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Tell me why I'm wrong about math


Lilikoi
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I heard a conversation on NPR yesterday that seems relevant. The host was talking to a child psychologist and author, who has just written a book on the science of parenting, I think called "The Gardener or The Carpenter," or something like that. They were discussing the trend of parents trying to "build" a certain type of child, as if the parent is a carpenter, who, if they can just get the plans right, they will achieve the desired result. The other type of parenting, being "The Gardener," was more about creating a rich, nurturing environment, in which a variety of results could occur, depending on the child. The auther discussed some of the science regarding how young child learn.

 

One study at her clinic involved giving a child a toy with many different ways to use it. In one scenario, the child was given the toy, with no instructions, and then the child was left alone with it. In another scenario, the child was given instructions on one way to play with the toy, and then left alone with it. Observers saw that with no instructions, children played with the toy in a wide variety of ways, and those children who were given instructions only played with it in the way they were instructed.

 

Last week, my daughter's science class just did the "spaghetti/marshmallow tower challenge," where small groups of students were given dried spaghetti, tape, string, and a marshmallow, and then told to build the tallest tower they could build in 30 minutes, using just those materials, and placing the marshmallow at the top. Historically, the type of student who does the best on this challenge is a kindergartener, basically because they have limited preconceptions, and they are very hands-on in their model-making. The are more likely to create a variety of prototypes, and develop a successful building method. The type of student who does worst at this challenge is a graduate business school student.

 

Anyway, my point is, I think you are wrong in your plan to pick a fixed curriculum and follow it. Work with the child in front of you. Play, question, discuss, explore. If you have just 30 minutes a day to devote to math, spend 10 minutes doing something interesting together, then you can take 10 minutes to assess where she is, and to pull out a relevant math assignment, and she can spend the final 10 minutes on whatever assignment you came up with. A standard math curriculum is not always a good fit, and a fast learner will have you scrambling to rework the curriculum plans all the time anyway.

 

So unless your plan is to teach her, at 5, that math is all about being focused on the goal, until she gets through calculus, I hope you will be open to less efficient options. It sounds like you and your spouse are capable of embarking on a great math journey with your child, given your backgrounds. Bon voyage!

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When Sacha and I are using BA (and our brains are melting), our mantra is "This is the Art of Problem Solving, not The Art of Calculating!"

 

But, there is just something so satisfying in the brain melting that BA induces. It really feels like an accomplishment to us if we can figure out the starred problems -- high fives, ice cream for lunch, and all. There was never any such feeling with MM, Khan Academy, etc. for us.  

 

 

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When Sacha and I are using BA (and our brains are melting), our mantra is "This is the Art of Problem Solving, not The Art of Calculating!"

 

But, there is just something so satisfying in the brain melting that BA induces. It really feels like an accomplishment to us if we can figure out the starred problems -- high fives, ice cream for lunch, and all. There was never any such feeling with MM, Khan Academy, etc. for us.  

 

Yes! Exactly! Spot on! Feels so good to crack a problem like that. But I think it's also fine to not be able to solve the problem at 5yo or even at 8yo. It is really the willingness to try. To actually know that you are going to do something hard without having all the tools necessary. Having faith that it's going to be fine. Moving forward.

 

My son only used AoPS sporadically for geometry after using Jurgensen so this wasn't with AoPS but Jurgensen had some pretty challenging problems in it too. His tutor assigned a problem that took my son more than 3 months to solve. He was 9 years old. It was very frustrating. And then the light dawned slowly. So very slowly but wow, the look on his face when he finally solved it. We celebrated at every little milestone, lots of positive,  reinforcing words and of course, ice cream. The tutor didn't help other than to just keep encouraging him. They didn't stop at that problem either. They moved on but son kept working on it in the background. And when he did, the tutor said something very, very sweet. He said, you are now a mathematician. That made my son's day. The entire effort felt so worth it. I didn't even have to reward him with ice cream kwim?

 

Think of all the skills in the process of solving that problem:

  1. Going into a difficult situation
  2. Applying what he had learned before
  3. Realizing that mistakes make him stronger
  4. Schooling himself to be patient
  5. Trying different approaches
  6. Being okay with leaving it aside for a while and moving on (it helped with perfectionism!)
  7. Learning how to ask for help
  8. Learning that sometimes the adults you live with cannot help you so you need to find other ways
  9. Realizing that you have something left unfinished and that you are going to grow by going back and trying to work at it again
  10. Writing proofs over and over only to discover you were on the wrong track (this was a child who hated putting pencil to paper and he wasn't willing to type proofs at that time either). Being okay with all that writing not being used. But also learning to write better proofs as a result!

Fast forward 4-5 years...he is doing the same but with harder research problems through AoPS Crowd Math. There are things he hasn't solved for more than 3 months now but no tears or frustration because it's really enjoyable work for him. He is also collaborating with other students/ college students and learning from them too. It's such a creative, collaborative endeavor.

