Saxon Math -- Early Impressions

[Free]

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.)

 

I think this is why I specifically quoted Ruth's post which said "Competition Math" is a red herring. That is not what she was talking about and that is most certainly NOT what I was talking about. I for one, could not care less about Math competitions. They are great for kids who are driven to compete but not for the rest. I also agree with Cathy O'Neil's post in its entirety, but this section deserves to be highlighted:

 

I have never been particularly fast at working out the details of something from the conceptual understanding — for example, it takes me a long time to solve a 7x7x7 Rubik’s cube — but it turns out the Rubik’s cube doesn’t mind. And in fact mathematics in real life isn’t a timed test — the idea that you need to be original and creative really quickly is just a silly, arbitrary way to select for talent.

It’s well documented that people seem to think that one is either born good at math or not, in spite of the fact that there’s ample evidence that practicing math competition-type problems makes you good at them.

 

In fact if you take Prof. Jo Boaler's course which I had linked in my earlier post, she repeats these very same points often.

What I was trying to get at in my post is not that one has to do puzzle type problems to excel in Maths, or that one has to work through AOPS (which like Saxon, I have never seen) but rather that children need to be encouraged to think deeper, detect patterns, make connections, and make sense of mathematical concepts in many ways. They need to work with challenging problems that stretches them to use their math muscles. The former can come from a good teacher who has profound understanding of maths or from a curriculum that focusses on conceptual depth. For the latter, I have found competition math books to be a good resource, but then my goal is not to prep my child for a competition, but rather to provide challenge which probably can be found from plenty of other resources as well.

[quark]

deleted for privacy

[Heathermomster]

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. 

 

 

If the OP were only pushing drills on her student, I'd agree with you.  

 

ElmerRex is not using Saxon as written.  As I understand it, the OP is applying a more Asian style scope and sequence using Saxon's problems sets.  I was also left with the impression that she uses manipulatives to teach.   To me at least, an Asian style scope and sequence automatically implies conceptual teaching, subitizing, and numbers sense activities.

 

I have seen the OP post elsewhere about adding more strategy games to the ones she already owns and uses with her children.  Maybe we should just give her the benefit of the doubt and assume that she plans to or is already incorporating some conceptual learning and deeper, mathematical thought inducing activities outside of Saxon.

 

Earlier in the thread, the OP mentioned pre-reading the math exercises in anticipation of any troubles with tricky problems.  She studies the problems ahead of time and then sits nearby and helps her son address them directly.  I do the very same thing with my eldest child.  She acts as a one on one tutor with her student, modeling the behavior that he will eventually incorporate through consistent practice.  She seems conscientious of her son's feelings, and it's clear she cares very deeply for him.   

 

As stated earlier, if the OP were only pushing drills on her student, I'd agree with you; however, she is not even using Saxon as written.  

[ElizaG]

What I was trying to get at in my post is not that one has to do puzzle type problems to excel in Maths, or that one has to work through AOPS (which like Saxon, I have never seen) but rather that children need to be encouraged to think deeper, detect patterns, make connections, and make sense of mathematical concepts in many ways. They need to work with challenging problems that stretches them to use their math muscles. The former can come from a good teacher who has profound understanding of maths or from a curriculum that focusses on conceptual depth. For the latter, I have found competition math books to be a good resource, but then my goal is not to prep my child for a competition, but rather to provide challenge which probably can be found from plenty of other resources as well.

 

Yes -- I didn't want to write too long a post, but should have said that there are a few different characteristics of "competition math" that were being questioned in the comments on that blog: 

 

1) the competitive aspect

2) the individual work vs. collaborative aspect

3) the speed aspect

4) the emphasis on solving specially written, often "tricky" problems 

 

and the first three don't have to be an issue if we're using these books at home.  But the fourth one might, unless we're looking at this approach as just one part of a larger picture.   

