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Sarah0000

Would this work for algebra?

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All three Arbor Algebra books 

HOE/HOE Fractions

Patty Paper Geometry

Alcumus

I know most people use these as supplements or introductions. If DS8 (ADHD) did this for a year or so, around where would he place afterwards? Are these resources organized enough that I can tell him to do the next lesson/section and he could do so independently after an initial learning period? Are they easy for me to check work for understanding?

I would prefer something more streamlined as our main daily math but I've eliminated common recommendations for a variety of reasons...

Derek Owens: don't think DS would stay focused through the long, drawn out videos

Jacobs: seems a little dry, maybe too much of a transition from fun, colorful BA. This is my first runner up though.

Singapore/MM: would like to try to transition DS into textbooks instead of work texts so he has more options available to him for beyond algebra.

Any live, online classes: he needs more maturity for that

Any thoughts and suggestions appreciated.

 

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I am only really familiar with the middle 2.  Those 2 are definitely supplements and not even close to being more than that.  My 4th grader will be finishing up HOE this yr and is currently in Horizons 6.   She will complete MUS alg/geo before taking Foerster's alg.  HOE is very simple alg, just an algebraic way of expressing the same sorts of problems found in the elementary levels of SM.  The Verbal Book has full solutions, so very easy for you to check.  (I'm not sure how long the VB would last if it was a focus.  It doesn't take that long to go through the problems.) Patty Paper is just physical representations of a minor number of geometry principles.   

So, in terms of those 2 and placement afterward,  I wouldn't consider placement to be really anything beyond however you are classifying him now.  He would solidify some concepts, but the focus of these 2 is so narrow, that I wouldn't consider it "progress" toward anything in particular.  

My ds was beyond the development of Alcumus when he used AoPS and my dd didn't use it, so no help there.  I have never heard of the other, so maybe others can fill in the gaps to give you a bigger picture.

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The Arbor books are pre-algebra/Algebra 1. One of DD's friends used it, and then moved into the last half of AoPS intro Algebra without issue. 

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I know you said that you had eliminated Jacobs and DO, but I just wanted to let you know what our experience was with them.

Jacobs works well for younger kids, but I wouldn't just hand him to book and expect him to do it.  When I used it with my older son at age 10, I presented the material myself and copied the problems out of the book for him to do worksheet style.

DO Prealgebra worked well for my younger son when he was 9.  I watched the conceptual videos with him, took notes myself, and then, rather than watching video after video, we worked through the examples together with him telling me what to write.  He then did the worksheets on his own.  I would think that you could use the algebra class in a similar way.

Edited by EKS

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At that age my oldest had finished all the beast academy books and Math Mammoth through level 6 (prealgebra).  He had also done Hands on Equations including the word problems book and Hands on Geometry.

We jumped right into AOPS Prealgebra.  I was very wary of what Richard Rusczyk calls "The Calculus Trap".  My goal was to slow DS down by using deep, rigorous, and non-traditional materials.  When he needed to take a break from AOPS Pre-A (because it is certainly a difficult, hefty tome) I would intersperse chapters from Jacobs' Mathematics - a Human Endeavor, Zaccaro's Real World Algebra, and alcumus.

It took DS almost two years to make it through AOPS Pre-A.  Very little of that was actually learning new math; most of it was learning and practicing much higher level math skills.  I think it was an invaluable use of time.

Looking back, I'm sure DS could have tackled (and aced) a less rigorous algebra back when he was 8.  But now he is 10 and thriving (and being intensely challenged) in AOPS Algebra which I consider to be a much more advantageous path for a strong, accelerated math student.

Wendy

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43 minutes ago, wendyroo said:

At that age my oldest had finished all the beast academy books and Math Mammoth through level 6 (prealgebra).  He had also done Hands on Equations including the word problems book and Hands on Geometry.

We jumped right into AOPS Prealgebra.  I was very wary of what Richard Rusczyk calls "The Calculus Trap".  My goal was to slow DS down by using deep, rigorous, and non-traditional materials.  When he needed to take a break from AOPS Pre-A (because it is certainly a difficult, hefty tome) I would intersperse chapters from Jacobs' Mathematics - a Human Endeavor, Zaccaro's Real World Algebra, and alcumus.

It took DS almost two years to make it through AOPS Pre-A.  Very little of that was actually learning new math; most of it was learning and practicing much higher level math skills.  I think it was an invaluable use of time.

