AoPS Pre-A Alcumus - Expecting too much?

[J&JMom]

Hi, we are 5 weeks into our first AoPS course.  Our methodology has been to work the pre problems, read the text, watch the videos, achieve blue on Alcumus, and then use the review/challenge questions (a selection, not all) as the test.  My son is enjoying the program, but the Alcumus is a time-suck.  He gets a few questions wrong (the second time) and he basically needs to start over having to complete an ever increasing number of problems to get back into orange, then green, and finally, blue.  Does he need to learn to take more care in his work, or is blue too demanding? He is spending upwards of 2-3 hours per section in the Exponents chapter.  He says he gets it, but is he really with this workload?  BTW - for Squares (2.1) his ratio is 30/45 and the result is green.  This seems like a LOT of work. I guess should I be content with Green or push for the Blue (which I consider to be "A" grade).

[sassenach]

I'm not super familiar with Alcumus. We're just getting started with pre-A this year and I was playing around on it yesterday.  I would say that blue is asking too much. Green would be what I would shoot for. Rusczyk (one of the authors) has spoken several times about the tyranny of 100%. He suggests that 70% is the number to aim for before moving on. 30/45 is not quite 70%, but it's pretty close.

[wapiti]

I'm unclear - is he taking the online course?  If not, there is no rush.

 

If he is doing all the regular exercises in the book, plus a selection of challenge problems, I would not be pushing him to make Alcumus blue at this point in time.  I like to use Alcumus for review.  I'd either leave it for later, as in a few weeks, or only have him turn it green at most.  Then later, in weeks or months, you can have him go back and turn everything blue.  That also makes for a nice review of everything at the end of the text.  (Amazingly, the early chapters seem so much easier by then :))

 

Realize that chapter 2 is one of the more difficult ones in the book.  One of the lessons there is probably the longest one in the book in terms of the time from start of the lesson problems (gray boxes) to completion of the exercises.  I would not have him working through one lesson per day - I'd go by time, say an hour per day.  The next day he would just pick up where he left off.  The videos can be time consuming so I'd probably only add those in when he felt the need for more explanation.

 

The lessons in the second half of the book are more consistent for length/time.  Still, there may be days where he is doing the lesson problems (and possibly adding the videos) on one day and then the exercises the next day.  The chapter review may take multiple days.

[J&JMom]

Thanks for the responses.  I am wanting to complete the program in an academic year (end of May for us Texans) therefore we need to keep to a schedule.  That's how we roll :).   So, would you consider a student to be working at an "A" grade if he or she earns Green on Alcumus as the assignment?  I like using Alcumus because the answers are explained for that problem only without needing to look it up in a book, thus he can work independently. We do not do the after section exercises in the book.  The test comes from the end of chapter review/challenges (he selects problems from each which are worth x points each with 2 attempts).  I average the Alcumus for the chapter as a test grade and average with the test for his grade. Yes, I use numeric grades which are grouped as A, B, C, etc. So I want to ensure he is working according to appropriate standards and that I am not grading unfairly.  I had planned to use Blue as A, Green as B orange as C and red as Fail.  Thanks.

FYI, our pacing schedule (we are working currently 1 week behind WTM online course and need to catch up!) is 1 day for working text discovery problems, reading the solutions, and watching the videos. Day 2 is for completing Alcumus. For "test" days, I set aside 2 days.  I have set aside 1 hour per day for this work. For this chapter, this is not enough time as he is working upwards of 2 hours a day.  Maybe this is just a rough patch and things will pick up faster. I hope to complete the course in 32 weeks.

 

Ideally, I would love to see the grading schema for the online class :)

[wapiti]

I may have misunderstood, but if you are using Alcumus in place of the end-of-lesson exercises in the text, IMO that is a mistake (ETA, other people will probably chime in with a different experience, so YMMV).  The exercises are designed a little differently from the somewhat random selection of Alcumus problems within a topic, which vary widely in difficulty level, sometimes easier, sometimes harder than the book problems.  Alcumus isn't likely to be enough practice for many of the topics.  I don't think that Alcumus and the end-of-lesson exercises are truly comparable.

