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Saxon Math -- Early Impressions


elmerRex
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It seems to me that it would be pretty unfair if some very highly gifted and hard-working students ended up being excluded because they weren't able to follow a special full-time curriculum for a few years beforehand.   I don't think this is how the contests worked in the past, and I hope it still isn't the case today.   

 

 

Last thing I will say, to compete successfully nationally or internationally in mathematics requires about 30 hours of study a week for about 5 to 7 years. Not any different from any other 'Olympian.' We are talking years of hard work and dedication. 

 

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Math isn't just about the challenge, it's about the speed, automaticity, and application.

 

Not slamming Saxon here, but I think 99% of mathematicians would disagree with this statement.  The best math problems take days, weeks, or years to solve.  Fermat's theorem took considerably longer than that.

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I'll take a stab at this, Courtney. Giving gifted average work teaches them 1) everything is easy, 2) I'm smarter than everyone else, and 3) I don't have to work hard to succeed. These are terrible lessons. This is why I ramp it up until the work is at a difficult level for my child. He needs to know struggle. 

 

Socially, having known struggle, he can actually better relate to his peers even if he is working years ahead. 

 

 

.

 

Courtney, some kids just aren't average, and no wishing that they were will make them so.

 

Ruth in NZ

 

Well, right, there are kids who teach themselves to read, etc. But I thought we were talking about non-gifted kids.  

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I'm perplexed. Are you joking, or are you serious? I honestly don't even know how to respond... This is certainly enlightening....

 

I'm not sure what you're responding to. Did my teachers try to drill our accents out us? Absolutely. Still happens. My husband finds it very disconcerting to hear my accent change when I'm tired or upset.

 

ETA: If you have other concerns please feel free to contact me directly. I'm going to stop following this thread. Too busy.

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I'm not sure what you're responding to. Did my teachers try to drill our accents out us? Absolutely. Still happens. My husband finds it very disconcerting to hear my accent change when I'm tired or upset.

 

ETA: If you have other concerns please feel free to contact me directly. I'm going to stop following this thread. Too busy.

 

No, it wasn't the teachers' drilling. 

 

I have no need to discuss concerns,  but I did want to let you know I saw your response to my post and your suggestion to contact you directly.

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This is a great point, and one of the reasons we keep our kids slowed down when they could move further ahead. If was a choice that made sense for our goals, and diversifying some of their math into more practice or a broader set of skills instead of just accelerating arithmetic has been a good way to keep them more balanced and less asynchronous.

 

This is exactly what I'm trying to do with my son. :) OP said she has been doing other enrichment as well and teaching her kids with her own instruction, so I believe this is her case, too.

 

I agree with lewelma that it'd be greatly beneficial to develop a good balance between arithmeric practices and the critical thinking/problem solving enrichment in math from early elementary years but I agree with you, boscopup and ElizaG more that the latter can come later at a student's pace and building a strong arithmetic foundation at earlier years can lesson the frustration of solving higher level conceptual problems. Too much challenge at earlier years can be a joy killer, too, for some smart kids.

 

There is also the tendency to keep accelerated kids accelerated.  To get so excited that your kid is xx many years ahead. To be proud.  To push.  I have so been there when my older took 3 years to get through the AoPS intro algebra book.   :toetap05:  So what I am hoping to convey is that you can accelerate your kids to calculus by age 12, without slowing down to do the other half of the math curriculum - the critical thinking/problem solving.  But then you have a kid in no-man's land -- into college-level courses without the skill to do the equally important other half.  Once again NOT saying this of the OPer, but saying it to those reading who may not fully realise (as I didn't ) that the other half is equally important and equally time consuming.

 

According to my not-so-long observation on this forum, what I see more frequently than such attitude/tendency of pursuing radical acceleration is a tendency that there seem to be a lot more general focus/interest on conceptual mastery & critical thinking development, rather than doing enough review or math fact drills. Anything boring, dry, repetitive or workbook-y seem to be regarded as something to be avoided, which I think is a mistake. Many people here seem to be looking for a "fun" math program and I was really surprised when I saw people often asking if they can use LoF only for their math. I see that many people choose just one single program for math and keep switching it to something else over the years.

 

FWIW, in South Korea I was taught in a similar way to the "Singapore way" at school but most kids including myself used at least 2~3 different kinds of complete programs in different methods/focus, depending on their levels, on their own to supplement the textbook. We couldn't spend 30 hours a week for math alone since we were also taking other classes in 12+ subjects in the same year, but the intensity of math study was pretty high. Going through a single approach/method was never enough because we never knew what kind of irregular problems would appear on the tests. We, including PG/gifted students, all went all the way through Kumon or other similar arithmetic drill programs from kindergarten (or earlier) in order to reach automatic, speedy and 99% accurate arithmetic mastery, and tackling with the harder, wordy problem solving in the math team didn't come until 5th grade. Of course, we did a lot more challenging materials in middle and high schools. And most of us did fine in the math olympiads, later at college and STEM occupations. I believe Saxon is a better, more comprehensive program than Kumon. While it may be true that a Saxon-type of program is not necessary for PG students (who are extremely rare), I believe Saxon could work for many smart students as one of their main programs or supplements, and not for many others. I think saying Saxon is not good for gifted kids is as much generalizaion as saying anybody with dedication and hard work can do 5th grade math at 6yo. I agree I wouldn't use Saxon as a sole program for my bright son, but think it might serve the purpose of building good discipline and daily practices for us, alongside with our other concept-based programs. We homeschoolers thankfully have tons of different math programs available to choose from, and it'd be up to us how to mix and utilize these "tools" to fit each child. :)          

 

Last thing I will say, to compete successfully nationally or internationally in mathematics requires about 30 hours of study a week for about 5 to 7 years. Not any different from any other 'Olympian.' We are talking years of hard work and dedication. 

 

 

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Not slamming Saxon here, but I think 99% of mathematicians would disagree with this statement. The best math problems take days, weeks, or years to solve. Fermat's theorem took considerably longer than that.

To add to this, at the elementary level especially, automacity is not the same thing as raw speed. Faster isn't smarter. My most math-gifted and most accelerated kid would never have passed a timed math fact drill in early elementary, even while he was able to calculate numbers to powers in his head. Fast he isn't, LOL.

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While it may be true that a Saxon-type of program is not necessary for PG students (who are extremely rare), I believe Saxon could work for many smart students as one of their main programs or supplements, and not for many others. I think saying Saxon is not good for gifted kids is as much generalizaion as saying anybody with dedication and hard work can do 5th grade math at 6yo.

 

This.

