Facebook nonsense

[Not_a_Number]

Just now, lewelma said:

I will have to argue with you a little bit.  Younger ds really struggles with mathematical science which has to do with his dysgraphia -- encoding ideas into math is still quite difficult. We spent the entire year doing organic chemistry to build up his science skills and stall for another year on putting the math overlay in.  You can do a LOT of organic chemistry without needing math.

OK. I'll rephrase that to "you can't have most STEM careers without knowing math." 

Can you give me an example of something that would be encoding ideas into math that's hard for him? 

[lewelma]

7 minutes ago, Not_a_Number said:

encoding ideas into math that's hard for him? 

We did mechanics last year and it was a disaster. He cannot understand basic Newtonian formulas because they don't mesh with his intuition.  He can plug and chug just fine, but the simplicity of the model won't work with his brain. So it became just a memorizing thing which was clearly a waste of time for physics. Sure he could have gotten a good grade, but I am actually after learning, and no learning was happening. He also really struggled with molarity calculations for titration last year. He is fine with chemical equations and ratios, but dealing with molar ratios is a problem. The wording of the questions is also hard for him to translate into action for things like equilibrium in aqueous solutions. He has the same problem with probability word problems. And these are not small problems, these are big problems.  It is the way his brain works, which is why I chose a science that he could succeed at that was still incredibly complicated.  Success breeds success. So I would rather abandon something that is just not going to work, and instead build confidence in science.

Edited January 4, 2021 by lewelma

[Not_a_Number]

1 minute ago, lewelma said:

We did mechanics last year and it was a disaster. He cannot understand basic Newtonian formulas because they don't mesh with his intuition.  He can plug and chug just fine, but the simplicity of the model won't work with his brain. So it became just a memorizing thing which was clearly a waste of time for physics. Sure he could have gotten a good grade, but I am actually after learning, and no learning was happening. He also really struggled with molarity calculations for titration last year. He is fine with chemical equations and ratios, but dealing with molar ratios is a problem. The wording of the questions is also hard for him to translate into action for things like equilibrium in aqueous equations. He has the same problem with probability word problems. And these are not small problems, these are big problems.  It is the way his brain works, which is why I chose a science that he could succeed at that was still incredibly complicated.  Success breeds success. So I would rather abandon something that is just not going to work, and instead build confidence in science.

Makes sense. Let me know if you ever need any brainstorming for how to get things to mesh -- I know you have plenty of practice, but we always do come at this from opposite points of view. 

(For example, I have lots of probability practice, lol.) 

[Shoeless]

29 minutes ago, wathe said:

My kids love Scratch.  But for us, it's not school; it's a free time activity.  They do learn quite a lot with it - I treat it as a species of creative play.

Scratch is a good intro to coding, IMO. We have played with it, too. You have to think logically and trouble shoot your code to get the desired outcome. I think scratch also gets into if/then statements and loops and has a debugging tool? It has been a while, so maybe I am misremembering. 

I think scratch is closer to real coding than the cute plastic caterpillar robot my nephew had, that you can "code" by changing the order of the body segments.It's fun, but... that's not coding.

 

[lewelma]

Just now, Not_a_Number said:

Makes sense. Let me know if you ever need any brainstorming for how to get things to mesh -- I know you have plenty of practice, but we always do come at this from opposite points of view. 

(For example, I have lots of probability practice, lol.) 

Thanks for the offer, and I will.  We have decided that this up coming year will be for mathematical science. We are NOT going back to mechanics because he came in with too much knowledge for the models to make any sense. So instead, we are doing Electromagnetism.  I'm hoping to show him that the equations actually make the science make more sense which was not true with high school level mechanics equations. 

As for chemistry, I am hoping that by doing a year of organic chemistry, that his brain will be better wired for equilibrium calculations. Basically, now he knows all the vocabulary and concepts and notation, so perhaps the math overlay will be easier. 

Probability is a no go. When calculations are determined by a single change in a preposition of the sentence, there is no way that he will be willing to do it. He feels it is a trick.  I can teach him how to code the language to computation, but it just makes him mad.  We will stick with statistics. But actually next year he will be doing complex numbers as we skipped that to do calculus. Complex numbers are just so beautiful that I thought that if we waiting a year that he would enjoy them more. 

[Not_a_Number]

1 minute ago, lewelma said:

Probability is a no go. When calculations are determined by a single change in a preposition of the sentence, there is no way that he will be willing to do it. He feels it is a trick.

Explain more? This is not corresponding to my experience of probability at ALL. 

 

1 minute ago, lewelma said:

We are NOT going back to mechanics because he came in with too much knowledge for the models to make any sense.

Interesting. Why don't the models make sense? Last I checked, you could do non-trivial calculations with basic high school mechanics... parabolas and whatnot, lol. 

[lewelma]

43 minutes ago, Not_a_Number said:

Interesting. Why don't the models make sense? Last I checked, you could do non-trivial calculations with basic high school mechanics... parabolas and whatnot, lol. 