 

Moereover, you are then using what should be regular homework practice (because you're not doing the exercises) for too much grade weight.  As far as online grading scheme, AoPS had info online though I'm not seeing it right now - if I find it, I'll post a link.

 

I don't know anything about the WTM online course, so I can't comment on the workload.  However, we've done many of the online courses at AoPS.  I have seen firsthand, in my own house, that a student who skips the regular book end-of-lesson exercises in order to finish the online assignments is shooting themselves in the foot.  IMO, the book exercises are the best way to get the concept down, to practice, before moving on to more challenging problems.  I can't emphasize this enough and it does have an effect on time efficiency - the less-well the student knows the material, the longer the Alcumus would take.

 

For a middle school age student, I doubt you'd have any difficulty getting the book finished by May even if you self-pace.  The second half goes much faster.  Chapters 2 and 5 were the slowest for us.  If you really need to cut down the time spent, I'd cut out the videos, which shouldn't always be necessary.  ETA, also note that some lessons have more, or harder, lesson problems than other sections and in a few cases should take more than one day.  OTOH, there are some lessons that are short enough to dive right into the exercises after finishing the lesson problems.

 

ETA, alternatively, how much time is spent reading the lesson problem solutions?  Is your student completely independent with this book?  You might be able to help speed things up there by doing it with your student, pointing out items of significance and helping your student go over areas of difficulty while more quickly breezing through areas that were understood well already via the doing of the lesson problems.  When we did the prealgebra text, that is how we approached the lesson problem solutions and typically we only spent a few minutes, as most of the important points were covered during the doing of the lesson problems.

[Julie of KY]

 We do not do the after section exercises in the book.  The test comes from the end of chapter review/challenges (he selects problems from each which are worth x points each with 2 attempts).

 

I think the section exercises are very important and then the meat of the chapter is the review section at the end. Students cannot be expected to know how to do all those problems if they haven't worked the problems previously in the chapter. The review problems are not just a sampling of problems throughout the chapter, but they go much deeper and this is where LEARNING occurs - they haven't already done this type of problems so they shouldn't get them all right. The solution book has complete solutions to all the problems. For my kids, it might take several days (up to a week) to finish some of the end of chapter reviews.

 

I use Alcumus as a review as we move on to future chapters.

 

[Roadrunner]

My son turned all the topics blue and each topic had on average about 8 to 10 problems. Forty is a lot! I would not be asking for mastery (blue) if I were in your situation. The class only asks kids to turn topics green (pass). You can go back in the summer and turn them blue. I can't imagine handling the book (and I highly recommend doing all the problems there), Alcumus, and class assignments if Alcumus is so time consuming. The class moves at about two weeks per chapter.

[SilverMoon]

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Edited September 23, 2023 by SilverMoon

[sassenach]

This thread has been very helpful to me as I learn about the different components in the AOPS universe. Thank you to all of the experienced parents who gave input!

[J&JMom]

OP Here.  Interesting take on the Alcumus problem set.  Just to be clear - We do work through the intro problems as intended.  He figures them out with me at the table, then we review the solution offered in the book.  I am attempting to replace the end of section exercises with Alcumus.  It appears to me that the problems are comparable - is there that much of a discrepancy in difficulty?  I will consider this, but I will most definitely accept Green from now on.

 Thanks for the replies. 

[J&JMom]

My son turned all the topics blue and each topic had on average about 8 to 10 problems. Forty is a lot! I would not be asking for mastery (blue) if I were in your situation. The class only asks kids to turn topics green (pass). You can go back in the summer and turn them blue. I can't imagine handling the book (and I highly recommend doing all the problems there), Alcumus, and class assignments if Alcumus is so time consuming. The class moves at about two weeks per chapter.

What are the assignments for the class?  Alcumus?  End of Section Exercises?  Combination?  I would like to get an idea of how the online does it.  I found a syllabus listing the topics covered per week for my pacing here at WTM course. Thanks in advance.

[Roadrunner]

What are the assignments for the class? Alcumus? End of Section Exercises? Combination? I would like to get an idea of how the online does it. I found a syllabus listing the topics covered per week for my pacing here at WTM course. Thanks in advance.

