Self-Teaching AOPS -vs- AOPS Online Classes

[TheAttachedMama]

Can anyone who is familiar with AOPS help me make an informed decision?  :) :)

My son (6th grade) has really taken off with AOPS Pre-Algebra this year.    I started out teaching him the course (basically reading through the book with him and working the problems with him)---however, he has since taken over the subject and is basically "self-teaching" at this point.   He reads the book (we have the ebook) and works through all of the example problems.   He also watches the videos which are embedded in the electronic book.   Then, he works through Alcumus until it is "blue" or mastered for the topic.....and repeats as necessary.    He takes about two days per topic to do all of this.    And over this summer, I will have him cycle back and work through all of the challenge problems from the book again.)  For review, he works through school and chapter level past mathcounts tests which give him practice with a variety of problems and give him "previews" to things he will cover in future AOPS books.  Plus, he also has the standard built-in practice in alcumus.  (I try to have him stay "blue" in all of the previously learned topics.)

My first question is:  Does it sound like he is doing OK in math?   I feel sort of weird that I am allowing him to self teach math.   It is one of our most important subjects....right?  But he seems to be doing OK by himself.   He is mastering the material on alcumus, sometimes working through over a 100 problems on a given topic in order to do that.  So I feel like he is getting enough practice with challenging problems.  Am I making some horrible mistake though?

 Side note:  I really like alcumus!  The solutions are so well written that even my 6th grader can follow them.   Plus, it prevents the kids from trying to cheat.   (They can't copy from the solution manual with alcumus!)   Plus, the video game aspect of it with the fun challenges are really motivating for kids.  It sort of gives them a chance to experience an online presence in a really safe, encouraging, well-moderated environment!   Plus, I like that it has online review built in.)  

My second question concerns next year:  Should I allow him to try to self-teach through the Algebra book too?   Or should I sign him up for an online course through AOPS?   Is it going to be worth the money in our case?  We could afford the online class if we really scrimp and save.    I would be willing to make some cuts in other places because we really consider math to be one of our most important subjects.   However, if he is going to be able to work through the books independently, is it worth the sacrifices?

Being self-paced is nice because we can work at our own schedule.   If we decide we want to focus solely on mathcounts for a while, we can!   Or if he needs extra practice on a subject, he can just hang out and work on it.   

My ONE concern is that he isn't getting any practice writing proofs at home.   According to the Introduction to Algebra A syllabus, "Grading: 40% Alcumus homework, 35% Short-Answer Challenge Problems, 20% Writing Challenge Problems (proofs), and 5% Class Participation. Alcumus is the AoPS online learning system that adjusts to student performance to deliver appropriate problems and lessons."    Could anyone tell me more what they mean by short answer challenge problems and proofs?   What types of problems are they talking about? I could have him write "proofs" at home, but I am not sure what I am looking for when I grade them.   Or what exactly they even mean by that.  (embarrassed)  Would he be better served to have an actual mathematician grade his work and guide him?   

Also, I've heard over and over again that the classes move fast.  Can anyone expand on that?  Does that mean that an average kid is going to be left in the dust?  Will he ever even get a chance to answer the questions?  Does my child need to learn to type really fast before taking the class?   Or does that just mean that they have to work a lot outside of class to stay with the pace (mastering alcumus, etc.)?  

Edited January 11, 2019 by TheAttachedMama

[SeaConquest]

I'm not going to be much help because we are in Pre-A as well, but I did want to chime in to reassure you that we are paying $$$$ for my kid to attend the local AoPS Academy, and what you are doing sounds great! (I'm mostly spending the money because my kid is an extrovert and likes learning with other kids.) My personal opinion is that, if it aint broke, there is no need to fix it. Unless there is a specific reason you need the online course, I would stick with what is working. And it really sounds like it is working well. The only issues I see going forward are that 1) you will eventually run out of videos -- can you teach him the material, or can he just self-teach from the book (my kid can't) and 2) can you grade geometry proofs and other higher level mathematics? 

But again, it sounds like, for now, things are working well. Great job! 🙂

Edited January 11, 2019 by SeaConquest

[Momto6inIN]

We didn't discover AoPS til oldest D'S was through Algebra I and II and Geometry, so he only used it for Counting/Number Theory, Precalc, and Calc. But he had absolutely no trouble at all self teaching. He would have been ground into the dust with the pace of the online classes because although the content itself was just the right amount of challenge for him, he sometimes needed two days to do one problem and just is not a fast worker in general.

He had already had Geometry though, so proofs were very familiar to him. Not sure how he would have done with those without instruction on how they are set up and supposed to work ...

