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concept-heavy but not discovery based pre-algebra and beyond


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I've read every thread about pre-algebra and algebra. DD is probably ready for pre-algebra in terms of operational skill set and conceptual understanding, but I'm holding back a bit to give her some more practice with word problems which frustrate her. She's 2e with some working memory and processing speed issues so if she forgets to keep track of key data/steps, she gets frustrated.

 

I use problems from pre-algebra workbooks as her daily practice--I just choose 4-8 problems for her to keep up with continual practice. 

 

We have used a variety of math programs to complete elementary level math. She's completed Singapore 5, used Danica McKellar books, bunch of the Key to series, all the BA books, and too many other things to list.

 

When BA 4C came out recently, we got it and finished it quickly. It was a nice review, and BA originally revolutionized her attitude towards math, and we're sad that we've outpaced it. It makes me think that AoPS might work. But, the things she love about BA probably aren't really replicated in AoPS--minimal practice sets, emphasis on puzzles, and awesome characters. It's probably not the discovery approach that appeals to her really. But, I think BA has actually boosted her confidence and ability to stick with things better than anything else.

 

Also, she tends towards perfectionism and gets frustrated and discouraged if she doesn't figure something out "soon enough" (as defined by her). She has an intuitive grasp of mathematical concepts, but I wouldn't describe her as gifted in math. I think she's just advanced in math, not gifted, if that makes sense. 

 

She ADORES and I mean this emphatically knowing why algorithms work. She's not strong on memorization (see working memory issues) so understanding why something works really works well for her. However, as I said, she loses patience with the discovery method.

 

I have on hand:

- Jousting Armadillos

- Mathematics a Human Endeavor

- Dolciani, pre-algebra

- Lial's college math

- Lial's pre-algebra

 

What's going to give her the best, most solid conceptual explanations (even if we derive them) without the frustration of having to discover it on her own? 

 

I'm leaning towards trying Jousting Armadillos after the holiday break, but I'm not feeling entirely confident about that choice.

 

 

 

 

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You do not have to use AoPS as discovery.  As the parent you can go through the Socratic reasoning steps with her so that she is not jumping into the problems blind.  It doesn't lose anything (for your situation) and still has tough problems without her having to discover.  It merely makes the program less independent.  It becomes a mentorship thing, as opposed to a student led endeavor.

 

AoPS PreA has minimal problems in sets, a focus on puzzles, and an emphasis on understanding concepts instead of memorizing.  There are no cute characters.  However, your explanation of what you want directly brought to mind AoPS.  If she is not directly in conflict with having you work with her, I would give it a shot.  She can also watch the videos before the problem sets to get an idea of how to solve the problems, too.

 

Know that she might get frustrated, and that is part of it.  However, anyone who expects all of learning to be intuitive is going to get frustrated.  More than anything else, using PreA with my son got him over his perfectionist, "know it immediately," meltdown stuff.  It was worth it just for that!

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The previous post is spot-on. AoPS has everything your daughter liked about BA, except the characters and dialogue, and can be adapted to be worked ''buddy-style'' or ''guided discovery'' as best suits each student. My son is working through the P.Alg book now, and in this transition between BA and textbook-style math, we do a combination of solo and guided discovery on a problem-by-problem basis. I've read repeatedly on these forums that that's not unusual for the first AoPS course, and that as students mature and gain experience with the discovery method, they become more independent. Expect frustration: productive struggle is to be desired. When struggle becomes unproductive, take a break and/or try another approach.

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I think starting with JA, since you have it, and then making a decision about AoPS would be a reasonable plan.  JA is very conceptual, not too many problems, lots of puzzles and problem-solving, and though it doesn't have characters like BA, the author is almost a character in his own right - he has such a funny and engaging voice!  It's a very gentle, guided discovery, so it might help you see if that method works with her, too.

 

ETA:  JA was my dd's favorite math, ever.  She is now thriving doing Jacobs and Alcumus, but decided against using AoPS for her main math, as she likes the gentler discovery method in JA and Jacobs vs. the jump-into-the-deep-end method of AoPS.  She loves the challenging problems on Alcumus, but after she has already practiced the concept.  Just to give you some context!

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I think starting with JA, since you have it, and then making a decision about AoPS would be a reasonable plan.  JA is very conceptual, not too many problems, lots of puzzles and problem-solving, and though it doesn't have characters like BA, the author is almost a character in his own right - he has such a funny and engaging voice!  It's a very gentle, guided discovery, so it might help you see if that method works with her, too.

 

ETA:  JA was my dd's favorite math, ever.  She is now thriving doing Jacobs and Alcumus, but decided against using AoPS for her main math, as she likes the gentler discovery method in JA and Jacobs vs. the jump-into-the-deep-end method of AoPS.  She loves the challenging problems on Alcumus, but after she has already practiced the concept.  Just to give you some context!

 

Do you regret not continuing with the Arbor Center books? I recall your comments about their costs, but I know from other recent posts you don't seem to have found anything that she's really connected with since then. 

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My 10th grade dd sounds a lot like your dd.  She wasn't thrilled with AoPS though.  The upper levels consume a lot of time and if you have a student that isn't really in love with math, the time factor can become an issue.   She thrived in Foerster's alg 1 and 2.  We switched this yr b/c pre-cal is beyond my abilities.  She watches DO's videos and takes his exams, but she isn't following his assignments or schedule.   She finds his workload too light and she works through a lot more of the problems on her own.   (Just sharing that b/c a lot of people are really happy with DO's classes, but we haven't found this math class to be a particularly good fit for a really strong math student.)