No friction and wind resistance makes many of the mechanics models only approximations of actual movement that my son has witnessed. He is particularly aggravated by models pulleys and levers, which he has deep intuition on. I don't remember the details, but I am NOT going there again. Learning disabilities are no small thing.  He cannot *encode* and math is a part of that. 

[Not_a_Number]

2 minutes ago, lewelma said:

No friction and wind resistance makes many of the mechanics models only approximations of actual movement that my son has witnessed. He is particularly aggravated by models pulleys and levers, which he has deep intuition on. I don't remember the details, but I am NOT going there again. Learning disabilities are no small thing.  He cannot *encode* and math is a part of that. 

Super interesting. 

You can still calculate stuff that's not obvious, though, right? But that doesn't convince him, I take it? 

[lewelma]

49 minutes ago, Not_a_Number said:

Explain more? This is not corresponding to my experience of probability at ALL. 

Here are 3 questions from the 11th grade probability exam based on a table provided.

What proportion of days over this time were windy?

What proportion of wet days over this time were still?

Only the single underlined word changes how the question is calculated. 

OR

Find the probability that it was dry in both Ashburton and Timaru on a randomly chosen day

Find the probability that, on a randomly chosen day, only one of the tows was wet. 

If it was a dry day in Timaru, what is the probability that it was also dry in Ashburton on the same day?

This kind of word game is just not going to work for my son.  He cannot code this kind of language into calculations.

[lewelma]

4 minutes ago, Not_a_Number said:

Super interesting. 

You can still calculate stuff that's not obvious, though, right? But that doesn't convince him, I take it? 

The models will either need to make sense with his intuition or he will need to have no preconceived notions to be able to use a formula that he actually understands.  He is not able to simplify complex scientific concepts into mathematical models that approximate the truth.  I think we will have way more success with molar calculations as they are actually more real life than high school mechanics equations.

[Not_a_Number]

7 minutes ago, lewelma said:

What proportion of days over this time were windy?

What proportion of wet days over this time were still?

This kind of word game is just not going to work for my son.  He cannot code this kind of language into calculations.

Interesting. I probably don't have a good understanding of the dysgraphic brain at all, but what happens if he tries? What doesn't click? Like, say, he tries to do the second question, with the wet days. What makes him mad about it? Where would he start? 

(I hope you don't mind the questions! I'm both theoretically interested and am also curious if I've seen anything like this before and could be of help.)  

Edited January 4, 2021 by Not_a_Number

[lewelma]

Just now, Not_a_Number said:

Interesting. I probably don't have a good understanding of the dysgraphic brain at all, but what happens if he tries? What doesn't click? Like, say, he tries to do the second question, with the wet days. What makes him mad about it? Where would he start? 

(I hope you don't mind the questions! I'm both theoretically interested and am also curious if I've seen anything like this before and could be of help.)  

Well, I experience it too. I have a complete shut down when I read questions like this. It is only because I had to tutor it (integrated math) that I had to find a way through.  I code the language. I bracket off the subset, and re-read the question.  And the 12th grade work is way worse.  I actually can teach it really well because I have struggled so much with it. I have multiple full notebooks that I worked on over 2 years to try to understand the wording and to learn how to code it into probability statements.  It is really a language game.  Sometimes they will have a which clause or sometimes an adverbial clause subsetting the data.  It is only because I know grammar that I can see these things.  My ds would rather do something else with his time because it really looks like people are purposely trying to trick him with a single word difference. And he is not wrong.  The national test has to be hard enough to fail 35% of the students, so they are putting in difficult wording on purpose. 

[klmama]

2 minutes ago, lewelma said:

The national test has to be hard enough to fail 35% of the students, so they are putting in difficult wording on purpose. 

Why?  

[lewelma]

The way my brain works with this kind of thing feels very much like when I turn on my 'art brain.' In order to be able to draw something I see, I have to focus on removing the interpretation that happens automatically between my eye and my brain.  I have to see exactly the shading that is there, not that it is a flower that my brain interprets as a flower.  So when I read these types of probability questions, I have to turn off my 'reading brain' and turn on my 'probability brain.' I have to see only the words that are there and not read what my brain automatically interprets the meaning to be.  It is a skill that I have learned, but even now, I have to 'turn it on,' it is not an automatic feature.  And when I am tired or flustered I can't do it at all.

[Not_a_Number]

Just now, lewelma said:

Well, I experience it too. I have a complete shut down when I read questions like this. It is only because I had to tutor it (integrated math) that I had to find a way through.  I code the language. I bracket off the subset, and re-read the question.  And the 12th grade work is way worse.  I actually can teach it really well because I have struggled so much with it. I have multiple full notebooks that I worked on over 2 years to try to understand the wording and to learn how to code it into probability statements.  It is really a language game.  Sometimes they will have a which clause or sometimes an adverbial clause subsetting the data.  It is only because I know grammar that I can see these things.  My ds would rather do something else with his time because it really looks like people are purposely trying to trick him with a single word difference. And he is not wrong.  The national test has to be hard enough to fail 35% of the students, so they are putting in difficult wording on purpose. 

