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Math Aptitude: Is this inherited only...or can it be encouraged?


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I've been thinking about this lately, and wondered if I could read what others think about this too. Do you think that some children have a certain level of math aptitude and that the curriculum you use should meet them or do you think that given the correct currriculum children will be able to increase their math aptitude? Does this make sense?

 

I'm undecided with what to do with my younger dd. She's using Singpore 4 right now. I do have other math curricula on hand that I'd like to start using more frequently with her (Hands-On Geometry, Patty Paper Geometry, CWP). I haven't had her tested but she is accelerated in other subjects. In math, she really seems bright but not more. She picks up on ideas fairly quickly, but over the last two years or so has had a couple of areas where we needed to spend more time than usual for her (long division, still forgets some facts sometimes but absorbed these quite well, fractions are important so I spent time here too). This is where I get the idea that she is bright but not gifted in this area. (But, I could definitely be wrong.) She has an unusual preoccupation with memorizing license plate numbers and is very observant about patterns in nature. These are the times when I wonder if I've missed opportunities to let her explore math more. Is it possible that a curriculum such as MEP or AOPS might encourage her math aptitude? Or can I relax and realize that I haven't made a huge mistake with her and know that she is bright and will be good in math, but doesn't necessarily need more? I'm so hard on myself sometimes, but I am truly the one that is in a position to make this good for her. It really is up to me.

 

What do you think?

 

She is a 4th grader.

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She has an usual preoccupation with memorizing license plate numbers and is very observant about patterns in nature.

 

I am just tickled by this because I was telling hubby my aunts are fantastic at remembering lottery numbers and matching them to license plate numbers. Imagine you are a passenger in their car and they tell you the license plate number in front of their car was a winning number in which years and how much the number won.

 

On a practical note, this kind of skill is very useful in data mining and actuary and I am sure there are other fields that I am not familiar with. Math aptitude in my opinion is both inherited and cultivated. I find that the math curriculum here is not pushing hard enough and cause the students to slack. While there are people like my dad and brother who needs a lot more practise to master math, plenty of students in asian countries do well with a "harder" math curriculum. Most of my extended family have an easy time with math so genetics does play a small part. We are much better at applied math than theoretical math though which is probably why there are plenty of engineers and accountants.

 

It can definately be encouraged of course :)

My kids have their favorite topics in math due to their aptitude/interest. I just help with reserving and checking out library books. I also print out math circle problems in their interest area.

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i dont think the question you asked is the question you need to ask. it sounds like the real question is, do you think she would get something out of (the curricula you named) or not. A child doesnt have to be 'gifted' to get something positive out of those. Try one and see how she responds . . let her know its something different and if she doesnt like it, you dont have to keep using it. what can go wrong? and even really mathy kids can find some math subjects easier than others.

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Another possibility-has she been formally tested?

 

I went through years of thinking that I was just not good at math. I was on grade level, generally solid there, but somehow, it just didn't work for me the way the more verbal subjects did, and I was constantly getting "You should be better on this". I did great on a lot of the aptitude tests, but it didn't materialize in class. My parents believed, for years, that the problem was math anxiety-that I'd absorbed an idea that "girls don't do math"-and used the fact that in many cases I COULD come up with the correct calculations in chemistry or physics as the reason why I obviously didn't really have a problem with math.

 

When I was in grad school, and was setting up a 504 for teaching the following year, I went through yet another neuropsych eval. And this one noticed something that all the evals the schools had done hadn't-that the spread on my IQ test sections couldn't be explained by motor skills (which is what it had always been ruled out to be-and since I was solidly in the gifted range anyway, no one worried about the fact that I had a close to 80 point spread in some areas and had 99% to 5% scores-it averaged out). So they did more testing.