Looking back, I'm sure DS could have tackled (and aced) a less rigorous algebra back when he was 8.  But now he is 10 and thriving (and being intensely challenged) in AOPS Algebra which I consider to be a much more advantageous path for a strong, accelerated math student.

Wendy

Was your son good at focusing at 8 and 9 years old? Did he do AOPS somewhat independently in terms of reading and writing answers? My son often gets sidetracked in the middle of a problem, both from outside stimuli and the math problem itself. I'm not sure he could handle the AOPS format yet even if he could handle the math. I cannot consistently sit with him and help him note take or write solutions like some posters. Giving him experience in that is something I'm hoping to gain, so that he can go to AOPS or whatever fits him. But maybe Jacob's would be a better choice for that purpose than Arbor Algebra. 

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17 hours ago, Sarah0000 said:

All three Arbor Algebra books 

HOE/HOE Fractions

Patty Paper Geometry

Alcumus

I know most people use these as supplements or introductions. If DS8 (ADHD) did this for a year or so, around where would he place afterwards? Are these resources organized enough that I can tell him to do the next lesson/section and he could do so independently after an initial learning period? Are they easy for me to check work for understanding?I

Any thoughts and suggestions appreciated.

 

 

I have actually used all or part of everything on your list. I may own too many math things. (Your proposed list, not your ruled out list.)

Arbor Algebra - we only used part of the first book. It turned out not to be as good a fit for us as I hoped, but it could serve as a base Algebra program. This could be the program that you use as a core. It does not go *nearly* as deep as something like AOPS, but it’s much, much better than something like Saxon.

HOE - great for learning to set up and work with basic equations. Doesn’t get deep enough into the more complex equations that Algebra starts working with, but a fantastic introduction. I would use this either alongside the first book of Arbor or before starting any Algebra program.

HOE Fractions - This is way more basic than I expected. Remind me what you’re using now? If he’s done fractions through about a 5th grade level using any other mainstream program, he is already past this.

Patty Paper Geometry - has no overlap with Algebra, but has been an amazing pre-formal-Geometry program.

Alcumus - I know nearly everyone disagrees with me, but we could have used this as our entire Algebra 1. DD watched the (short!) AOPS videos, then worked on Alcûmus. She was about halfway through the Algebra 1 topics when she decided to take the online class. The class offered nothing new. She had learned it well enough from the videos and Alcumus that she didn’t need more. She did have to pull out the book when it came to the graphing chapters, since she had never done graphing before, but otherwise the videos were enough.

Edited by Jackie

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9 minutes ago, Sarah0000 said:

Was your son good at focusing at 8 and 9 years old? Did he do AOPS somewhat independently in terms of reading and writing answers? My son often gets sidetracked in the middle of a problem, both from outside stimuli and the math problem itself. I'm not sure he could handle the AOPS format yet even if he could handle the math. I cannot consistently sit with him and help him note take or write solutions like some posters. Giving him experience in that is something I'm hoping to gain, so that he can go to AOPS or whatever fits him. But maybe Jacob's would be a better choice for that purpose than Arbor Algebra. 

As to the bolded, OH MY GOODNESS NO!!  My son has ADHD, ASD and anxiety.  He gets sidetracked by specks of dust in the air, a sibling humming two floor away, and pressing matters like considering what color toothbrush he will request the next time he goes to the dentist.

I did not sit with DS at all while he worked on AOPS Pre-A, but I also wasn't completely hands-off. 

The format of each section is very consistent.  First there is a short introduction - very short, often just a couple paragraphs.  After that there are a number of carefully chosen, increasingly difficult problems.  Immediately after the problems are what I consider the meat of the book: the solutions.  Each problem is solved in detail, including different strategies, tips and tricks, mistakes to avoid, etc.  Then, after the problems and the solutions, there are exercises for the student to practice with.

For my DS, the hardest part was convincing him to read and value the solutions.  He would often attempt one of the problems, get it correct seemingly through intuition, and then not read any further in the solution to reap all of that important teaching.  Then, when he got to the exercises, if he could not immediately "see" the answer he would flounder because he had not taken the time to dig deep and actually understand the concept.

So, at the beginning of every math session DS and I would flip through the book and determine a minimum requirement, a stretch goal and check in points.  Initially he would do one problem, read the solution, and then immediately check in with me to discuss the solution.  Lather, rinse, repeat to ensure he was taking the time required.  Then he would complete all the exercises (with me in the vicinity making sure he did not get too distracted, but not sitting with him or helping), we would check them, and he would redo any he had gotten wrong.