[SoCal_Bear]

I'm not sure if you mean 2 column formal proofs or inductive proofs. If the latter, that's already in some of the challenge problems in PA. I would think that he's likely doing it already even if you haven't called it writing a proof. I don't make my son write it out formally. We let him do it orally with us and explain his thinking because the dialogue seems to help him process. These tend to be about the only problems that I have to stop him and go back over with him. I often tell him that I get that you know this is true...but it's important to understand why it's true. Unless I am mistaken, those are the problems where it says show....explain...or why....

My son has self-taught himself the PA book as well. He likely will finish before the end of the month. I think the books are written to the student and lend themselves to self teaching since it's discovery method. I had originally planned to let him work through it slowly and take a year or even a year and a half. He surprised me by setting his own pacing and is on track to complete it in about 7 months. Right now because of his age and because I'm not in any rush, I am planning to have him divert and work through Jacobs' MHE book as there is a lot of interesting math topics in there that he won't see again. He saw me flipping through the text and the billards table chapter caught his eye, so he is excited. I just haven't made up my mind if we will do AOPS Algebra after that or do two passes with Jacobs and then AOPS through like others have on the boards here who have a ton more experience. Sort of leaning towards the latter because I did two passes with PA with JA followed by AOPS and what I did with SM and BA. The system seems to have worked so far in that he masters the basics and then diving deep isn't too hard. The kiddo is in 4th grade so I know that we have plenty of time on our hands.

@TheAttachedMama are you committed to AOPS beyond Algebra? I am not sure if I want to encourage ds in continuing on if AOPS is the time sink it sounds like, but then I think maybe he is the kind of kid who AOPS is written for because he does self-teach and has worked through PA at a faster pace than I expected so then maybe AOPS won't be as much of a time sink which would prevent him from putting time in all the other things he enjoys.

 

Edited January 12, 2019 by calbear

[lewelma]

If he can self teach from the textbooks, I think that is better than the online courses. It's late, and I'm off to bed, so hopefully I can write more tomorrow. 🙂

Ruth in NZ

[Monica_in_Switzerland]

DS is in the algebra book now, and I would say his ability to self-teach improves with each lesson.  In PA, I was still doing a ton of hand-holding.  Now, he asks me about two questions per section.  I still have him read me his exercise answers while I look in the Solutions Manual- this helps me keep an eye on progress and accuracy and misunderstandings, hopefully avoiding those stories you hear of parents suddenly discovering self-teaching kids are weeks or months or years behind where the parent thought they were.  

My son does 50 minutes of the textbook + 15 minutes of alcumus, 5x a week.  Typically he takes two days per section (one for problems, one for exercises) and I don't attempt to have him align the alcumus, I figure that's just a spiraling review.  Review sections sometimes take a full week.  

So far, this is working great because I have no issues teaching algebra on the fly when he does have a quesiton.  My pre-calc/calc are a lot more rusty though, so I'll have to probably at least skim each section if he still needs help at that point.  

[KSinNS]

So my experience with this is my oldest (now 14) did prealgebra and the first 2/3rds of algebra largely self-taught (age 10-13). Like you, he started doing it with us, and then moved to self-teaching. He did the problems in the book rather than alcumus as the only difference (he is extremely trustworthy). My husband would sit down with him to look at his work every now and then, or when he was struggling. He did fine, though I was a bit concerned about his pace (which was a bit slow-close to 2 years/book) and accountability. He did every single problem (including every challenge problem). We got busier this year, so we put him in the AOPS counting and probability course. It took him a couple of weeks to change his style of doing math, but he quickly had no problems and really enjoyed the class. He was very well prepared. My second is ready to start PA, and she's going to do the online class (because of my time limitations). I think both can work, and certainly I'm very happy with how my son did. I think he took substantially longer doing it himself than doing the online class, but otherwise he did really well. (He did start PA much less well prepared than my daughter, so I think the extra time he took was well spent). 

[daijobu]

You and your student are doing great.  Our pace was more like 1 section per day with 1-2 days on each on the end of chapter review and challenge problems.  But we didn't do Alcumus, and they weren't self taught, they worked with me.  I wouldn't sweat the proofs because the books contain plenty of those.  

The online class is fast-paced so he'll be moving along at faster than 2 days per section.  I would say if he's comfortable with the current pace, then keep him there.  

One benefit of the online classes is your student may make some online friends in class.  OTOH, the discussion forums are free, so he can always make connections outside of class.  There is an active MathCounts discussion group he may find interesting.  

It's great that you are having him do old MCs.  I agree with your observation that it gives him both review and preview.  You can also try the AMC-8's which are available for free form the AoPS website.  It's at about the same difficulty as the chapter level MC.  If you want to bump up the difficulty, you can give your student the state or even national level MC or the AMC 10.  

But mostly, keep up the good work!  