I mean, these are all really boring probability. But for these "uniform probability" questions, it's pretty much all "find the subset they are taking the probability over, then figure out what proportion of them match the condition they gave." What makes it hard? 

[Not_a_Number]

Just now, lewelma said:

I have to see only the words that are there and not read what my brain automatically interprets the meaning to be. 

So what would your brain automatically interpret the meaning to be? Say, take something like 

"Find the probability that it was dry in both Ashburton and Timaru on a randomly chosen day." 

What exactly does that say to you if you just read it? 

[lewelma]

Just now, klmama said:

Why?  

The national exams here are tough.  15% A, 20%B, 40%C, 35%F.  There is no grade inflation here.  If you are going to pass the exam, you need to have a certain level of core competency.  To pass a class, you have to pass 4 of the 6 exams.  They don't average.  So you drop your bottom two exam marks for any class. 

[lewelma]

1 minute ago, Not_a_Number said:

So what would your brain automatically interpret the meaning to be? Say, take something like 

"Find the probability that it was dry in both Ashburton and Timaru on a randomly chosen day." 

What exactly does that say to you if you just read it? 

It doesn't say anything of value because it is not standard english. To me, it says this is a question about probability and about 2 towns that are dry.  

[lewelma]

4 minutes ago, Not_a_Number said:

I mean, these are all really boring probability. But for these "uniform probability" questions, it's pretty much all "find the subset they are taking the probability over, then figure out what proportion of them match the condition they gave." What makes it hard? 

It is hard because you have to code english words and sentence structure in to math.  That is not easy.

[Not_a_Number]

Just now, lewelma said:

It doesn't say anything of value because it is not standard english. To me, it says this is a question about probability and about 2 towns that are dry.  

Would you be able to rephrase it in standard English? 

[Not_a_Number]

Just now, lewelma said:

It is hard because you have to code english words and sentence structure in to math.  That is not easy.

I really don't know. I do it all the time and prioritize it highly when I teach. I know it's not easy for kids from the start, but I have enough practice that I have a lot of mental shortcuts for it. 

[lewelma]

Just now, Not_a_Number said:

Would you be able to rephrase it in standard English? 

Nope. Because it is math coded in english language.  We then turn it around and take the english language and code it back into math.  This is not a sentence that you would find in a novel or even a science textbook. It is purposely designed to be a coded math statement. 

[Not_a_Number]

Just now, lewelma said:

Nope. Because it is math coded in english language.  We then turn it around and take the english language and code it back into math.  This is not a sentence that you would find in a novel or even a science textbook. It is purposely designed to be a coded math statement. 

Well... you can approximate it with English, though 🙂 . It does have a meaning. 

[lewelma]

1 minute ago, Not_a_Number said:

I really don't know. I do it all the time and prioritize it highly when I teach. I know it's not easy for kids from the start, but I have enough practice that I have a lot of mental shortcuts for it. 

Oh so do I, but I have worked very hard to remember how confusing it was at first.  I couldn't make heads or tails of it for a few months.  This is how my students and my younger boy feel.  

[Not_a_Number]

2 minutes ago, lewelma said:

Oh so do I, but I have worked very hard to remember how confusing it was at first.  I couldn't make heads or tails of it for a few months.  This is how my students and my younger boy feel.  

There's lots of math I remember being confused by, but math has been utterly interwoven with language for me for longer than I can remember, and that is how I teach it. So I don't remember there being a disconnect between language and math. 

The way I teach is why DD8 has been writing proofs for a year now. Of course, she's very gifted, but the fact that we explain everything linearly in words means it's all verbal and visual and interwoven for her. 

Edited January 4, 2021 by Not_a_Number

[Wheres Toto]

34 minutes ago, lewelma said:

No friction and wind resistance makes many of the mechanics models only approximations of actual movement that my son has witnessed. He is particularly aggravated by models pulleys and levers, which he has deep intuition on. I don't remember the details, but I am NOT going there again. Learning disabilities are no small thing.  He cannot *encode* and math is a part of that. 

Sounds like he wants the math to work in real-world applications and most high school/early level stuff is more theoretical and often not taking into account all the real world factors (friction, air resistance, gravity, etc.), and instead assumes things are taking place in a vacuum, etc.   I had the same problem with Physics.  

Although I did find Chemistry very logical and "real".   Stoichiometry in particular just made sense.  

[Not_a_Number]

I think probability is easiest to model with a bit of suspension of disbelief. Like, you have to believe you can actually DO the experiments. You can actually show up to check up on Timbuktu and Ashburton on some random day over and over and over again, and you can see whether it's dry or not. 

That's not where I would ever start building the mental model, that's for sure, lol. It's much easier to do suspension of disbelief of that sort with a coin or a die or a deck of cards. You really can imagine doing it for all eternity, and then you can think about what probability means and build up a model that you can describe in words and pictures. ("A model you can describe in words and pictures" is always where I start.) 

[lewelma]

Just now, Not_a_Number said:

Well... you can approximate it with English, though 🙂 . It does have a meaning. 