 

What it came down to was this-I have super, super low scores in visual-spatial processing, and while I'm fine with content in one axis, I struggle with content in more than one at a time. Guess what math is? HIs only question was that he couldn't see how I could be a musician, and as far as we can tell, the difference is that, somehow, my brain processes music notation differently than it processes an algebra problem, a long division problem, a map, or a graph. And since almost all my math work was focused on not only getting the final answer, but getting all the steps down in the correct format in the correct order, and especially once I got to graphing, I was struggling not because I didn't understand it conceptually, but somehow, it was just plain getting messed up between the page and my brain and the paper in front of me.

 

I did have a trigonometry teacher who caught on and gave me a few tips and ideas that helped-he was dyslexic himself and had a dyslexic child-and recognized the signs of an LD when he saw them-but couldn't justify referring for a borderline A/B student in a grade level class who already had an IEP.

 

I suspect a curricula like SM, with it's focus on mental math, would have been great for me, because so much of the focus is mental math, and I was fine as long as I didn't have to write it down. I think I would have loved Fred, and probably would have been better able to pull the concepts out of the text in Fred than in the written out problem examples of Saxon, which is what I went through school under. And I love math manipulatives (and have a kid who HATES them with a passion) because they match the way my brain works. But most of all, I wish I'd known and been told all the way through that "This is hard for you because of the way your brain works. You're figuring out ways to do it, but it's taking you a lot more effort than for most people, and sometimes the things teachers tell you are going to be just plain wrong for you. So, we're proud of that B in Algebra II over the As in everything else and the wins at quiz bowl and all the other stuff you do-because WE KNOW it took you more effort to get that B than basically everything else combined".

 

FWIW, I ended up staying in grad school longer and getting my certification in math ed and math remediation. Once I knew WHY I was struggling, I wanted to figure out how it could be better-and I kind of wanted to remediate myself.

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I haven't had her formally tested...so I can't even say for sure that she is gifted. She displays a number of the traits that causes me to wonder if she is gifted. She has a very mature and usual way of looking at the world. She's very accelerated in language (Reading, writing and spelling are all subjects that I've barely had to teach her...she just absorbed it all and needed more. She's reading at an early high school level easily...and if pushed could probably take on more.)

And it's not really that she struggles with math. No, I actually think that she's quite quick to pick up on the concepts, but it's that she's never needed to be accelerated in math. I have never had to be diligent or consistent with her in language (and yet it has always been difficult for me to keep up with her).

 

I have tried harder lately to increase the amount of time and attention that we spend in math (we went through a very rough time period where we struggled to spend enough time on our schoolwork...we moved across the world...literally.). She is quickly making up for some lost time and I plan to continue to be spend more time in math for her. I think she will respond well to this.

 

I have often wondered how she'd like Life of Fred...hmmmm, I'll have to think about this more seriously.

 

Thank you ladies so much for your help and advice. Getting some feedback has helped me sort out my thoughts and has helped me tremendously! :)

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math aptitude, can it be encouraged?

 

I am not a psychologist of learning and these are only my personal observations.

 

First, I believe that everything can always be encouraged, and that encouragement is the best thing we can do for a student.

 

Second, aptitude in math or anything else, is a (movable) point on a spectrum and seems strong or weak only relative to someone else. Of two children, one may seem not to have math aptitude, but only in comparison to the other, or to a parent. In our family one of our children was assessed by a school teacher to "just not have the math aptitude of the other members of the family ". That child of relatively low aptitude, as viewed by that teacher, became the only member of our family to score 800 on math SAT, including the parents. There are also at least two kinds of math aptitude, speed oriented computation, versus creative problem solving.

 

I was thought to be extremely fast by some of my college students, but when I myself interned at an elite university math dept, I felt like a snail in comparison. (I told a friend I felt like the "Rocky" of algebraic geometry, slow and plodding, but never giving up.) Once during that visit I asked for help from an expert who wrote a few lines on a pad and stopped, which I assumed was because he was stuck. I mumbled it was all right since I "didn't really need it". He remained silent, but looked at me slightly oddly, so in leaving I asked for his page of writing. After studying it in my office for an hour, I realized he had completely solved my problem. After a year visiting in that environment I also became faster in comparison to some people elsewhere. So even "aptitude", or its usual signs, such as speed of comprehension or computation, can be encouraged and enhanced. When I returned to a setting where few people knew enough to discuss my work or even question me, I again lost that sharp edge. So math alertness and speed can also be discouraged.

