dereksurfs
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Posts posted by dereksurfs
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Great advice so far. Between MM, AoPS videos/Alcumus and Dolciani I don't think you can go wrong with these affordable, high quality options. One more great free resource is Khan which we've used for Pre-A and Algebra supplementation. They have both lessons and associated problems which worked well for ds11.
Here is the section on percents: http://www.khanacade...hmetic/percents
Questions: http://www.khanacademy.org/math/arithmetic/percents/e
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Derek thank you! i will purchase Foerster just for comparison's sake, and I also like to mix and match problems from different books so my child has the ability to process problems no matter how they are presented. When we hit anything tricky, I will be sure to visit Derek Owens videos. I have seen them before and like them, and have considered usiing him for Algebra when we are done with Pre A. What do you thinnk about supplementing with some Zaccaro?
That's a good question which I wanted to think about a little more before answering. You see I am in the midst of looking over 6 Pre-Algebra and Algebra books right now, comparing, contrasting, and evaluating them in light of where ds11 is currently at. I am considering various senarios or paths ahead including some combination of these resources. Zaccaro definately falls in the Pre-Algebra category I've discovered. So in looking at it again today I can see that some of the initial chapters would be redundant and actually easier than what ds11 has already done in TabletClass Pre-A. He is very vocal about doing things which he deems too easy. I think he is kind of like I was at his age. I would get bored if things seemed too easy. TabletClass is really doing a great job of stretching his brain right now diving deep into multi-variable linear equations. So in short I would recommend Zaccaro, but not too late into Pre-Algebra. Right now we could probably use at least half of it. However at the same time I am considering a model which actually begins to weave in AoPS Intro to Algebra. My son is looking over chapter 1 as I write this. I may have him start one day a week while finishing up Pre-A this year. At the beginning of the school year I would have said No Way! But his brain has developed so fast in such a short time its been amazing to watch.
Sorry for the long ramble. You just happened to catch me in the midst of one of my evaluation and planning stages. I'm such a planner. Yet I'm discovering that the best way to plan is to have a general idea of direction, then leave the door open for change based on reassessment of status. For example when ds11 started linear equations he hit a wall initially. So it was time to slow way down and look at various supplimentals. Khan and AoPS Pre-A really worked well in providing additional perspectives. Now that he's got it he's really taking off. At this point I'm looking ahead to his next challenge.
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Yes, the videos are awesome. My daughter works through the textbook, watches the videos and uses Alcumus for review. Do you know about Alcumus? If you create an account, you can have Alcumus "follow the book". So, Alcumus gives problems to your student that correspond to the order of topics in the textbook. Also, there are Quests. If they answer a certain number correctly, they can earn like a "virtual badge" for their account. My kid works through the section in the textbook, watches the videos that correspond to the topics and then she uses Alcumus for extra review problems. When she completes a topic, she stops Alcumus and moves on in the textbook...
Thanks for this ellaboration on Alcumus usage. I didn't know there was a 'follow the book' feature. The time we tried it over a year ago we used it in kind of a random fashion which quickly frustrated my ds at the time. Of course we went on later to discovery that it challenges and frustrates by design. :tongue_smilie: Yet if it could be aligned with a current lesson it would probably frustrate ds11 less now.
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I have Dolciani Pre-Algebra and Algebra 1 (1992) edition. As others have mentioned the various editions are somewhat different. But I actually liked the somewhat newer one after reviewing them online at OpenLibrary. Although the 1970s book was my Algebra text I liked some of the layout refinements in the newer edition.
Slight text differences aside I think the main advantage is very clear, straighforward math instruction. The scope and sequence seems to follow most of the current common core standards from which standardized tests are based. Its a no nonsense math textbook which covers all the bases.
Disadvantages for us would be its concise nature which is really designed as a 'student workbook' to be supplimented by direct teacher instruction. There is simply not a lot of concept development and explanation in the book itself. There's a brief overview of the concept with a few examples and then mostly problems to solve. Unlike programs geared more toward independent learning like AoPS this traditional book is not. My wife does not want to lecture/teach from a book during the day. So if we went with Dolciani as the spine we would look for supplimental lectures. I think Derek Owens bases his Algebra 1 course upon Dolciani, though he expands on it quite a bit. In your case since you already are going through Dolciani Pre-A this might be a non-issue. I'm not sure how different families approach this with traditional workbooks only. But I would imagine it varies quite a bit depending on the student as well as the parents in terms of how much direct instruction is provided.
Foerster is very nice as well. I may even like it a bit more when comparing the two side by side, especially if we were to only use one as a spine. I think Foerster provides a bit more in terms of concept development and elaboration, though still concise. I recommend picking one up to compare if you do go this more traditional route. They are both very affordable on the used market. Foerster also has Math without Border Lectures which can be purchased and expand upon the concepts presented in the book, similar to the way I think it was designed to be used.