I can probably be convinced that kids in the upper .01, or .001% will NOT be served by Saxon, but simple statistics put most gifted kids in the 1-2% (or even 1-6 or 8%, depending on how generous we are) range and observation has shown that many (most?) of those kids will be perfectly satisfied with the results they get from Saxon.

I couldn't care less about math olympiad or anything like it. That's not even *available* in rural America. I just want to know that my kid will have the basis for engineering, physics, or something similar.

Given the number of parents and teachers who sent their bright students off to engineering schools with Saxon, and continue to recommend it, I have to believe that my observations aren't too far off the mark that it'll give most gifted kids a perfectly good foundation.

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Last thing I will say, to compete successfully nationally or internationally in mathematics requires about 30 hours of study a week for about 5 to 7 years. Not any different from any other 'Olympian.' We are talking years of hard work and dedication.

 

A person who eat sleep think math is not going to find a single math book that works. It would be a mish mash plus lots of interaction with intellectual peers.

Olympics training starts earlier than three in some countries. Maybe look at the documentary on Nadia Comaneci (the first perfect 10 gymnast) and just think of something similar to the children who represent their country for math Olympiads.

 

For gifted kids who are not interested in being theoretical mathematicians but have other interests, Saxon as a get it done math for an hour a day isn't going to be a killjoy.

 

ETA:

2014 IMO questions. Question 6 is suppose to be the fun one.

2014 IMO in Cape Town, South Africa

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We have used Saxon math for grades 1-Algebra 1.  We have strayed here and there, but always come back to Saxon.  My older two went to public school in High School, and did well.  They missed Saxon Math though, because they truly understood it.  My 15yo is at a Christian School, and Math is her favorite subject. The Christian School uses Saxon. ALL 3 have done well on PSAT/SAT math scores.  The best math is the one that the child truly understands... for us, that is Saxon.  Sure, there are "more advanced" math programs out there, but I am not in a race... I just want my kids to understand math. Saxon does that for our family.... but may not for another family!!  Find your math niche and stick with it!!

 

My younger three will be using Saxon as well.  4yo will begin math 1, 7yo math 3, and 10yo math 65.

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Injecting myself into the drill debate here.  :tongue_smilie:

I think Singapore has a loooot of drill. I am surprised that some of you think it's not enough. We have done a combo of textbook, IP and CWP, and frankly some of those pages in IP books are just packed with "do it over and over and over" type of exercises. I couldn't imagine adding more.

 

Has anybody seen Russian Math 6 textbook? If you have, this was a standard type of textbook in our schools. We did no additional drill at all and I wouldn't say we were weak at computation. I think some kids need more drill than others, but there are success stories out there for general public without much drill as well. 

Also, it's not like once you learn how to add, you never do it again. You use arithmetic to solve 'advanced" problems, so you do get your drill, in a different way.  :D

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I'll take a stab at this, Courtney. Giving gifted average work teaches them 1) everything is easy, 2) I'm smarter than everyone else, and 3) I don't have to work hard to succeed. These are terrible lessons. This is why I ramp it up until the work is at a difficult level for my child. He needs to know struggle. 

 

Socially, having known struggle, he can actually better relate to his peers even if he is working years ahead. 

 

Ruth in NZ

 

I agree with this.  And, I do the same thing for a different reason.

 

I dont think I know much about giftedness so I will refrain from that. My daughter is a strong VSL and seems accelerated.    The curricula that we use at home challenges her at appropriate levels. This learning makes her feel confident.

 

While I think she would understand the struggles of her peers, she needs enough challenges and learning to not let her   perfectionism (coupled with being a strong VSL) damage her self-esteem.  Being a VSL, she prefers a different learning approach and when she gets it at home she has her proud moments giving her self-confidence.   She has become more active at her day care after we started doing our curricula at home (just an hour in a Montessori way)

 

I would never want to move up so fast unless her emotional maturity and academic abilities align well. Please dont quote me, I sincerely apologize if I haven't phrased it right - its just being ESL or my inabilities to convey it.

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Injecting myself into the drill debate here.  :tongue_smilie:

I think Singapore has a loooot of drill. I am surprised that some of you think it's not enough. We have done a combo of textbook, IP and CWP, and frankly some of those pages in IP books are just packed with "do it over and over and over" type of exercises. I couldn't imagine adding more.

 

Has anybody seen Russian Math 6 textbook? If you have, this was a standard type of textbook in our schools. We did no additional drill at all and I wouldn't say we were weak at computation. I think some kids need more drill than others, but there are success stories out there for general public without much drill as well. 

Also, it's not like once you learn how to add, you never do it again. You use arithmetic to solve 'advanced" problems, so you do get your drill, in a different way.  :D

 

I guess, to me, using a multiple program is more due to a "methodology" issue than the number of drills. I want my student to be able to solve basic arithmetic and word problems presented in any other different order/method/layout/format and not fixated with one certain way of doing it, and his accelerated pace allows us time to explore wider. If my students were whizing through Singapore IP and CWP, of course, it'd be time to move on to the next grade level. But I see a lot of people including us using those books a semester or a year behind. But then again, that's just me and there's nothing wrong with using a single solid program if it works well since being a curriculum junkie like me is not really cost-effective  :D nor necessary for some kids.

 

It's no good to us if they can solve complex puzzles but can't factor proficiently.

 

This speaks volumes to me. 

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I agree with this.  And, I do the same thing for a different reason.

 

I dont think I know much about giftedness so I will refrain from that. My daughter is a strong VSL and seems accelerated.    The curricula that we use at home challenges her at appropriate levels. This learning makes her feel confident.

 

While I think she would understand the struggles of her peers, she needs enough challenges and learning to not let her   perfectionism (coupled with being a strong VSL) damage her self-esteem.  Being a VSL, she prefers a different learning approach and when she gets it at home she has her proud moments giving her self-confidence.   She has become more active at her day care after we started doing our curricula at home (just an hour in a Montessori way)

Not wanting to sound like a know-it-all -- because I really don't know much about anything -- but I bought heavily into this idea when my eldest child was four, and now think differently.    In hindsight, I'm not sure why I put so much stock in it, except that I was a nervous parent and it sounded plausible.   That's why I mentioned "theories" above.

 

Based on six more years of experience with that child, and several with younger siblings, two things have been brought home to me:

 

1) If bright/gifted children are having emotional or social difficulties, this isn't necessarily going to be solved by giving them additional challenges.

 

2) If they do need more challenges, academic challenge isn't necessarily going to be the most appropriate kind.

 

At this point, when it comes to acceleration and advanced work, I can relate most to what Courtney and Hunter are saying in this thread.  