 

Finally it does not matter how much aptitude we have if we enjoy a subject and can adjust our expectations to reality. There is a place for us somewhere to contribute with our own level of ability.

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...

And it's not really that she struggles with math. No, I actually think that she's quite quick to pick up on the concepts, but it's that she's never needed to be accelerated in math. I have never had to be diligent or consistent with her in language (and yet it has always been difficult for me to keep up with her).

 

...

 

This was interesting to me ... if my older child didn't require regular, challenging math for his mental health, I would never have known what a strong aptitude he has.

 

Regarding the inherited/encouraged thing, of course there is a largeish genetic component -- there always is -- but if the child is above-average bright & especially if she is otherwise neurotypical (that is, barring specific disabilities or processing issues) I think there is good evidence that it is her hard, focused work (more than sheer "talent") that will have the strongest effect on her success.

 

I do think that excellent math skills are personally enriching as well as extremely useful in the world, and for that reason alone I'd encourage you to enrich her math life. Perhaps gently accelerate her until she hits the level that really challenges her; ideally have her on two math tracks, perhaps one math curriculum and ongoing living math books or something hands-on. livingmath.net can help you find resources that parallel her history studies, for example. And if you posted a thread here for living math ideas specific to her interests/age/skill level, I think you would get helpful responses.

 

finally -- you certainly haven't messed anything up, or missed any crucial opportunities yet! I wish my parents had been so alert to enriching my education & encouraging my talents :) .

 

ETA:

RE math curricula, in addition to MEP and AoPS please consider Galore Park (they have Junior Maths and then the So You Really Want to Learn Maths series). The math is excellent, and I've noted it in my mind as esp. "female-friendly" because of the ties made to history and other interesting facets of real life -- also, the author of SYRWTLM is a woman. Not that it is such a Big Deal. Still, just sayin'.

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math aptitude, can it be encouraged?

 

I am not a psychologist of learning and these are only my personal observations.

 

First, I believe that everything can always be encouraged, and that encouragement is the best thing we can do for a student.

 

Second, aptitude in math or anything else, is a (movable) point on a spectrum and seems strong or weak only relative to someone else. Of two children, one may seem not to have math aptitude, but only in comparison to the other, or to a parent. In our family one of our children was assessed by a school teacher to "just not have the math aptitude of the other members of the family ". That child of relatively low aptitude, as viewed by that teacher, became the only member of our family to score 800 on math SAT, including the parents. There are also at least two kinds of math aptitude, speed oriented computation, versus creative problem solving.

 

I was thought to be extremely fast by some of my students, but when I visited the Harvard math dept, I felt like a snail in comparison. Once during that visit I asked for help from an expert who wrote a few lines on a pad and stopped, which I assumed was because he was stuck. I mumbled it was all right since I "didn't really need it". He remained silent, but looked at me slightly oddly, so in leaving I asked for his page of writing. After studying it in my office for an hour, I realized he had completely solved my problem. After a year visiting in that environment I also became faster in comparison to some people elsewhere. So even "aptitude", or its usual signs, such as speed of comprehension or computation, can be encouraged and enhanced. When I returned to a setting where few people knew enough to discuss my work or even question me, I again lost that sharp edge. So math alertness and speed can also be discouraged.

 

Finally it does not matter how much aptitude we have if we enjoy a subject and can adjust our expectations to reality. There is a place for us somewhere to contribute with our own level of ability.

 

 

This was wonderful to read! Thank you!

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This was interesting to me ... if my older child didn't require regular, challenging math for his mental health, I would never have known what a strong aptitude he has.