 

I think I'm going to try having my 9 and 10 year olds do a few of the contest-type problems collaboratively (with my participation as well), and also try to include more open-ended activities for all ages.   This is pretty much what I remember doing one year in an elementary pull-out program, and it was very enjoyable.   If they want to keep going deeper in some areas on their own, so be it. 

 

There are activities out there that give more of the sorts of experiences that Lockhart talks about -- math camps, festivals, etc. -- but I think it's harder to do this stuff at home, because there's more direct teaching/guiding and social interaction.  But that's the part that's so valuable for some students.  

 

I think it would be great to have online video classes for various levels of leisurely math enrichment/discussion, as we do for literature discussions.  (Maybe there are some out there, and I'm just not clued in.)

[Arcadia]

4) the emphasis on solving specially written, often "tricky" problems

Take a mishmash/assortment from different sources as different competitions have different emphasis. My kids are now debating strategy for a graph theory kind of problem the non-theoretical way.

 

Also look at past math circle problems. These tend to give children a taste into math not commonly taught in class. It also means lots of rabbit trails in my home.

 

ETA:

Math circle locator for anyone interested. They fill up very fast

http://www.mathcircles.org/Wiki_ExistingMathCirclePrograms_view?field_status_value_many_to_one=Active

[quark]

I think it would be great to have online video classes for various levels of leisurely math enrichment/discussion, as we do for literature discussions.  (Maybe there are some out there, and I'm just not clued in.)

 

If you can find some of the math Great Courses in your library, you're set for some time. AoPS videos could help somewhat too...you don't HAVE to watch them as part of a lesson. Also look up Numberphile. Really cool stuff.

[ElizaG]

If you can find some of the math Great Courses in your library, you're set for some time. AoPS videos could help somewhat too...you don't HAVE to watch them as part of a lesson. Also look up Numberphile. Really cool stuff.

Sorry for not being clear -- I was thinking about interactive online classes.  Like the group discussions and "Socratic seminars" that several companies are offering for literature and history.   And not so much for my own family, as for families in general, even if they aren't particularly inclined toward math (at least, not yet  :001_smile: ).   

 

I haven't come across anything like this.  Even the brick & mortar classes and camps are usually focused pretty heavily either on contest math, or on remediating or solidifying school skills.  There are exceptions, such as MathPath, but they're only available to a few highly gifted students.  

[Alte Veste Academy]

I do think the OP sounds like a conscientious, thoughtful homeschooling parent. I was responding to her point about tricky math problems taking maturity, just as a possible stumbling block to be aware of, especially as she specifically says she isn't looking at the long term.

 

But seriously without a hint of snark or negativity, if she is doing all this...

 

ElmerRex is not using Saxon as written. As I understand it, the OP is applying a more Asian style scope and sequence using Saxon's problems sets. I was also left with the impression that she uses manipulatives to teach. To me at least, an Asian style scope and sequence automatically implies conceptual teaching, subitizing, and numbers sense activities.

...I do not think her OP comes from a typical, achievable perspective for most homeschooling parents considering the use of Saxon, gifted child or not. However, I am also not aware of an Asian scope and sequence that puts drill and problem sets ahead of conceptual understanding.

 

I understand what you say about her working on problem solving with him. From my own (admittedly bitter and tainted, LOL) point of view, I see memorizing facts and procedures and working large problem sets as an artificial bolster to mathematical self-esteem. I am NOT saying many (most?) kids don't benefit from drill and repetition, by the way. I get that part is ideal for her DS. Perfect execution of algorithms was, unbeknownst to me at the time, a way to claim my own giftedness in mathematics. I was "good at math" by side-stepping the frustration of figuring out what the problem actually meant.