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Hey Guys! I have a 5th grade student that is almost done with pre-algebra. Last year was our first homeschool year and we landed with Singapore for math. This year, I'm using Singapore 6A, 6B, MUS pre-algebra, a little bit of AOPS, and the Making Algebra Child's Play manipulatives. The MUS pre-algebra isn't as challenging as I had hoped, so I'm supplementing as needed. Basically, we start with the MUS pages and then move on to more challenging problems, even if I have to make them up. I expected pre-algebra (all of the curriculum mentioned) to take us a year and a half to get through, taking us through fall of 2013. BUT, my DD will be done by the end of January. I've looked at the Saxon placement tests and she would easily test into Saxon algebra. I'm not a big Saxon fan because of the way it jumps around. The sequence doesn't make sense to me and she thinks a lot like I do. She isn't fond of AoPS because she "needs" (in her mind) to be able to complete a lesson, and that isn't always possible in AoPS, which is why we only use it occasionally. I've purchased used copies of Foerster's and Saxon (even though I haven't been a big fan in the past) to look at, but they haven't come in yet. Our school administrator recommends Saxon, which is why I even gave it any thought. DD is very good at math, but doesn't love it. I want something challenging, but not to the point that she can't complete all of the problems (like AoPS) because that only frustrates her. Any suggestions?
Hi, I was in a similar situation as you with our ds11 earlier this year. We started with MUS Pre-A and I quickly discovered I wanted more depth along with greater scope. The main reason we selected it initially was because he has used MUS up until this point and its S&S is different from others elementary programs. Anyway after reviewing various programs which could offer more we decided to give TabletClass a try. I didn't feel he was ready for AoPS discovery yet or the writting style of the book. TabletClass Pre-A has been great in terms of rigor and scope including excellent lectures. ds11 is hitting similar topics as AoPS such as linear equations and even beyond with functions. We also suppliment with AoPS at times for another perspective.
I'm not sure if you have considered several great online /DVD lecture programs. Here a few worth looking into:
TabletClass
Derek Owens (Based on Dolciani)
Jann In Texas (Lials)
Math without Borders (Foerster)
I also bought Foerster, Dolciani and AoPS Algebra and am reviewing them to prepare for what is next. Though I would like to utilize Zaccaro's Real World Algebra between Pre-A and Algebra 1. I was definately impressed with the Foerster book as I think you will be once you recieve it. The others are great as well. But honestly ds11 is thriving so well with TabletClass currently that we will most likely continue with it for Algebra 1, then integrate one or more of these other great texts in as we go.
With young learners you have plently of time. And Algebra is such a foundational subject that its ok to spend more time on it. That is why I will most likely use more than one resource and extend it up to two years depending on how things go.
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Does the PM feature still exist? I guess I need to search for it to find out what you have to say, lol!
Yes, just highlight the user's name in the thread and you will see 'send message.' Alternatively if you click on their picture and go to their profile you can send a message from there as well.
I also think if Sharon has info from MUS which addresses her initial question it could benefit the group to hear their response. There may be others in this same boat either now or in the future.
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Derek,
You are right about it being hard to find used price. I will wait one more month since we are still doing 5B. I really hope ds10 will like Dolciani. I am very excited that it is just ONE book instead of Singapore's two textbooks, two workbooks, two intensive practice books and one challenging word problem for each year (some people used HIGs which is two more books). I am really wanting to simplify my math teaching life. But if I use both AoPS and Dolciani, it won't be that simple. We will start with just Dolciani in the beginning.
Thanks for your encouragement!
aomom,
I can highly recommend several more resources that are free which we use in conjunction with our Pre-Algebra spine (TabletClass). While its nice to have one book or online program in our case (TabletClass) it is also nice to pull from other areas when needed. During Pre-A this year my son hit a wall when encountering linear equations for the first time. It was then that I looked for outside supplimental resources in order to help him better understand the concepts and then practice solving these types of problems. I hadn't received Dolciani yet and I'm sure that would have helped as well. We found these to be the most helpful:
1. AoPS Pre-Algebra videos. These are really good and align with the book. But you don't have to own the book to benefit from the instruction. The video and free sample chapter were great on this subject: http://www.artofprob...type=prealgebra
2. The free AoPS Excerpts such as this one: http://www.artofprob...lgebra/exc2.pdf
3. Khan Academy. We used the lessons on linear equations and accompanying online problems. My son really enjoyed these. Sal Khan is gifted at explaining sometimes difficult concepts to kids. Here is an example from Linear Equations: http://www.khanacade...ear-equations-1
Problems: http://www.khanacade...ear_equations_4
I hope these resources help if you need them.
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A few comments:
1. There is a good reason not to use the same author for science - because you want a textbook written by somebody who is an expert in his field. The author of a great biology text would not be qualified to write a decent physics text, and vice versa.
2. In math, the issue is not so much that one wants to keep the same author (if that were the case, AoPS would not fit the bill, as the books of the series have different authors), but rather that one wants a program that has no gaps. The goal of using materials from the same series is to ensure that the student has the prerequisites from the preceding volumes to be successful in the next one - something that is much harder to do if you switch series. Since math builds organically on itself, this is a unique requirement not present in other subjects. You can still learn Renaissance history of you have gaps in Ancients, but you can not study precalculus if you have gaps in algebra.
(As an aside, the compartmentalization of math into neat packages labeled "algebra" and "precalculus" is a unique US phenomenon - elsewhere it would simply be "math", with a more organic approach.)
I agree that there are advantages in using different approaches. But the most important ingredient for success to me seems to be that the student has mastered the material that poses the prerequisite for his current textbook, something easier accomplished if one follows the same series, because the books are coordinated to be used in sequence.
Btw, if one is taught by a teacher who possesses subject expertise, it is pretty irrelevant what book is used, if the teacher is good. I have not the slightest idea who the authors of my high school textbooks were, but I also did not have to learn the material by studying from the books: I had a teacher who taught me.