 

Regarding the inherited/encouraged thing, of course there is a largeish genetic component -- there always is -- but if the child is above-average bright & especially if she is otherwise neurotypical (that is, barring specific disabilities or processing issues) I think there is good evidence that it is her hard, focused work (more than sheer "talent") that will have the strongest effect on her success.

 

I do think that excellent math skills are personally enriching as well as extremely useful in the world, and for that reason alone I'd encourage you to enrich her math life. Perhaps gently accelerate her until she hits the level that really challenges her; ideally have her on two math tracks, perhaps one math curriculum and ongoing living math books or something hands-on. livingmath.net can help you find resources that parallel her history studies, for example. And if you posted a thread here for living math ideas specific to her interests/age/skill level, I think you would get helpful responses.

 

finally -- you certainly haven't messed anything up, or missed any crucial opportunities yet! I wish my parents had been so alert to enriching my education & encouraging my talents :) .

 

ETA:

RE math curricula, in addition to MEP and AoPS please consider Galore Park (they have Junior Maths and then the So You Really Want to Learn Maths series). The math is excellent, and I've noted it in my mind as esp. "female-friendly" because of the ties made to history and other interesting facets of real life -- also, the author of SYRWTLM is a woman. Not that it is such a Big Deal. Still, just sayin'.

 

 

Thank you Ana!

 

I accidently hit the wrong button on your post...I was trying to hit quote but hit unlike instead. I fixed it immediately, but I hope it doesn't show up this way for you! I liked you post very much! :)

 

I'm greatly encouraged that putting more math in front of her can only benefit her as long as she's not feeling overly unhappy or stressed about it. I'll also keep Galore Park in mind when I next order some math curricula.

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Interesting question. Neither of my kids seems particularly "mathy," though I think they would like to be. Things just aren't clicking automatically as they seemed to when I was young. However, this could be because the concepts seem to be introduced to them a bit younger.

 

I think my kids need to go back and re-learn how to think about math. My advanced dd is always in such a hurry to skip ahead, I think she has missed some building blocks that would make things click more easily for her. My slower dd is in dire need of remediation and practice, but I feel that once she gets the concepts, she will be the one for whom mathematical thinking will come "naturally." She probably won't ever be a super math student, but I think it will become intuitive for her once taught properly. (Does that make any sense?) So I think you can probably teach a child to think mathematically, provided she is open to learning.

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I was going to answer in detail but noticed that Ana has already said so much of what I wanted to say. Interest and effort...these are the two things I'm constantly trying to encourage in my home. I try not to think about genes. There are strong genes for laziness in my family lol.

 

I've noticed that once there is interest, effort can be quite easily encouraged. So I spend most of my time planting little seeds of interest, namely by making quality resources easily available where affordable (not necessarily plentifully available though because I've found that doing too much can also backfire). Then I watch as my son puts in the effort and I'm careful to offer just enough praise when necessary, or I dangle a carrot in the form of another cool math book, to keep the effort going. But otherwise, I keep out of the way. The bulk of the effort needs to come from him.

 

Genetically speaking, we have a few poets and writers in the family, but without interest, it has been extremely difficult to encourage my son to write. Wish me luck on that one. :)

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So I think you can probably teach a child to think mathematically, provided she is open to learning.

 

Open mindedness is key and I'm glad SKL brought it up. To extend this point, it is important also to be open to different approaches, trying not to be discouraged that a math solutions key shows a different way of solving a problem, trying not to be discouraged by the problem itself, and being open to the fact that you can ALWAYS come back to a problem. Be open to the idea that you don't need to finish a math book in one year or grade level, be open to the fact that there could be something new for you to learn even if a book is pitched at a younger grade level (something we're still working on!).

 

And this open mindedness can be cultivated through role modelling. When I find myself fearing something or not being able to cultivate my own open mindedness, it's all the more important that I co-learn with my son.

 

To add to my response above, one more approach, apart from interest and effort, is to learn and research fun math ideas with your child, should time permit.