 

Again, I get that you have picked up (here and in other threads) that she is working on problem solving with him, but I just wanted to tell her (from a nice place, not a finger-wagging place) what I wish some of my teachers had known: that a cheerful attitude, procedural competency, and even perfect execution of problem sets (even advanced ones) do not ensure conceptual understanding and a true reflection of mathematical capability (as opposed to competency in arithmetic, which I had and still have in spades). At present, having done Miquon, Singapore K-6B, Beast Academy, supplements too numerous to mention, and working through AoPS ahead of and alongside my kids, I can say I actually AM good at mathematics, not just arithmetic! Even with novel problems! ;) Maybe I will go study architecture when I am finished homeschooling! LOL

[kiana]

Sorry for not being clear -- I was thinking about interactive online classes.  Like the group discussions and "Socratic seminars" that several companies are offering for literature and history.   And not so much for my own family, as for families in general, even if they aren't particularly inclined toward math (at least, not yet  :001_smile: ).   

 

I haven't come across anything like this.  Even the brick & mortar classes and camps are usually focused pretty heavily either on contest math, or on remediating/solidifying school skills.  There are exceptions, such as MathPath, but they're only available to a few highly gifted students.  

 

I wish I had time to do this. There are so many interesting ideas in mathematics that don't require an advanced level of thought per se, but just aren't useful enough to be included in the March To Calculus that typifies current school mathematics.

[wapiti]

Sorry for not being clear -- I was thinking about interactive online classes. Like the group discussions and "Socratic seminars" that several companies are offering for literature and history. And not so much for my own family, as for families in general, even if they aren't particularly inclined toward math (at least, not yet :001_smile: ).

 

I haven't come across anything like this. Even the brick & mortar classes and camps are usually focused pretty heavily either on contest math, or on remediating/solidifying school skills. There are exceptions, such as MathPath, but they're only available to a few highly gifted students.

If/when your kids are about ready for prealgebra level, another resource to add to your list is the set of online courses Elements of Mathematics. We started the first one earlier this summer and I thought it was nicely done. Lots of code breaking and such. Unfortunately life intervened and my boys haven't gotten back to it, but I think it's worth at least ezploring the samples. There was a thread on the Logic board with more details.

[Arcadia]

 Maybe I will go study architecture when I am finished homeschooling! LOL

 

The math part is easy. it is the drawing part in the entrance exam that I can't clear.  Don't know if they have entrance exams for architecture here but they do have in Asia.

E.g.

"Drawing Test

This is a two hour paper where candidate has to attempt three questions. The drawing aptitude is judged on the following aspects -

ï‚Ÿ Ability to sketch a given object proportionately and rendering the same in visually appealing manner.

ï‚Ÿ Visualising and drawing the effects of light on the object and shadows cast on surroundings.

ï‚Ÿ Sense of perspective drawing.

ï‚Ÿ Combining and composing given three dimensional elements to form a building or structural form.

ï‚Ÿ Creating interesting two dimensional composition using given shapes and forms.

ï‚Ÿ Creating visual harmony using colours in given composition.

ï‚Ÿ Understanding of scale and proportions.

ï‚Ÿ Drawing from memory through pencil sketch on themes from day to day experiences."

 

and what to bring

"Three or four sharpened soft-lead (2B & HB) pencils and a good eraser.

ï‚Ÿ Set of colours (Water/ Poster colours, crayons, pastels) with appropriate instruments (Brushes, dish, etc.).

ï‚Ÿ Geometry instrument box

ï‚Ÿ Blue ink pen / Blue ink ball point pen"

 

Architecture is one of the STEM/technical field that needs Art skills even with the advancement of computer graphics  :lol:

[Alte Veste Academy]

The math part is easy. it is the drawing part in the entrance exam that I can't clear. Don't know if they have entrance exams for architecture here but they do have in Asia.

E.g.

"Drawing Test

This is a two hour paper where candidate has to attempt three questions. The drawing aptitude is judged on the following aspects -

ï‚Ÿ Ability to sketch a given object proportionately and rendering the same in visually appealing manner.

ï‚Ÿ Visualising and drawing the effects of light on the object and shadows cast on surroundings.

ï‚Ÿ Sense of perspective drawing.

ï‚Ÿ Combining and composing given three dimensional elements to form a building or structural form.