They are assuming that you are working through the book yourself, so they aren't grading that, but

 

They assign a set of problems that aren't in the book to complete as well as Alcumus problems. Your grade depends on those two components. Again, if you don't work through the book first, you won't do well on those. Honestly Alcumus was the easiest part of it all even though we got mostly questions above level 17. Sometimes DS mastered the topic with just three or four questions. I am surprised to hear about your experience.

 

I don't know about WTM prealgebra schedule. I looked at the Algebra and saw they call the first 10 chapters Algebra 1. I think with the exception of couple of chapters, the entire book is Algebra 1 on steroids. It would take more than two years on their schedule to complete an entire Algebra 1 course.

[Julie of KY]

OP Here.  Interesting take on the Alcumus problem set.  Just to be clear - We do work through the intro problems as intended.  He figures them out with me at the table, then we review the solution offered in the book.  I am attempting to replace the end of section exercises with Alcumus.  It appears to me that the problems are comparable - is there that much of a discrepancy in difficulty?  I will consider this, but I will most definitely accept Green from now on.

 Thanks for the replies. 

 

I thnk there is a big difference in the end of chapter review problems and alcumus. Compared to Alcumus, I think the end of chapter review problems generally start easier and get harder than Alcumus. They build on themselves and incorporate a lot of theory and understanding of the concepts. Alcumus tests problem solving using the chapter concepts, but it is not the same. Once my kids struggle through the chapter reviews, they find Alcumus to be relatively easy.

[EndOfOrdinary]

We have done four of the Intro AoPS books. By far, PreA was the wonkiest to schedule. In NO way were you able to take the chapters, divide them up over the school year, and be good. You can't even take the number of problems in each chapter and do it. Trust me, I tried. I am a neurotic planner. I tried everything I could analyze and searched out other schedules. No dice. It is flat out not designed to be paced that way. The author has been explicit about that in numerous places. The chapters are designed to take as long as they take, period. In fact, toward the end of the book (chapters 11-15) are brisk, concise, and not difficult in their theory. They are just touching on beginning foundations of various descrete math concepts or later geometry. The beginning chapters (1-4) are imperative. They are not only necessary to know stone-cold solid, they take significantly longer to master because you are dealing with theory to an extreme degree. Not only that, you are dealing with theory from multiple angles as the crux of further study. They all build on one another (which is the point of the review problems as stated above and why you should not remove them.)

 

To be pushing pace at all is doing a significant disservice to your student. This is a book series designed to mull over. It is designed to seep slowly into the student's brain and be absorbed. It is not process. It is not repetitions for mastery. It is creative problem solving where the point is to be baffled and stand in the unknown. The entire design requires faith on everyone's part. If that makes you uncomfortable as the parent (as it appears by your need to schedule without consideration to the learning style) you need to choose a different curriculum. That said, a student in middle school (not an accelerated student who is chronologically younger) would more than likely finish easily by May. Many significantly younger kids (once through age appropriate maturity issues) quickly progress through PreA.

 

If you are switching up a curriculum, cutting out various parts in place of others, pushing and smushing into a schedule, and the results are not what you thought, perhaps it is either time to trust the curriculum as written or it might not be the curriculum for your family.

[J&JMom]

Ok, Ok.  Let's say I'll play the game properly, would you eliminate Alcumus and simply do the end of section problems? Would that be enough?  I am also hearing that this chapter 2 is a bear, and it would prudent to give it another few days to percolate. 

I am not trying to be difficult. I am used to math (and other curriculum) to being simply open and go with daily lesson plans and clear objectives for mastery. This seems a bit more convoluted, and the fact that many of the problems make me want to run screaming from the room doesn't help matters. [i have a masters degree in social sciences - math isn't my thing, so to 'play' in math other than just 'get-it-done', is a foreign concept, but one I will indulge my son in, hence this program entering the house at all :)]

And my son likes the program.  I have asked if he wants to go back to what we have used in the past, but he emphatically says no. He laments that he won't be able to continue this program into high school (as we plan to send him to public at presents).  He is in seventh grade so he is not 'accelerated', but bored by the typical middle school text program we were using. He scores consistently in the top 10% and even 5% on ITBS math subsections, so he should be able to handle the work. I am guessing the problem is me, so I must accept this paradigm shift, and let it be. Thanks for the help!

