And 'Rithmetic: 6 years in 20 weeks

[Hunter]

What do you all think of this article? I'm not saying anything until I hear what some of YOU have to say :lol:

http://www.scribd.com/mobile/doc/14389275

[Spy Car]

What do you all think of this article? I'm not saying anything until I hear what some of YOU have to say :lol:

http://www.scribd.com/mobile/doc/14389275

I think it is a huge load of bull that may just help some people attempt to rationalize educational neglect.

 

Bill

[forty-two]

The link isn't working for me, but, assuming it is the Sudbury school article, I read it a while ago, so here are some random thoughts of mine:

 

I'm sympathetic to the basic idea that motivated learners can learn waaaaaaaay faster than unmotivated ones. I'm also sympathetic to the idea, promoted by John Holt and pretty core to unschooling, that students learn waaaaaaaaay better when they haven't been socialized into seeing school subjects as unconnected to "real life", and so give up on the idea that school learning ought to make any sort of "normal" sense, end up effectively trained out of using their normal real-life intuition in their school work, because they were explicitly or implicitly taught to follow the teacher's method whether it made sense to them or not. (And I've learned how *easy* it is, even as a person who really values understanding, to be tempted to say, "it just *is*", after the twelfth clarifying question. And that is one on one, with a flexible schedule.)

 

The biggest issue that occurred to me as I read the article was the question of how many prerequisite skills had to be in place for the formal learning to proceed so efficiently. In addition to plenty of number sense and math intuition (developed how? through what sorts of self-directed activities?), this was a bunch of highly motivated and curious students, very self-starting, with plenty of grit and perserverence - all of the character strengths promoted in How Children Succeed, in fact. Unschoolers seem to expect math intuition and those character strengths to flower automatically if not stifled, but what if they don't?

 

The idea is intriguing to me, but I see it as much like "one day potty training" - sure, with all the prereqs in place I have no doubt the actual formal learning goes very well. But it's a formidable number of non-trivial prereq's, and unlike the potty-training book, which at least spelled them all out explicitly, the article takes them all for granted as naturally flowing from the unschooling process. Which is great when it works, but gives you zero help for proactively working on getting all the prereq's in place when the unschooling process falters.

[GoVanGogh]

It isn't an avenue I would take with my own child, but I have a somewhat similar math background.

I grew up in a dysfunctional family, passed around between extended family and, unfortunately, passed through the school system with failing grades. I worked full-time in high school to put a roof over my head, often skipping school. The only school official that ever inquired about my home life and failing grades was the school nurse, who housed me for a week when I was 16. I graduated from high school dead-last.

As a young, married adult, I decided to attend college. I started at a community college, and failed the math portion of their entrance exam. I was placed in their self-paced math/tutoring center. I was able to take four semesters of remedial math in one semester.

I do agree with what PP said about intuition, grit, determination - and having prerequisite skills in place. I probably had a good math foundation from real life experience.

From that, I would agree that it is possible. Ideal? No.

[regentrude]

This, or something like this, gets quoted every year or so. So, I write my opinion every year or so, and it is still the same (if I could only find my previous post and save the typing)

 

My main issue with the approach:

The time may be sufficient to introduce older students to the procedures, but is not sufficient to create enough practice so that the math becomes automatic, which would be necessary for progressing to higher math. The years spent on arithmetic are not wasted; through time on task students develop the familiarity with numbers that enables them to see relationships easily. In 20 weeks, I can teach the procedures; I will not familiarize my students with numbers to the degree that they "see" prime numbers, factors, perfect squares, cube roots, cancellations, simplifications - this comes from knowing numbers, from having worked with them over time, not from having been explained an operation.

I marvel how people, who readily accept that playing an instrument is a skill that requires practice, will consider math something that does not. If somebody claimed a music student could learn in 20 lessons what other students normally learned in 6 years, it would be seen as preposterous.

