdened by "math facts" and mindless worksheets. If the child is not motivated, intuitive or gifted, he still has an opportunity to grow up without hating math and his confidence intact--which is one of the biggest precursors to being successful in math later on.

 

Obviously, in my opinion there's much to lose in teaching a child who is not intersted or not ready too early.

 

I do agree that there are risks involved in both approaches. Some are easier to digest than others, especially in our culture of achievement. Different people take different risks.

 

It's not an either/ or scenario.  You can teach the child you have.  And I assume that most parents can figure out (with some help from the HIve!) where their child fits on the math spectrum.  I have a late bloomer.  I did not push math with her.  And when she was ready, it clicked and she took off like a rabbit.  This only happened this last year.  But we still did math from K to 8th grade.  We did games and ran her quickbreads business and did some Khan academy at a slower pace that suited her.  All that less intensive math work from K to 8th grade gave her the vocabulary and concepts so that when she was ready she had the foundation so that she could rabbit ahead.  If she hadn't had that, I suppose that she could have built it up, but we would have been wasting time building up what could have been already there waiting for her to bloom. 

 

And honestly, I wasn't 100% sure if she would bloom.  LDs were a possibility.  Though I have a special ed. degree and had a gut feeling from working with her that it was a late blooming thing and not an LD thing.  Plus, I knew that she had my genes and I was a late math bloomer.  If she hadn't started to click with things this year then I would have continued working with her at her level but I would have stepped up the therapeutic ways of working with her instead of letting her lead the pace. 

Edited April 22, 2017 by Jean in Newcastle

[Guest]

Possiblity #1: Teach the child math systematically from Kindergarten. If the child is math-intuitive, motivated or gifted, he might start resenting math because the early years of arithmetics and "math facts" can be absolutely soul sucking, especially to gifted children. If the child is not intuitive, motivated or gifted, he might resent math even more and might start feeling like he "can't do math."

 

Possibility #2": Don't teach the child systematically from Kindergarten. If the child is math intuitive, motivated or gifted he'll be picking up math anyway, he has a chance to grow up loving math when he is ready to study it beyond arithmetics. Meanwhile, the child might have enjoyed other things and developed other passions without being burdened by "math facts" and mindless worksheets. If the child is not motivated, intuitive or gifted, he still has an opportunity to grow up without hating math and his confidence intact--which is one of the biggest precursors to being successful in math later on.

 

Obviously, in my opinion there's much to lose in teaching a child who is not intersted or not ready too early.

 

I do agree that there are risks involved in both approaches. Some are easier to digest than others, especially in our culture of achievement. Different people take different risks.

I actually think the danger of being bored and resentful when you are good at something is incredibly small, much less if you're good at something and have the freedom of homeschooling as well. People generally enjoy doing things they are good at. Sure, if your child could skip pages and pages of review because - got it, let's move on - then it would be idiotic to keep passing them pages in some uptight attempt to fill out every paper. But working with a systematic curriculum is not automatically boring or resentment-inducing to bright, intelligent children. It gives them exactly what they desire - knowledge.

 

Take a parallel - playing a musical instrument. One of my children loved instruments from a very early age. I gave this child many opportunities to explore music non-didactically. BUT! There are systematic things to learn in music as well. It's not ALL just diddling around and playing what sounds pleasing. People don't master musical instruments that way. So there were also years and years of didactic lessons and that included years and years and years of intentional, daily practice. Sometimes it was difficult. Sometimes the kid was sick of playing piano. But that's part of learning discipline - you keep going. The child plays beautifully now.

 

I have never heard of a master musician who did not learn the didactic part of music theory, who only just played what they could pick up and became a master at it. Never heard of an accomplished musician who just dabbled at an instrument once in a while when the mood struck. A musically intuitive person does not become bored and resentful when someone teaches them the staff and what all those circles mean and why it says "largo" or "allegro" at the top of the piece. All that info is just a key that unlocks greater mastery and thus, greater joy in the instrument.

 

See, I think this whole "gifted kid is bored with didactic teaching" is a myth. Gifted children love to learn. They are hungry for knowledge and thrilled when they can obtain more of it in their area(s) of interest. What a gifted kid doesn't want to do is sit in a room with 20 other kids who are being taught something they already know. But homeschooling has the advantage of not having to be that way at all, but not because the solution is that they shouldn't be instructed on purpose at all. Just that you don't dwell on 2+2 when they have already mastered that and are ready to explore 4-x=2.

[Bluegoat]

RU involves unparenting.

 

I'd say that distinguishes it quite a lot from the unschoolers busy strewing info on the rock cycle and great composers and math games, while at the same time, reserving the right to tell your kid to brush their teeth.

 

I suspect they wouldn't like me suggesting that. 

[Arcadia]

It's the "Sandra Dodd" unschooling that I am frankly opposed to. I think it's a terrible idea, risks something that isn't the parent's to gamble (their child's future options), and makes a lot of excuses for its shortcomings.

I am not familiar with Sandra Dodd nor this lady that I am linking but I guess they are similar in the type of unschooling?

 

http://www.giftedunschooling.com/coming-of-age/

 

My strengths aren't my passions and can feel more like a burden sometimes. So yes, it is possible for a person to have no joy in doing what a person is good at.

 

I suspect they wouldn't like me suggesting that.

 

It is a parental right and duty to nag kids to brush their teeth according to my kids' pediatricians and dentists. It can take me an hour (ETA: of nagging my kids) some nights :P Edited April 22, 2017 by Arcadia

[luuknam]

I am not familiar with Sandra Dodd nor this lady that I am linking but I guess they are similar in the type of unschooling?

 

http://www.giftedunschooling.com/coming-of-age/

 

 

I didn't finish reading the entire thing, but yes. RU of the type where if a young child chooses to run in front of a bus they should have the right to do so, because they'll learn from natural consequences and it isn't right for anyone, even a parent, to control another human being.

 

ETA: I should probably clarify that I haven't seen SD say that literally, but I have seen her make similar-ish statements about very young kids' rights to refuse medical treatments for potentially lethal conditions. Now, in all fairness, it's been about 10 years since I was on her email list, so I have no idea what her current views are.

Edited April 22, 2017 by luuknam