You asked why it is hard.  It is not actually english as english was spoken for a 1000 years.  It is actually math written with grammatical structures.  That is why it is hard.  For someone like my son who has dysgraphia, it makes no sense.  It doesn't work with the way his brain works.  He just won the national creative writing competition because of his beautiful style. He learned it through a holistic process of absorbing how language works through reading.  He can't parse it. He can't break it into tiny bits. These kinds of probability sentences are about identifying what language piece goes with what mathematical piece. He can't connect them. His brain connects things through intuition not direct linking.

[Not_a_Number]

7 minutes ago, lewelma said:

You asked why it is hard.  It is not actually english as english was spoken for a 1000 years.  It is actually math written with grammatical structures.  That is why it is hard.  For someone like my son who has dysgraphia, it makes no sense.  It doesn't work with the way his brain works.  He just won the national creative writing competition because of his beautiful style. He learned it through a holistic process of absorbing how language works through reading.  He can't parse it. He can't break it into tiny bits. These kinds of probability sentences are about identifying what language piece goes with what mathematical piece. He can't connect them. His brain connects things through intuition not direct linking.

I disagree that the way you should interact with it is by breaking it into teeny bits, that's all. I would never teach it like that. I agree that it's kind of tortured English, but it still means things. The only "math word" is probability, and that's the part I'd grapple with, in terms of making it into English. What does this "probability" thing even mean? What is it asking me for? How do I fit into my actual lived experience? 

Those are hard questions, anyway 🙂 . I think people grappled with the idea of probability (surrounding games, naturally) for a very long time. That's where there were all the crazy "get rich" schemes in which people were SURE they could figure out a way to win. That's why the Monty Hall problem breaks people's brains, including scientists' brains. 

I wouldn't teach questions like this to begin with for ages, though, because they do NOT elicit the scaffolding that make probability make any sense whatsoever. They are very confusing. The model is all broken. 

Edited January 4, 2021 by Not_a_Number

[lewelma]

7 minutes ago, Not_a_Number said:

There's lots of math I remember being confused by, but math has been utterly interwoven with language for me for longer than I can remember, and that is how I teach it. So I don't remember there being a disconnect between language and math. 

The way I teach is why DD8 has been writing proofs for a year now. Of course, she's very gifted, but the fact that we explain everything linearly in words means it's all verbal and visual and interwoven for her. 

My older boy once told me that the young boy is like the way Ramanujan was described.  Deep intuition with no structure. It has been a hill that I have been willing to die on to get him to structure his mathematical thinking. He is where he is because of 12 years of 1 on 1 tutoring for an hour a day on structuring his thoughts in mathematics.  This has brought him up to average. Learning disabilities stink. The way he perceives on math is deep and profound and without language. 

[Not_a_Number]

1 minute ago, lewelma said:

My older boy once told me that the young boy is like the way Ramanujan was described.  Deep intuition with no structure. It has been a hill that I have been willing to die on to get him to structure his mathematical thinking. He is where he is because of 12 years of 1 on 1 tutoring for an hour a day on structuring his thoughts in mathematics.  This has brought him up to average. Learning disabilities stink. The way he perceives on math is deep and profound and without language. 

What kind of structure would you want out of him, in terms of his ability to talk about mathematics? What were your goals for this for, say, arithmetic? 

[lewelma]

Just now, Not_a_Number said:

I disagree that the way you should interact with it is by breaking it into teeny bits, that's all. I would never teach it like that. I agree that it's kind of tortured English, but it still means things. The only "math word" is probability, and that's the part I'd grapple with, in terms of making it into English. What does this "probability" thing even mean? What is it asking me for? How do I fit into my experience? 

Those are hard questions, anyway 🙂 . I think people grappled with the idea of probability (surrounding games, naturally) for a very long time. That's where there were all the crazy "get rich" schemes in which people were SURE they could figure out a way to win. That's why the Monty Hall problem breaks people's brains, including scientist. 

I wouldn't teach questions like this to begin with for ages, though, because they do NOT elicit the scaffolding that make probability make any sense whatsoever. They are very confusing. The model is all broken. 

He understands probability intuitively, the kid is a brilliant mathematician like his brother. But he cannot connect the language with the math. There is an *encoding* problem which is why we will still working on being about to write The Cat in the Hat at the age of 12. It is not like the math is any different. What age could your daughter write The Cat in the Hat from dictation with lets say only 20% of the words misspelled? I can put my ds in a language rich environment, I can get him writing every day, we can work on the structure of language, I can be diligent, and yet he still can't do it after 2000 hours of work. Something simple like spelling CAT at the age of 12.  It is not that if I taught it better or used a different technique he would have had it.  It is no different with math for him. He can't do probability because it is not the way his brain works, and no amount of wishing otherwise will fix that. Sometimes it is worth focusing on what you are good at.

[lewelma]

7 minutes ago, Not_a_Number said:

What kind of structure would you want out of him, in terms of his ability to talk about mathematics? What were your goals for this for, say, arithmetic? 

Nope. My goal for him is the confidence to be able to forge his own path.  My goal is success because that leads to motivation to try when things are hard. 