These are good points Regentrude. I think that as long as parents/teachers are aware of the potential scope and sequence differences from one program to the next it shouldn't be too much of an issue. I always examine these carefully when making curriculum decisions. However I can see how it would be easier to stay with only one program - all Saxon, MUS, TT, AoPS, etc... You really wouldn't even have to think about the transition from one year to the next.
I also know what you mean about being taught by a teacher with subject matter expertise. I had two excellent math teachers whom I will never forget, one who taught Algebra and the other Calculus. Yet I coudn't remember the texts they used. It was only after performing a search for various quality Algebra books that I realized I had used Dolciani. The texts didn't teach me, the teacher did. But that is also the way those books were designed, more as student workbooks to be supplimented by direct classroom instruction. That is also why I wouldn't use Dolciani or Foerster alone for independent learning. Although other programs such as Saxon, TT, AoPS, TabletClass, etc... are designed to be done independently. I actually think that my son's current teacher, John Zimmerman of TabletClass, is really good at explaining algebraic concepts to him. I know parents can do this also. But for me I like letting these well regarded teachers provide the lecture portion. That's also why I like the AoPS videos.
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Here is the link to Intro to Algebra videos: http://www.artofprob...pe=introalgebra
I haven't seem any official usage statement regarding these. But I think most who want the fullest discovery experience start with the book, do the chapter's initial challenge problems, wrestle with them, then watch the video lesson after. Though I could see how watching them first would be a good way to go for someone needing a little jump start. Also using the videos could substitute at least in part with you trying to create your own lessons from scratch, especially since they are designed to align with the book already. That's not saying you wouldn't have to do some supportive teaching. But I think it could minimize some of the frustration in terms of lesson plan design.
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I really do see it as an option. If you are a math teacher, you just teach the material, and then the kids do the problems in class, and the exercises for homework. In my experience as a math teacher, I saw very few kids that ever read a textbook. They just waited for the teacher to explain the material. When I hear that high schools are using AoPS, I am guessing that a lot of them are doing this. The discovery method takes time, and I think that a lot of schools are under increasing time pressure for teaching the curriculum. Direct instruction is efficient.
I was actually thinking more terms of homeschoolers vs the public/private school teachers. I think it would be interesting to hear if teachers using AoPS would try to keep the focus discovery based like the online classes or make them more direct instruction.
Yes it does work. It is just inefficient as a base curriculum, and reading through the entire text book as a supplement would be a pretty impressive feat.
Ah, I just am making the big cuts, not the subcuts. Shortened they are:
1) Either you learn the material from a source or you discover it yourself
2) If you learn the material from a source, it could be through text or orally
Ok, I understand. I have heard of kids using AoPS in addition to their regular pubilc/private school workbooks. Some take the courses as extracurricular activities. I think many at this level are really into math, think math clubs, competitions, etc... My coworker's son is like that. I'm not sure any of my kids would ever be that driven. Though I could still see using AoPS as supplimental to gain another perspective and for added challenge.
Derek, I don't know anything about the videos. Looks like I should look into them. I think that videos first sounds like a wonderful idea for students needing a little extra help. What I don't like is reading the text which is the answer to the problems, and then doing the exercises. It is just not efficient.
I'm quite surprised you haven't watched the videos yet since they are so darn good! RR is a great instructor and I think kids can relate to his upbeat presentational style, more than most. Sal Khan is another naturally gifted math teacher. Though their styles are quite different. The videos were one of the things that initially drew me in to AoPS to want to learn more. They only go through Algebra right now Though he has plans to produce Geometry in the future.
ahhhh, but it just so easy. :001_smile: I love the idea of having math all set out. And I do think that the AoPS books build on themselves. My son is using algebra concepts he learned in Intro Algebra in the geometry book. And he is using problem solving techniques previously learned also. It would be interesting to hear from others how easy it is to jump into AoPS at a later date. I'm sure it depends on the kid. My older skipped PreA with no trouble, but would you want to go into intermediate algebra without doing AoPS's Intro algebra? not sure. I am also in a different situation here in NZ because my children must take the Cambridge math exams to gain university entrance, and there is a set curriculum with set books. I am very hopeful that working through AoPS will be overkill, but my younger might just use the cambridge math books if AoPS is a no go. I simply forgot the differences in the educational practices between the countries. NZ has a standardized curriculum for all 5 years of high school, so typically you choose 1 series of books and work through them. They build quite tidily on each other.
Still, I am a long term planner. And I have found that sometimes people need to be reminded to consider the big picture. I have definitely appreciated that same advice from other more seasoned homeschoolers.
Ruth in NZ
Sorry, I sort of overlooked that you are in an entirely different country! :tongue_smilie: I guess that does change a few things in relation to university enrollment and quite a bit else I would imagine. It sounds like NZ has a standardized test based on their standardized curriculum. In that case that is a consideration as well.
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When I go looking for a math curriculum for my kids, I prefer to stick with a single series if I can. Just a bit more continuity. Fewer gaps etc. So if you plan to use AoPS with direct instruction, I would suggest you think about some long term plans. These are the long-term options I see for using AoPS with direct instruction:
1) You teach them all the way through High School and not have them read the book. This would be like what happens in most high school math classes; students are taught in class and do homework but never read the textbook. The negatives being the lack of independence and passion that develops when a student self-studies. Also, you will have to be up on the material to act as full teacher.
2) If your student is going to self-study but retain a direct instruction style, he will have to read the text first and then go back and do the problems. As I have stated, there are better texts out there for this approach.