 

(It turns out that this homeschooling/child-rearing thing is a lot more complicated than I was expecting.   But also more fun.    :001_smile: )

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I think it is extremely narrow to plan for every student capable of acceleration, to use a curriculum designed to prepare them for a competition, that takes 30 or more hours a week to prepare for.

 

Just because a student can doesn't mean they should.

 

Some religions and worldviews frown on competition and focus on personal pursuit of excellence and/or group benefit. I don't know that these groups are wrong.

 

Some students are globally gifted and capable of accelerating in all subjects, but there just is not time to do that. I don't believe that we should choose math as the default time gobbler for all students. There are so many options for a student to focus on.

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I think it is extremely narrow to plan for every student capable of acceleration, to use a curriculum designed to prepare them for a competition, that takes 30 or more hours a week to prepare for.

 

Just because a student can doesn't mean they should.

 

Some religions and worldviews frown on competition and focus on personal pursuit of excellence and/or group benefit. I don't know that these groups are wrong.

 

Some students are globally gifted and capable of accelerating in all subjects, but there just is not time to do that. I don't believe that we should choose math as the default time gobbler for all students. There are so many options for a student to focus on.

 

For the record, AoPS isn't just to prepare for competitions. My dd has no desire to do math competitions, but it is still a good fit for her. She doesn't spend 30 hours a week on math--not by a long shot.

 

We are doing 10+ subjects plus extra-curriculars, volunteering, and social time. AoPS isn't always a time gobbler. :)  It's a tool, just like everything else. Use it how your family sees fit. (Or not. ;) )

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Some religions and worldviews frown on competition and focus on personal pursuit of excellence and/or group benefit. I don't know that these groups are wrong.

 

 

 

I wanted to pull this out specifically. AoPS focuses on personal pursuit of excellence.in.spades.  It even has quotes that we stop to discuss and ponder. It's not a stretch to say AoPS plays a part in making us better people. I don't disagree with a wordview that focuses on personal pursuit of excellence. I do disagree with the notion that this is counter to the goals of AoPS. The competitions are fun for the people who do them. Games, child's play, if you will. They love the challenge and the hard work. The ultimate competition is within yourself as you strive for excellence.

 

(I would also like to note that many churches have Bible Bees and the like which are competitions.)

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I think it is extremely narrow to plan for every student capable of acceleration, to use a curriculum designed to prepare them for a competition, that takes 30 or more hours a week to prepare for.

 

Just because a student can doesn't mean they should.

 

Some religions and worldviews frown on competition and focus on personal pursuit of excellence and/or group benefit. I don't know that these groups are wrong.

 

Some students are globally gifted and capable of accelerating in all subjects, but there just is not time to do that. I don't believe that we should choose math as the default time gobbler for all students. There are so many options for a student to focus on.

 

I think this is not the point being made.  AoPS provides a curriculum, but it also has a couple of books / courses that are designed for competitions.  When people discuss AoPS, they're usually talking about the former.  Honestly, it isn't for everyone, but it is excellent for kids who abstract well and need to understand why as well as how.  Some of the AoPS problems can get very, very hard, but are clearly labeled as "challenge" problems, and not strictly required.

 

For kids who need drilling, AoPS does not stand by itself very well.  It is really aimed at a particular breed of student.  I haven't yet met a kid that really likes both -- it's pretty much one or the other.

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AoPS is used by students that aren't doing math competitions. It also doesn't require 30 hours of study per week. Lwelma was talking about studying for IMO, not the AoPS curriculum. Two totally different things! My student spends 30-45 minutes per day on AoPS, plus 10-15 minutes a day on a spiral elementary curriculum a couple grade levels below his working level. He likes this combo, and the hour per day spent on math is perfectly appropriate for a 5th grader. He's not interested in math competitions. He likes math and enjoys the hard problems that AoPS provides. He also likes just practicing easy math sometimes. He is ok with drill as well (during the exponents chapter, he needed more practice, so I pulled out Dolciani Prealgebra, and according to her Wikipedia entry, she was a big proponent of drill and kill... her textbook certainly suggests that statement to be true).

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 What nut jobs we all are on these boards, and hopefully our kids survive our nuttiness!

:smilielol5:

 

 

I'll be very interested to hear how the OP progresses with her course of study with her child. You just never know what might benefit some poor parent searching for help on the forums, if they can wade through all our individual opinions, experiences, and biases to do it. This has been a really interesting thread and I've enjoyed it :)

 

Me too! :cheers2:

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I think a point was made that AOPS should be used instead of Saxon, because Saxon did not prepare a student for the MO and AOPS did. Did I misunderstand that? If I did, I'm sorry.

 

Sigh, these are my posts you are referring to.  Yes, you misunderstood, probably because I simply cannot explain what I am trying to say.  extra sigh.

 

First of all, I hope everyone here sees me as a generally helpful, nice person.  I am NOT trying to say everyone has to be like my kid, or even every mathematically gifted kid has to love math or want to do a lot of it, or even that every mathematically gifted kid who does love math has to do competitions.  No no no.  I just suck, apparently, at explaining myself.

 

Of course, different kids are different.  My younger is 3 years advanced in math and will NOT use AoPS. I just got out the Saxon book with him today because of this thread, and he loved it.  We won't use it every day, but I think it will be a nice augmentation to the curriculum we are using.

 

I got involved in this conversation because I saw some very advanced students flying through a program.  I wanted to caution both the OPer and any others that *if* your student is moving so fast through Saxon, that they are likely to end up finishing early.  And if your student has the possibility of finishing early, then it is worth your time to include at least a part of the other half of the math curriculum, a part that Saxon does not contain.  Obviously, not all kids need hard core problem solving skills, and clearly Saxon is enough for most students. But a very gifted math student (however you might want to define it, and possibly the OPer's kids) is likely to finish Saxon by the age of 12 or 13. As I said earlier, this puts the student into the no-mans land of university math without hard core problem solving, and at age 12 (or 13 or 14 or 15) where the student would still need more math credits to fulfil most highschool graduation requirements.  You can rectify this by either mixing Saxon with a program that contains more problem solving, or by using a program where problem solving is integrated in with the subject material.