 

ETA: I have heard the rationale "if they need it and want to learn it, they will learn it quickly" over and over - and I have never seen it work with math. I teach at a STEM university, and my students are all science and engineering majors, so clearly people who need math and want to be in their field- so they should be able to learn it. But fact is, most who have gaps in their math education from their school days are incapable of remedying these gaps that hinder them from succeeding in their other classes. They can't do it. Because they are lacking the "time on task" of several years.

(Nor have I seen it with music. Even a motivated adult beginner will not catch up in skill level with a violinist who trained since age 4 and has spent hundreds and thousands of hours in time on task.)

 

[Arcadia]

:

The time may be sufficient to introduce older students to the procedures, but is not sufficient to create enough practice so that the math becomes automatic, which would be necessary for progressing to higher math.

From the article, it seems that for this particular group, the math did become automatic.

"It was a math primer written in 1898.Small and thick, it was brimming with thousands of exercises, meant to train young minds to perform the basic tasks accurately and swiftly.

.......

 Hundreds and hundreds of exercises, class quizzes, oral tests, pounded the material into their heads"

[regentrude]

From the article, it seems that for this particular group, the math did become automatic.

"It was a math primer written in 1898.Small and thick, it was brimming with thousands of exercises, meant to train young minds to perform the basic tasks accurately and swiftly.

.......

 Hundreds and hundreds of exercises, class quizzes, oral tests, pounded the material into their heads"

 

It says the worked the drill book. It did not say anything about the long term results.

The brain needs time to let concepts settle. I am skeptical that cramming all the exercises into a short span of time will create the same sustainable effect as steady work over years with times for the brain to process.

It would be interesting to see if they had perfect recall of their math twenty years later, and if they had been able to apply the math they learned in higher math and science courses.

[Cosmos]

Why on earth do the students have to beg to learn arithmetic? And why does the teacher discourage them? What on earth?

 

I am familiar with Sudbury, but, but . . . I can't get my head around that.

[Hunter]

I think it is a huge load of bull that may just help some people attempt to rationalize educational neglect.

 

Bill

Why on earth do the students have to beg to learn arithmetic? And why does the teacher discourage them? What on earth?

 

I am familiar with Sudbury, but, but . . . I can't get my head around that.

:lol: I knew this thread would be fun.

 

What I was thinking when reading this article, was what if a student were doing math for several hours a week, but mom was disorganized, and using bits gathered from here and there? GASP! Department store workbooks. Worse yet, department store workbooks picked up at a yard sale and missing pages. With...even...Twinkie cream smeared on the pages (that one is for you Bill :lol: )! And a some living math books from the library that got read in no proper order. And the kid cooked with mom and figured tips at the restaurant, and all that stuff that makes non unschoolers gag when they hear it. A few expensive card games that collected dust more than got played, but the real board games like Monopoly did get played.

 

Then at say the 7th grade, mom picked up a remedial college Basic math text from the same yard sale (this one has beer spilled on it :lol:) and worked through it with the child, for a full 36 weeks, closing any gaps, and then tackled Algebra right after that, so the student didn't take a break from math afterwards?

 

Is DISORGANIZED but STEADY work before 6th grade so bad, if followed up by an intensive and explicit and organized 6th or 7th or 8th grade course?

[Hunter]

This, or something like this, gets quoted every year or so. So, I write my opinion every year or so, and it is still the same (if I could only find my previous post and save the typing)

 

 

Sorry, Regentrude :lol: But it's just so much fun!

[Mergath]

It looks like the article was written five years ago.  I would love to know just how much of the arithmetic that was so unceremoniously crammed into their heads is still there today. (I'm guessing not a heck of a lot.)  They might be able to understand the basic principles after twenty weeks, but I doubt they'll retain much of it.  To each his own, though. 

[Hunter]

Why on earth do the students have to beg to learn arithmetic? And why does the teacher discourage them? What on earth?

 

I am familiar with Sudbury, but, but . . . I can't get my head around that.