BTW , to beat the dead horse, - how do the online classes pace themselves then if it is to be self-paced?  Especially the one that AoPS themselves offer?  I would love to pass the reins to them, but are unable to swing the $600 for the courses...

[Julie of KY]

It would be perfectly okay to eliminate Alcumus.

 

I typically do one section per day - mom working through the section with the student and then the student doing the exercises. If it is a long or hard section (or we are just having a bad day) then we take two days for that section. I then take several days (up to a week) on the chapter review and challenge problems. I can easily see an "A" student only getting 3/4 of the chapter review problems and 1/2 of the challenge problems. I would count the starred problems as bonus, but not count them against the student if he can't get them.

 

I use Alcumus as review. We do it on lazy days that we don't want to do other math. We also do it on days that we want to go more slowly through a chapter review so that math is still being done. I always work on Alcumus behind where my student is in the book. As you move along, Alcumus is not an easy thing. We may go weeks (or months) without touching Alcumus and then pick it up again.

[J&JMom]

It would be perfectly okay to eliminate Alcumus.

 

I typically do one section per day - mom working through the section with the student and then the student doing the exercises. If it is a long or hard section (or we are just having a bad day) then we take two days for that section. I then take several days (up to a week) on the chapter review and challenge problems. I can easily see an "A" student only getting 3/4 of the chapter review problems and 1/2 of the challenge problems. I would count the starred problems as bonus, but not count them against the student if he can't get them.

 

I use Alcumus as review. We do it on lazy days that we don't want to do other math. We also do it on days that we want to go more slowly through a chapter review so that math is still being done. I always work on Alcumus behind where my student is in the book. As you move along, Alcumus is not an easy thing. We may go weeks (or months) without touching Alcumus and then pick it up again.

Thank you for posting!  I like metrics, and you have offered me some I can work with.  I believe I am finally understanding (sorry about the thick skull) that Alcumus is the review, and the exercises are the course.  Got it! However, the thought of spending an entire week on 'review' seems counter-intuitive as it would be assumed the learning would have already been accomplished by the time of review, but I'll go with it. 

 

[Julie of KY]

"Review" section is a misnomer as I think that is where the meat of the chapter is. The chapter sections walk you through the teaching, but the chapter review is often where you put it all together and apply it to new and harder problems. AoPS does  not have an end of chapter test or anything similar.

 

By the way, I consider the challenge problems optional for some students. My students that are better at math always do the challenge problems. With my students that are just good, but struggle through the review section, I may skip the challenge altogether. I would not move on if students don't understand much of the "review".

[wapiti]

Just as a point of clarification, when you say end-of-section, I'm assuming you mean the exercises for the numbered lessons.  For many lessons/sections, the exercises are far fewer than what one would find in a traditional prealgebra text.  There is need for further practice putting the concepts to use.  Along these lines, I agree with Julie that the end-of-chapter "review problems" that come in the "summary" section are really important to do.  When we have rushed through the review, we are sorry later.  It's ok; there will be time to finish the book by May.  (I don't usually assign all the challenge problems either.  After my student is through the book, I like to go back and select a few challenge problems from each chapter for review.  It's amazing how much easier the challenge problems seem later once they've had more time for everything to sink in and more practice problem solving.)

[The Governess]

Well, I will offer you a slightly different perspective. My dd took the pre-A class with AoPS last year as a fifth grader. The assigned homework was to read the chapter sections (anywhere from 2 to 4 per week) and work through the problems, turn the Alcumus bar green for the chosen topics (although she usually worked until it was blue or came back later to turn it blue), and complete about 10 challenge problems per week, one of which had to be a written step-by-step solution, walking someone through the problem. Most weeks there was simply not enough time left to do any of the other exercises or reviews.

 

My dd is very good at the mechanics of math, but the problem-solving focus of AoPS was a challenge for her. The class definitely stretched her. I think she ended the year with a pretty good grasp of the concepts even though we weren't able to do all of the exercises. One thing to keep in mind is that AOPS pre-A covers topics much more deeply than any other curriculum would... I taught Saxon Algebra I in a co-op last year and the content of AoPS pre-A went well beyond what Saxon's algebra text covered in many areas.

