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Hello!

I'm trying to find a really good, even rigorous, Alegebra 2 (Intermediate Algebra) course.

Any thoughts? BYU-Online offers the course in two parts. JHU-CTY offers the course too, but it's more expensive. Is it worth the price? Are there other options? She needs to get through it in about two months. We would sign her up for the UW Robinson Center's Summer Stretch course, but she has a conflict so will not be able to attend.

Other options or opinions that you can share would be very much appreciated!

Thanks!

You don't mention the Art of Problem Solving one, which would seem like one obvious choice; looks as though one instantiation of it started yesterday, but she might be able to join in! I have no experience of their courses (the timing doesn't work from Europe) but I love their books and Alcumus.

At the other end of the spectrum, my DS just did ALEKS Algebra 2. Depending on what "rigorous" means to you, this might not be suitable - all students have to do is enter answers, so it's no good for practising writing proofs etc., and the questions all fit into neat boxes, so there's no open-ended problem-solving element. I felt it was useful as a way to give DS a largish toolbox of techniques, though, and that this combined with using Alcumus and other problem-solving materials was good for him.

DS6 has used ALEKS over the past few weeks off and on. The reason I specifically picked it was that I wanted to give him some time to brush up on his skills, without forcing him to do too much drill. (For nearly this entire spring semester he has not only been taught nothing mathematical at school but we haven't been afterschooling him, and we only fitfully afterschooled for the first half of the year. I'm just trying to get him back in form so we can proceed at this point.)

I don't know how much practice he is really getting. He goes through 5-10 topics per hour, based on difficulty and attention to detail at the time, even including drink and potty breaks. This has caused two areas of concern. First, I don't know that he's actually getting a decent amount of practice in each topic if he can complete them that quickly, although I guess I should just take this as a signal that his retention is high and his ability to fill in holes quickly is decent too. Second, every session ALEKS queues up a new interim assessment for him, and I have to call and get it cancelled (they are working to add support for parent cancellation of these, but the assessments were apparently implemented with the idea that a normal student would encounter them less frequently because they would do fewer topics per session).

One could say that these are just symptoms of mastery, but I know that DS gets a few wrong here and there and that he does need a brush-up. This makes me feel ambivalent about ALEKS. It doesn't seem ideal as skills practice for a highly gifted kid because of lack of customizability coupled with assumptions about learning at a normal pace; but it also doesn't seem ideal as a way to actually learn or teach new math concepts, because the bare-bones explanations don't qualify as lessons, though I am in favor of letting kids noodle through things on their own a good part of the time.

5 topics an hour wouldn't worry me unduly, but if he's doing 10 topics an hour regularly, I suggest that he already knows the material and is working on things that are too easy. At least in the courses I'm remembering from recently, it usually takes 3 questions correct (with none wrong) to get a topic on your pie; if he's doing 30 questions in an hour that also includes the odd break, he's obviously not having to think about the questions much.

Huh? Why? I've always just let DS do the assessments the system schedules, even if it's frequently, because they aim to fix exactly the problems you're talking about, and IME do it pretty well. (By the way the underlying "knowledge space" theory is cool, too.) Because the assessment not only asks you questions on what you've already done (at most one question per topic, if you get it right) but also asks you questions on things that are not on your pie yet, answering on an assessment something you haven't officially done yet is the way to get over the boring stuff that's obvious if you really understand what you've done so far and to the genuinely new stuff. (Especially in the earlier courses, where the increments were often tiny, it often happened that the system would ask DS a question on a topic that wasn't on his pie and he wouldn't even notice, he'd answer it based on what he'd understood. He could skip whole prerequisite chains of topics that weren't necessary for him, that way. That's fine, because those are exactly the topics I don't want him to have to get one at a time by answering three questions on each.) Similarly, that's where you find out whether more practice is needed - if he can't answer the question, the topic'll get taken off his pie and he'll get more practice. Does your DS object to doing assessments frequently? Why? Is it possible that this is fixable?

I'd love to have the full teacher interface available to select additional topics and maybe leave out the odd one (synthetic division! crazy thing! although I have to admit DS enjoyed it), and there'd be no harm in being able to fiddle when it assesses, although I don't think I'd use it even if it were there. What other customization would you want, just out of curiosity? (For context, my DS is still certainly not "learning at a normal pace" - in our most recent subscription episode, he was signed up for 4 months, during which he worked on it only at weekends and a little during the holiday, was logged in for I think 50-odd hours total, and in that time did both Geometry and Algebra 2. However, it was pretty rare for him to work for more than an hour at a stretch in it, and also only in the holidays did he ever do more than 2 consecutive days, so I suppose we didn't encounter the really frequent assessment issue that you may have; he usually got a week at least between them.)

For learning I like it a lot (I think a set of gradually harder problems such that in fact you can often work out how to do the problem without any actual teaching is great), but for teaching I agree it's no use. We basically never use the explanations in ALEKS; if DS has trouble he asks me or DH.

Some probably are, but there's no way for me to just find and plug the holes. Holes certainly exist due to mismatch in the scope and sequence with what he's done before (Singapore and assorted problem solving), but it's not only time-consuming but prone to error to make assumptions based on abstracts of the scope and sequence of each.