[hellen]

Your child is doing so well self-teaching that I would let him continue as long as it is working.  The videos do eventually run out.  I don't recall which level.  

The proofs are just answers with explanation.  It's like the answers in the solution manual or Alcumus.  

[Kathy in Richmond]

On 1/11/2019 at 11:11 AM, TheAttachedMama said:

My ONE concern is that he isn't getting any practice writing proofs at home.   According to the Introduction to Algebra A syllabus, "Grading: 40% Alcumus homework, 35% Short-Answer Challenge Problems, 20% Writing Challenge Problems (proofs), and 5% Class Participation. Alcumus is the AoPS online learning system that adjusts to student performance to deliver appropriate problems and lessons."    Could anyone tell me more what they mean by short answer challenge problems and proofs?   What types of problems are they talking about? I could have him write "proofs" at home, but I am not sure what I am looking for when I grade them.   Or what exactly they even mean by that.  (embarrassed)  Would he be better served to have an actual mathematician grade his work and guide him?   

Also, I've heard over and over again that the classes move fast.  Can anyone expand on that?  Does that mean that an average kid is going to be left in the dust?  Will he ever even get a chance to answer the questions?  Does my child need to learn to type really fast before taking the class?   Or does that just mean that they have to work a lot outside of class to stay with the pace (mastering alcumus, etc.)?  

Have you seen their Assessment in the Online school article? It explains the difference between short answer problems and proofs and how they're evaluated.

It sounds like you and your son are doing wonderfully right now! You're doing just what I'd recommend to self-learners: doing Alcumus for fluency, going back through the text later to tackle the challenger problems, and doing MathCounts type problems on the side for mixed review and a fun challenge.

I was a long time AoPS mom when my kids homeschooled, starting when the school first opened.  We did the original texts (Vol1 & 2) on our own at home, and we took several classes online: most of the contest math offerings, but also number theory, intermediate algebra, precalculus, WOOT, and olympiad geometry.

Some thoughts:

You don't have to do all or nothing. You could let him do intro level classes at home, and do the online school when he hits the intermediate level. Or you could do the main courses at home, and let him do the extra classes (number theory, C&P, AMCs) online. My daughter enjoyed the group experience very much, and made some lasting friendships in her classes. Participating in the forums also led directly to math team (incl ARML) invitations when she hit high school age. Now she even works for AoPS, so I'm super happy in retrospect that she had those opportunities...I'm a mathematician & could easily have done it all at home...

Proofs are nothing more than well reasoned and well written answers to problems requiring more than a calculation. There are plenty in the textbooks - they just don't appear in the two-column format that we all learned in school in geometry class. If your son is studying the solution book and comparing his written answers to theirs, he is learning how to write a proof. You know him best! For kids who tend to skip that step, for those who don't like to admit what they don't understand fully, or for those who tend to skip steps when it involves writing more than a line or two, then having an AoPS mathematician grade their proofs can be very helpful. They hold the kids to high standards, both in accuracy and style.

As for class speed, take a look at the syllabi online to get an idea. The Intro Alg book is covered in two 16 week sessions (A and B), so approximately one school year in length. The book is very meaty, though, and many kids do better having more than a year to get through it.

In an online class, you'll be doing a problem set a week. These are not the textbook problems, but special sets made for the classes. For some kids, it keeps them "marching along" and not getting bogged down. Some do better on their own pace at home, and some benefit from that "push."

My kids were average typists when they took the classes online, but not super speedy. Anyone who wants can submit answers to the teacher's questions, and the teacher selects a subset of those answers to display. There is a bit of a speed issue if you want to have your answer be correct & displayed, but we found it was as much about fast thinking as fast typing. One thing that helps is to read the chapter in the text before class. You want to grasp the basic ideas before wrestling with the in-class problems. And it helps to realize that a lot of the AoPS students are after-schoolers and may already have taken the basic course in their schools. So it's hard to be the top of the class, and that bothers some students more than others. Again, you know your kid best...

 

[mathnerd]

I recently got a notification from AOPS that they are introducing a "stretch" Algebra course for a longer duration than their fast paced regular courses in case anyone is interested in a slower course for their kids:

Stretch Introduction to Algebra A covers the same topics as Introduction to Algebra A, but at a more methodical pace (22 two-hour classes versus 16 ninety-minute classes). Topics covered include exponents and radicals, linear equations and inequalities, ratio and proportion, systems of linear equations, factoring quadratics, complex numbers, completing the square, and the quadratic formula.

Edited January 17, 2019 by mathnerd

[whangty]

I asked almost the same question on accelerated learners forum as well as on artofproblemsolving.com forum several months ago.  