 

I brought up the competition stuff ONLY to try to clarify that there is a lot of high school level math out there that is not in the Saxon books.  *I* did not realise this when I started down this path.  I did just fine, thank you, with a standard high school math curriculum, but then I hit university math in university and I. could. not. do. the. work.  I did not have the problem solving skills.  Clearly, in school I had to use the books that were given to me, but if someone had slowed me down (I was 3 years ahead) by teaching me the problem solving, I might have continued in math in university because I loved it as a teenager. Given that we are homeschoolers, we have the opportunity to augment *if* the student wants it or *if* we think it is necessary. There appears to be a lot of homeschoolers (and I was one of them) who do not realise that there is an entire extra half of high school math that can be taught if desired, and that half is NOT in Saxon.  I only brought up the *highschool* level competitions as a way of trying to back up my statement that there is *more* math for high schoolers out there that is not just *more* subject matter, but rather another way of thinking.  I brought it up because *I* did not know about it until Kathy in Richmond explained it to me 2 years ago. Obviously you can study this way of thinking and still have absolutely no interest in competitions.

 

So please assume the best of me.  I am not out to slam Saxon!  Saxon does very well what Saxon does.  But there is *more* for those who want it.

 

Ruth in NZ

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I don't believe that we should choose math as the default time gobbler for all students. 

I strongly don't believe math is the default time gobbler for most American students. I just have never, ever had this impression at any point in my life.

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Last thing I will say, to compete successfully nationally or internationally in mathematics requires about 30 hours of study a week for about 5 to 7 years. Not any different from any other 'Olympian.' We are talking years of hard work and dedication. 

 

How do public school kids do this?  :ohmy:

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Sigh, these are my posts you are referring to.  Yes, you misunderstood, probably because I simply cannot explain what I am trying to say.  extra sigh.

 

First of all, I hope everyone here sees me as a generally helpful, nice person.  I am NOT trying to say everyone has to be like my kid, or even every mathematically gifted kid has to love math or want to do a lot of it, or even that every mathematically gifted kid who does love math has to do competitions.  No no no.  I just suck, apparently, at explaining myself.

 

Of course, different kids are different.  My younger is 3 years advanced in math and will NOT use AoPS. I just got out the Saxon book with him today because of this thread, and he loved it.  We won't use it every day, but I think it will be a nice augmentation to the curriculum we are using.

 

I got involved in this conversation because I saw some very advanced students flying through a program.  I wanted to caution both the OPer and any others that *if* your student is moving so fast through Saxon, that they are likely to end up finishing early.  And if your student has the possibility of finishing early, then it is worth your time to include at least a part of the other half of the math curriculum, a part that Saxon does not contain.  Obviously, not all kids need hard core problem solving skills, and clearly Saxon is enough for most students. But a very gifted math student (however you might want to define it, and possibly the OPer's kids) is likely to finish Saxon by the age of 12 or 13. As I said earlier, this puts the student into the no-mans land of university math without hard core problem solving.  And at age 12 (or 13 or 14 or 15) where the student would still need more math credits to fulfil most highschool graduation requirements.  You can rectify this by either mixing Saxon with a program that contains more problem solving, or by using a program where problem solving is integrated in with the subject material.

 

I brought up the competition stuff ONLY to try to clarify that there is a lot of high school level math out there that is not in the Saxon books.  *I* did not realise this when I started down this path.  I did just fine, thank you, with a standard high school math curriculum, but then I hit university math in university and I. could. not. do. the. work.  I did not have the problem solving skills.  Clearly, in school I had to use the books that were given to me, but if someone had slowed me down (I was 3 years ahead) by teaching me the problem solving, I might have continued in math in university because I loved it as a teenager. Given that we are homeschoolers, we have the opportunity to augment *if* the student wants it or *if* we think it is necessary. There appears to be a lot of homeschoolers (and I was one of them) who do not realise that there is an entire extra half of high school math that can be taught if desired, and that half is NOT in Saxon.  I only brought up the *highschool* level competitions as a way of trying to back up my statement that there is *more* math for high schoolers out there that is not just *more* subject matter, but rather another way of thinking.  I brought it up because *I* did not know about it until Kathy in Richmond explained it to me 2 years ago. Obviously you can study this way of thinking and still have absolutely no interest in competitions.

 

So please assume the best of me.  I am not out to slam Saxon!  Saxon does very well what Saxon does.  But there is *more* for those who want it.

 

Ruth in NZ

You couldn't be any more clearer. Honestly, sometimes I wonder if people are confused because they haven't ever seen "the other half of the math curricula." 

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Just to be clear, this is an aside and has nothing to do with the conversation about problem solving.  Don't want confuse anyone with another red herring. :lol:

 

How do public school kids do this?  :ohmy:

 

I know quite a few gymnasts that train for 25 hours a week and then have comps.  Same thing I guess. Just really long hours.  I also know that a large number of the kids that attend the USA math training camp come from a certain subset of schools.  They attend the advanced classes that are taught by real mathematicians who have an eye on these competitions and know the kind of thinking that needs to be worked on.  Exeter is one of them.  In NZ, 70% of the kids attending the camp come from 3 schools (all public).  If the school has these specialized teachers, they can identify the student talent and get the kids studying right from 9th grade or earlier if it is a K-12 school. So it is a part of their school/homework rather than a 30-hour tack-on. The 2 school kids from our town were taught by their parents in what I guess you could call afterschooling.

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How do public school kids do this? :ohmy:

from a canadian news article,

"Underlying Shanghai’s stellar test scores, though, is something far more difficult to transplant elsewhere: what happens outside the classroom. Chinese math performance, for better or for worse, is driven in large measure by a cultural commitment to pouring hours into math, eschewing soccer games for quadratic equations."

 

Actually if a child afterschool at least 3hrs per day on math (or science/gym/music/dance/swim/tennis/squash ....) and spend most of the weekend hours on math, 30hrs is easily reached. A friend was a competitive swimmer, swam before breakfast and after school (public school), did her homework after dinner, still made it to med school and became a pediatrician.

 

now we are derailing the thread again :lol:

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from a canadian news article,

"Underlying Shanghai’s stellar test scores, though, is something far more difficult to transplant elsewhere: what happens outside the classroom. Chinese math performance, for better or for worse, is driven in large measure by a cultural commitment to pouring hours into math, eschewing soccer games for quadratic equations."

 

Actually if a child afterschool at least 3hrs per day on math (or science/gym/music/dance/swim/tennis/squash ....) and spend most of the weekend hours on math, 30hrs is easily reached. A friend was a competitive swimmer, swam before breakfast and after school (public school), did her homework after dinner, still made it to med school and became a pediatrician.

 

now we are derailing the thread again :lol:

Sorry, but had to ask! :)

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Before I dive in, in this thread a disclaimer: I do NOT have any experience with Saxon, so my comments are strictly a general response to several posts on this thread and not about any curriculum in particular.

 

Competitions are a red herring to the point I was trying to make.  Sorry for the confusion.