Because the main reason for the interim assessements, as opposed to the regular ones, is to cement what's been recently learned. These are the great bulk of questions on them, perhaps the entirety-- they're more quizzes than level-setting assessments like the initial bigger one. But even though they're supposed to just cement knowledge, he doesn't need this every session, and it winds up wasting time he could be using to plow on ahead. It's more review than he needs, and the main reason is that he goes too quickly to suffer the lapse of time and memory which is the main reason for the existence of the interim assessments/quizzes in the first place, but also has much better long-term recall than average.

It's not useful to pile cement on top of cement, and I'm using ALEKS because I thought it would avoid this. It does to some extent, but it's just not ideal for someone who goes quickly and needs less review than normal. It would be better if there were more fine-grained control over the amount of review presented, and/or if the system had been more intelligently designed. Perhaps the system could tune itself over time for each student by tracking how little review each needed. Instead what seems to happen is that at predetermined intervals all students get a certain amount of review; they're just let out of the bulk of it if they re-demonstrate mastery (which for a fast learner might be done on a topic covered just the day before or even the same day).

The system's not totally inefficient, just not optimally efficient for kids at the higher end of the spectrum. And while ALEKS was designed with a good end in mind, a system that would adapt to the needs of the student, assumptions obviously based on the needs of more ordinary students have resulted in an implementation geared more to their needs.

He gets bored when he's forced to do extra questions on things he may have demonstrated mastery on just the previous day. I don't think it's a problem that needs to be fixed, since he has a good work ethic in general and his time could be better spent.

I could work up a full list based on system design principles, but don't have the time. It's one of those situations where I was noticing tons of improvement opportunities as I used the interface, but didn't write them all down. They obviously tried to keep it simple for end users with the goal of improving the user experience, and to the extent that it obviously works fine for many people, they must have succeeded.

ETA: I'll leave what I've typed below, but actually it looks as though I should eat some of my words, because looking back at this thread that I started when DS was 5, I am reminded that at that stage we did have similar issues with ALEKS. FWIW, our resolution was that DS did ALEKS up to Level 6, then did ALEKS Chemistry, taking a long time over it (just over a year, IIRR) then went straight on to ALEKS Algebra 1, and didn't feel the bump - he did Alg 1 in a few days in fact, as a "let's use up the subscription we've paid for" exercise. (He had, of course, learned a bit of maths elsewhere in between.) So if part of the issue is that you're feeling your DS should do all the courses in sequence - I don't think you've said which it is that he's doing just now - let me urge you to be a devil and consider alternatives :-) Gaps can be positively helpful, sometimes.


In fact, the algorithms that ALEKS implements do IME do a pretty good job of accounting for scope and sequence mismatches, if you let them.
I think this description is misleading, perhaps indicating that you've been misled. The way the underlying theory works, and it appears to me to be implemented pretty straight, is essentially that the system selects each question based on what will give it maximum information about what the student knows, or to put it another way, it selects a question where the calculated probability that the student will get the question correct is as close to 50% as possible. During a course it uses prior information about what the student has done in learning mode (which of course it doesn't have in the initial assessment) but other than that, the process is identical in all kinds of assessment.

What it doesn't do, AFAIK, is to adapt to individual students, or allow customisation of the prior probability that a student will answer correctly on the most recently added topic. It could be that for our children, the most informative question might actually be on a "you are ready to learn next" topic rather than on a "recently added to pie" topic that might be the result of the calculation with default parameters.

However, this doesn't normally matter too much, since the number of recently added topics will, with the default assessment schedule, always be fewer than the number of questions in an assessment so there is room to ask on all recently added topics and still have at least a little space to explore beyond. Come to think of it, if you are cancelling assessments, then the assessments you do let it do are indeed likely to get filled up with questions on topics that are on the pie, just because it limits it to 25-30 questions and if there are that many new topics, those are likely to win. Also, if your DS is doing scattered topics from all over the pie, the algorithm will work less well than if he does a long strand in a session e.g. sticks to one slice of the pie. To give a simple example, if he does 5 topics each of which depends on the previous one, then what the algorithm will (most likely) do is to ask him a question on the last one; if he gets that right, the probability it assigns to his being able to answer questions on the earlier 4 goes up so it probably won't ask him on those, leaving more spare questions for other topics.

But really, an assessment will only ever ask one question per topic, at a maximum, unless the child is making mistakes. There seems to be an inconsistency between you saying that that's too much review and you wondering whether he's getting enough practice - which is your main concern?

Have you actually watched him doing the assessments? Is it possible that, being 6, he's actually making slips that are causing the system to ask him repeated questions on the same topics? At that age, I did sometimes sit next to DS and go "Ahem" at crucial moments to avoid this, though I did this sparingly and more often gave him enough rope to hang himself, as it were...

+1 Colinsmum here. There is a contradiction in the issue of too much/too little repetition.

We worked with Aleks very differently (one topic per day, two max), but I tracked his progress rather carefully and automated assessments are triggered once 20 new topics have been added to the pie. You also get (optional, thanks Colinsmum ) review on topics added the previous session when you come back to Aleks.