 

She is using Forester for Algebra I this year. The first few chapters are a review of Pre-A and she is flying through them very easily. We may go back to AoPS in the future but she wanted a more straightforward text this year. I will still supplement with the AoPS videos and Alcumus.

[Sebastian (a lady)]

OP Here.  Interesting take on the Alcumus problem set.  Just to be clear - We do work through the intro problems as intended.  He figures them out with me at the table, then we review the solution offered in the book.  I am attempting to replace the end of section exercises with Alcumus.  It appears to me that the problems are comparable - is there that much of a discrepancy in difficulty?  I will consider this, but I will most definitely accept Green from now on.

 Thanks for the replies. 

 

If you are looking for independence, why not let him do the end of chapter summary exercises and then check his work in the solutions book?  If you are worried that he'll see the next problems, you could copy the solution pages for the summary, cut them apart, fold them and number them on the outside.  

 

Pre-Algebra wasn't out yet when my older kids went through that level.  They started with the Intro to Algebra book.  There was a certain process to working through the book that they and I had to learn.  Each lesson isn't the same length.  I couldn't just split the book up by chapter and figure x days per chapter.  Some lessons needed more than one day.  Sometimes they got to a point and realized that they hadn't understood a previous concept to the depth necessary to move forward.  So they looped back and repeated a chapter.  At one point I decided that their difficulty with quadratics stemmed from insufficient fluency with multiplying polynomials, so they spent a couple weeks going through ever increasingly complicated problems from an older Dolciani book before returning to AoPS.

 

I think that using Alcumus as the end of chapter review and grading criteria risks using a supplement in place of what is designed as an intrinsic part of the instruction.  I agree with others that the end of chapter exercises aren't just a compilation of what came before, there are extensions of concepts that require the student to put together what he/she's learned.  Some of these problems are preparatory for the instruction that will come in the next chapter.

 

It also sounds like you are using the mastery level (blue on Alcumus) of an already challenging program to determine A level.  I have had a similar tendency myself in the past.  But I don't think that is the purpose of the level coding on Alcumus.  It was created to challenge and motivate students who are potential competitors in national and international math competitions, meaning the upper level of the problems presented may be quite a bit higher than what is typical.  In other words, a student working through Alcumus may have reached A level quite a bit earlier and be working at A+ or A++ level.

 

Finally, while I did start grading work my older kids did in 7th and 8th grade, remember that a grade for Pre-Algebra isn't something that goes anywhere outside the family in most cases.  Even folks who put high school math done before 9th grade on a transcript start with Algebra, not Pre-Algebra.  So trying to figure out a grade isn't a hill to die on IMHO.  In the long run, I think you would be best served to ensure that he works through and understands the math in the book, even if that takes a little longer than until May.  

[Clear Creek]

OP Here.  Interesting take on the Alcumus problem set.  Just to be clear - We do work through the intro problems as intended.  He figures them out with me at the table, then we review the solution offered in the book.  I am attempting to replace the end of section exercises with Alcumus.  It appears to me that the problems are comparable - is there that much of a discrepancy in difficulty?  I will consider this, but I will most definitely accept Green from now on.

 Thanks for the replies. 

The problem sets in the book that include the solutions and how to solve them are only 10% of the teaching on the concept. The other 90% of the teaching is actually in the exercises at the end of each section, or at least that is how it felt for us. The exercises look deceptively like groups of problems that have the student use the learned concept over and over, but that is not it at all...the first several problems might be that way, but the ones after that are ordered so that the student discovers how the concept works in all sorts of new situations and together with other concepts, and the main concept is explored deeper with each successive problem. Same thing with the review exercises at the end of the chapter...it is not really a review of the concepts covered, but more of a bringing together of the concepts that were taught and seeing if the student can use them together. The book actually has little in the way of explicit review (the student is supposed to be able to retain concepts through repeated use in later chapters), so my daughter used the challenge problems as review two chapters behind where she was working (so when she finished chapter 8, she went back and did the challenge problems for chapter 6).

[daijobu]

My kids don't do Alcumus, probably for the reasons cited by OP.  But they attempt all problems, exercises, review exercises and challenge problems.  If it's in the text, we at least attempt the the problems and review the solutions.  We gave up on the videos and don't do alcumus, or really anything else other than the text.  