3) You are going to use direct instruction just temporarily while training, modelling, waiting for maturity, etc. You are going try to convert your kid from a direct-instruction type to a discovery type (like I will try to do with my younger). And then they will use the texts as written - in the discovery style.
So if you have a direct instruction kid, there are many questions to consider (all of which I am asking about my younger). Will you be satisfied with #1 or #2 if #3 fails? Or would you switch textbooks? How long will you keep trying #3? Will your efforts at #3 turn your child off of math? Obviously, the answers to these questions will vary for each family depending on too many factors to count. But these are questions that you need to consider before heading down this path (and I am in the same boat).
As I have said, I do believe that the discovery method is superior to direct instruction. I think it creates a very strong mathematical thinker. My older is a perfect example of this. However, and this is a big however, you do NOT need it in high school to succeed in a STEM career. And I will be very very careful with my younger to make sure that I do not turn him off math in my effort to change the way he approaches learning math. He does not need AoPS. He does need passion and confidence.
HTH,
Ruth in NZ
I would hazard a wild guess that no one does #1, ever (all the way through High School). It just sounds too crazy, like trying to fit a round peg in a square hole, over and over and over. Why do that?
I think most will probably use a combination of these approaches in varying degrees initially to try to introduce the program and find a fit. #2 would be less common longer term, unless one uses AoPS as a supplimental. In that case I think it can work.
I also think there are more than these three options. For example, one could watch the videos first, then go through the book including wrestling with the intial problems *before* reading the text. I'm not saying this pattern is recommended. However if that works for some kids who are struggling too much without the instruction, why not?
For our children I do not feel compelled to use only one program, especially all throughout High School. I view courses and their associated curriculum at this level as more independent (Algebra, Geometry, Trig, Calculus, etc...). I don't think I ever used the same author twice while in High School or in College for math or even science. And I never found that a stubbling block in any way. In fact I think there can be some advantages such as looking at things from a different prespective, being challenged in a different way when facing similar or related subject matter, etc... But that's just my perspective based on my own experiences. Maybe if you had all the same author throughout HS or possibly during some college courses you discovered a benefit? I am also considering dual enrollment once at the High School level. So for example our kids could take AoPS or any other curriculum for Algebra and Geometry, then a college course in Algebra II or Pre-Calc. Many HS families I know do that (dual enrollment) very successfully. AoPS could even continue as extracurricular if time and desire permits.
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I got a used copy of Dolciani Prealgebra: An Accelerated Course 1985 for $8 including shipping. The first three lessons are done in pen. So I will type the exercises out for ds to use for the three lessons.
After using Singapore for so many years, I like the change of having just one book and it looks very easy to use. I can't wait to start. Ds10 is finishing up 5B now. I hope to start early next year.
I still would like to find a relatively cheap used set of AoPS Prealgebra book and solution manual to use sometimes. Please let me know if you want to part with yours. Thanks!
Glad you like the Dolciani. I purchased both the Pre-A (1980s) and the Algebra (1992) and like them both. They are pretty cheap used.
With regards to AoPS I also purchased the Intro to Algebra text new. However I first looked for both the Pre-A and Algebra texts used and did not find anything. Since these are newer books and *very* popular the odds of finding affordable used copies are pretty low IMO. But you never know. You may get lucky. Based on the samples, online videos and overall quality I decided this was one book I would be willing to pay full price for. I even asked the author if they had annual books sales first and he politely said no. :tongue_smilie:
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Wow, this is a long thread! I'm new to the forums (and to homeschooling) -- would someone please list what the acronyms used for identifying curricula actually stand for? I'm in the planning-before-we-switch-to-homeschooling stage of things right now, and would like to better understand which curricula are being discussed here.
Thanks!
Hi AMJ,
Glad you are planning ahead. All the acronym slinging seems a bit overwelming when you first join I know.
So here is the list which includes multiple subjects:
http://www.welltrain...-abbreviations/
And another:
http://whythereyouar...breviations.htm
I got these from the Abreviations Sticky at the top of the Parent K-8 forum.
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I was over at our virtual charter's lending library today and I looked at their selection of algebra 1 texts. I still was very underwhelmed by the ones titled "California Algebra 1" (Glencoe, McDougal-Littell, CGP) but I did find an interesting looking text. It's Larson's Elementary Algebra 4th Ed. and I gather the 5th ed. is the text used in ChalkDust. I really liked the word problems in the Larson text.
Now I'm leaning towards using the word problems in Larson to supplement Singapore DM 8A/B instead of Horizons Algebra 1. I'm waiting on clarification from the charter school whether this combo will be acceptable for their purposes or whether I'd still have to give the end-of-chapter tests for one of the CA Algebra 1 texts. I'm getting sticker shock on the CD videos so I'm probably going to attempt teaching it myself.
I may be wrong, but I thought I read somewhere that you can buy the CD video lectures by Dan Mosely in a less expensive manner. Here is one thread briefly discussing it:
http://forums.welltrainedmind.com/topic/262888-cheap-chalkdust-algebra-usersheads-up/
It seems while some students enjoy these lectures other kids really don't like them. But that is probably true for most video lectures. So maybe teaching from the book yourself would be the better option. I guess its hard to say unless you were to demo the lessons with your dc.
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Just thought I would clarify that the above is not what I do. ;)
All 5 of my older kids have used MUS's alg/geo as a pre-alg/pre-geo program. All of them have followed MUS with Foerster. I did not discover AoPS until our 4th child had already finished MUS alg/geo, Foerster alg 1. Houghton Mifflin's geo (Chalkdust), and was in the middle of Foerster alg 2. He started AoPS w/counting and probability while finishing alg 2. His first "sequential" AoPS course was AoPS alg 3 (intermediate alg).