ï‚Ÿ Creating interesting two dimensional composition using given shapes and forms.

ï‚Ÿ Creating visual harmony using colours in given composition.

ï‚Ÿ Understanding of scale and proportions.

ï‚Ÿ Drawing from memory through pencil sketch on themes from day to day experiences."

 

and what to bring

"Three or four sharpened soft-lead (2B & HB) pencils and a good eraser.

ï‚Ÿ Set of colours (Water/ Poster colours, crayons, pastels) with appropriate instruments (Brushes, dish, etc.).

ï‚Ÿ Geometry instrument box

ï‚Ÿ Blue ink pen / Blue ink ball point pen"

 

Architecture is one of the STEM/technical field that needs Art skills even with the advancement of computer graphics :lol:

Wow! I coulda' been a contender! I remember thinking that no one would have wanted me being the one to figure out how to keep their building standing up! :lol:

[lewelma]

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.

 

 

This.  And you said it so succinctly. :001_smile:

 

I have fought this battle with my younger from the beginning.  From about the age of 6, he shyed away from any conceptual challengers, and if we'd tried a bit without success, I'd just move to something he could do, which in hindsight I realise was always procedural math.  This had him doing preA at 8.5, and only then did I realise my mistake.  He was not ready for anything that required difficult thinking. He was not ready to struggle.  He thought math should be easy and straighforward.  And now I was stuck with him wanting to learn *new* material so heading into preA, but not being able to deal with the preA's challengers. What a mess! 

 

We have now spent 2 years flitting from program to program trying to keep him in the new material that he craves, but giving him the chance to develop the problem solving/frustration tolerance that he needs to move forward.  We have used Life of Fred, Jacobs Mathematics a Human Endeavour, Singapore Math 7, Singapore Math Challenging Word Problems 6, MEP 8, AoPS preA, and Saxon.

 

If I could do it again, I would make sure that his problem solving/frustration tolerance/axiomatic math skills were on par with the level of math he was doing. I just took the easy way.  And now I am still cleaning up the mess.

[lewelma]

Axiomatic thinking is really the better term for it.

Awesome. I needed a word for it.

 

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.

I agree. I thought you would get a kick out of a little vignette about my older. Because he went into AoPS so early and without supplementation in basic math, he asked me one day at the age of 12 how to multiply decimals. I kind of went :huh: and then :scared: and then :001_rolleyes: . To put it in perspective, this is the question he was working on the week he asked me:

 

"In a sequence of positive integers an inversion is a pair of positions such that the element in the position to the left is greater than the element in the position to the right. For instance the sequence 2,5,3,1,3 has five inversions – between the first and fourth positions, the second and all later positions, and between the third and fourth positions. What is the largest possible number of inversions in a sequence of positive integers whose sum is 2014?"

 

You really need both - axiomatic maths and 'repeated practice of the developed tools.'

 

Ruth, your voice is one of the ones I most respect on this board.

Thanks for this

[quark]

Sorry for not being clear -- I was thinking about interactive online classes.  Like the group discussions and "Socratic seminars" that several companies are offering for literature and history.   And not so much for my own family, as for families in general, even if they aren't particularly inclined toward math (at least, not yet  :001_smile: ).   

 

I haven't come across anything like this.  Even the brick & mortar classes and camps are usually focused pretty heavily either on contest math, or on remediating or solidifying school skills.  There are exceptions, such as MathPath, but they're only available to a few highly gifted students.  

 

Ah, yes, those are hard or expensive to come by. Perhaps not so much if you have a good math circle near you though...you can check locations of math circles on www.mathcircle.org -- the ones run by profs are usually of a higher caliber. We attended one run by high schoolers and it was much more of a contest prep circle than an interactive, discussion-style circle. (ETA: oops, sorry, I see that Arcadia already shared the link upthread!)

 

This also why we engaged the math tutor/mentor. His style is very Socratic and kiddo has benefited so much from it.