[Allearia]

One of the reasons I disliked the online AOPS classes was that it gave no online credit for doing the problems in the book, so my son would just try to do the challenge problems and work through Alcumus and mostly skip the book. Even though when he was having problems, I would take him through and help him find the section in the book that taught it. He was always surprised that it was right there in the book. But it was a bit hit or miss what he would have learned or if he was missing something obvious from the book. so I would just prioritize the book over everything else, and have Alcumus for some extra review if he wants to etc. Right now I am not having ds doing any Alcumus because it takes time away from the book. The problems in the book are really carefully thought out to teach the concept in a progressively deeper way.

[Sebastian (a lady)]

Again we have experience with starting in the Intro to Algebra book, but I wanted to mention that my older kids did algebra 1 and algebra 2 using that book then did most of the Intro to Geometry book. They then tested into precalculus at our community college. My oldest is now in CC Calculus.

 

They did the books only not the online class. They rarely see Alcumus.

 

Just meant to encourage that the books alone are pretty good.

[Roadrunner]

Again we have experience with starting in the Intro to Algebra book, but I wanted to mention that my older kids did algebra 1 and algebra 2 using that book then did most of the Intro to Geometry book. They then tested into precalculus at our community college. My oldest is now in CC Calculus.

 

They did the books only not the online class. They rarely see Alcumus.

 

Just meant to encourage that the books alone are pretty good.

You mean he didn't do Intermediate Algebra book?

[Sebastian (a lady)]

You mean he didn't do Intermediate Algebra book?

Correct.

Algebra 1. Intro to Algebra book chapters 1-13

Algebra 2. Intro to Algebra book chapters 14-22*

Geometry. Intro to Geometry

 

Precalculus dual enrollment at community college

 

* My original intention had been to use part of Intermediate Algebra for the later part of Algebra 2, but we didn't get to it. Ds did have to play catchup with a few topics like logarithms.

 

My main point is that I think Alcumus is a supplement and not a substitution for the exercises in the text. Also that AoPS is pretty beefy and it can be easy to forget that.

[Sebastian (a lady)]

One other thought, algebra at our house tended to happen around the same time as puberty. Increasing independence at the same time that math got a lot more complicated at the same time that hormones got unpredictable was problematic.

 

We were more successful when I was very present during math. I'm working my own way through Intro to Algebra for the second time with my youngest. I also learned to knit to keep patiently busy while I wait for them to do problems I'm done with.

[ErinE]

I wrote an overview of how ds used AoPS pre-algebra and my review of the program here:

 

http://forums.welltrainedmind.com/topic/536672-aops-pre-algebra-detailed-review/?hl=%2Breview

 

I absolutely would not skip the end of chapter exercises. This was where I assessed my son's understanding of the concept. DS considered Alcumus fun, but the book was for learning. It took him 18 months to complete the book, but he was in 5th/6th grade. As other posters have said, the first half of the book is fundamental, and the latter part progresses quickly.

 

DS is currently taking Algebra in public school while concurrently working on the AoPS Algebra text. He finds the class very easy, and of course, the book is hard.

[EmilyGF]

My son just finished Chapter 1's Alcumus in 30 minutes. I had him do it in two 15 minute chunks after he'd done all the main chapter work (as a sort of review) and while working the challenge problems. He only got it to green.

 

I think if a child needs 30 min per day to do Alcumus, there is some sort of lack of understanding (or inability to type? or distraction while using the computer?) that may need to be dealt with. I would consider my child sharp but not off the charts. I consider the book the main learning and Alcumus as a good way to get extra practice and review as needed. I probably won't have him start Ch 2 Alcumus until he is at least half way through the chapter.

Emily

[J&JMom]

Op Follow Up:  Okay.  We have switched things up in the week since I originally posted this.  He has now completed all the section problems for 2.3 and 2.4 over 2 days (30 minutes per day). These past two days (~1 hour each) he worked through the 20 or so end of chapter review problems. He got about 90% of them correct by the second attempt (~70% on the first).  I think he's got it.  I will not have him work through the challenge problems for this chapter to save time. He was much more relaxed, hence our homeschool was relaxed and we have ended on time! I think for now, I am confident he is understanding the material with the textbook alone and will put a hold on Alcumus for now.  Thanks!