Slowly over time he became much, much better at learning independently from a book (and he did not need to check in nearly as often).  We were about 3/4 of the way through the book before I tackled his other big hurdle - he despised writing down any math work.  At that point I started 1) requiring a full, comprehensive, written solution to one exercise a day, and 2) refusing to help with exercises that stumped him unless he had shown his work.

AOPS Pre-A was a huge challenge for my son...and there were plenty of times I questioned whether he would be able to rise to that challenge.  Sometimes it did get to be too much and we had to work on something else for a bit before diving back in.  But in the end, he did preserver and he learned and grew SO MUCH.  For him it was the right choice.  He was forming more and more bad math habits - habits that persisted because he had always been able to "wing it" and had never encountered math that truly stumped him.  At some point he had to learn the hard way that he could not intuit and mentally calculate his way through upper level math - reading to learn and writing out his work were simply unavoidable in the long run and he had to be pushed into accepting that.  I am profoundly grateful that AOPS Pre-A offered us a way to tackle those lessons at a math level that was mostly review for DS rather than having the additional stress of also learning new math concepts.  I cannot believe his algebra journey would be going as smoothly if I had chosen an easier pre-algebra path and he was now being faced with new and difficult material without the necessary underlying skills.

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18 minutes ago, wendyroo said:

As to the bolded, OH MY GOODNESS NO!!  My son has ADHD, ASD and anxiety.  He gets sidetracked by specks of dust in the air, a sibling humming two floor away, and pressing matters like considering what color toothbrush he will request the next time he goes to the dentist.

I did not sit with DS at all while he worked on AOPS Pre-A, but I also wasn't completely hands-off. 

The format of each section is very consistent.  First there is a short introduction - very short, often just a couple paragraphs.  After that there are a number of carefully chosen, increasingly difficult problems.  Immediately after the problems are what I consider the meat of the book: the solutions.  Each problem is solved in detail, including different strategies, tips and tricks, mistakes to avoid, etc.  Then, after the problems and the solutions, there are exercises for the student to practice with.

For my DS, the hardest part was convincing him to read and value the solutions.  He would often attempt one of the problems, get it correct seemingly through intuition, and then not read any further in the solution to reap all of that important teaching.  Then, when he got to the exercises, if he could not immediately "see" the answer he would flounder because he had not taken the time to dig deep and actually understand the concept.

So, at the beginning of every math session DS and I would flip through the book and determine a minimum requirement, a stretch goal and check in points.  Initially he would do one problem, read the solution, and then immediately check in with me to discuss the solution.  Lather, rinse, repeat to ensure he was taking the time required.  Then he would complete all the exercises (with me in the vicinity making sure he did not get too distracted, but not sitting with him or helping), we would check them, and he would redo any he had gotten wrong.

Slowly over time he became much, much better at learning independently from a book (and he did not need to check in nearly as often).  We were about 3/4 of the way through the book before I tackled his other big hurdle - he despised writing down any math work.  At that point I started 1) requiring a full, comprehensive, written solution to one exercise a day, and 2) refusing to help with exercises that stumped him unless he had shown his work.

AOPS Pre-A was a huge challenge for my son...and there were plenty of times I questioned whether he would be able to rise to that challenge.  Sometimes it did get to be too much and we had to work on something else for a bit before diving back in.  But in the end, he did preserver and he learned and grew SO MUCH.  For him it was the right choice.  He was forming more and more bad math habits - habits that persisted because he had always been able to "wing it" and had never encountered math that truly stumped him.  At some point he had to learn the hard way that he could not intuit and mentally calculate his way through upper level math - reading to learn and writing out his work were simply unavoidable in the long run and he had to be pushed into accepting that.  I am profoundly grateful that AOPS Pre-A offered us a way to tackle those lessons at a math level that was mostly review for DS rather than having the additional stress of also learning new math concepts.  I cannot believe his algebra journey would be going as smoothly if I had chosen an easier pre-algebra path and he was now being faced with new and difficult material without the necessary underlying skills.

That sounds exactly like my son. And hovering nearby keeping him on task but otherwise hands off except for new routines is how we operate as well. I'm definitely going to consider AOPS Pre-Algebra, but still after a solid review, maybe with a few MM units. Thank you for taking the time to explain all that!

