S/O - Math Intuition/Thinking about Math Tools...

[Woodland Mist Academy]

I didn't want to derail the other thread...

 

My daughter doesn't want to be a mathematician. She is strong in math, but not profoundly gifted in it by any stretch. She seems to want the tools to be given to her so she can use them. They are the means to an end. She doesn't want to play around developing the tools herself. She wants to be able to pick them up and use them for what she does want to play around with....

 

There have been times she has screamed, "WHY WON'T THEY JUST TELL ME SO I CAN DO THIS?" She doesn't want to contemplate math; she wants to contemplate other things. Yesterday it was surgery. ;) She spent her lunch break reading about surgical procedures. Some days she talks about how she thinks chemical equations are cute... :001_huh:   Isn't it OK for her to save her mental energy for places she wants to spend her time grappling? Does everything need to be a struggle? She needs the math to do what she wants to do. Taking up time and mental energy making her struggle to reach the tools is an odd approach, isn't it?

 

Is it so wrong to just hand her the tools and explain what they are called and how to use them? Does she really need to forge them herself? I honestly can't say that I see a difference between what she learned by "discovery" with AoPS and what she was taught elsewhere....   In some ways, she is much stronger and confident in the latter. It makes me wonder if discovery is overrated...

 

Sometimes I think she just wants an explanation and a name for what is going on in her head...

 

 

 

[regentrude]

I do not think she must discover and develop all tools herself.

I do, however, consider it vitally important that a student understands WHY the tools work. A student who is just handed a tool to use it, without thorough understanding of the why, will flounder in higher math and science. I see it every day with my college students: if they have just been trained how to do a certain procedure, they will make mistakles, will forget when they have not used the tool in a while, and will be unable to solve problems that require creative thinking and an extension, unless they also understand why it works.

 

You do not need to use a discovery aproach. But you should derive and/or prove everything the student is given to use.

 

ETA: Prime example: dividing fractions. It is not sufficient that the student is drilled to multiply with the inverse. He will forget eventually and mix things up. A student who understood WHY that is the way to divide fractions will never forget, because he can always rederive the procedure.

 

[Woodland Mist Academy]

I do not think she must discover and develop all tools gerself.

I do, however, consider it vitally important that a student understands WHY the tools work. A student who is just handed a tool to use it, without thorough understanding of the why, will flounder in higher math and science. I see it every day with my college students: if they have just been trained how to do a certain procedure, they will make mistakles, will forget when they have not used the tool in a while, and will be unable to solve problems that require creative thinking and an extension, unless they also understand why it works.

 

You do not need to use a discovery aproach. But you should derive and/or prove everything the student is given to use.

 

Thank you! She actually doesn't mind showing/proving if she has the words to do so. Once she has been given the concepts and vocabulary she relishes using them.

 

Her understanding is actually sometimes deeper if she has been directly shown as opposed to discovering. She has many more holes and misunderstandings in what she hasn't been directly taught.

 

Thanks again for sharing your thoughts and experiences with your students.

[Chrysalis Academy]

Dang, Woodland Mist, you are totally describing Shannon!!! 

 

And, coincidentally (?), we have found that hard-core discovery isn't a good fit for her.  Deriving the why behind an algorithm - yes.  But reinventing the tool, not so much.

 

Anyway, it's always nice to hear about kids that are just like yours.

[Woodland Mist Academy]

 

ETA: Prime example: dividing fractions. It is not sufficient that the student is drilled to multiply with the inverse. He will forget eventually and mix things up. A student who understood WHY that is the way to divide fractions will never forget, because he can always rederive the procedure.

 

This is actually a good example. At one point there was a fraction concept that my daughter was misunderstanding partly because of an overly vague discovery approach... 

 

I do agree that students need to understand. I think the problem is that sometimes there is a presumption that what is discovered is automatically better understood. Not so.

 

Thanks, again!