[Not_a_Number]

1 minute ago, lewelma said:

He understands probability intuitively, the kid is a brilliant mathematician like his brother. But he cannot connect the language with the math. There is an *encoding* problem which is why we will still working on being about to write The Cat in the Hat at the age of 12. It is not like the math is any different. What age could your daughter write The Cat in the Hat from dictation with lets say only 20% of the words misspelled? I can put my ds in a language rich environment, I can get him writing every day, we can work on the structure of language, I can be diligent, and yet he still can't do it after 2000 hours of work. Something simple like spelling CAT at the age of 12.  It is not that if I taught it better or used a different technique he would have had it.  It is no different with math for him. He can't do probability because it is not the way his brain works, and no amount of wishing otherwise will fix that. Sometimes it is worth focusing on what you are good at.

Well, as I said, I don't understand his brain, because I'd probably need to see it to understand it. 

So what's his understanding of probability, intuitively? Where's the disconnect? Why does the question not elicit any kind of picture? Do other probability questions get understood via pictures? What's wrong with "a random day" as opposed to "a random roll of the dice"? 

 

Just now, lewelma said:

Nope. My goal for him is the confidence to be able to forge his own path.  My goal is success because that leads to motivation to try when things are hard. 

I understand, but you said you wanted him to "structure" it. Can you explain to me what that means for you? 

[Not_a_Number]

I'm having a tough time understanding the issue, because I'm not sure what makes this question about "encoding" and other math NOT about "encoding." What's the difference? How does he understand other word problems or other mathematical objects? How did you find scaffolding for his natural intuitions for other things? 

[lewelma]

29 minutes ago, Wheres Toto said:

Sounds like he wants the math to work in real-world applications and most high school/early level stuff is more theoretical and often not taking into account all the real world factors (friction, air resistance, gravity, etc.), and instead assumes things are taking place in a vacuum, etc.   I had the same problem with Physics.  

Although I did find Chemistry very logical and "real".   Stoichiometry in particular just made sense.  

Yes, he has very much loved statistics here because he has to write 15 page research papers on complex statistical data. He has written on :

The causes of Hotel occupancy rate time series data

The causes of auckland train transportation time series data

The relationship between open road efficiency, motor size, and vehicle type

The relationship between age and length in Tuatara also accounting for island and sex. 

---

These reports are way way better for him than any probability test. 

 

 

[lewelma]

6 minutes ago, Not_a_Number said:

I'm having a tough time understanding the issue, because I'm not sure what makes this question about "encoding" and other math NOT about "encoding." What's the difference? How does he understand other word problems or other mathematical objects? How did you find scaffolding for his natural intuitions for other things? 

The key is that he does not want to try.  Motivation is everything. He will fight the long fight for calculus, but those questions are much more straightforward than probability. Without the will, any effort is doomed to fail.  As I see it, there is limited time, so let's do complex numbers!

[Not_a_Number]

12 minutes ago, lewelma said:

The key is that he does not want to try.  Motivation is everything. He will fight the long fight for calculus, but those questions are much more straightforward than probability. Without the will, any effort is doomed to fail.  As I see it, there is limited time, so let's do complex numbers!

I'm not really asking about whey he's not trying to figure out how to pass the probability exam, because those questions look incredibly tedious to me, too. I'm just trying to understand the disconnect, because I'm a curious person 😉 . 

What kind of pure probability question would he be able to do? If it's dice or cards or coins, does that make sense to him? 

I feel like whenever we talk teaching, I can't get through, somehow. I think I've been very forthright about the fact that I don't know the answers for complicated kids (I'm not even sure I know the questions), but I've also taught lots of kids who ultimately didn't understand any math, and I'd like to think that some small thing from my experience may possibly be applicable. 

From my perspective, I say something like "That's not how I teach it," and then we have a conversation about how the way I teach it would never work. I mean... I really have no clue if anything I tried would or wouldn't work. I'm an inventive person, which is why I wound up teaching DD4 to read in a COMPLETELY different way than DD8. But when I try to invent things, I do try to spin off from things I know, because those are my reference points. So then I try to connect things to my reference points, and I never can, because we have a long conversation about how it would never work instead 😞 . 

Edited January 4, 2021 by Not_a_Number

[Not_a_Number]

Anyway, I'm not arguing he should learn probability. I was just trying to figure out why it didn't work, because I like probability (although not that kind of probability!).

[lewelma]

Ok, I just asked him. Sounds like he has come very very far since we did this a year ago. He now says these questions are easy!  So I am glad that I didn't push through last year and gave him a year to mature. He just said "the probability they are test here is so easy." So I asked him why he doesn't like it and he said. 

"The problem is that these questions are a combination of a word problem and not a word problem. They translate a word problem into 'word math' which then they want me to translate into math.  It would be so much better for me to translate a word problem into math directly, without this awkward step.  Here is a better question: Bob is doing a research paper as to what the probability of it raining in the summer on a day that he wants to go surfing. He can only surf on the weekends, and his two spots are Asburton and Timaru. What is the probability that it will be sunny on either or both of these two spots on the weekend? This is more what you would actually ask yourself in real life and the language makes more sense. The 'word math' of these test questions bothers me on an innate level.  It is very irritating." 

