math woes - considering AoPS again, or what else?

[kristin0713]

I just sent the following question to AoPS:

_________________

Hi,
I am very interested in the Pre-Algebra course for my son. He is extremely math minded and can do math in his head in ways that I can't wrap my brain around.  However, he is an extremely reluctant reader.  I looked at the AoPS Pre-Algebra text from a friend and I know that the book would scare him away.  Is there a way to do this course without all the reading?  He needs an instructor that will explain things clearly and then problems to work through, without pages and pages to read.  Thank you for any insight you can give me.  

_________________

 

More info.  DS is 12.5 and completed Singapore Standards through level 6 very successfully.  I added Evan Moor Daily Math Practice last year for him in 6th grade so that he was getting some review with fractions and general arithmetic.  His mental math is excellent and he has a very intuitive understanding of how to solve problems.  This year, I put him in Horizons Pre-A.  It has been a bit of a disaster.  First, although I do think he needs more consistent review than Singapore had, the spiral format is just terrible for him.  He is frustrated with only learning a bit at a time and without the conceptual depth that he wants.  I have used Math Mammoth in the past, but the amount of problems are a huge turn-off for him.  (I think that part of this was that he had vision problems that we have since corrected, but he thinks back in horror to the very crowded MM pages with never-ending problems.)  

My concern with AoPS -- it has been indicated here that AoPS is for kids who live for math and could do math all day.  Um, no, that is not him.  Also, like I stated above, I think he would run away from home if he had to read the AoPS textbook.  But I just feel in my gut that the AoPS way might be the best way for him to learn. 

Help??

[Not_a_Number]

I'm going to PM you 🙂 . I work at AoPS, but I try not to post about it in public nowadays. 

[Shoeless]

Have you looked at Jousting Armadillos for pre-A?  There are 2 other books in the series; Crocodiles and Coconuts, and The Life and Times of Chuckles the Rocket Dog. I don't think the series is a complete pre-A course, but it will get you a good portion of the way there.  Google Books has a full length "preview" of the book, so you can see if it would be a good match for you son.

[8filltheheart]

If MM turns him off, I would definitely not recommend AoPS.  AoPS is going to require a lot of work and unless they have recently changed, even their online courses use textboxes (students don't speak.  They type.)  

If you want white space and limited reading in the text, I use MUS alg and geo (in a single yr) as pre-alg and pre-geo.  It has worked as a good transition for my kids between 6th grade and alg. 

[Momto6inIN]

My oldest DS loved, loved, loved AoPS, it made his soul sing LOL ... but all my other kids would run screaming if I even attempted it. I'd show him a sample and see what he thinks before I bought it and tried it. My other kids all had an immediate negative reaction to the discovery method, and I do too, TBH.

We use Video Text and it's very conceptual - definitely not spiral - but very incremental. I don't know if I'd use it for a 12 year old or not though.  I'd probably do what 8 suggested above and then move to Algebra when you think he's ready.

[Not_a_Number]

5 minutes ago, Momto6inIN said:

My other kids all had an immediate negative reaction to the discovery method, and I do too, TBH.

I would guess that since you don't like it, I won't convince you, but I've never gotten as good a result teaching in any other way. It doesn't have to be AoPS, either... there's really something about figuring out where "rules" come from and their logical inevitability. 

[8filltheheart]

And yet there have been plenty of math-oriented posters on here over the yrs that have shared that the AoPS approach is not for all students.  Definitely plenty of students successfully master mathematical concepts and go on to STEM careers from direct instruction.  Students can also go from direct instruction and jump into AoPS mid-stream and thrive.  Way more ways to mastery than a single methodology.

[Not_a_Number]

Never mind, sorry!

Edited October 27, 2020 by Not_a_Number

[kristin0713]

Thanks for all the feedback.  Here is my big problem with him.  

I really can't tell if

1) he craves a deep understanding and is resistant because wants to know more of the "why", not just the "how"

2) he is being stubborn and lazy (definitely true in some areas of school)

3) he is just not ready for algebra, despite being very competent in all arithmetic leading up to algebra

I have noticed in other subjects that when he perceives his instructor to be an "expert", he ups his effort and cooperation to another level.  This has happened with him in writing and science which I'm outsourcing this year.  Even though his writing instructor is giving him the same feedback that I have given him all along, suddenly it has credibility because she's a writing teacher.  🙄  So I'm thinking that a math instructor who can engage him and answer all of his deep questions might be what he needs.  Or maybe he needs to just stop whining and do his work.  Ugh, I don't know.  