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48 minutes ago, Jackie said:

 

I have actually used all or part of everything on your list. I may own too many math things. (Your proposed list, not your ruled out list.)

Arbor Algebra - we only used part of the first book. It turned out not to be as good a fit for us as I hoped, but it could serve as a base Algebra program. This could be the program that you use as a core. It does not go *nearly* as deep as something like AOPS, but it’s much, much better than something like Saxon.

HOE - great for learning to set up and work with basic equations. Doesn’t get deep enough into the more complex equations that Algebra starts working with, but a fantastic introduction. I would use this either alongside the first book of Arbor or before starting any Algebra program.

HOE Fractions - This is way more basic than I expected. Remind me what you’re using now? If he’s done fractions through about a 5th grade level using any other mainstream program, he is already past this.

Patty Paper Geometry - has no overlap with Algebra, but has been an amazing pre-formal-Geometry program.

Alcumus - I know nearly everyone disagrees with me, but we could have used this as our entire Algebra 1. DD watched the (short!) AOPS videos, then worked on Alcûmus. She was about halfway through the Algebra 1 topics when she decided to take the online class. The class freed nothing new. She had learned it well enough from the videos and Alcumus that she didn’t need more. She did have to pull out the book when it came to the graphing chapters, since she had never done graphing before, but otherwise the videos were enough.

He's doing BA and always excels in fractions. Thanks for the heads up that HOE Fractions will probably be too low level. 

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This is just personal experience with my daughter, so take this with a grain of salt, but what will work for algebra really depends on what your kid's level of understanding of arithmetic operations, the relationships between them, and variables is. In some sense, if you're solid on all of those, then there isn't all that much in algebra, and lots of possible programs will work. 

We're just starting algebra with my 7.5 year old, but she's been using variables (mostly in the form of "shapes"), equations in many forms, and the properties of the operations for a very long time, because that is how she figures out all calculations (we didn't do algorithms for years.) I've found so far that there's lots and lots of algebra she can just DO without needing an explanation. It was really obvious to her that you can manipulate equations by doing the same thing to both sides. She knew that to get from 25x to x you need to divide by 25. She easily figured out that 

(a+b)(c+d) = ac + bc + ad + bd

and uses it successfully for quadratics. There are quite a few other examples. 

Personally, I would think about which concepts from algebra you are trying to communicate, and then think about which programs fit him best :-). And if he's relatively solid in the conceptual stuff already (at least, if he is solid at the level of arithmetic, and if he'd be able to generalize), then probably even low level stuff would work for now, while you wait for him to mature and get ready for tougher programs. 

Edited by square_25

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12 hours ago, square_25 said:

This is just personal experience with my daughter, so take this with a grain of salt, but what will work for algebra really depends on what your kid's level of understanding of arithmetic operations, the relationships between them, and variables is. In some sense, if you're solid on all of those, then there isn't all that much in algebra, and lots of possible programs will work. 

We're just starting algebra with my 7.5 year old, but she's been using variables (mostly in the form of "shapes"), equations in many forms, and the properties of the operations for a very long time, because that is how she figures out all calculations (we didn't do algorithms for years.) I've found so far that there's lots and lots of algebra she can just DO without needing an explanation. It was really obvious to her that you can manipulate equations by doing the same thing to both sides. She knew that to get from 25x to x you need to divide by 25. She easily figured out that 

(a+b)(c+d) = ac + bc + ad + bd

and uses it successfully for quadratics. There are quite a few other examples. 

Personally, I would think about which concepts from algebra you are trying to communicate, and then think about which programs fit him best :-). And if he's relatively solid in the conceptual stuff already (at least, if he is solid at the level of arithmetic, and if he'd be able to generalize), then probably even low level stuff would work for now, while you wait for him to mature and get ready for tougher programs. 

Honestly, I'm not hugely concerned with content since he gets everything so quickly anyway and has years ahead of him. I'm mostly interested in format, engagement, and some level of daily independence. On the one hand an easier program would help with the study skills aspect but a harder one would be more engaging.

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21 minutes ago, Sarah0000 said:

Honestly, I'm not hugely concerned with content since he gets everything so quickly anyway and has years ahead of him. I'm mostly interested in format, engagement, and some level of daily independence. On the one hand an easier program would help with the study skills aspect but a harder one would be more engaging.