[wapiti]

One of my boys just wants to get on with things and be told how.  The problem with him is that when he is told how without having to think deeply about the why, he is able to use the procedure (using only those two little brain cells way in the back corner) and then forget it immediately.  On the dividing fractions example, I can't tell you how many times he was taught this and how much drill his teacher had him do.  And then months later, I slap my forehead and say *dude*.... why are you flipping the first number.  The first time he learned this, his teacher had assigned him the plug and chug practice in Keys-to.  I have explained the concept over and over again, but for him, unless his *whole brain* is deeply engaged, it goes in one ear and out the other.  So in his particular case, that is the utility of a discovery approach.  I admit I'm not always sufficiently patient (we are really struggling to get some afterschooling done, long story), but in the long run I think it is the way to go for him.

 

It's almost as if his high intelligence is a detriment when it comes to being told the how and forgetting the why if the explanation isn't sufficiently engaging (that would be me; my oral explanation is not sufficiently engaging LOL).  It's as if the experience *needs* to be somewhat intellectually painful to make a dent.

 

I do think there may be a delicate balance when it comes to how much is discovered the hard way vs how much concept is explained by direct instruction and that is why I prefer to be involved, to keep close tabs, as much as possible.  It can be a little tricky for us (as in, I have to be patient enough to let him figure things out for himself, but involved enough that he'll actually do it).

 

Eta, so to answer the main question, how much discovery is helpful would depend on the student.  The two aspects I'd consider are (1) how well the student absorbs the concept through direct instruction (direct is faster, after all!) and (2) how well the student can apply the tool in new and different scenarios for further development of the depth of understanding.

[Woodland Mist Academy]

It's interesting how different brains work, isn't it? What engages one, may shut down another...

 

[Woodland Mist Academy]

 

Eta, so to answer the main question, how much discovery is helpful would depend on the student.  The two aspects I'd consider are (1) how well the student absorbs the concept through direct instruction (direct is faster, after all!) and (2) how well the student can apply the tool in new and different scenarios for further development of the depth of understanding.

 

I sometimes wonder if what really matters is what is done with the information. Just because someone "discovers" it doesn't mean she can just do a few problems and she'll have it down solid for life. The more I think about it, the more I think it's not about "discovery" for everyone. For some people it's about using the concepts in different situations, frequent exposure, and practice. Discovery is not an automatic route to thorough, lasting understanding.

[Chrysalis Academy]

Yeah, I don't find that just because Shannon derives/discovers something, that means she never forgets it or can remember how to do it in other situations!  :lol:

 

I agree that for her, spaced repetition, interleaved practice, and using the concept in different/unfamiliar ways is more effective.  This is one of the reason we've always used multiple resources for math, which we would absolutely not have time to do if we were using AoPS!

 

 

[wapiti]

Rose, I was just thinking that maybe you don't have enough algebra resources yet.  I think you need to buy Gelfand.

 

 

 

Just kidding (mostly)!

[Woodland Mist Academy]

Rose, I was just thinking that maybe you don't have enough algebra resources yet.  I think you need to buy Gelfand.

 

 

 

Just kidding (mostly)!

 

:smilielol5:

 

[Chrysalis Academy]

You know, I actually think I do.  :huh:

 

A pox on both your houses!!!!!

 

:lol:  :lol:  :lol:

[quark]

Deleted...I didn't express myself accurately.

[mathwonk]

I am myself conflicted on when one should insist on a teaching technique the student rebels against, even if one is sure of its value, but I do recall that the best teachers I have known, would never tell a student the answer.

[Woodland Mist Academy]

But isn't there a difference between telling an answer and providing an explanation? She just wants the tools so she can use them...is that so very wrong a thing to ask....

[Woodland Mist Academy]

She doesn't have trouble using the tools, she just tires of crafting them herself...

[quark]

Actually, my pp didn't come out the way I intended it to. I think that if it is meaningful to her area of interest then the struggle to discover and craft the math will be extremely beneficial to her, despite how frustrating it is. But it shouldn't become something so negative that she starts to hate math. And I also feel it would be very helpful for her to speak to as many scientists she meets as possible to ask them about their own journeys with math.

 

I meant that her struggle could come from lack of repetition and application, not only understanding. Providing the explanation while she has more practice doing and applying the problems might be very valuable. Then, giving her a challenge e.g. working on some problems without the explanation might increase her confidence with the discovery aspect of it (when you think that aspect is meaningful to her). Holding her hand as much as you see fit, setting her up for success then slowly releasing her to work things out herself so that she eventually has that strength under her belt (but it doesn't have to come now)?