 

Sometime back I came across in my student's Math textbook a blind rule which he was to memorize and it annoyed me to no end. The rule was that you can compute (n+1)2 by adding 2n+1 to n2. Knowing algebra, I knew how they had computed that, but then I had to make this rule accessible to my student without the Algebra. A google search brought up many visual representations of that rule, and when I saw that I was gobsmacked. Duh! The pattern was obvious. To see a visual confirmation of the algebra which was all I had learnt was mind-expanding. It was my personal Aha! moment. That led me to make sense of a number of other rules, e.g. the sum of n odd numbers is n2. Devoid of the visual context, this rule sounds so esoteric and mystical and magical. But when you actually try to make sense of why this is so, it becomes so obvious!

 

I think this particular incident had me looking for curricula that help students make sense of the maths they are learning and that was when I came across Paul Lockhart's A Mathematician's Lament (link opens PDF). When I first came across this piece a few years back, I must admit I found it mildly interesting and did not understand much of what he was lamenting about. But this time around I was hanging on to his every word and nodding along.

 

So, yes I understand the point you were trying to make Ruth. I think there is a general idea expressed in this thread that competition math is for the particularly gifted, the ones in the top 2%. That most others just need the "get it done" variety of Maths. But I have come to believe that this need not be true, and indeed in most cases, this thinking may even be counterproductive. Maths is not just a way of adding up numbers. It is instead, a way of making sense of the world through a unique lens. I don't see why we should deprive our children from developing this wonderful mathematical sense.

 

Curricula geared towards treating Mathematics as a creative endeavour, a tool for problem solving and a way of comprehending patterns we see around us, are also the curricula that can get you through math competitions. But you do not need to have only that end in mind when using such Curriculum. Undoubtedly there will be some kids who are profoundly gifted with Maths. Morever, to do well in a competition, additionally one would have to put in a lot of work which not all children may be driven to do. But even so, all kids can immensely benefit from engaging with Maths and getting down and dirty and grappling with challenging problems and working on their innate mathematical sense.

 

I have also been going through the open course "How to Learn Math" geared towards Parents and Educators and I think Prof. Jo Boaler makes an excellent case for exposing children to Mathematics in a creative and challenging way. I highly recommend it.

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I think it is extremely narrow to plan for every student capable of acceleration, to use a curriculum designed to prepare them for a competition, that takes 30 or more hours a week to prepare for.

 

Just because a student can doesn't mean they should.

 

Some religions and worldviews frown on competition and focus on personal pursuit of excellence and/or group benefit. I don't know that these groups are wrong.

 

Some students are globally gifted and capable of accelerating in all subjects, but there just is not time to do that. I don't believe that we should choose math as the default time gobbler for all students. There are so many options for a student to focus on.

 

I don't think acceleration should be the goal at all for any but the most obviously prodigious kids and I do not see anybody advocating for acceleration for all kids. If anything, I have often seen advice that asks parents to slow down and allow children to go deep. On the other hand thinking deeply in all subjects including Mathematics is most definitely a worthy goal for all kids.

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But a very gifted math student (however you might want to define it, and possibly the OPer's kids) is likely to finish Saxon by the age of 12 or 13. As I said earlier, this puts the student into the no-mans land of university math without hard core problem solving, and at age 12 (or 13 or 14 or 15) where the student would still need more math credits to fulfil most highschool graduation requirements.  You can rectify this by either mixing Saxon with a program that contains more problem solving, or by using a program where problem solving is integrated in with the subject material.

 

 

 


 
I did just fine, thank you, with a standard high school math curriculum, but then I hit university math in university and I. could. not. do. the. work.  I did not have the problem solving skills.  Clearly, in school I had to use the books that were given to me, but if someone had slowed me down (I was 3 years ahead) by teaching me the problem solving, I might have continued in math in university because I loved it as a teenager.

 

 

This very neatly sums up my perspective, as well.  I know DS12 hates Saxon because he doesn't like repetition, but the repetition is good for him, to iron out flaws in his skill sets.  DS7 will probably enjoy it.  Both do well with AoPS, and both need it.  Both will likely end up doing quite a bit of Saxon, as well.

 

I was fortunate as a kid, because my father had a PhD in mathematics.  We have a long line of scientists on both sides of our family.  So, we received enrichment without textbooks.  If I was stuck on any problem, my father made me resolve the misunderstanding axiomatically.  That is the "other half of mathematics" that is often referred to, but is also often obfuscated by the term "problem solving"  (Rusczyk himself uses that phrase, btw).  Axiomatic thinking is really the better term for it.  I honestly didn't like math until the last half of calculus 3.  But, at that point, I was free to see the beauty that lay underneath it all, and with the benefit of an axiomatic upbringing, I was free to run around in a new playground.  The harder the math, the more fun I had (I still hate statistics, though ;) ).
 

What Saxon is NOT good at is axiomatic mathematics.  It misses it entirely.  No ifs, ands, or buts.  Some of its definitions are so unique to its own curriculum that they cannot be used in conjunction with other, purer math curricula, because the terminology is nonstandard.  AoPS, on the other hand, is heavy on axiomatic mathematics.  The language and development follows classical lines.  Many of the "challenge" problems are, in fact, classic problems throughout the history of mathematics (which is why they can be so tough).  What AoPS is NOT good at, but where Saxon excels in spades, is the repeated practice of the developed tools.  AoPS is one of the very best at building the axiomatic foundation, but Saxon is one of the very best at building skills for basic applied mathematics.  For advanced applied mathematics, Saxon needs to be supplemented in some way -- often just by a good teacher or mentor.

 

Ruth, your voice is one of the ones I most respect on this board.  Sometimes we are all misunderstood, and it is all the more likely when our words are exchanged in print.  Don't fret about it too much!

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You couldn't be any more clearer. Honestly, sometimes I wonder if people are confused because they haven't ever seen "the other half of the math curricula." 

 

This.

 

I'm one of those moms who never saw "the other half of the math curricula" until my two oldest (13 and 12) just did the Gauss Math Contest this past year.

 

Here is a link to past contests. Look especially at the last section of the contests. The first 2 sections are covered in excellent detail in Saxon Math. The last section isn't touched. If anyone has specific resources that teaches these kind of problem solving skills I'd LOVE to have links. Thanks!

 

www.cemc.uwaterloo.ca/contests/past_contests.htlm

 

 

 

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This.

 

I'm one of those moms who never saw "the other half of the math curricula" until my two oldest (13 and 12) just did the Gauss Math Contest this past year.

 

Here is a link to past contests. Look especially at the last section of the contests. The first 2 sections are covered in excellent detail in Saxon Math. The last section isn't touched. If anyone has specific resources that teaches these kind of problem solving skills I'd LOVE to have links. Thanks!