I don't know about Sudbury, but I pulled something similar with my oldest. He wanted to read a Charles Dickens book for "school" and I Insisted on nonfiction and Bible only. I told him I would consider it if he could write me a persuasive essay convincing me of the educational merits of fiction. He did that and got his uncle to harrass me, and got his cousins and aunts involved. I was attacked at the family holiday meal, while just my father in law and I laughed. When everyone ran out of steam, I just asked my son why he didn't just read the book on his own time if it was so all fired wonderful. He looked at me, and said, "FINE! I will!" And he did. :lol: So DS ended out reading the nonfiction AND Dickens AND read the Dickens book with more interest.

 

NOTE: This was in the 90s and I have mellowed. DS is happily married and self-supporting and seems to have survived the incident fairly unscathed.

[forty-two]

Is DISORGANIZED but STEADY work before 6th grade so bad, if followed up by an intensive and explicit and organized 6th or 7th or 8th grade course?

That scenario sounds like it would have more in common with Benezet's experiment than the Sudbury class - intentional but mostly informal math prep, instead of self-directed activities providing the "math prep". Though Benezet spread the formal arithmetic teaching over 2-3 years instead of one.

[Mergath]

Is DISORGANIZED but STEADY work before 6th grade so bad, if followed up by an intensive and explicit and organized 6th or 7th or 8th grade course?

 

Bad?  No.  But not nearly as effective as systematic and structured learning over time, starting in the earlier years.  (I'll forgo sharing my opinion on how early that should be. ;) )  I've done quite a bit of intensive learning over the last fifteen years, but the things in which I hadn't gotten a solid foundation in elementary school never did stick.  Especially when it came to math.  I have to keep learning them over and over again.  

[dbmamaz]

This was a self-selected group of students who were highly motivated.  Its not like EVERY student who went through the school did this.  

 

However, I do believe that most kids can do light, living math for most of elementary and still master the basics of arithmetic.  

 

OTOH, i have heard of kids who were unschooled and decided they could not major in science in college because they didnt know the math.  

 

I do think you need a combination of motivated kids and competent teachers (note, any adult who understands math is imo a competent teacher)

[Monica_in_Switzerland]

I don't think the take-away message from this article is that math can be delayed for years and then "caught up" in a few hours.  I think the take-away is that motivated children learn faster than unmotivated ones. 

 

The goal then, would not be to put off math until a child suddenly says, "Oh gee, I sure with I could find the slope of this curve at point X!".  The goal would be to make math meaningful to a child so that he has an internal motivation to continue. 

[Haiku]

I think the author's smug attitude undermines whatever message he was trying to get across, and for the most part I think his article is hooey.

[Dmmetler]

I imagine retention depended on what happened next. Since the kids were still elementary ages, I'm not sure you can say that they're late-especially not the younger ones. If they continued into a solid pre-algebra program in middle school, I could see them being just fine in high school math and science.

 

I also imagine that if they did this 20 week class and then went back to not formally doing math and practicing it, they lost it quickly.

 

To make the music analogy, it's true that someone who starts later is not going to catch up to an early starter who practices consistently and continues studying. But I've seen a lot of early start, talented kids begin high school orchestra in a high chair, because they're light years ahead of the kids who started in 6th grade-but that by 12th grade, the first chair player may well be someone who started in 6th grade and who's instrument went home every day for additional practice, while the early starter left theirs in their orchestra locker and only played in the group rehersals.  And many music majors reached their peak in college or grad school-in most cases, even a full-time music job isn't going to have you playing at the level you need to grow from that point, and often, you end up spending most of your time at lower levels, and it's very, very easy to lose those hard won upper level skills when you don't have time to practice them or need to use them. If your full-time job isn't music, it's even harder to keep those skills up.

 

[LucyStoner]

I think it is a huge load of bull that may just help some people attempt to rationalize educational neglect.

 

Bill

What he said.

 

Can you learn arithmetic in a condensed way? Yes. Can you gain the sort of math fluency and comfort needed for many educational and career paths by shoving 6 years into a 1/2 school year? Hells no.

[In The Great White North]

The most interesting part of the article would have been which 1898 arithmetic text he used - but they didn't give that.

[Hunter]

The most interesting part of the article would have been which 1898 arithmetic text he used - but they didn't give that.