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Loving this conversation! A favorite story I share is about Brian Cox, a particle physicist on BBC documentaries (our family loves this man). He got a D on his Maths A-Level. He says he was distracted with his music interests at the time, but also realized that all you need to do with math is practice, practice, practice.

 

A few random thoughts:

 

I have 4 kids. Until 6 months ago, I thought for sure my kids were humanities types. After being inspired by documentaries and stories of other scientists, I have a college son who is majoring in math, a 13 year old son who is obsessed with physics/astronomy and is doing Algebra 2 with AoPS and a dd10 who now loves math and science and dreams of being a scientist after being a professional ballerina. ;)

 

OP, for my youngest, I exposed dd to things like ViHart on youtube, science and math documentaries, Design Squad and Sci-Girls on pbsgo, Education Unboxed, Scientists in the Field books etc. If I am excited about something, my kids eventually catch on. This doesn't suddenly make for a math or science genius, but it opens the doors of possibilities. She attends ps which uses Everyday Math (aargh). As a supplement, we have always used MEP, which she loved. We now use Math Mammoth; it's easier to concentrate on one subject. She tends to have gaps and confusion to due to the school program and teachers. In the summer, she makes great headway in math, until she is slowed down by school math and a busy schedule.

 

Ds13 always aced his traditional math courses. He was willing to try AoPS. The online class was way too fast for him and he immediately felt defeated. He is a kid who struggles with anything less than 100%. I knew it might be a problem. With resistance, he started going through the textbook on his own. Finally, after a week, he started to really enjoy the way it teaches - now, he likes going deeper and he's getting used to working through difficult problems.

 

I don't know how college boy got interested in math. He is a huge self-learner. Somehow, he found out about a subject called complex systems. The more he learned, the more inspired he became. He was much like my 13 year old - always scoring As in math, but never having to stretch himself. Well, now with college math courses, he has learned that he's not as good at math as he originally thought. But, he loves it enough to figure it out. One interest led to another, and he is now talking about going to grad school for physics. He is only a freshman, so anything can happen of course.

 

I wanted to share my random stories because inspiration and encouragement had a lot to do with my kids' interests. And it is similar to what Brian Cox says. My kids aren't math competition type kids. They don't see numbers in everything. But, they're not going to let math stop them from their passions. :)

 

Oh - and I have to add that dh and I are NOT "math people". ;)

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This is actually a topic I think about quite a bit. I think "how" a student thinks about math can be influenced by how they develop their math skills. For example, I believe that AoPS really trains students to think about the proof behind the math they are doing. That trains the mind to understand the theory vs. just the application or even just the conceptual. (understanding what/how they are doing is still not the equivalent of proving the theorems behind what they are doing.)

 

I do not believe all students need that level of exposure or "mental training" for math. However, for really strong math students with the aptitude to spend the time on the theory, I see strong benefits. It is very unlikely that those skills will be well-refined/trained without exposure to resources like AoPS.

 

The development of those theoretical cognitive skills are also not going to be confined just to math. It really is mental training.

 

But for students that don't love math or don't have a strong aptitude, I think it that sort of approach is actually "over-complicating" math for them and may cause more harm (like hating math or thinking they are dumb) than good. Those sorts of cognitive skills can be developed via other subjects/materials that spring from their inherent skills/interests/aptitudes.

 

I'm really tired, so I apologize if the above is not clear. I just know that our oldest ds is very much our youngest ds and he would have thrived doing AoPS if I had known about it. It would have really developed his theoretical thinking skills more vs. focusing so much on his analytical/application oriented math program. Yet, I see our strong -at-math-but-does-not-like-math dd developing the same sort of elevated critical thinking skills via intense language/literature/poetry studies. (I'm probably not making any sense at all. :p )

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The development of those theoretical cognitive skills are also not going to be confined just to math. It really is mental training.

 

But for students that don't love math or don't have a strong aptitude, I think it that sort of approach is actually "over-complicating" math for them and may cause more harm (like hating math or thinking they are dumb) than good. Those sorts of cognitive skills can be developed via other subjects/materials that spring from their inherent skills/interests/aptitudes.