 

www.cemc.uwaterloo.ca/contests/past_contests.htlm

 

Saxon will cover that, as well.  It is just a more advanced set of problems.  To solve those ahead of the material, though requires precisely the thought processes developed by AoPS and its ilk.  Really old math textbooks are great, too (pre-Dolciani).

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Lewelma, I'm sorry if I made you feel personally attacked. I didn't mean to do that.

 

Stripe, even at many American public schools that are providing pretty inadequate math instruction, over half the homework assigned is often math homework. But I wasn't talking about all of AMERICA. I was talking about the pressure on homeschooling families to devote a disproportiniate amount of time and money to math compared to other subjects.

 

I'm just trying to say that just because a child shows promise in math, doesn't mean that math has to become so CENTRAL to the child's education and possibly a burden to the entire family. Math is ONE subject. There needs to be balance. And this is a BIG country and even a bigger WORLD as more and more countries join the homeschooling community.

 

If you read vintage books, spending a disproportionate amount of resources on math has been going on for a long time. It was questioned then, and I question it now. Back then, the thought was that things that can be measured most easily will be attractive to teach, and math skill is easy to test and measure. That's why we have MO.

 

Competition is a way of life for some families. Some families have a history of careers that require extensive math backgrounds. This is a big country and world though, and a math heavy curriculum is not always the best way to triage the family's resources.

 

Doing our best is not painful. When we are in pain, we are practicing self-neglect, not doing our best. All forms of neglect are wrong, including and maybe especially self-neglect. Moms/instructors need to teach a complete and balanced curriculum to all their children at their own personal best, and no more.

 

For certain children in certain families it would be negligent not to provide instruction that leads to competition. But that type of education is a burden for many families instead of a joy and oppurtunities.

 

Lewelma, thank you for all your posts. You did a great job in helping me understand a few things better than I previously did.

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I am struggling to respond on my phone today but thought I might point out that competition math ultimately isn't about competing but about problem solving and that "other half"of mathematics that isn't typically taught in school, a means to an end rather than an end in itself. It's about a fuller, deeper education, perhaps analogous to the depth sought in WTM language arts. The value of problem solving experience is discussed in Rusczyk's talk that I may or may not have linked earlier in this thread - I can't check now... It is also discussed in an article that I posted on the general ed board a few days ago, a value that goes way beyond the world of math.

 

Also, it is worth pointing out that there's more than one way to skin this cat. Disproportionate time and resources spent on math don't need to be the case. (LOL, my boys will probably never compete and certainly aren't likely to spend more than an ordinary amount of time on math. Still, tbey will have at least some experience withis problem solving and discrete math topics)

 

Eta we are on the road today but I am thinking about ways to work on problem solving. It is not easy to tap into the motivation to do the hard thinking that is necessary. Brain-tickling, for lack of a better term, would be one such angle, if anyone knows what I mean by thatthat. I would guess that there might ne a fair amount of problem solving involved in programming,say, though perhaps it is not coincidental that some discrete math is involved there too. Maybe a spin off thread is in order - I would enjoy hearing more ideas.

Edited by wapiti
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Not wanting to sound like a know-it-all -- because I really don't know much about anything -- but I bought heavily into this idea when my eldest child was four, and now think differently.    In hindsight, I'm not sure why I put so much stock in it, except that I was a nervous parent and it sounded plausible.   That's why I mentioned "theories" above.

 

Based on six more years of experience with that child, and several with younger siblings, two things have been brought home to me:

 

1) If bright/gifted children are having emotional or social difficulties, this isn't necessarily going to be solved by giving them additional challenges.

 

2) If they do need more challenges, academic challenge isn't necessarily going to be the most appropriate kind.

 

At this point, when it comes to acceleration and advanced work, I can relate most to what Courtney and Hunter are saying in this thread.  

 

(It turns out that this homeschooling/child-rearing thing is a lot more complicated than I was expecting.   But also more fun.    :001_smile: )

 

Thank you. I totally understand it.   It does feel complicated but also feels good to do it.  I will keep this in mind.  Just like OP said, its informal instruction for my DD.  Its more of having fun playing games than any academic learning. Curricula is for me to serve as a guideline. 

 

When I see "readiness" clues from her, we do activities in a visual style so she gets to enjoy and learn her way.  Absolutely no intentions of boasting, but just sharing what we do (not even sure if its good enough to share).  Here's an example of our math (parking rods game). The idea is from this forum when a poster explained how she taught her VSL kid using number lines. 

https://drive.google.com/file/d/0BzhYJLMgCI4kR0tXa29XUl8zM00/edit?usp=sharing

She can do addition with Crods without realizing them as addition, so we play with this number street and see how if 2 helps 8 to get to 10 faster, 8 returns the favor by helping 2 to get to 10 (and this mutual friendship makes it faster to reach 10 than crossing one house at a time).  When she has a visual, she is comfortable with oral discussions and doesn't feel lost. So we take it at her pace based on how she enjoys it.

 

She lights up and enjoys such games. PAL-reading is the only program we do as designed. She loves the activities and pace (her school teaches phonics and she is able to read beginner books so I continue do it at home to give a strong foundation and to help her with comprehension).

 

I dont have any intentions of boasting and I do apologize if I come across that way.  Sorry to derail the thread.

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Hunter, I have read your cautions about over emphasizing math before, and I do understand your concerns, but I really feel there are few people who actually are spending a lot of time on math, and when they do, I think very few of those do it to the detriment of other subjects. But I do agree with you that one's mental health and balance are important.

I like discussing math with my kids. But it was my favorite subject in school, what I studied at a higher level, and it was how I was raised (one of my mother's favorite subjects), but I don't go crazy with it and it feels balanced to me. Or at least as balanced as I can get.

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I am struggling to respond on my phone today but thought I might point out that competition math ultimately isn't about competing but about problem solving and that "other half"of mathematics that isn't typically taught in school, a means to an end rather than an end in itself. It's about a fuller, deeper education, perhaps analogous to the depth sought in WTM language arts. The value of problem solving experience is discussed in Rusczyk's talk that I may or may not have linked earlier in this thread - I can't check now... It is also discussed in an article that I posted on the general ed board a few days ago, a value that goes way beyond the world of math.