An assessment has 25-30 questions, and I think it will only have *one* question per topic, no second chance (I have seen topics removed from my son's pie after one careless computation error in the assessment). The extra questions will be on new items, offering the chance of acceleration.

If you want extra review you can print worksheets and do them offline. They don't count within the interface, but they do provide extra review (and, for my son, an opportunity to practice writing longer answers and to learn to use a real ruler and protractor).

I think we're having this discussion because they don't do such a great job. My son took the initial assessment, and theoretically was let out of learning what he already knows, and yet you've correctly noted that a lot of what he's doing is probably too easy for him. This is a waste of his time.

Maybe, but I don't think so.

http://www.aleks.com/about_aleks
"As a student works through a course, ALEKS periodically reassesses the student to ensure that topics learned are also retained."

This was explained as a primary use for the interim assessments, by two different support people. It's also what I've seen and what my son reports. It's a key part of the system to incorporate review; this is a good feature of any traditional math curriculum as well, except that when you use a traditional curriculum you can compact (skip excessive review). It's not the exploration of readiness for new concepts that I'm against, but the extremely frequent review that can't easily be bypassed, when the main selling point of the system was essentially the easy ability to use compacting.

The description for the initial assessment also claims that it provides an overview of everything the student does and doesn't know. If so, and it's accurate, the only deviations as the student progress should be based on learning things without needing ALEKS instruction (during coverage of similar topics or outside of ALEKS), or losing mastery. If the former, I'd still want to have him test out of the block of material by the same sort of coverage as when he encounters a supposedly unknown topic and quickly masters it. The latter doesn't happen.

The most sensible way to conduct curriculum compacting is to administer a pretest-- which is essentially done in ALEKS by coverage of the subtopic itself after it's assigned, if not during the initial assessment-- and let a student test out. This is completely separate from review. Review is not antithetical to compacting, but it's the review with which I find fault in ALEKS.

The system was implemented to give fairly continual review, in addition to its other facets, based on assumptions made about how children learn. The review doesn't seem to be customizable or adaptable enough to avoid wasting a bit of time for a child who moves quickly and with higher retention than normal. It's not the end of the world, just suboptimal for my son.

I think it's a good point that someone might fill in gaps by working on related topics, and to that extent it is useful to have a reassessment every so often. Every day, with review of just-mastered content mixed in, shouldn't be necessary.

One obvious way they could improve this is by splitting out the review questions from assessments designed to allow compacting, and allowing one to skip the review, or allowing one to configure the amount of review. It's the review of recently covered topics that is most boring, not so much getting assessed on something not yet covered by ALEKS even if known.

As one goes through a curriculum one will cover many sub-topics. Even at one periodically presented question on each previously covered subtopic, the number of unnecessary review questions may grow to be large. No matter how they're spaced out, the total minimum review burden for each subtopic doesn't seem to be adaptable enough to different students-- I doubt that ALEKS only asks one review question, ever, on a subtopic without revisiting it periodically. I'm not worried about there being an interesting or varied mix of review; I'm worried about there being a such a high overall proportion of review, based on the needs of ordinary students, that it wastes time for higher-spectrum students. I simply don't want time wasted on review every day.

Although I'm a little disconcerted by the speed with which ALEKS initially determines mastery, I could live with it as long as my son continues to plow ahead without difficulty. But if mastery is attained, he doesn't need such frequent review. I'm not worried about him getting enough practice on topics previously mastered through ALEKS-- that's what mastery means to me, that one need not revisit it for quite some time and can move on. He doesn't like being forced to redo things he has done already. I'm just trying to use ALEKS to make sure he's solid before moving on to the next grade; in a sense, except for the hole-plugging concern, I'm using it with the intent that he do minimal review. This mismatch with the common use might be part of the problem, but it would be easy to get around if the system were more flexible. It ought to allow for this sort of use, since it's not good as a primary learning resource.

I have in the past, though I get the assessments cancelled now. He made only very infrequent errors on review questions, but he still got plenty of them.

The issue is too much repetition after a topic's mastered, constituting a waste of time. Ideally, one would be able to eliminate it, but that's not possible without skipping the interim assessments. I'd prefer a higher ratio of learning time to mixed assessment/review time; and the initial assessment supposedly provided a comprehensive assessment for the whole grade level.

This is a much more informative (but still non-technical) description of how ALEKS works than you'll find in the typical-user-facing pages.

But yes, rereading my very old thread does remind me that we've had the same feelings you're having now. I wish I could remember more about why we felt so much less positive at that stage than now - what changed? Some combination of the topics getting "bigger" and DS's maturity increasing.

A suggestion I got in that thread, which I didn't actually use but thought was brilliant, was to do the assessments myself "as" DS. You might want to do that: next time it give an automatic assessment, instead of cancelling it, do it yourself based on what you know your DS can do. (Maybe have him standing there telling you whether he could do a question, and then do it yourself rather than making him do it - it would be quicker and easier for him, and if he's anything like my DS it would tickle him! If you're good at identifying the questions that are on stuff that's he's not already done in ALEKS, you could hand over to him for those questions only.)