Just want to share our experience RE your 2nd question (self-teach vs. online class for intro to algebra book).  After finishing prealgebra 1 on his own in summer of 2018, my son has been taking online classes (prealgebra II, intro to algebra a, and currently intro to counting and probability).

So far I have observed or learned the following:

1.  Beyond prealgebra, it gets harder.   My son is having to work very hard in intro to counting and probability, esp. on alcumus problems.   Even Intro to Algebra a grew harder for my son in the 2nd half.  I heard that intro to geo is the most challenging class out of the intro series.   Esp. in intermediate classes, I have been told that online class can def. make it easier to learn the mat'l vs. self-teaching.  

2. Mastery comes from solving a lot of "hard" problems.   In intro to cp, my son has not had much problem understanding the theory or the concept, but when faced with hard problems on alcumus, he would get stuck very often and had to ask for help on many problems.  However, I believe these struggles have helped him to learn the material deeply and develop intuitions.  Therefore, although an imperfect measure, math competitions like AMC 8/10/12 can be a good test of how well a student has learned and mastered the material.  

3. Although I believe online classes are worth the money, the costs can quickly add up.  Even without sending your kids to a quality but expensive summer camp like Mathpath or AwesomeMath, you may be spending few thousands of dollars on aops classes alone, esp. if multiple siblings start taking online classes at the same time.  Also, the price of online AoPS classes went up this year by $30 or so per class. 

Overall, I feel that your son is doing very well, and I feel that either online class or self-teaching can work out for him re intro to algebra book.  

 

 

[whangty]

Forgot to add one more thing.   RE your concern about proofs, I think writing problems that are part of online class can be a very valuable teaching tool for students.  The AoPS staff take grading very seriously and provide very detailed yet encouraging and helpful comments, all of which I believe and hope will strengthen my son's proof-writing skills down the road.  As a matter of fact, one parent strongly advised me to take online classes mainly for the writing problems.  

 

 

[Jackie]

My daughter is in the Algebra A class now. We chose to go with the online class because an official grade from a provider will be helpful for specific reasons for her, but otherwise she was doing just fine without the class, and I doubt we will continue with the classes. She may want to do the competition prep classes enough to take them.

Specific to the question about the Challenge Writing Questions: They consist of one question per week in which the student has to write up a full, thorough answer, similar to what you find in the book when it is teaching how to do a new problem. The student should assume they are writing it for someone who is capable, but hasn’t learned that particular material yet, and explain things well. They need to use correct grammar and full sentences, as well as (obviously) having the math right.

The class format is really a poor fit for my kid. They are fully text-based, no audio or video at all, and 90 minutes long. It’s a stretch for her attention, especially because once she types in her answer to a question she will let her mind wander and then not notice when the answers get pushed through and the class starts to move on. Something, anything audio at all, even a ding when they post a new problem to the class or push the answers through, would be really helpful. Also, the workload is simply more than she needs to “get it”. Once she hits mastery on Alcumus, she’s gotten the concept down and is ready for challenge problems or to move on. The online class requires Alcumus *plus* about 10 extra questions per week at about the same level as Alcumus. She can do them, but she’s not fast, so those 10 additional questions require a substantial chunk of time for a kid who is ready to move on.

[mathnerd]

I posted a similar question on the accelerated learners board some time ago. In our case, my son does every problem in the book and all the challenge problems as well. I have always been the parent who is cautious about not creating gaps in knowledge and understanding and also developing underlying fluency in concepts. The sheer number of problems, the discussions we had on certain topics in addition to the time it takes to do correction work was not only huge but also keeping my son from geometry and competition math questions that he wanted to tackle. He was ready to move on to upper level math and our slow pace was frustrating to him. I wondered if it would be easier to sign up for the online classes and move through the books quickly. The general advise that I got was that working on every problem in the review and challenge part of each chapter builds problem solving stamina and logical thinking skills and if possible, AOPS through self study was beneficial. 

So, I modified our strategy for self-study of Aops as follows:

1. For each chapter: Complete all the exercises. Complete all the odd numbered problems in chapter reviews. Complete all the odd numbered challenge problems at the end of the chapter.

2. When half of a text book is completed, go back and work on all the even numbered problems in all the chapters covered. This also served as our review on older concepts.

3. Simultaneously start Counting and Probablity and Number Theory and let him go at his own pace (this took away his main complaint of being made to sit on a single book for months and months without access to more formal math).

4. In the summer, work on Alcumus for review and my son sets it to "insanely hard" level as he practices for math competitions in the summer. He says that some of the alcumus problems are harder than the challenge problems at the end of each chapter.

That being said, we will move on to online classes for higher levels of AOPS in the future where there might be benefits to moving quickly through the curriculum and having an instructor to teach the child.

Edited January 18, 2019 by mathnerd