 

Also, it is worth pointing out that there's more than one way to skin this cat. Disproportionate time and resources spent on math don't need to be the case. (LOL, my boys will probably never compete and certainly aren't likely to spend more than an ordinary amount of time on math. Still, tbey will have at least some experience withis problem solving and discrete math topics)

 

Eta we are on the road today but I am thinking about ways to work on problem solving. It is not easy to tap into the motivation to do the hard thinking that is necessary. Brain-tickling, for lack of a better term, would be one such angle, if anyone knows what I mean by thatthat. I would guess that there might ne a fair amount of problem solving involved in programming,say, though perhaps it is not coincidental that some discrete math is involved there too. Maybe a spin off thread is in order - I would enjoy hearing more ideas.

Here you go.

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I think there is a general idea expressed in this thread that competition math is for the particularly gifted, the ones in the top 2%. That most others just need the "get it done" variety of Maths. But I have come to believe that this need not be true, and indeed in most cases, this thinking may even be counterproductive. Maths is not just a way of adding up numbers. It is instead, a way of making sense of the world through a unique lens. I don't see why we should deprive our children from developing this wonderful mathematical sense.

 

Curricula geared towards treating Mathematics as a creative endeavour, a tool for problem solving and a way of comprehending patterns we see around us, are also the curricula that can get you through math competitions. But you do not need to have only that end in mind when using such Curriculum. 

 

I agree with a lot of what you're saying, but I'm starting to wonder if the best way of "developing this wonderful mathematical sense" is really through practice with competition-style problems.  I realize that it's motivating and enjoyable for some students, and does develop certain skills and traits.   And it's certainly becoming more accessible, with AoPS and all the practice problems out there.  But it isn't something that's emphasized in the paper by Paul Lockhart (thank you for posting that, BTW!), and I just came across this blog post and its many comments, which raise some interesting concerns.  (There's a thoughtful response to Cathy O'Neil's original post here.)

 

This is just me thinking out loud, because I had the same experience of "hitting the wall" that's been described by Richard Rusczyk (and lewelma in this thread), and automatically bought into the AoPS approach as the solution.   But I've also had the experience described by some people on the  Mathbabe blog, of deciding in high school that I wasn't cut out to be a mathematician -- not so much because I didn't always win, as because I didn't enjoy the "contest" and "puzzle" type of problem-solving as much as some classmates did (and yes, they were all boys).  

 

Without wanting to put down those who enjoy competitive math, I'm encouraged to find that some mathematicians doubt that this sort of problem-solving is strongly linked to math success in the longer term.  This opens up a whole new perspective for me.  Maybe I will stop seeing myself as such an "English person" when it comes to homeschooling, and go back to being a "math person" as well.  

 

Yes, Arctic Mama, I am nuts, LOL.

 

And I think it's normal for threads like this to get a bit uncomfortable and confused, because they're getting close to the heart of the subject.   Sort of like threads on "how to teach writing," and "the purpose of literary analysis."   With all of these topics, I've had times where I felt almost completely lost (and out of step with other posters), and it's sometimes taken years to even begin to sort out a plan.   I guess that makes it a hard problem, but in this case, hopefully not a competitive one.   :001_smile:  

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I don't know. I can't keep up with all this quick talk with jargon I don't know and ideas I'm not familiar with. I don't even know if the people here are arguing or not right now. All of this is too confusing for me to respond with helpful suggestions or clarifications.

 

I started this to be a help to other peoples wanting to know more, so the next may apply to current posters and readers with experience already, but is aimed at those still exploring and looking for math curriculum, especially if they have dismissed Saxon best on negative impressions that they get from others or because they think Math 5/4 is for 9-11 years old kids in 3-6th grade or something like that. If that last sentence is you, then this message is intended for you...

 

The math that our son does at 6.5 years and just getting ready for official 1st grade in September isn't about competition in middle schools and high schools or college. The math he is doing at 6.5 years of age is about the foundation to do math at 7yo, and 7.5 yo. I know some people who do over complicate their life or their kids lives because they look at their infant drinking breast milk and fret over where they will attend HS or college, but that isn't us. I don't worry about that. Maybe because of the child we lost, but we try very hard to focus on the now with our kids and their academics is no different.

 

If you are wondering about Saxon Math details when you read this, please feel free to PM me directly. Especially if this is months old topic when you see it, because I am writing this for you--the undecided parent. The parent who may hear many, many bad things about Saxon Math and dismiss it without a careful look.

 

 

We communicate with the son and work closely with our son. I know that, if he does, then he will let us know when he is out-grown the way that we use Saxon Math or just the Saxon Math way of teaching, the same way he out grew his baby version math lessons. His behavior will tip us off before his mouth will. I think that maybe some parents are throwing away Saxon Math once their kid out grows it and instead of celebrating their childs growth and grateful to the way Saxon served the child, they are blaming Saxon Math for not lasting longer or going further or changing with their child. Saxon Math books are jus books. They can't change in response to the childs growth in real time.

 

We are not trying to raise a little boy to be Math Contest Master, and if he is inclined that way we will not hold him back. But middle school and high school math contest isn't our goal, rock solid understanding and rock solid skills (using that understanding) is. I don't think that because a kid doesn't do serious problem solving or logic lessons via math in grade 1 he will not learn those skill successfully later on or from something besides math so this isn't a concern for us. Problem solving with tricky math problems takes more maturity than just plain old math.

 

My son likes math enough that he will work for a good time at it IF THE LEVEL IS RIGHT. Right now, today, he is capable of learning 3-digit addition and subtraction with regrouping.He is capable of simple multiplication and learning divisions. We are targeting our lesson for him based on what he is capable of. In our culture, this capability isn't exclusive and we don't have any special terms for it that I can think of. In our minds--it is expected that kids will receive the support they need to do work that they are capable of. Not just what they want to do and not just what the state school expects them to do.

 

My son is capable of this basic math, but he also needs regular review, he needs time to work and make his basic skill set solid and to help him not be frustrated or discouraged. He has the focus and interest to do 20+ math problem at the right level. He is ready for a math book instead of mom-and-pop work sheets now, he is wanting to write his work and have something tangible for his pride and confidence.

 

That is what Saxon Math 5/4 and our methods of using it with him is systematically giving to him, no matter what number/grade is on the cover or how old he is or isn't and that is why we are using it.

 

Again, when I say that it our belief that success in school mathematics is about 1) appropriate instruction, 2) diligent practice and 3) time on task. I really do mean it. I think appropriate instruction is to some Americans/Anglophone minds a broad sub-topic that includes learning styles, teaching ideals, etc...but I use one tidy term "appropriate instruction" to embody it all.

 

That is all, well no its not all. This is off-topic but so is everything else now anyway so I will add my opinions and anyone can disagree and it is still okay, but to me: (And my thoughts are more on the K-3 stage and excluding trouble-makers who do not WANT to learn.)