Since our dd (#5) is similar to her brother, when she finished MUS alg (pre-alg in our home), I asked her if she wanted to try AoPS alg and she said yes. However, it did not take long for her to say she didn't like the approach. (I think it was through chpt 3?? I can't remember exactly now.) She did not have problems w/the math, just the way things were approached. We switched to Foerster. She was finished w/Foerster sometime around Feb. (again, I don't remember exactly) Anyway, I asked her if she wanted to do one of AoPS online courses and take the alg 1 b/c she would finish around the end of the school yr and she could just give AoPS one more try and it shouldn't be difficult b/c it would be her 3rd time through alg 1.
Well, she had zero difficulty w/the math, but her view of the approach remained the same.......she just really does not like the texts. So, there you go. This is the view pt of a strong math student that didn't struggle with the work and just flat out doesn't like it.
I don't know if knowing how to solve the problems prior to using the text diminished its appeal (b/c she would approach the material with full knowledge of where it was going) or what. I just know it is a complete flop with her. She has absolutely no desire to pursue anything related to math, so I'm perfectly content in sticking w/Foerster.
While my previous post about the distinctions in my kids is accurate......the big picture is that not everyone needs to be able to deductively prove math at high levels. For ds who wants to major in theoretical aspects of physics......it is definitely a good tool. For dd, who at this pt is more interested in foreign languages and linguistics, it isn't a need. Even our oldest as a engineer didn't "need" the AoPS approach (Foerster was great preparation for him).
Honestly, from my POV, it AoPS fits the student, run with it. If it doesn't, I would not exert a lot of effort trying to make it fit.
Woops, sorry 8Fill! I guess I have a hard time keeping all your kiddos' math paths straight. :tongue_smilie: I knew you used MUS as Pre-A and that some used AoPS which you've discussed in this thread (dd & ds). I guess I was a bit fuzzy on the rest.
You do make a good point for all the AoPS interested parents reading this thread. There should no guilt or shame in using another fine program when AoPS is simply not a good fit. Keeping that in mind is liberating, especially if/when that is the discovery. There can be the impression that if one does not use AoPS they are only settling for second best or less. And as caring parents we obviously want the *best* for our children.
I think what interests many parents also is the *way* in which AoPS is introduced, and if that way at least partially influences outcome.
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I can't tell you how helpful this, in particular, is to me. From reading posts on this Forum, I was getting the impression that "The Discovery Method" was the key to AoPS, and if you don't do it this way (i.e. have AoPS be your child's first exposure to X topic via discovery) then you might as well not use it at all. This was frustrating, because I can see that my dd will be ready for more advanced/challenging math, conceptually, before she is ready to wrestle with thie level of problem entirely independently. What I'm reading now confirms my own intuition that much - so much - can still be gained by going through AoPS, either later after concepts have been introduced in other ways, or with another method than pure discovery.
So thanks for starting this thread and thanks to all who have posted!
I agree Rose, that is actually the reason I started the thread. I felt frustrated by the portrayal of a 'one size fits all' approach which doesn't, even if you like *some* aspects of AoPS. So hearing these different experiences along with clearification from the author has helped me gain a wider understanding of AoPS uses.
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So instead I think that we will go with an alternative PreA book (like first part of Jacobs) and then start the discovery method with AoPS Algebra, but just moving very slowly. As a pp mentioned, The first 5 chapters of AoPS Intro Algebra covers a lot of the same topics as PreA, just in a more concise manner. So if I want my ds to try to develop the ability to read the book himself, it seems that fewer pages would equate to more success even if the problems are harder because he would have completed a different PreA program.
Hope that makes more sense,
Ruth in NZ
Ruth, I was going to recommend the same thing. There is a time and a place for everything and sometimes its better to conquer one hill at a time. Mukmuk made an excellent point speaking to this very thing:
I'm listening to SWB's audio and she makes a good point - separate the various elements. Eg, math level, frustration level, and the stress of learning a new mode of learning. The less one infringes on the other, the higher the chances of success with the subject.
In starting with one of the elements first (e.g. comprehending algebraic reasoning) its takes something very difficult (AoPS Discovery Pre-A) and simplfies it somewhat. This is also very much the way us math geeks solve more complex problems through breaking things down into their simpler parts. It makes perfect sense to me. The other *big* factor in this equation is the rapidly developing brain. So as one part advances - understanding abstract math, other parts begin to catch up - reading comprehension and reasoning skills. Of course this could be done using AoPS twice or another program first then AoPS. It really depends more I think on the indivdual child at that point in terms of what may work best, first. I do think two seperate programs can compliment each other well in certain cases. 8Fill for example used MUS Algebra 1 to prep her kids for AoPS Intro to Algebra which seemed to provide a good mental bridge for them.
I'm really enjoying the collaborative thought and discussion on this topic. So many good points are brought forth as we each consider the best approaches to take for our unqiue children. I think we all want the same thing, and that is for them to succeed in whatever they do. If by chance its AoPS then what will facilitate the success of their unique journey from point A to point Z? In many cases, especially with young ones, its ok to take non-linear or non-traditional paths to get there.