 

 

[lewelma]

My younger boy is like so much like your dd. He likes math and is good at it, but he does not want to derive and prove every tool he uses.  He has other interests, and does not have the time nor the inclination to put 2 hours a day to AoPS. He does not like the discovery method, and it confuses him more than anything else.  It reminds me of a class my dh took for his MBA.  It was accounting taught in the discovery approach.  The class would discuss the issue, brainstorm all the different possible ways to account for something and why each would be useful, and then the professor would say that #4 is the way that we have chosen to do it. But what happened is that dh remembered *every* idea, and their pros and cons, and could not remember *why* #4 was chosen.  He just remembered it all and even to this day gets muddled.  Clearly accounting is not exactly like math, but I think that for some people, discovery is *not* effective.  For these kids you can explain directly the concept, link it to a conceptual understanding and even a formal proof if desired.  But the kid does not have to come up with it *herself*!

 

What I think that AoPS does is get kids to develop the problem solving and critical thinking that is so important in STEM.  But I think there are other ways to go about it.  For my younger, we are using MEP and I am making sure that he does one investigation in every 2-week topic.  These investigations have no one answer, have many steps that must be managed, and take a lot of thinking and persistence. I feel like it is a good substitute.  Here is an example, ds (age 11) did last month in the angles/maps/bearings unit.  They gave a scale drawing of the UK with the cities marked:

 

You are the flight director of a new small airline based at Manchester. You have leased
4 identical planes which fly at an average speed of 450 km/h, and need refuelling after a
maximum distance of 600 km. You would like to provide at least one daily return flight
from Manchester to each of the other cities marked on the map.

Design:

(a) timetables for the daily use of each plane (starting no earlier than 0700 hours,
and finishing no later than 2200 hours; allow at least 40 minutes between
arrival and departure at any airport).
(b) flight paths for all flight movements, ensuring that they do not conflict with
one another.

 

For the ds, the practical nature of this work is so much more interesting.  So instead of creatively deriving all the math tools he knows, we put our energy to creatively *using* them.

 

Different strokes for different folks!

 

Ruth in NZ

[Steppenwolf]

Actually, my pp didn't come out the way I intended it to. I think that if it is meaningful to her area of interest then the struggle to discover and craft the math will be extremely beneficial to her, despite how frustrating it is. But it shouldn't become something so negative that she starts to hate math. And I also feel it would be very helpful for her to speak to as many scientists she meets as possible to ask them about their own journeys with math.

 

I meant that her struggle could come from lack of repetition and application, not only understanding. Providing the explanation while she has more practice doing and applying the problems might be very valuable. Then, giving her a challenge e.g. working on some problems without the explanation might increase her confidence with the discovery aspect of it (when you think that aspect is meaningful to her). Holding her hand as much as you see fit, setting her up for success then slowly releasing her to work things out herself so that she eventually has that strength under her belt (but it doesn't have to come now)?

 

This.

[Woodland Mist Academy]

Holding her hand? Hmmm...maybe I'm not expressing the situation clearly....this is the last thing she needs...

 

Right now I feel I've leadened her with weight and clipped her wings....it's not a good feeling...

[Chrysalis Academy]

My younger boy is like so much like your dd. He likes math and is good at it, but he does not want to derive and prove every tool he uses.  He has other interests, and does not have the time nor the inclination to put 2 hours a day to AoPS. He does not like the discovery method, and it confuses him more than anything else.  It reminds me of a class my dh took for his MBA.  It was accounting taught in the discovery approach.  The class would discuss the issue, brainstorm all the different possible ways to account for something and why each would be useful, and then the professor would say that #4 is the way that we have chosen to do it. But what happened is that dh remembered *every* idea, and their pros and cons, and could not remember *why* #4 was chosen.  He just remembered it all and even to this day gets muddled.  Clearly accounting is not exactly like math, but I think that for some people, discovery is *not* effective.  For these kids you can explain directly the concept, link it to a conceptual understanding and even a formal proof if desired.  But the kid does not have to come up with it *herself*!