 

Would difficulty be what makes it engaging for him? I'm genuinely asking. For my daughter, difficulty doesn't make it more fun -- what makes it fun is having more conceptual and structural material to chew over. She doesn't enjoy puzzles all that much, despite being more than competent at them. For me, when I was her age, puzzles were definitely the thing that motivated me. So I know that the motivating factors vary a lot between mathy kids. 

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1 hour ago, Sarah0000 said:

On the one hand an easier program would help with the study skills aspect but a harder one would be more engaging.

For what it is worth, the bolded is the exact opposite for my son.

It seems like common sense that an easier program would be less taxing math-wise, and therefore he would be able to devote more attention to study skills.  In actuality, an easier program isn't taxing enough math-wise and therefore the study skills are completely unnecessary for DS and he fights against them tooth and nail.

My kiddos will always choose the path of least resistance.  If they can get away with winging math sans reading, writing, deep thinking or persevering, then that is exactly what they will do.   The only way I have found to force them to learn and practice the study skills is to go harder - not faster or farther, but deeper and more conceptually challenging.

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1 minute ago, wendyroo said:

For what it is worth, the bolded is the exact opposite for my son.

It seems like common sense that an easier program would be less taxing math-wise, and therefore he would be able to devote more attention to study skills.  In actuality, an easier program isn't taxing enough math-wise and therefore the study skills are completely unnecessary for DS and he fights against them tooth and nail.

My kiddos will always choose the path of least resistance.  If they can get away with winging math sans reading, writing, deep thinking or persevering, then that is exactly what they will do.   The only way I have found to force them to learn and practice the study skills is to go harder - not faster or farther, but deeper and more conceptually challenging.

I did just assume the study skills would be easier to learn with an easier program, but now that I think about it he has only written down math when he absolutely had to. So that does make sense.

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52 minutes ago, square_25 said:

 

Would difficulty be what makes it engaging for him? I'm genuinely asking. For my daughter, difficulty doesn't make it more fun -- what makes it fun is having more conceptual and structural material to chew over. She doesn't enjoy puzzles all that much, despite being more than competent at them. For me, when I was her age, puzzles were definitely the thing that motivated me. So I know that the motivating factors vary a lot between mathy kids. 

He definitely likes puzzles and multi step word problems. Things that are difficult in terms of thinking through the problem engage him more but problems that are difficult only because of lot of routine arithmetic steps bore him. 

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40 minutes ago, Sarah0000 said:

I did just assume the study skills would be easier to learn with an easier program, but now that I think about it he has only written down math when he absolutely had to. So that does make sense.

Yeah, the same has been true for us -- she only writes things down if she absolutely has to. So I wouldn't assume that an easier program would be better for that. 

When you say "algebra," what do you want him to get out of the program? If you aren't worried about him learning algebraic ideas, per se, since you're absolutely right he has lots of time for that, what is it you're looking for? 

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10 hours ago, square_25 said:

Yeah, the same has been true for us -- she only writes things down if she absolutely has to. So I wouldn't assume that an easier program would be better for that. 

When you say "algebra," what do you want him to get out of the program? If you aren't worried about him learning algebraic ideas, per se, since you're absolutely right he has lots of time for that, what is it you're looking for? 

Just the next math to do since he's wrapping up BA. I know there are options for going wide and deep, and we do have some resources for that but none of it is particularly conducive to long term, daily, mostly independent work. If there's something else out there I'm interested. I'm definitely not stuck on algebra. I had considered geometry (not proofs, something like RS). I do sporadically do wide and deep stuff but right now I'm focusing on my 5yo since he's learning foundational stuff.

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Have you considered the self-paced AoPS Prealgebra course? We did the demo at some point and it seemed pretty engaging. It's interactive, at least. You can sign him up and drop for a full refund within two weeks if it isn't a good fit. Prealgebra is probably the one AoPS book I think a very math-intuitive student could learn without ever cracking the book open, especially with an online class (self-paced or live), the AoPS videos, and Alcumus. 

The other thing I'm considering for DS 10 to do for pre-a after he finishes BA 5 is Thinkwell. I think he could get some degree of independence (as long as I'm nearby, in the same room, and have some degree of attention focused on him, lol) with the videos and online practice. I'd probably follow up with Alcumus, possibly buddy-solving.

There's also Elements of Mathematics: Foundations (EMF). That could totally be an independent program, and it approaches math in an extremely interesting way. My DS 10 actually really liked it, except there was too much in the way of large blocks of text, and he needed me to read it all aloud to him.

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