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One more thing I forgot to Mentioned. RR replied in a follow-up email that younger kids sometimes go through the same AoPS material *twice*. The first could be more direct instruction/non-discovery with the second time being discovery. In thinking this over I could also imagine the first time being *another* program such as for Pre-A or Algebra, then following with AoPS in the same subject area. This was actually my initial thought for an Algebra 1, option year 2. However now I'm considering a hybrid approach also which consists of parallel integration or weaving in of two separate programs, over an extended period of course.
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Well, Derek, because of this discussion, I actually went and got my AoPS prealgebra book off the shelf and looked through it. Hummmmm. It is clearly a "no go" for my younger. I think it is very esoteric.
My older worked for a full year to get through the first 5 chapters in AoPS intro Algebra independently. He was adamant that he did not want help and he was successful in making the AoPS program his own. So, I got to thinking, if I want my younger to be able to do the discovery method, how can I mimic my older's experience. What struck me is that my older read through 150 pages of Intro algebra in his first year (prealgebra was not out), wheras my younger is looking at 500+ pages in his first year of AoPS if we use prealgebra. Originally, I was thinking of using prealgebra to introduce him to working through discovery independently, by slowly walking him through what is expected and how to do it. But now, I'm thinking that my older's success had to do with the fact that he had fewer pages to get through. There is a big difference between 150 and 550 pages. So, if I want to teach my younger how to do the discovery method, I'm thinking that perhaps moving very slowly through the intro algebra book is the answer. Its the speed that's the problem, because that means more pages. It is simply overwhelming. If I want him to have success with discovery and independence, there needs to be less to get through.
I think that your next big thread to start is how Intro Algebra users are teaching their students to use this wonderful curriculum. We will be ready by August (I think) to start the process. He will be starting as a direct-instruction type kid and I will be guiding him into the discovery method. My personal goal (which may not be shared by all) is to train him to be independent and use the discovery method, and I would be happy to discuss successes and failures with other hive members.
Ruth in NZ
Ruth, this sounds like the same conclusion I arrived at with my d11s earlier this year when evaluating AoPS Pre-Algebra. In reviewing the samples online and considering his maturity and math level it was just too much. However, now that he is well into Pre-A this year in another program (TabletClass) and learning a ton of new abstract skills I see his overall maturity and confidence rising. At some point in the future I can imagine him attempting AoPS Discovery to some degree at least. That includes reading through the lessons independently and working the problems.
This also goes back to an earlier point you made about a child being *ready* vs. possibly too young. Maybe for some Pre-Algebra *is* too early, yet by the time they are a bit older, more mature, Algebra may not be so bad. This of course also depends of their Pre-A preparation. But this worked fine for many kids including 8Fill's who didn't even have AoPS Pre-A at the time. RR seems to think maturity can also play a role in Discovery readiness. See his email I quoted above.
You mentioned you may take your dd through AoPS Intro to Algebra next year. She still seems very young. Yet I guess if you adapted it where you somehow teach her then do the problems at least initially it could work. I would be interested in hearing your experiences. If we start ds11 it won't be until later next school year. And I'm still looking at what that mix would be. He's really thriving in TabletClass Pre-A right now. So we will probably continue with that as well.
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All, thanks for your great input! I am still going through the replies and thinking about them.
Today I got a response from the author regarding this question with some clarification on recommended AoPS uses:
Greetings,
I'm not a huge fan of labels like "discovery approach", since terms like these are typically ill-defined and loosely-used, but I suspect that people are referring to the fact that we give students the option of trying to solve problems before explaining to them how to solve the problems. We do so by presenting all of the problems that will be covered in a section before presenting the solutions to those problems. However, students who would prefer a more traditional approach can simply skip straight to the presentation of the solutions and the ensuing discussion in the text. So, the books can be used either as what people call a "discovery" approach, or in a more traditional "read the material first, then try some problems" approach. The "discovery" approach will help students develop more general (not math-specific) problem-solving skills that will be essential to success down the road (and arguably may be more important than the math skills), but some younger students may really struggle with it and need to get a little more mature before taking it on.
Sincerely,
Richard (Rusczyk)
One of the keys here for me is that the more direct approach still has the the student going through the textbook as it was writtent toward them. Of course this is not to say that other approaches couldn't also be adapted if a young learner for example wasn't ready for the language yet. But I think having the student go through on their own would be the easiest way to teach it.
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I have no problem with direct instruction. I would just use a direct instruction textbook if that is the method I would be using with my child. I think that a student needs to be able to use his textbook to learn independently. I good math student should not wait around to be taught. There has to be some passion and interest and desire to self-teach. I am not a hands off type of homeschooler; however, I do think that you put your child at a disadvantage if you choose a text that can only be accessed with the help of a teacher. When I was in school, I always worked ahead and did my homework in class so I did not have to bring it home. I could only do this because I was using Jacobs (a direct instruction text) and I was a kid who learned from direct instruction. As I said, discovery would have killed my love of math. My older boy is the opposite. He cannot learn from direct instruction. It MUST be discovery. And when he used a direct instruction text (singapore) he turned it into a discovery curriculum by refusing any direct teaching. This speaks to the importance of working with your student's style of learning.
However, and this is a big however, I had to learn the discovery method eventually to have a STEM career. And it was a shock to my system when I realized in university that I did not know how to do it. I was a plug and chug type, and now needed to be more intuitive with answering difficult questions. The first physics class I *ever* took, was calculus-based physics for engineers at Duke University. Talk about sinking. I tried to continue with my plug and chug methodology by memorizing the entire physics text book and every single type of problem in it. But boy oh boy did that take a lot of time. I did well in the class, but realized then and there that I needed a new approach.