 

What I think that AoPS does is get kids to develop the problem solving and critical thinking that is so important in STEM.  But I think there are other ways to go about it.  For my younger, we are using MEP and I am making sure that he does one investigation in every 2-week topic.  These investigations have no one answer, have many steps that must be managed, and take a lot of thinking and persistence. I feel like it is a good substitute.  Here is an example, ds (age 11) did last month in the angles/maps/bearings unit.  They gave a scale drawing of the UK with the cities marked:

 

 

 

Sounds like our three are very similar.  And I agree that the bolded is absolutely essential.

 

Which is why I just bought *both* Gelfand and Crossing the River With Dogs.  On the same day.  In separate transactions.  Yep, I am Amazon's dream customer.  :leaving:

 

It's also what I like about doing a straightforward Algebra as a spine.  We have time and space for these digressions!  We just decided to take the first week of the new year to work on translating word problems into equations, for all different kinds of word problems.  Because this is a really critical tool that she needs to get solid with, before pressing ahead.

 

And I'm not worried or stressed about getting behind at all - I know we have plenty of time to get through Jacobs plus this other stuff.  Whew!

[Woodland Mist Academy]

Yes! There are many, many ways to get there. The idea that there isn't is a bit ironic in a discussion about problem solving, isn't it?

[lewelma]

  We just decided to take the first week of the new year to work on translating word problems into equations, for all different kinds of word problems.  Because this is a really critical tool that she needs to get solid with, before pressing ahead.

 

Yes!  I completely agree.  We are just dabbling at this, but I have it front and center as a goal.

[quark]

 

 

You are the flight director of a new small airline based at Manchester. You have leased

4 identical planes which fly at an average speed of 450 km/h, and need refuelling after a

maximum distance of 600 km. You would like to provide at least one daily return flight

from Manchester to each of the other cities marked on the map.

Design:

(a) timetables for the daily use of each plane (starting no earlier than 0700 hours,

and finishing no later than 2200 hours; allow at least 40 minutes between

arrival and departure at any airport).

(b) flight paths for all flight movements, ensuring that they do not conflict with

one another.

 

For the ds, the practical nature of this work is so much more interesting.  So instead of creatively deriving all the math tools he knows, we put our energy to creatively *using* them.

 

Different strokes for different folks!

 

I swear I wish I had another kid to use MEP with. I miss MEP. :001_wub:

Holding her hand? Hmmm...maybe I'm not expressing the situation clearly....this is the last thing she needs...

 

Right now I feel I've leadened her with weight and clipped her wings....it's not a good feeling...

 

Maybe holding her hand isn't the best way to say it...I don't hold DS's hand either lol. He'd look at me really funny and maybe hold mine instead and also feel my forehead just to be sure lol.

 

It's hard for me to understand your context not knowing what you are facing...maybe just let her fly? What's the worst that can happen? Some of our best moments were moments that were completely unscripted and unplanned and really risky when I come to think of it.

[lewelma]

Can I just say that my kids are chalk and cheese, especially when it comes to math.  Older ds just spent 22 hours solving 2 geometry problems. :blink:

[lewelma]

WMA, did I miss where you said what your dd is using?  If it is AoPS, is there a reason you are sticking with it if it is causing so much grief?

[lewelma]

I swear I wish I had another kid to use MEP with. I miss MEP. :001_wub:

 

I think we might be using it all the way to the A-levels.  Having tried 8 different textbooks/programs in the previous year, we finally came back to MEP in June.  Never sure why we left. :huh:  He loves it.  Mastery but within a 2-week rotation of topics.  Just what he wants/needs.

[Woodland Mist Academy]

WMA, did I miss where you said what your dd is using?  If it is AoPS, is there a reason you are sticking with it if it is causing so much grief?

 

Good question! :huh:  :laugh:  Peer pressure, I guess... ;)   Well, that and the fact that there is a lot about AoPS we love.