[Not_a_Number]

Well, you could also post here and see if you can get his questions answered 🙂 . I do think kids benefit from feeling like their instructors are ahead of them, plus kids are simply less snotty for people who aren’t their parents!!

If he’s fluent in the whys of arithmetic, I’d guess he’s ready for algebra. What kinds of questions is he asking?

[kristin0713]

It's not really specific questions.  It's arguing with me about why it matters and saying it's not real math, etc.  Yesterday he was complaining about solving inequalities because there is not only one answer.  I said yes, there is an answer, the answer is X is greater than four.  I gave him real life examples of when the answer is not just one number.  I showed him some examples of graphing. He didn't want to hear it, he was just being difficult.  But that's why I'm wondering if conceptually he is not ready for concepts that seem more abstract even though I don't see them as abstract, or if he had a teacher to give him incredible mind-blowing explanations would he suddenly be "able" to do his math without complaining?  I'm not sure.  I am going to give him placement tests from a bunch of different programs and take it from there.  

[daijobu]

19 hours ago, kristin0713 said:

Is there a way to do this course without all the reading?  He needs an instructor that will explain things clearly and then problems to work through, without pages and pages to read.  Thank you for any insight you can give me.  

 

My concern with AoPS -- it has been indicated here that AoPS is for kids who live for math and could do math all day.  Um, no, that is not him.  Also, like I stated above, I think he would run away from home if he had to read the AoPS textbook.  But I just feel in my gut that the AoPS way might be the best way for him to learn. 

 

This is exactly what I do with my AoPS students, week in and week out.  I read through the problems and work through them online for them, modeling  the way one studies difficult material, so they learn how to study as well as the math. 

I did not hand over the textbook to my daughters and expect them to self-study, though I don't doubt that some students are capable of this.  Mine weren't, though by high school they were autodidact experts because of the study skills they learned from AoPS.  

My kids also do not live for math and certainly did not do math all day long.  

[Not_a_Number]

1 hour ago, kristin0713 said:

It's not really specific questions.  It's arguing with me about why it matters and saying it's not real math, etc.  Yesterday he was complaining about solving inequalities because there is not only one answer.  I said yes, there is an answer, the answer is X is greater than four.  I gave him real life examples of when the answer is not just one number.  I showed him some examples of graphing. He didn't want to hear it, he was just being difficult.  But that's why I'm wondering if conceptually he is not ready for concepts that seem more abstract even though I don't see them as abstract, or if he had a teacher to give him incredible mind-blowing explanations would he suddenly be "able" to do his math without complaining?  I'm not sure.  I am going to give him placement tests from a bunch of different programs and take it from there.  

Inequalities are kind of a hard idea 🙂 . So are variables. So the "answer" of x > 4 might just feel unsatisfying, you know? I don't think graphing helps with that at all -- graphs are hard, even when you're graphing an equation, and graphing inequalities is just a disaster, it's so difficult. 

I think the right way to talk about it "well, we're trying to find all numbers such that (for example) 2*x + 1 > 9. Can you name ONE number like that? Do you think there are more? How could we describe ALL numbers like that?" You'd want to listen and think about how he's conceptualizing a variable, by the way. Lots of kids aren't quite aware that a variable can stand for ANY number, not just a specific number. One way you could check if he understands that is to see if he can think about whether 

3x = x + x + x 

for any x, and what he would say if asked to explain why. 

I think it's less about "mind-blowing explanations" and more about making sure it all fits in his head in a coherent way. And giving him space to interpret things in a way that makes sense to him. 

Edited October 27, 2020 by Not_a_Number

[8filltheheart]

Based on your above description @kristin0713 you might want to look into Derek Owens.  His videos explain everything clearly.  You can register in 2 ways: 1-$58/mo and you send homework to them to grade, can email questions, etc or 2-$29/mo and you self-grade but they will provide you the SM.

[daijobu]

5 hours ago, kristin0713 said:

Yesterday he was complaining about solving inequalities because there is not only one answer.  I said yes, there is an answer, the answer is X is greater than four.  I gave him real life examples of when the answer is not just one number.  I showed him some examples of graphing. He didn't want to hear it, he was just being difficult.  

I agree; I also find the solutions to inequalities to be vaguely dissatisfying.  Because you want one answer, right?   A range of answers just seems wishy-washy in comparison.  