I was wondering the same thing! I don't think it really matters which one, though. The turn of the 20th century texts are pretty similar.

[SorrelZG]

I was wondering the same thing! I don't think it really matters which one, though. The turn of the 20th century texts are pretty similar.

Baird's, for example, has only 100 brief lessons per year up as far as I've specifically checked and many of them are review. It may not always apparent that there are specific teaching methods behind these books, though, and I am not so sure the book itself is key so much as the method of teaching it is intended to guide (not that they're complicated).

[kiana]

And what happened to the students who did not want to join the arithmetic class?

[shinyhappypeople]

I see value in any approach that turns what we think we know about education on its head. 

[swellmomma]

I think for some students it is completely plausible but not for all students.  I know of a homeschooler that unschooled until high school.  She never had formal math instruction until age 12 when she decided she wanted to start with saxon's algebra 1/2.  She covered all basic math in less than a month and then jumped into that book and did just fine and continued with the series through high school never missing a beat.  My own dd14 just outright refused to math for the last several years, so she stalled out after MUS gamma and did nothing.  Since september she has done 3/4 of Delta and will finish by the end of November I am sure.  Then onto Epsilon and Zeta, bringing her to the end of elementary math.  No it is not 20 weeks only based on her current speed and progress I would say closer to 30 weeks BUT if I opted not to have her work through a curriculum and just taught the concepts we could finish much sooner but since I don't trust my own math background I opt to go this route.  Basically she is spending about 10 weeks per level.  So yes I think it is totally possible for intelligent, motivated learners with a teacher strong in math to cover all the basics of elementary math in 20 weeks.

[WishboneDawn]

I think it is a huge load of bull that may just help some people attempt to rationalize educational neglect.

 

Bill

It's a Sudbury school so it's pretty far from educational neglect.

 

These children likely come from fairly well off and well educated families with a rich home life. Their school is most likely filed with resources and opportunities most public schools can't offer.

 

This is NOT a story of educationally neglected children who, given some intense work and a caring teacher managed to tackle tough concepts in a few weeks.

 

This is a story of already bright and enriched kids who've likely had years of informal math experience in and out of the school and are simply formalizing and extending knowledge they already have. This is all arithmetic. It's not calculus. For those who haven't been neglected its pretty natural stuff that they've been dealing with for years.

 

I did much the same with my daughter and it worked well.

 

The article should not be used as any kind of guide for those looking at kids who HAVE been neglected. I have a feeling it wouldn't go as smoothly. It should also not be seen as evidence that introducing formal math earlier isn't a valuable approach. It's an anecdote about a success, that's all.

[WishboneDawn]

I should note that I tried the same approach with my middle son and it was not a success. We're now working through Liping Ma's Knowing Mathematics Intervention program and after that well be moving to the math program I think he now should have had all along, the dreaded Saxon. My little Singapore heart is breaking.

 

Anyhow, the article isn't hooey. But it's not a magical cure-all either.

[mama27]

I didn't read the article but I have read similar ones and I do think it would be possible to learn all of arithmetic in less than 6 years. I had a very hard time understanding math as a child but as an adult it makes more sense. Mental maturity had a lot to do with it, seeing how it's useful helped.

I'm only speaking of arithmetic, not algebra and higher, obviously.

 

[mama27]

Yeah and take older math books.  I wonder if they cover fewer topics.  I look at the books I have and I find myself either skipping some of the chapters or condensing them significantly because it just doesn't take that much time and practice to go over the concepts.  For example, SM and MIF spend time on telling time.  Neither of my kids needed that.  I skipped it.  They spend a long time on shapes, but in the beginning it is so basic that it's hard to imagine a kid not having encountered a triangle or square.   Five minutes.  Then entire chapters are spent on reading graphs, but the absolute most elementary graphs that you would probably never see anywhere.  That takes five minutes to explain, and not pages and pages of practice.  Then there are some weird chapters on stuff like tessellations and drawing shapes with dots.  After a page of that my kids both had enough.  

This is why I have never really used one math curric exclusively for my elementary kids. Too much silly stuff.