 

We got through Chapter 7 of AoPS Intro to Algebra and decided to switch. She had been using Saxon as well for a few weeks because of some weaknesses we noticed with AoPS alone. Seeing her response to Saxon was one reason we decided to change everything.  The original plan was to keep doing both, but that didn't work for a few reasons... The decision was to find a happy medium. She started Foerster this week. So far she is just reading and testing through the chapters. Most of the beginning chapters are review given how far she got in AoPS.

 

The only comment she's made so far was being impressed with his writing style... :lol:   I think the column approach to proofs may be exactly what she needs. Exactly. There also seems to be an emphasis on knowing how and why to do procedures, as well as what they are called. AoPS downplayed the latter (at least the do as far as we've done in AoPS). I think my daughter will actually love knowing and using the correct terms...

 

 

[Chrysalis Academy]

Oh man, you guys are so tempting me to pick up a copy of Foersters!  

 

It might be the only Algebra book I don't own???  :001_rolleyes:

[Woodland Mist Academy]

Oh man, you guys are so tempting me to pick up a copy of Foersters!  

 

It might be the only Algebra book I don't own???  :001_rolleyes:

 

You don't have Foerster??? :svengo:

 

How is that even possible?

 

[wapiti]

I thought she had it too!  (Really!)

 

IIRC the order of topics is slightly different.  There are more topics than in Jacobs.  There are more practice problems.  It's different.  I thought it was useful.  I don't think I could ever use one text, LOL, and we always find ourselves back with AoPS at points in time (gosh why can't I get anyone - of my kids, that is - to stay in Jacobs?) but I think it's helpful to see what's in a rigorous non-AoPS algebra 1 text.  Hmmm... maybe ds should do a few lessons out of Foerster over winter break, which starts tomorrow, just for "fun" (am I mean or what).  Maybe I should pull it out and look... this is so much more fun than wrapping presents.

[quark]

Here's one peer who isn't going to pressure you. We didn't use AoPS as a core ever. I love their style but DS just can't seem to settle on using just AoPS alone or even being consistent. If he uses it at all it's either a class (and so far he's only taken 2 AoPS classes in his whole math journey) or it's just the review and challenge sections of the book. Didn't use it for geometry or algebra 2 at all. He cannot stomach the other explanatory bits. It's an on-again, off-again supplement. You know what we've used as a core for high school math? Wait for it.... :eek: textbooks! Good ones mostly but a not so good one this semester and I'm so glad he's switching instructors next year to one who uses a better text. The textbooks present the math clearly enough. There are sections with challenging problems (usually enough to give him a good workout). He learned to write two-column proofs, and only then switched to paragraph style.

 

I don't know if he will grow to be a respected math authority or if this lack of AoPS will come back and bite him but I do know that this (wrenching decision though it is for me to not be more AoPS based) path has freed him to do math his way and love it and continue loving it. AoPS is not the be-all and end-all.

 

We jumped around a lot too. I explored Saxon and Foerster at one time as well but decided to let them go in favor of what he was using with his tutor (Dolciani, Jurgensen).

[quark]

Rose, look deep in your shelves. Perhaps you had it at one time and sold it (like I did) or forgot and even bought a second copy (like I did with another book).

[Woodland Mist Academy]

Yes, I imagine our future choices will be influenced by tutors/instructors.

[Chrysalis Academy]

Rose, look deep in your shelves. Perhaps you had it at one time and sold it (like I did) or forgot and even bought a second copy (like I did with another book).

 

:lol:  I do keep finding things I didn't remember I had.  I just found Mildred Johnson's How To Solve Word Problems in Algebra.  Love that book!

[Woodland Mist Academy]

Thanks, quark! I had forgotten your ds didn't use AOPS all the way through!

[quark]

:lol:  I do keep finding things I didn't remember I had.  I just found Mildred Johnson's How To Solve Word Problems in Algebra.  Love that book!

 

Hey, me too! :)

[Gratia271]

Good question! :huh:  :laugh:  Peer pressure, I guess... ;)   Well, that and the fact that there is a lot about AoPS we love.

 

We got through Chapter 7 of AoPS Intro to Algebra and decided to switch. She had been using Saxon as well for a few weeks because of some weaknesses we noticed with AoPS alone. Seeing her response to Saxon was one reason we decided to change everything.  The original plan was to keep doing both, but that didn't work for a few reasons... The decision was to find a happy medium. She started Foerster this week. So far she is just reading and testing through the chapters. Most of the beginning chapters are review given how far she got in AoPS.