Teaching is about the student.

The teacher is there to serve the student in the students efforts to learn. The teacher should be a humble and dedicated servant to the students needs, not the student subjected to the teachers whims. This is one reason why I don't want to send my boy to 1st grade at our public school. The teachers do not view themselves as the students servers, but I think that they should.

 

If students need magnets, blocks, paper, pencil, puppet, repeated telling of the same thing, direct instruction, indirect instruction, or special manipulatives then fine. If they need 2 explanations or 20 to learn then the teaching system be set up to support them getting it and should give it to the student without stigma or a fit.


Students aren't there to aid teacher in Teaching, but to get a service from the teacher (or the institution).

 

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I don't know. I can't keep up with all this quick talk with jargon I don't know and ideas I'm not familiar with. I don't even know if the people here are arguing or not right now. All of this is too confusing for me to respond with helpful suggestions or clarifications.

 

 

I think that your thread here has sparked something further reaching than your initial intent. I don't see any of the posts as arguments at all. You are at the beginning of your homeschool journey with a very young child. Some of us are farther along, have multiple children, and are, like you, exploring and interested in various math curriculum options. We've all had different experiences teaching math to our various children and many have taught other children as well. That's the beauty of homeschooling and having forums like this available, we can learn as we work with our children, and access input from other parents further down the road than we are. Because our children are all individuals, we may never reach the same places as others' do, but it's very interesting and can be helpful to learn about other's journeys.

 

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I am struggling to respond on my phone today but thought I might point out that competition math ultimately isn't about competing but about problem solving and that "other half"of mathematics that isn't typically taught in school, a means to an end rather than an end in itself. It's about a fuller, deeper education, perhaps analogous to the depth sought in WTM language arts. The value of problem solving experience is discussed in Rusczyk's talk that I may or may not have linked earlier in this thread - I can't check now... It is also discussed in an article that I posted on the general ed board a few days ago, a value that goes way beyond the world of math.

 

Also, it is worth pointing out that there's more than one way to skin this cat. Disproportionate time and resources spent on math don't need to be the case. (LOL, my boys will probably never compete and certainly aren't likely to spend more than an ordinary amount of time on math. Still, tbey will have at least some experience withis problem solving and discrete math topics)

 

Eta we are on the road today but I am thinking about ways to work on problem solving. It is not easy to tap into the motivation to do the hard thinking that is necessary. Brain-tickling, for lack of a better term, would be one such angle, if anyone knows what I mean by thatthat. I would guess that there might ne a fair amount of problem solving involved in programming,say, though perhaps it is not coincidental that some discrete math is involved there too. Maybe a spin off thread is in order - I would enjoy hearing more ideas.

 

I don't think anyone here has implied that they are spending their time only prepping their dc for math contests.

 

Here's a neat website from the University of Kent that I found regarding employment and problem solving areas. There certainly is more than one field to "skin" the problem solving cat, and if a student is a lover of math, why not go for it in the various fields of math - whether through contests or other resources?

 

www.kent.ac.uk/careers/problem-solving-skills.htm

 

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I don't know. I can't keep up with all this quick talk with jargon I don't know and ideas I'm not familiar with. I don't even know if the people here are arguing or not right now. All of this is too confusing for me to respond with helpful suggestions or clarifications.

 

I don't think you're alone. :lol: I imagine most are in agreement, but we've all gotten different things from certain posts, and that caused disagreement where there isn't necessarily disagreement. It happens. :)

 

Keep doing what you're doing, and let us know how it goes later on!

 

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I don't think that because a kid doesn't do serious problem solving or logic lessons via math in grade 1 he will not learn those skill successfully later on or from something besides math so this isn't a concern for us. Problem solving with tricky math problems takes more maturity than just plain old math.

 

My son likes math enough that he will work for a good time at it IF THE LEVEL IS RIGHT.

 

My son is capable of this basic math, but he also needs regular review, he needs time to work and make his basic skill set solid and to help him not be frustrated or discouraged. He has the focus and interest to do 20+ math problem at the right level.

 

I don't have anything against Saxon, for the record. I think it is a perfect fit for many kids. I also don't think it is concerning that you are doing 4th/5th grade math with a 1st grader. I even think doing "tricky math problems" with 1st graders is not necessary...for 1st graders doing 1st grade math. But there is a huge difference between a tricky 1st grade math problem and a tricky 5th grade math problem. Generally speaking, the 1st grader has the tools to manage the 1st grade tricks and slowly but surely, over time, develops the skills and patience to solve the 5th grade problems by the time he has reached 5th grade math. 

 

The potential for problems comes when working far ahead and avoiding "tricky problems" merge. Just as you say you have worked on basic math with regular review at each level, it serves kids well to progressively advance in conceptual problem solving. The risk you run (and lewelma's point, that got lost in the mix) is that when you hit the end of the runway with basic math, you may well be left with a technically advanced kid who is rock solid in basic skills but has not developed the habit and skill set of facing conceptual challenges and, yes, (a developmentally appropriate level of) frustration, head on.

 

When you said earlier in the thread that his conceptual understanding was at the 2nd/3rd grade level but he is working at the 4th/5th grade level...well, that sounds very much like a child working without understanding, which is precisely how I got straight A's all the way through high school and then abandoned my (pipe)dream of being an architect because, frankly, I just flat out didn't understand math and know how to work through novel problems. Now, at the end of your DS's education, maybe he'll be a liberal arts guy and possessing the patience and skills for solving novel math problems won't be necessary. But maybe he won't and maybe they will. It is hard to back up with a kid at X level to A level for teaching that could have been taught at A level along with the A level basic skills. 

 

I don't think anyone is saying don't use Saxon. A lot of people here do use Saxon successfully and love it. Many of us who don't use Saxon don't use it precisely because of what you say below about serving your particular student. Saxon isn't the problem here in my mind so much as moving on with algorithms and drills before securing conceptual understanding. 

 

Teaching is about the student.

The teacher is there to serve the student in the students efforts to learn. The teacher should be a humble and dedicated servant to the students needs, not the student subjected to the teachers whims. This is one reason why I don't want to send my boy to 1st grade at our public school. The teachers do not view themselves as the students servers, but I think that they should.

 

If students need magnets, blocks, paper, pencil, puppet, repeated telling of the same thing, direct instruction, indirect instruction, or special manipulatives then fine. If they need 2 explanations or 20 to learn then the teaching system be set up to support them getting it and should give it to the student without stigma or a fit.

 

Students aren't there to aid teacher in Teaching, but to get a service from the teacher (or the institution).

 

I agree with this 100%.

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