 

 

You make perfect sense, 8. This "mental training" is what I find most rewarding, especially when crossing over into other areas of life (academic or not). Thinking through a problem. Considering all of one's options. Not being afraid to approach a challenge. Allowing yourself the the time and patience to struggle. Being proud of climbing that hill or mountain.

 

I am not a lifelong homeschooler and only hs one right now. But, I have learned through these boards, that it's a necessary skill for my kids to have. And I am trying to develop it in a few different ways.

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The development of those theoretical cognitive skills are also not going to be confined just to math. It really is mental training.

 

Yet, I see our strong -at-math-but-does-not-like-math dd developing the same sort of elevated critical thinking skills via intense language/literature/poetry studies.

 

 

Actually, these are some of the thoughts that brought me to ask this question. I'm concerned that since language/literature/poetry is stronger for me and for my older dd (who is very passionate and vocal in this area) that we may have, unintentionally, caused her to revert any skills in math she might have had into language. Does this make sense? I don't want to give the impression that we neglect interest in math in our house or even speaking negatively about it (although my older dd struggles with math and this is seen). I'm just wondering if our families over-enthusiasm ( :) )with language caused her, somewhere over the years, to just get math done and put her greater efforts in language. On the other hand, she does have a lot of natural interests in language too, so maybe this was a natural progression for her anyway.

 

She has separated herself enough from her sister's identity (a good thing for her....she's matured a lot over the last two years in becoming her own individual person) to have shown that she finds science interesting and wishes to pursue this area. I think the combination of her strong interest in science, how life/nature works, patterns in nature and interest in numbers all lead to a need for more math. I'm wondering, now that she has a stronger math foundation (4th grade math really begins to lay some foundations), if she might be ready to start thinking more mathematically. (She watches her sister's algebra dvds because she finds them interesting. :))

 

I'm going to stay with Singapore, increase her math time (using Hands-On Geometry, Patty Paper, CWP) and consider looking at one or two other math supplements (maybe Hands-On Equations? or something else? MEP? ) When would it be the right time to try something like AOPS? I would probably know this when I see it, right? I'll have to look at the AOPS site again. I've forgotten what their earliest math level is? (Besides Beast .... or something like that?)

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I'm concerned that since language/literature/poetry is stronger for me and for my older dd (who is very passionate and vocal in this area) that we may have, unintentionally, caused her to revert any skills in math she might have had into language. ...... I'm just wondering if our families over-enthusiasm ( :) )with language caused her, somewhere over the years, to just get math done and put her greater efforts in language. On the other hand, she does have a lot of natural interests in language too, so maybe this was a natural progression for her anyway.

 

 

It is possible to be strong in both language/literature/poetry and math. Both requires critical thinking skills to be honed. I always find it interesting when people I meet think that LA and math "talents" have to be mutually exclusive.

 

After all Thomas Edison said "Genius is one per cent inspiration, ninety-nine per cent perspiration"

 

Canada's Math Kangaroo page has past years contest questions and solutions for 1st to 12th grade. Maybe your daughter might want to try solving.

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I agree with Math Kangaroo-Dd has been doing released tests to practice for the contest (tomorrow, here), and they're pretty good-and a lot of them touch on less commonly taught types of problems. On grade 3/4 tests, DD has had a lot of geometry and visual problems.

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It is possible to be strong in both language/literature/poetry and math. Both requires critical thinking skills to be honed. I always find it interesting when people I meet think that LA and math "talents" have to be mutually exclusive.

 

After all Thomas Edison said "Genius is one per cent inspiration, ninety-nine per cent perspiration"

 

Canada's Math Kangaroo page has past years contest questions and solutions for 1st to 12th grade. Maybe your daughter might want to try solving.

 

 

Thank you so much for sharing this. DD will love it. I've heard people mention Math Kangaroo, but I still don't know what it is. I guess I better check!