 

The only comment she's made so far was being impressed with his writing style... :lol:   I think the column approach to proofs may be exactly what she needs. Exactly. There also seems to be an emphasis on knowing how and why to do procedures, as well as what they are called. AoPS downplayed the latter (at least the do as far as we've done in AoPS). I think my daughter will actually love knowing and using the correct terms...

My oldest DD really enjoyed Foerster materials. I had her try to AoPS, and she didn't care for it at all (I understand that is heresy).  I am wading into AoPS again, this time with son who has also used (and enjoyed) Foerster materials.  They are both naturals at math as well as conceptual learners. They have spent most of their educations learning through discovery.  They simply don't care to ponder math. 

 

So I think I understand what you are going through, and I would definitely let her do it in the manner she is comfortable with.  At least for my oldest DD, forcing AoPS would have killed her interest in math. Just my .02

[kiana]

Honestly, Foerster's is a good and solid algebra text that will prepare a student for any major, including mathematics. AOPS is not for everyone.

[Arcadia]

 

My daughter doesn't want to be a mathematician. She is strong in math, but not profoundly gifted in it by any stretch. She seems to want the tools to be given to her so she can use them. They are the means to an end. She doesn't want to play around developing the tools herself. She wants to be able to pick them up and use them for what she does want to play around with....

 

 

...Right now I feel I've leadened her with weight and clipped her wings....it's not a good feeling...

 

Maths doesn't require much effort from me but science can tax my brain. Still that is where I rather spend my energy and thankfully I was able to find enjoyable jobs in.  My boys seems the same way and they are using AoPS because I am a slacker mom.  The Larson and the Lials algebra textbooks doesn't hold their attention or I would have just used them.

 

Discovery, problem solving, resilience/grit can be in anywhere, doesn't need to be from maths. If science is what makes your daughter happy, then let her spend her mental energy on science.  I have a ex-classmate who all along wanted to be a cardio surgeon.  She aced her maths exams but all her energy is in medicine. Same for another lady classmate who became a neuro surgeon.  Almost half my classmates in an all girls school became surgeons and we used standard public school textbooks.  Hubby is in R&D and he doesn't need to do all the discovering; he just needs to understand other people's discoveries, synthesise and come up with his own discoveries which in turn is expand upon by other R&D people.  I know many parents in my kids German school who are great at maths but their jobs and passions are in other fields :)

[Mike in SA]

I wanted to quote, but there were so many relevant lines to quote that I couldn't decide on one.  :)

 

To me, the idea that different brains think differently is a real key point.  I often find myself trying to understand how people at work think, because it tells a lot about what they like to do, why they like to do it, and consequently, what they will do well.  A good team is composed of a variety of skill sets, some who like to dream up approaches, and some who actually drive things to completion.  Lots of people like to think they are both, but in reality, it's rare to find someone who excels and is comfortable in both realms.

 

Math isn't any different.  There is pure math, and applied math, and statistics, and on and on.  If your child loves to dive into the details of surgery, then this child probably is not engaged by theory, and may never be.  Although comprehending theory is important, creating theory is not as important.  If this is your child, then it may help to think of the proof as part of the task to be done.  Instead of strategizing on "the right" approach, just hit the ground running on several approaches, and see which one yields fruit.

 

If she likes this approach, she might be better at one of the applied math branches or statistics.  Statistics in particular requires a keen eye for detail.  That's why it was never my strong suit.  ;)

 

[Woodland Mist Academy]

My oldest DD really enjoyed Foerster materials. I had her try to AoPS, and she didn't care for it at all (I understand that is heresy). 

 

:laugh:  I know! I felt like I was confessing to losing my religion or leaving a cult by even starting this thread...

 

 They are both naturals at math as well as conceptual learners. They have spent most of their educations learning through discovery.  They simply don't care to ponder math. 