[lewelma]

37 minutes ago, Not_a_Number said:

So then I try to connect things to my reference points, and I never can, because we have a long conversation about how it would never work instead 😞 . 

Aw, sorry that I made you upset.  I really struggle to explain how I teach because I am so intuitive about it.  I adapt to what each day and each student gives me.  I also have a terrible memory, so I can't even remember the struggles I went through to get this boy structuring his math.  I have written about it in detail on the board, and I've spent the last 10 minutes looking for what I wrote as I know I liked how I explained it. But so far I can't find it. 

I also think that I am very close to this struggle of his as I have sacrificed my sanity over many years to clean up his math mess. So it feels kind of yucky to have someone suggest that if I had just done xxx, then it would have been fine. I know that it not what you mean, but it has just been oh so hard to help this boy that I don't really want to go back and relive it and wonder if I could have done better. 

[lewelma]

Found it!  That took a while! I was responding to someone asking about a kid showing 'her' work.

An event 3 years ago really impacted how I perceive of showing your mathematical workings. My younger son was struggling to write, so we took him in to get tested for dysgraphia. They worked him through a battery of tests that took 2 days and about 5 hours. I was in the room because he wanted me to be. He was 11 at the time. For the math section, the final question was something like you have 5 oranges and 8 apples costing $20, and 8 bananas and 6 oranges cost $18, and 9 applies and 3 bananas cost $21. How much does each fruit cost? (this is not the question, just something like it). I got out a piece of paper and simply coded it as three equations and three unknowns, but then realized I was going to get fractional answers.  Yuck!  Well, my ds had not started algebra certainly had never done simultaneous equations, had never seen a problem remotely like this, plus he could not write. Although he was allowed to use paper, he did not touch it. It took him 15 minutes to get the answer. He did it in his head.  To say that the examiner and I were flabbergasted, would be to undersell our response.  Neither of us could figure out how he did it. It was an amazing display of both raw intelligence and memory. When we got home, I was really curious about how he did it.  So we talked. I pulled out a piece of paper so I could actually write down what he did since he could not write, and what he explained made no sense.  Clearly, he was using ratios in some way. But we had not yet covered ratios, so he had no words to describe his intuition.  His 15 minutes of insight could not be coded into standard mathematical language. At least not by me. I was at a loss.

Because my ds could not write, he did all of his math in his head, and had for years.  I often scribed for him, but it was more me showing him what to write down rather than just writing verbatum what he told me to write.  So that week during math, I tried to scribe for him by just writing exactly what he told me to write, and it became very clear that he had no idea. None.  He could get the answer because of his mathematical insight, but he could not code it.  Over the next year I came to understand that this was a piece of his dyslexia.  He could not *code* his thinking into mathematical language of expressions and equations. He thinking was web-like and based on intuition, it was not linear or really logical, and certainly not structured in a standard way.  And I came to believe that this was going to be a bigger and bigger problem as he advanced in math.  Given his amazing mathematical intuition, it would be sad for him to be limited in math because he could not write it down. His mathematical insight needed a strong linear, logical foundation of writing to be put to great use in higher math.

This was the beginning of my journey to *teach* him *how* to show the work.  It was absolutely not about showing *his* work because *his* work was a jumble of insight that could not be written down.  It was about rewiring a piece of his brain so that he could take that jumble and code in into linear logical steps.  This took 3 full years. But this process showed me that there is more than one reason why students don't show *their* work. My son had to be trained not just which steps to write, but how to *think* like a mathematician. Intuition is a wonderful ability to have, but it simply won't get you far in math without proper mathematical thinking.  And writing is thinking made clear.  If you cannot write it, you are not thinking it.

My point is, to ask a student to show *her* work, is the wrong approach in my opinion.  You need to train a student to write the workings in a certain way, and that certain way when repeated day after day, year after year, will train a student to see math differently.  It is no different than practicing scales in violin, over many years you train the ear to hear if notes are out of tune. Drill is what was required for my ds.  So for him, he had to drill proper workings to be able to train his brain to think linearly and logically. To do it the other way -- show your jumbled workings so I can see what you are thinking -- is to miss half of what teaching kids math is all about.

Ruth in NZ

Edited January 4, 2021 by lewelma

[Not_a_Number]

53 minutes ago, lewelma said:

Aw, sorry that I made you upset. 

Nah, don't worry about it. It's mostly that I've had a long day, including a brief screaming fight with my MIL 😛 . I'm glad we're visiting my in-laws, because it makes my pandemic-bound kids much happier, but sometimes months of my in-laws are just a bit much. 

Plus, you know, COVID. We're all a bit stressed over here. 

 

53 minutes ago, lewelma said:

I really struggle to explain how I teach because I am so intuitive about it. 

I'm intuitive about my teaching as well, but I'm also naturally very analytical. So I find things that work, then I try to find a framework for what MAKES them work. It's not always the same thing, but I've come up with a few interesting principles that I now find it impossible to explain to anyone 😛 . 