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The development of those theoretical cognitive skills are also not going to be confined just to math. It really is mental training.

 

But for students that don't love math or don't have a strong aptitude, I think it that sort of approach is actually "over-complicating" math for them and may cause more harm (like hating math or thinking they are dumb) than good. Those sorts of cognitive skills can be developed via other subjects/materials that spring from their inherent skills/interests/aptitudes.

 

I'm really tired, so I apologize if the above is not clear. I just know that our oldest ds is very much our youngest ds and he would have thrived doing AoPS if I had known about it. It would have really developed his theoretical thinking skills more vs. focusing so much on his analytical/application oriented math program. Yet, I see our strong -at-math-but-does-not-like-math dd developing the same sort of elevated critical thinking skills via intense language/literature/poetry studies. (I'm probably not making any sense at all. :p )

 

 

This makes perfect sense and is one of the main tenets of liberal education. It is the reason that the College of Arts and Sciences concept exists and is unified under one umbrella rather than being split off into separate colleges of thought like business and education schools.

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I know our MK testing site still has spots available. I don't know if they allow late registration or not. 4th grade US seems to have a lot of visual problems and logic (3rd and 4th use the same materials). DD's enjoyed it-and is looking forward to tonight for the T-shirt (she loves the Kangaroo carrying the pi-she's obsessed with irrational and imaginary numbers).

 

I will say that the Math Kangaroo Canada site is MUCH nicer than the US one-I've bookmarked it. I think DD will enjoy the Canada practice papers :).

 

Continental Math League (www.cmleague.org) is another option. For a homeschooler to register individually, it's $15 for the meets. They're more numeric and less visual/logic than MK (at least, at DD's age/grade level), but are still beyond what is typically expected for the grade level. The practice materials are great. I do wish they'd take credit cards and online payments, though. The season is done for this year (the final round was March 14), but registration will open again in the fall.

 

Next year, she'd be eligible for the Mathnasium Tri-mathlon (mental math, magic square, counting game) which is more numeric as well. It's free, and the kids get a goody bag for participating. It's easier than MK or CML by quite a bit. In the Fall, the American Math Challenge is online, and in the Spring, World Maths Day is part of the World Education games. Both of these focus on computation and speed almost exclusively and are done at home on the computer. The certificates are nice, especially if you have a color printer (I use resume paper for certificates). I think my DD has been more inspired by these to actually memorize her math facts than anything else.

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There are a lot of great thoughts here. Reading them I am reminded again that encouragement is perhaps the key concept. In my own high school there was a trophy case where the math team's trophies were displayed as prominently as those of the basketball team. In my children's fine private school the staff regarded math as less holy somehow than English which they worshipped, and math was done more in secret, while music and theater and English were celebrated publicly.

 

One parent whose child played on the football team and was a star there asked me why I thought it important for kids to compete in math - wasn't it enough just to enjoy doing it? A similar atmosphere existed in one son's earlier public elementary school. Perhaps since not everyone is equally gifted or accomplished in math it was considered inappropriate to celebrate those who were, as if it meant unfairly slighting the average or below average math student.

 

At the same time all other abilities, including physical ones were trumpeted aloud. There was even a chart posted on the door where children's heights were drawn for public comparison and on display every day. Every later-growing child had to look at that every day perhaps with less than delight. But academic accomplishments were to be a secret. It is amazing when a child keeps up his/her love for a subject under the conditions that obtain in many schools.

 

So we might try to celebrate, encourage and value the abilities a child displays or even aspires to. This requires skill and tact, since over - celebrating an obvious gift may lead a child to ignoring other areas where she needs more work to excel. I struggled with this, but if we try to keep the child's welfare and happiness in view, over our own special area of pride, it may help.

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I don't know if they are or not, but the US one only has papers from tests several years back, and the Canadian site has different ones (including the worked solutions from last year's test), so it's a different set of problem sets for DD to play with. The Canada site has online practice, too.

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