 

:001_wub:

 

 

 

So I think I understand what you are going through, and I would definitely let her do it in the manner she is comfortable with.  At least for my oldest DD, forcing AoPS would have killed her interest in math. Just my .02

 

Thanks so much for your post!

 

 

[Woodland Mist Academy]

Honestly, Foerster's is a good and solid algebra text that will prepare a student for any major, including mathematics. AOPS is not for everyone.

 

Thanks for saying this. It helps keep the doubt monsters in my mind at bay... 

 

[Nicholas_mom]

thanks Woodland Mist for starting this thread.  You have explained my ds for me!  :)

[Woodland Mist Academy]

I wanted to quote, but there were so many relevant lines to quote that I couldn't decide on one. :)

 

I'm running into this problem, too! Each poster has given me something important to consider... I wish I could comment on everything as I process my thoughts...

To me, the idea that different brains think differently is a real key point. I often find myself trying to understand how people at work think, because it tells a lot about what they like to do, why they like to do it, and consequently, what they will do well. A good team is composed of a variety of skill sets, some who like to dream up approaches, and some who actually drive things to completion. Lots of people like to think they are both, but in reality, it's rare to find someone who excels and is comfortable in both realms.

 

Math isn't any different. There is pure math, and applied math, and statistics, and on and on. If your child loves to dive into the details of surgery, then this child probably is not engaged by theory, and may never be. Although comprehending theory is important, creating theory is not as important. If this is your child, then it may help to think of the proof as part of the task to be done. Instead of strategizing on "the right" approach, just hit the ground running on several approaches, and see which one yields fruit.

 

If she likes this approach, she might be better at one of the applied math branches or statistics. Statistics in particular requires a keen eye for detail. That's why it was never my strong suit. ;)

Thank you. Thank you. I think I've been so focused on trying to make something fit against her natural inclination that I've somewhat neglected the gifts that are unique to her. Maybe partially because they are less easy to define and thus seem somehow feel less worthy or important? (ouch...it's tough to suddenly realize that...)

 

You mentioned statistics...By coincidence, (what are the odds?!? ;) ) we listened to a lecture on statistics during our commute to the lab yesterday...my dd was filled with giggles and wide-eyed wonder...

(The lecture was discussing when statistics are used incorrectly. She likes to casually mention various stastics in conversation, so she found the lecture particularly entertaining and informative.)

 

Instead of strategizing on "the right" approach, just hit the ground running on several approaches, and see which one yields fruit.

This suddenly sounds so simple and sane. Sometimes it's hard to see the forest for the trees. Thank you.

[Woodland Mist Academy]

 

 Hubby is in R&D and he doesn't need to do all the discovering; he just needs to understand other people's discoveries, synthesise and come up with his own discoveries which in turn is expand upon by other R&D people.  I know many parents in my kids German school who are great at maths but their jobs and passions are in other fields :)

 

:001_wub:  

 

[Woodland Mist Academy]

thanks Woodland Mist for starting this thread.  You have explained my ds for me!  :)

 

 

I feel like I've been to therapy or had a math intervention... :lol: 

My brain hasn't evolved with the technology though - at one point yesterday I had the odd feeling that I really should be offering warm drinks and finger foods...

 

:cheers2:

[Mukmuk]

WMA, I feel your pain. We've been down this road before, and I had actually switched my son out to Dolciani last year (from AOPS Alg 1 the previous year) with a wonderful tutor. I just wanted to preserve my sanity! A year later, Ds asked to switch back to AOPS, and boy was I nervous, which is why I added the support (classes, tutor). It's the one year of maturity, relative calm, and the fact that he made the choice, perhaps, that is allowing for this growth. After all we've been through, my philosophy is, any curriculum is a good curriculum as long as he's happy with it.

 

I haven't talked about our writing woes, which makes math seem like a piece of cake :o. But I just found the perfect teacher ... :D.

[Chrysalis Academy]

Rose, I was just thinking that maybe you don't have enough algebra resources yet.  I think you need to buy Gelfand.

 

 

 

Just kidding (mostly)!

 

wapiti,  :cheers2:   This just arrived today.  Wow.  That's just about all I can say. Wow.

[Woodland Mist Academy]

Details! Don't keep us in suspense!!!