Whenever I get a hobby, I seem to wind up being able to write a Ph.D dissertation on it by the end 😕 . Which also precludes me from talking to people about it, really, because I'd have to start somewhere around 4 years ago, when I started doing intensive experiments on a variety of kids. And all the results are in my head, anyway, so it's not like I even have convincing data -- just whatever it all cohered into after lots of experimenting and thought. 

I was talking about this with DH, and he pointed out that I wouldn't have any more luck explaining my Ph.D thesis, either 😛. Maybe that's a good comparison, because I've gone so far down this rabbit hole I can't even see where I started. (It's not even that I think that this is THE way to teach. It's more like I've tried so many iterations and tested so many things that I don't think I'm even using words in a normal way anymore.) 

 

53 minutes ago, lewelma said:

I adapt to what each day and each student gives me.  I also have a terrible memory, so I can't even remember the struggles I went through to get this boy structuring his math.  I have written about it in detail on the board, and I've spent the last 10 minutes looking for what I wrote as I know I liked how I explained it. But so far I can't find it. 

If you find the links, I'd love to see. 

 

53 minutes ago, lewelma said:

I also think that I am very close to this struggle of his as I have sacrificed my sanity over many years to clean up his math mess. So it feels kind of yucky to have someone suggest that if I had just done xxx, then it would have been fine. I know that it not what you mean, but it has just been oh so hard to help this boy that I don't really want to go back and relive it and wonder if I could have done better. 

No, I totally get that. I really am not trying to imply that, because I think you are a great teacher. It's more from the perspective of... "Hey, maybe you didn't try this thing! We teach pretty differently, so maybe something new would CURRENTLY stick to the wall that you haven't tried yet?" Like... I definitely learn that way myself. it's the reason brainstorming in groups can be better than people working on their own. 

It's not a smug "I could have taught him better," because I don't think I could have. I can see that you've worked INCREDIBLY hard and you obviously got amazing results. 

[Not_a_Number]

50 minutes ago, lewelma said:

So that week during math, I tried to scribe for him by just writing exactly what he told me to write, and it became very clear that he had no idea. None.  He could get the answer because of his mathematical insight, but he could not code it.

I wish I could have seen what it was that he told you to write down!! I'm very curious. 

I agree with you, by the way. Even with my very accelerated kiddo, I spend a LOT of time "straightening out" her thinking. It's not that she writes down what she's thinking. It's that we make sense of her thinking and linearize it, and then we write it down. 

And she's actually my more linear thinker. I'm curious how it'll go with DD4. 

[Not_a_Number]

1 hour ago, lewelma said:

Ok, I just asked him. Sounds like he has come very very far since we did this a year ago. He now says these questions are easy!  So I am glad that I didn't push through last year and gave him a year to mature.

I'm glad he's figured it out by himself!

 

1 hour ago, lewelma said:

He just said "the probability they are test here is so easy." So I asked him why he doesn't like it and he said. 

"The problem is that these questions are a combination of a word problem and not a word problem. They translate a word problem into 'word math' which then they want me to translate into math.  It would be so much better for me to translate a word problem into math directly, without this awkward step.  Here is a better question: Bob is doing a research paper as to what the probability of it raining in the summer on a day that he wants to go surfing. He can only surf on the weekends, and his two spots are Asburton and Timaru. What is the probability that it will be sunny on either or both of these two spots on the weekend? This is more what you would actually ask yourself in real life and the language makes more sense. The 'word math' of these test questions bothers me on an innate level.  It is very irritating." 

Super interesting. That makes sense to me, actually. 

Did you ask him a question about "one of" the two cities being sunny? Because your original question was about both of them. I wonder how he'd want that one phrased? 

For what it's worth, I agree with him, lol. These questions don't even make sense as probabilities. For one thing, they've already happened so... what are we doing here? Throwing a die with the number of sides equal to the total number of days, with the number of sides corresponding to "dry in both places" in a different color? Like, what IS this problem asking, anyway?? Where's the randomness coming from? 

Actually, "where is the randomness coming from?" is a surprisingly deep question. There is more than one probability question I've seen where you have to be VERY careful to explain how you're randomizing, and different ways give different answers. Probability is a slippery beast. 

I tend to like to work at the intersection of combinatorics and probability best, where I can still simply count and divide. But I'd also like to actually have a model of the process that is yielding the randomness... specifically, I worked on Markov chains, and it was at least easy to fit the randomness there into my head. At each point, you took a step, and you wanted to figure out what happened after k steps. I could figure out why that was random. I could even model it on a computer :-D. That's much better than "picking a random day." 