I think it's okay to not like certain things, as long as he isn't using it as an excuse to not study.  Sometimes kids just want to be heard.  And sometimes they are looking for an excuse to avoid work.  

I actually have a blog post about an AMC problem that you solve using triangle inequalties, twice, so arrive at a single answer.  

[Not_a_Number]

6 minutes ago, daijobu said:

I agree; I also find the solutions to inequalities to be vaguely dissatisfying.  Because you want one answer, right?   A range of answers just seems wishy-washy in comparison.  

I think it's okay to not like certain things, as long as he isn't using it as an excuse to not study.  Sometimes kids just want to be heard.  And sometimes they are looking for an excuse to avoid work.  

I actually have a blog post about an AMC problem that you solve using triangle inequalties, twice, so arrive at a single answer.  

You too, eh? 😄 You do really want to come up with an answer (or two) you can just plug back in and check!! 

[Janeway]

Derek Owens sounds like exactly what you are looking for. And he has an option where you can get the answer keys and grade yourself, but you need to request it specifically.

[Plagefille]

One of mine has done AOPS the other two, while also good at math, have done other programs.

A possible way to do AOPS Pre-A is to watch the videos first and then work through the problems. You could skip reading most of what's in the book that way, just make sure to read what's in the highlighted boxes. The videos go halfway through the Intro Algebra book. I know this is not the ideal way to do AOPS, but still a good option for using the program.

We really liked Jousting Armadillos like others have suggested, but it has a lot of reading too. Jacob's Algebra is great as well (JA is based off of it) and he may be ready to start that. My DD has used these programs and has scored very well on the Math section of the SAT.

My youngest has stuck with Singapore Dimensions 7 so far. It is good too, but probably my least favorite of the ones we've done. That may just be because we haven't done it long though.

[Btervet]

We are a few chapters into AoPS for PreAlgebra, but we do not do the discovery method as in the book. I will read over the lesson first, then provide a lesson using my own examples to the kid, and we will derive all the rules together - I will prompt him to see if he can come up with the right solution, but if not I just help. Then he quickly reads over the problems/discovery section, which is easy and quick since we did a lesson on that info already. Then he will do the problems, and we do the challenge problems together. IMO the value in AoPS is in understanding all the rules, and how to derive new rules, not necessarily in the discovery method. I figure if the online classes provide instruction, there is no reason I can't also provide direct instruction. It is more work, but not a ton.

[Not_a_Number]

8 minutes ago, Btervet said:

I figure if the online classes provide instruction, there is no reason I can't also provide direct instruction. It is more work, but not a ton.

The classes do prompt the kids to try to figure it out themselves, but I'm sure you're right that it feels a lot more like direct instruction than just going through the book. 

[Familia]

Math majors here, but almost messed that up being too creative with teaching early on.  

Our children liked more explorative math when younger, then something switched and went awry during/after pre-algebra.  After several unexpected and uncharacteristic failures, we switched to Saxon w/Art Reed DVDs to get over the crisis, but Derek Owens was IT!   I could confidently hand math over to him and know my children were getting direct teaching, grading, and help.

Doing math in a more traditional way gave back confidence and left lots of time for the passion and exploration of math to take place during non-school hours.   

[kristin0713]

I appreciate all the replies!   The taking notes aspect of DO concerns me for this child in particular.  I just started a trial of Unlock Math.  

[Not_a_Number]

49 minutes ago, Familia said:

Our children liked more explorative math when younger, then something switched and went awry during/after pre-algebra.  

Mind telling me what went wrong? 🙂 What made things less successful? 

[Familia]

@Not_a_Number Puberty?  Not certain, but, at that time, suddenly, the concepts were not being seen through creative means.  Especially with our son, who went on to get BS in math & now pursuing PhD.  He tutored at a national chain and saw the same shift in thinking.  Students needed ONE thing, he observed, in order to succeed in algebra and beyond - rote memorization of the math facts - all four operations.  

He said that time and time again, students were failing at algebra b/c their brain power was being zapped on figuring the operations.  Memorize the operations, the algebra was focused on and made sense.  

Whatever means you all use to teach lower level math, we wholeheartedly recommend that the students learn the facts of the four operations by rote.  YMMV, but, it was successful here and at the center with many, many students...discovered later than I would have preferred.

ETA, I say puberty, b/c, again especially in our DS, thinking methods changed.  Not only did he think differently about math and want to work on the basically presented problem, but EVERYTHING...he suddenly forgot where the dishes went in the cabinet, he forgot basic family patterns.  Odd, but true.  Maybe the brain is being used in another way and needs more concrete information??