If a student can handle the discovery method, I think it is superior. But not all kids can, for whatever reason. As I said, I don't think I could have. So clearly you do not need to use AoPS to succeed in math, but IMHO eventually you will need the methodological skills it teaches if you plan to go into certain STEM careers.
So I think there are 2 different issues:
1) Should you encourage your student to develop the ability to learn through discovery?
2) If you are planning on using a direct instruction method, should you choose to use AoPS?
Hope this clarifies my thinking and helps you in some way,
Ruth in NZ
This does help Ruth. To your first point regarding working independently I wholeheartedly agree. That is a philosophy we adopted pretty early on in our homeschooling with math especially. We actually started with the Robinson approach which emphasizes self-learning. He is also a scientist and a number his children went on to do the same after he homeschooled all six of them by himself. Robinson used Saxon primarily which lends itself toward independent learning. He also emphasizes the importance in allowing students to wrestle with difficult problems vs. helping them right away. Although we never followed his approach strickly we did like some of his ideologies regarding learning and discovery. The funny thing was although a scientist he didn't believe students should even study science until they had finished Calculus. Math was his big thing until then, which they did a lot of and usually finished early. But that's another story.
I think learning via discovery can happen in other ways beyond AoPS. Though it was obviously designed to facilitate that thought process. My idea of using AoPS in a modified way is probably different than what some have in mind when we talk about direct instruction. I would never attempt to teach from the book, ever. But rather I would have ds go through it himself. The only difference might be whether to have him listen to the lesson first and possibly read some of the lesson before working the problems. That is different from direct instruction in the more traditional sense (e.g. parent teaching lesson from the book, then child working problems). I could see how trying to do that would be difficult since the text is written to the student with self-learning in mind.
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There is of course the discovery aspect of it, but it's not the only aspect. I don't know that some kids are quite ready for that self teaching "discovery" method, but the problems aren't like anything I've seen. They flicked a switch in my brain and I think they did for my son (despite the fact he never used it on his own). So there is also that aspect of the challenge. A lot of books don't challenge. They present a topic and you practice predictable problems. Maybe at the end they throw in a challenge problem or two.
When he moans about it, I tell my son math training is like weight training. You don't strengthen your muscles with finger bends. You have to do something harder than that.
That said, I didn't enjoy using it to teach from.
Wendy,
Thanks for sharing both your pain and successes with AoPS. I like your analogy in comparing tough problems to weight lifting. I also enjoy the challenging aspect of the questions along with the thorough examples and explanations provided. It sounds like you had a hard time teaching from the text more directly. Did you use the videos to suppliment the book as well?
When I had my son go through the chapter on linear equations I had him listen the lesson first, then read through the text on his own and try the problems. This approach worked pretty good for him in working through the material himself. He is used to working on his math independently which is the approach we took with him and our dds pretty early on. We've never taught from a book but rather looked for programs which lent themselves toward independence. And that is something I think AoPS does as well.
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Hi Derek,
I tried something sort of like that w/our dd. I tried using the AoPS alg text w/her after finishing MUS's alg/geo book. Even though she was familiar w/the content in the beginning of the text, she still did not like how it was presented. She could do the problems, but she didn't feel like how she had to get to the pt helped her understanding of alg any better.
After completing Foersters (which she finished in about 2/3 of the following school yr), I enrolled her in AoPS alg 1 online course just to give it one more try. (She is just as strong of a math student as her brother, but she doesn't love math like he does.) Anyway, she finished the course w/very little difficulty (only a few of the challenge problems challenged her in a way that I would say required more than just a little mental exertion.) At the end, she just plain out said that she didn't like the way they teach and that she even going through it when she understood what they were teaching was unappealing and not helping her understand it any better than she already did.
So......take this as simply one student's experience vs. anothers.......I personally believe the strength in the AoPS texts is learning the material via the methodology. Direct method teaching just doesn't produce the same impact and AoPS used via the direct method doesn't seem to produce the same impact either. B/c while I can absolutely state that my dd is as strong of a math student as my ds, she is not his equal in deductively arriving in the same place. Ds can prove just about anything that he uses mathematically (and does all the time for his advanced classes) It is the deductive reasoning that is fostered via the AoPS approach. Direct teaching mutes that skill to a certain extent. At least that is what I see in my own kids.
ETA: FWIW, I did not attempt to start AoPS too early by any stretch of the imagination. ;)
HTH
8Fill, as always this is a very thoughtful and helpful post. I really do enjoy hearing the different experiences your children had with AoPS, especially this dd. It was very clear that AoPS wasn't for her in hindsight, though maybe not so much earlier on. She was able to complete a challenging class without too much trouble. Yet it didn't do much for her. I guess like many other bright kids, direct instruction is best for her.
This also makes one ponder the benefit of taking an AoPS course following another challenging class in the same subject matter. I could see starting with an easier Algebra then possibly attempting AoPS in a second year. For my son I'd like to spread Algebra 1 over two years including something rigorous in the mix. If we stick with TabletClass into Algebra 1 it is rather meaty. So I'll have to think about how to integrate something else in such as AoPS, either sequentially or more in parallel. I'm starting to consider the interweaving idea more, though I know its not for everyone as its extra work. But I don't mind using more than one thing at a time and actually enjoy the variety as I think my son does. I could even stagger the content. I'll have to think on that a bit more.