 

Maybe OP's DD is not going to be interested in becoming a mathematician but the approach is applicable in any area.

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Echoing previous comments: the toolbox should come second - not first.

 

A child is intrinsically logical and capable of extraordinary abstraction. No need to force it, but you can teach theory of arithmetic or set theory even now, as long as you eliminate all formality or expectations.

 

If she enjoys small problem sets, then just stay content with that for now. Prize the "fun," and forget about the depth until she asks for more. She will, when she is ready.

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Think of all the skills in the process of solving that problem:

  1. Going into a difficult situation
  2. Applying what he had learned before
  3. Realizing that mistakes make him stronger
  4. Schooling himself to be patient
  5. Trying different approaches
  6. Being okay with leaving it aside for a while and moving on (it helped with perfectionism!)
  7. Learning how to ask for help
  8. Learning that sometimes the adults you live with cannot help you so you need to find other ways
  9. Realizing that you have something left unfinished and that you are going to grow by going back and trying to work at it again
  10. Writing proofs over and over only to discover you were on the wrong track (this was a child who hated putting pencil to paper and he wasn't willing to type proofs at that time either). Being okay with all that writing not being used. But also learning to write better proofs as a result!

 

Maybe OP's DD is not going to be interested in becoming a mathematician but the approach is applicable in any area.

 

:iagree:

(1) to (9) works very well for music and sports too (other than rackets, clubs and music bows comes a flying from my kids, much milder than John McEnroe's tantrums on the tennis courts).

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I'd go with MM. 

 

Might get flamed, but I really don't see what is so special about BA other than it's fun and great for peaking interest (which of course is not nothing).  I think it actually doesn't do the best job teaching all the topics though, and I too found myself having to add in more explanation than what was offered.  Also, some of the topics covered I found to be rather random and odd (I didn't use all levels though).   I wouldn't consider using it as a stand alone, but that is just me.  I am sure some people do great with it as a standalone. 

 

 

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I'd go with MM.

 

Might get flamed, but I really don't see what is so special about BA other than it's fun and great for peaking interest (which of course is not nothing). I think it actually doesn't do the best job teaching all the topics though, and I too found myself having to add in more explanation than what was offered. Also, some of the topics covered I found to be rather random and odd (I didn't use all levels though). I wouldn't consider using it as a stand alone, but that is just me. I am sure some people do great with it as a standalone.

We don't either - I love it as a supplement just as I love logic puzzles of varying types, for thinking and problem solving. But I really like a nice mix of algorithm and critical thinking for my NT but highly capable kiddos. They're not even HG, I don't think, but they are bright and love thinking. So we just try to match tools to problems for the age they're at. And we got a LOT more mileage out of concept-heavy, manipulative heavy programs at that young age than anything that involved straight number crunching. We don't really start that until they're 7-8-ish and that's as early as I'd dare.

 

Play and fun and thinking are fundamental to success with these little kids. Print out some of these awesome posts and memorize them - they're bang on.

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I don't think any of my kids would have been able to spend 30 minutes on math at a high level every day. They all love math. They're all good at math. But 30 minutes... not at age 5. My 4th grader's math limit is about 30 minutes. :)

 

My oldest wasn't homeschooled until the middle of first grade, but prior to starting school, we did zero math curriculum. We just talked about math in daily life. He would play with numbers while we drove in the van. The stuff he came up with at 4 and 5 years old just blew my mind. Then he started school (where they used Saxon K in K - b-o-r-i-n-g), and his fun math discussions started to wain. I did let him accelerate when I pulled him from school, but at the same time I've learned as my younger children came along that it's good to relax a bit in the early elementary years. Absolutely go sideways. It sounds like she isn't ready for BA3. That's totally ok. My second son did most of 3A in 1st grade and got stuck when they started playing with squares. He just wasn't ready for that level of thinking yet. So we set it aside and did something else. I haven't even brought it out for my 2nd grader yet.

 

What I would do with a 5 year old like yours... Spend time playing logic/strategy games, talk about math in daily life. Read good math literature that gives her math to think about. Play with math. Let math come up on a whim. For example, the day that my oldest said, "You can't do 2-5." I said, "Yes, you can" and I pulled out a napkin and showed him negative numbers. I never had him do ANY worksheets on negative numbers. I never drilled him on negative numbers. I didn't give him any math curriculum using negative numbers. When he got to negative numbers in 4th grade math (when he was in 2nd grade), he remembered how to add and subtract negative numbers. He had played with them from the age of 5, and that stuck with him.