Edited October 29, 2020 by Familia

[Not_a_Number]

1 minute ago, Familia said:

Puberty?  Suddenly, the concepts were not being seen through creative means.  Especially with our son, who went on to get BS in math & now pursuing PhD.  He tutored at a national chain and saw the same shift in thinking.  Students needed ONE thing, he observed, in order to succeed in algebra and beyond - rote memorization of the math facts - all four operations.  

He said that time and time again, students were failing at algebra b/c their brain power was being zapped on figuring the operations.  Memorize the operations, the algebra was focused on and made sense.  

Whatever means you all use to teach lower level math, we wholeheartedly recommend that the students learn the facts of the four operations by rote.  YMMV, but, it was successful here....discovered later than I would have preferred.

Hmmm, I'd say you need the four operations by rote to be good at algebra, but it's not enough 🙂 . I see lots of kids who are good at the operations, but genuinely missed a concept (like equations or variables) that keeps them back in algebra. Or, say, a lack of understanding of the distributive property... even if you have everything by rote, if you've never used it with numbers, it's quite tricky to remember how to expand out (a+b)^2 🙂 . 

I tend to do creative stuff for a while, then solidify via drilling. So I do agree with you about the operations! I just don't think it's the whole story. 

[Familia]

2 minutes ago, Not_a_Number said:

Hmmm, I'd say you need the four operations by rote to be good at algebra, but it's not enough 🙂 . I see lots of kids who are good at the operations, but genuinely missed a concept (like equations or variables) that keeps them back in algebra. Or, say, a lack of understanding of the distributive property... even if you have everything by rote, if you've never used it with numbers, it's quite tricky to remember how to expand out (a+b)^2 🙂 . 

I tend to do creative stuff for a while, then solidify via drilling. So I do agree with you about the operations! I just don't think it's the whole story. 

Completely agree with you.  Our children were gifted at math, so the operations, not covered with more creative means, were all that was needed to make math soar.

[Not_a_Number]

23 minutes ago, Familia said:

Completely agree with you.  Our children were gifted at math, so the operations, not covered with more creative means, were all that was needed to make math soar.

Yes, DD8 is also gifted at it 🙂 . We’re both mathematicians so it’s genetic. I can’t say if just the operations would suffice — it’s possible!!

[SoCal_Bear]

I quickly scanned through the responses and thought I would suggest you consider Singapore Dimensions 7 & 8 since you said he did well with SM. This would cover pre-algebra and algebra. If he responded well to SM, then the design of the books is still very much in the style of SM Primary Math series.

I would not suggest using AOPS with a student who does not like to read. AOPS is very text dense with very little white space.

[Familia]

57 minutes ago, Not_a_Number said:

Yes, DD8 is also gifted at it 🙂 . We’re both mathematicians so it’s genetic. I can’t say if just the operations would suffice — it’s possible!!

Well, the operations, covered in a more ‘old-fashioned’ way that our more creative pursuits didn’t allow for, along with grade appropriate instruction as they progressed through grammar school.  What I mean, overall, is that students may get by without learning the basic four operations by rote, still doing well in grade appropriate instruction in grammar school.  Then, at a later time, when more difficult concepts get introduced, the brainpower utilized to figure those basic facts ‘eats up’ the brainpower needed to focus on more complicated material.  

[Not_a_Number]

15 hours ago, Familia said:

Well, the operations, covered in a more ‘old-fashioned’ way that our more creative pursuits didn’t allow for, along with grade appropriate instruction as they progressed through grammar school.  What I mean, overall, is that students may get by without learning the basic four operations by rote, still doing well in grade appropriate instruction in grammar school.  Then, at a later time, when more difficult concepts get introduced, the brainpower utilized to figure those basic facts ‘eats up’ the brainpower needed to focus on more complicated material.  

Ah, yes. We do drill basic facts AFTER the creative stuff. Definitely not optional!! 

[aeolianharp]

My 12yo is doing AoPS prealgebra. He doesn’t do any reading in the textbook. We watch the corresponding lesson videos on the website then work through all the practice problems in the book.

[Clemsondana]

If your student is struggling with the 'when would I ever use this' issue, you might try Life of Fred.  In pre-algebra it teaches the subject in the context of science content.  We've used it as a supplement for older an are using it more than that with younger.  

[kiwik]

My son quite liked the format for the self paced courses.