Its interesting how you notice the difference in your ds and dd's deductive abilities. I wonder if there is also a difference in their computational skills? Do you think that even though AoPS seems to work on fewer problems than other texts the depth of the problems combined with wrestling with the content (discovering it) makes up for this?
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My younger child is one of the "other" students you refer to, so I'll discuss my plans for him.
My goal for my younger is to initially use AoPS with direct teaching, and slowly over the year transition my son into the discovery learning approach. This transition might look like this: 1) direct teaching 2) guided discovery 3) direct teaching difficult problems and discovery method the easy problems 4) discovery method with lengthy overview in the beginning by me 5) independently discovery method. If he hates the discovery approach, I plan to do a traditional text for a year and wait for maturity and then try again. I really believe that older children do better with these texts. And I refuse to give up on the approach, just because my child is young. After all this, if the discovery method is just not to be, then I would use a traditional text and perhaps have him work through some of the starred review problems or challengers in AoPS in additional to a different text. But honestly, I doubt I would do this. There are a lot of good algebra texts out there and typically they have some very nice challengers. I would embrace a program that I know my child loves and appreciates, and steer clear of the grass is greener syndrome.
This is an interesting way to introduce or ease into this whole new way of discovery learning. I may consider this approach vs. all at once or not at all. I agree that there are a lot of other really solid traditional programs available. Personally I really like Dolciani and Foerster which I also have copies of to compare.
You have not commented on *my* experience with AoPS. And I stand by it. The explanations are WORDY if used for direct teaching and the exercises are too few. Obviously, I am not a child, but I would think that these 2 problems would be accentuated in children. Some of the sections in AoPS Intro Algebra could be set out in about 1 page, and AoPS takes 12 pages. I just want to know *how* to do the problems so I can go practice on the exercises. And I have to wade through so much text. Often I find myself skipping over stuff I think looks like extra, only to find out I needed it. But then when I get to the exercises, there are just not enough of them. Because I have not struggled through the discovery aspect, I need to spend more time on practice. And there are not enough there. It. is. just. frustrating. Personally, I would have hated this series as a kid, and I went into mathematical modelling as a career!
Ruth in NZ
Althought quite removed from a child's level of mathimatical reasoning :tongue_smilie: you make some valid points regarding your experience and frustrations with the AoPS writing style. I find your last sentance revealing in a number of ways. First, even as a mathematical modeller you would have hated this Discovery approach as a child. Yet now you see so many of its benefits. Obviously you did fine in math without it. And many other STEM students will do well using direct instruction.
I haven't heard of as many using AoPS with the direct instruction approach. But the ways you described above easying into discovery with your youngest does address the variation I am referring to. I just don't see it necessarily as all or nothing with AoPS. For example even if we use Dolciani as the spine I would like to use some of the AoPS problems and explanations of certain subject areas simply because I like them and they are well done. The videos are another great teaching tool which align directly with the text as well. Sometimes when a child hits a wall in understanding its nice to present things in a different light. AoPS's section on Linear Equations was great example of this and supplimental for ds11. The wordiness in that case was a welcomed perspective which 'added' to the instruction he had received from his spine program (TabletClass). Also for the kids going to ps who use AoPS as extracurricular many times along with their primary texts this information is at least partially introduced to them. A Russian coworker of mine has his son doing weekend Russian math which also uses a discovery approach along side his High School coursework. From what I've heard there are quite a number of PSers in the AoPS classes. This is more like parallel integration.
Math Question
in Logic Stage & Middle Grade Challenges
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Hi Susie, great question to which I think there are a number of paths to take. However since we just went through this with ds11 in MUS Pre-A I'll share what worked for us. ds11 used MUS all the way from Primer to Pre-A. He also has a strong interest in science and specifically programming. In fact I'm teaching him Java programming right now. :D I'm also a software engineer. So I think that contributes to his interest. Anyway after Zeta and starting MUS Pre-A I noticed he was forgetting some things as well.
We did increase his time a bit. He averages now ~ 1.5 hours. We also gave specified assignments to complete per day vs. simply time. This we had to estimate and adjust a bit based on a good steady pace. The incentive was that if he worked efficiently he could finish a little early and conversely if he goofed around/daydreamed he would work longer, which he did in the beginning. And some things just take longer which also extended his time a bit. Whatever he doesn't finish in the morning we have him complete in the afternoon. My big emphasis with ds11 and our younger dds is that its great if you like science. But Math is the basis of science and required to ever advance in science. So doing more is ok and fundamental for future learning.
The other thing we did is supplement MUS with another program, in our case TabletClass. Even if you stay with MUS through all secondary math I highly recommend supplementing. Since MUS is mastery based it doesn't have as much review as other Pre-A programs. We also supplemented with Khan Academy and even AoPS eventually. However after evaluating MUS secondary math I decided I wanted to switch to another program based on our goals for ds. Even though MUS added honors questions I just didn't find it to be as strong as other offerings such as AoPS, Dolciani, Foerster, TabletClass, etc... Right now we are using TabletClass Pre-A which was a fantastic change for him. He's not only reviewed fractions/decimals but is now working on more advanced algebraic topics - multivariable linear equations. I also picked up a copy of Dolcinia's Pre-Algebra to use if/when we need supplementation. I really find it helps to show problems along with methods to solve from a variety of sources.
You will find folks who say their dc did fine with MUS, TT, Saxon, etc... with no other resources/supplementation. But for STEM oriented students for whom math is fundamental to future academic success it certainly cannot hurt. ;) This is especially true if they are struggling with a particular concept or forgetting once learned subject matter.