 

I know what it's like to want to get further ahead with the first kid. BTDT. I'll bet many of us have. :) Thankfully, we have all these wise people here to learn from. I don't see any benefit at all to a 5 year old doing MM4, and I think it would be a quick route to burnout. 5 year olds are still babies. I know they look like big kids when they're your oldest, but they really are still babies. Two years from now, you'll likely have a different child, and she may be more ready to accelerate. But for now, I'd say just play with math. Keep it fun. Keep it relaxed.

 

My 3rd child was an early reader and really is precocious across the board (even had beautiful cursive handwriting in 1st grade! something my other boys absolutely did NOT have :lol:). Since he was reading so well and reading independently, I didn't do any "reading" curriculum with him the last couple years. This year he's doing a language arts class that uses literature to teach grammar, handwriting, spelling, everything, so he's reading for that, but I didn't even do a phonics course with him. He had already picked up phonics naturally and was a good speller, so why bore him with a phonics curriculum? I don't at all regret "skipping" subjects with him that weren't needed at a younger age. He was an eager student (being the youngest during that time), but I limited what we did and focused more on read alouds with him. I started him in K math at 4 on a when he asked basis - 10 minutes a day, if he wanted to do it (he usually did). In K we did a grade 1 lesson each day. Now he's going through a grade 3 book in grade 2. So he's not radically accelerated in the least. He's good at math, he enjoys math. He can solve the tricky Singapore word problems and do the mental math. Could he have gone faster through the curriculum? You bet! He could probably easily be 3 grade levels ahead right now. But he wasn't pushing for that. And in fact, when he was 5, he didn't like a lot of challenge. I've noticed that my kids can't really handle real challenge until 7 or 8, and when they get to that point, they start asking for challenge and really enjoying it. That's when I ramp things up. At 5? Nope. They want easy. Not challenging my oldest at 5 didn't hurt him any. Last week, he was spending an hour a day on Alcumus (Art of Problem solving online game), trying to do the missions... after he already had done a problem set in AoPS Intro to Algebra. I never told him he needed to do Alcumus. I just let him know it was available. Now he likes to challenge himself with it. He enjoys math and still likes to play with math. :)

 

Two engineering parents here who love math and believe it's very important (and fun!). I don't push a 5 year old to accelerate drastically. If they already know K/1/2 math at that age, I focus more on things they don't know (like reading) or I spend the time reading aloud good quality books. I liked the idea above of starting with CWP 1 and doing 3 problems a day. Make that math for the year. Or do MEP year 2, maybe even only doing half a lesson a day. If you want to spend a whole 30 minutes, make it MOSTLY logic/strategy games, online math games, or math oriented literature.

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I don't push a 5 year old to accelerate drastically. If they already know K/1/2 math at that age, I focus more on things they don't know (like reading)

 

That was what I was thinking too. I don't see a point in accelerating a kid 4 grades in math to develop character or w/e if the other subjects aren't also 4 grades ahead. If a kid is begging to learn long division etc, then I would indulge her, but not for character purposes.

 

The other thing is that just because you and your husband are STEM people doesn't mean your kid will be a STEM person too. It probably increases the odds, but it's far from a guarantee. Which is another reason why I mentioned adding other subjects rather than accelerating more math for a kid who isn't begging for more math.

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I know what it's like to want to get further ahead with the first kid. BTDT. I'll bet many of us have. :) Thankfully, we have all these wise people here to learn from. I don't see any benefit at all to a 5 year old doing MM4, and I think it would be a quick route to burnout. 5 year olds are still babies. I know they look like big kids when they're your oldest, but they really are still babies. Two years from now, you'll likely have a different child, and she may be more ready to accelerate. But for now, I'd say just play with math. Keep it fun. Keep it relaxed.

 

Oy vey is this true! I am still torturing my oldest because....well, he is the oldest. :lol: He just seems so old to me. And then I look back on pics of him from a few years ago (when he seemed so old to me at the time), and I think, gosh, he was just a baby! Ah, to be the first born! Poor Sacha!

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  • 5 weeks later...

As for BA, a friend kindly gave me a BA 3D workbook spare she had. My kids did the pages they like for fun. For a five year old, maybe just let her use the BA workbooks as fun puzzle books that can be completed later. So she can do those she is able to and shelve the rest for later.

 

While my DS10 is not weak in algebra, it was the geometry topics that gave him joy.

 

The Oliver Byrne version of Euclid Elements is something a young child can peruse and enjoy as a fun read. Link below

https://archive.org/details/firstsixbooksofe00byrn

 

We use Lego as math, physics and genetics/DNA manipulatives.

 

 

MEP is a lot more customizable in terms of topics and levels than SM :)

I had download all of MEP pdfs and just let my kids pick what MEP pdf they like on their ipad to do for hotel entertainment. It is very portable and my kids enlarge the page on their iPads so it is easier for them to read when they were much younger. Sure beats bringing SM books on a road trip.

 

This is genius.  Robby is going to flip!

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