[Clemsondana]

@lewelmaThanks for that description - I've said several times that I have a kid who sees math in a way that I don't but I haven't been able to explain it clearly, and solving problems like that in their head is exactly what I'm talking about.  They did it with those 'Fred is 2 years older than John was 5 years ago and 6 years older than twice as old has he is now' sorts of problems.  When we first encountered them, I would sit beside my student and do something normal, like decide what X was going to be and then start adding, subtracting, multiplying, and dividing to get the various expressions.  Kid would look at it a few minutes and then blurt '15'.  🙂  Sometimes kid did something with ratios, and sometimes I think kid saw a balance and added or subtracted from each side - I remember kid explaining that since there was a difference of 6 between them, they added 3 to one side and subtracted 3 from the other.  I listened to enough explanations to see that kid was doing some mathematical reasoning and not just super-fast guess-and-check, but I still never would have seen that approach.  But, kid is also compliant and has no reason that they can't write things down, so when I taught the usual method it was fine...but I think that with most problems they still do the in-their-head method first if they think it'll be faster.  They usually show their work correctly these days, so I think that the traditional method is their check rather than how they initially do the problem.

But, they aren't intuitive about everything - if they get a complex equation and are supposed to realize that if they represent part of it as a and part as b, then they have a difference of squares...well, they might or might not recognize that.  Which is not bad - learning to recognize it is the skill that they are learning and once they have it they know how to work with it, but it takes work.  

And, my other kid is completely different.  My 2 kids have never gotten stuck on the same concept, so I don't think it's my approaches to teaching them - it's something quirky in their brains, and we work through it, sometimes with repetition and sometimes with a new approach and sometimes by taking a break.  🙂  When I teach my bio students, I know that there are common mistakes and ways to get confused, but there are also occasional unique confusions that I have to sort out.  

 

 

[Not_a_Number]

20 minutes ago, Clemsondana said:

They did it with those 'Fred is 2 years older than John was 5 years ago and 6 years older than twice as old has he is now' sorts of problems.  When we first encountered them, I would sit beside my student and do something normal, like decide what X was going to be and then start adding, subtracting, multiplying, and dividing to get the various expressions.  Kid would look at it a few minutes and then blurt '15'.  🙂  Sometimes kid did something with ratios, and sometimes I think kid saw a balance and added or subtracted from each side - I remember kid explaining that since there was a difference of 6 between them, they added 3 to one side and subtracted 3 from the other. 

I occasionally have tricks for these, too... if you see enough of this kind of question, you do notice patterns that kind of let you fit things together. 

The people I’ve known who are really good at math have a mix of the approaches — they have flashes of intuition and they also can organize their ideas if needed.

Have you ever had your kid write down what they are actually doing in their head? I don’t really teach specific methods, only overarching principles, so I’ve definitely had DD8 write stuff that’s not the “standard method.” But I do need it in logical order.

Edited January 4, 2021 by Not_a_Number

[Danae]

Oh wow.  This is my younger son too.  There are so many times when I’ve had to explain “this lesson is about teaching you to set up equations. Even if you can just know the answer by looking at it I need you to set up the equation so that when you get to a problem you can’t just see the answer to you’ll know how to do it.” 
 

Unfortunately that has sometimes come out as “No! Don’t do it with thinking, do it with math.”

Edited January 4, 2021 by Danae

[Clemsondana]

At the time, kid wasn't ready to write the problems down using their method.  They would intuitively know to add or subtract 3 'outside the parenthesis' but I don't think they would have been able to reproducibly translate it into equations.  Years later they can write it in a reasonable way.  But, learning to write the equations and show some steps is probably more a function of getting frustrated when they miss a problem and have to start over than anything else...they finally learned to show work and if they miss a problem, they (and, if they get desparate, I) can go back and check their work and find that they added instead of subtracted or misread their 4 as a 9.  But, they often take a different approach than what the AoPS solutions guide shows.  Sometimes it's the same thing but I can tell that they saw it differently in the original setup so their numbers are lumped differently, and sometimes we have to check their reasoning to see that they also used a valid approach, but it's different (and sometimes less tedious).  

[Not_a_Number]

1 minute ago, Clemsondana said:

But, they often take a different approach than what the AoPS solutions guide shows.  Sometimes it's the same thing but I can tell that they saw it differently in the original setup so their numbers are lumped differently, and sometimes we have to check their reasoning to see that they also used a valid approach, but it's different (and sometimes less tedious).  

Yeah, I'm not  surprised. I think kids who are fluent with the concepts have their own approaches a lot of the time. 

 

1 minute ago, Clemsondana said:

 They would intuitively know to add or subtract 3 'outside the parenthesis' but I don't think they would have been able to reproducibly translate it into equations. 

I don't mean equations exactly... more like "explaining it out." You can certainly talk this kind of thing through without setting up equations, although it's of course more onerous. 

 

3 minutes ago, Danae said:

Oh wow.  This is my younger son too.  There are so many times when I’ve had to explain “this lesson is about teaching you to set up equations. Even if you can just know the answer by looking at it I need you to set up the equation so that when you get to a problem you can’t just see the answer to you’ll know how to do it.” 
 

Unfortunately that has sometimes come out as “No! Don’t do it with thinking, do it with math.”

I try not to discourage those kinds of approaches, especially when it's clear they've found the ONLY answer. I just give questions where it's harder to see the answer immediately so that they see the point of what we're doing 😉 .