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I have been using the Dolciani Mathematics books.  Their content is similar to the Dolciani Pre-Algebra book.  Pre-A is a one year survey text of most of the content taught in the two Mathematics books.

 

I like the combination of exercises, which include problems that use skills from various angles, word problems and other application type problems.  I also have Dolciani Algebra texts that I really like, although these are harder to find matched sets of student and teacher books.

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Do you regret not continuing with the Arbor Center books? I recall your comments about their costs, but I know from other recent posts you don't seem to have found anything that she's really connected with since then. 

 

Oh, she does really like Jacobs, and it's working well so far.  I just worry it doesn't have enough hard problems, at least so far.  I don't exactly regret not using the next Arbor books, it just seemed silly to spend that much money when I had Jacobs sitting right here on my shelf (since the Arbor books are based on Jacobs).

 

Says the girl that bought *two* new math books just last week . . .  :leaving:

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Oh, she does really like Jacobs, and it's working well so far. I just worry it doesn't have enough hard problems, at least so far. I don't exactly regret not using the next Arbor books, it just seemed silly to spend that much money when I had Jacobs sitting right here on my shelf (since the Arbor books are based on Jacobs).

 

Says the girl that bought *two* new math books just last week . . . :leaving:

That's good to know. I am trying to just focus on pre-algebra, but it's hard not to imagine the long-term goals.

 

I was on our high school's competitive math league (in the mid '80s), but I think I was a mistake. I was good at math, clearly better than most of the other teen girls which is why they chose me. But, I have phenomenal memorization skills. I am realizing how little conceptual understanding I had and the stress it apparently left behind! I had AP calc senior year and got an A but to this day I still have nightmares that I bombed the final! I did grad school in neuroscience and did many years of advanced statistics but I hated it. I don't like geometry either.

 

I also work full time and don't particular want to go through math again. DH is a gifted math intuitive which translates to being a really bad instructor for DD.

 

I am babbling, but I think it's clear to me that I'm going to outsource after algebra I so am just imagining the online and in-person options.

 

In other words, I'm willing to really work with her on something like JA or AoPS for pre-algebra and algebra and then I need someone else to take over!

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Well, we worked closely together for the first 3 chapters of JA, then she did the last 3 pretty independently.  She's been totally independent with Jacobs through ch. 5 so far.  We do work on Geometry together, but she hasn't really needed help with the Algebra so far.

 

AoPS, OTOH, was not independent at all!  

 

She does do Alcumus on her own, but after she's studied the topic, not as an introduction to it (i.e. discovery method).

 

I definitely think that Arbor books are discovery/constructivist in a way, but much more guided than AoPS.

 

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I finally sat down and went through Jousting Armadillos in detail. I think it looks like a wonderfully gentle approach, but I almost think some of it is going to be too easy after she's chewed up and spit out elementary math using BA and other stuff. So, I went ahead and ordered AoPS pre-algebra too. It's obvious to me now that we do need to move ahead with pre-algebra. She's ready.

 

So, I'm going to continue with my mish-mash approach to math, which has managed to work well for us so far and see how I can bring elements of both programs plus the other supplemental stuff I have. I have all those other books too if we need practice. 

 

She's a young 5th grader (early Sept. birthday) so we have plenty of time to meander together on this journey. I feel really good about this now. Thanks, everyone!

 

 

 

 

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You do not have to use AoPS as discovery.  As the parent you can go through the Socratic reasoning steps with her so that she is not jumping into the problems blind.  It doesn't lose anything (for your situation) and still has tough problems without her having to discover.  It merely makes the program less independent.  It becomes a mentorship thing, as opposed to a student led endeavor.

 

AoPS PreA has minimal problems in sets, a focus on puzzles, and an emphasis on understanding concepts instead of memorizing.  There are no cute characters.  However, your explanation of what you want directly brought to mind AoPS.  If she is not directly in conflict with having you work with her, I would give it a shot.  She can also watch the videos before the problem sets to get an idea of how to solve the problems, too.

 

Know that she might get frustrated, and that is part of it.  However, anyone who expects all of learning to be intuitive is going to get frustrated.  More than anything else, using PreA with my son got him over his perfectionist, "know it immediately," meltdown stuff.  It was worth it just for that!

 

So how does one do that if they themselves aren't strong with the concepts?  I really wanted to make it work, but I couldn't make it work.  I wish someone had warned me so I didn't waste money on it so I'm putting this out there. 

 

I don't love Saxon, but there are a ton of support materials so it's working out well for us.  I do wish I could find something else after Algebra 2 (that is where we are at now).  We are using one of the AoPS math competition books as a supplement.  It's kind of like their bigger books, but with less time spent on each concept. 

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My DD will be starting pre-Algebra next year.  We have been using Horizons from the beginning, and I had planned on using it through Algebra.  However, I've been rethinking that and now am leaning towards a different program.

 

I want to have DD learn math in a more sensible way.  I don't want to do the traditional Pre-Algebra, Algebra 1, Geometry, Algebra II dance.  For a while I've known that I would rather she learned all of Algebra together and then move on to Geometry.  However I've never found anything to use.

 

Well, recently I stumbled upon this curriculum: http://videotext.com/algebra-a-complete-course/

It's exactly what I've been looking for and, in it's teaching, stresses the "why" of math.  The only problem is that it's extremely expensive.  For that reason, I'm thinking of just trying the first module as an online class (Module A which is pre-Algebra) and see how it goes.  If the program is a hit and works, I'll progress by purchasing one module at a time.  While that ends up being more expensive in the long run, it's an incremental payment we can handle every now and then rather than the whole thing at one time.  Then we'll proceed with their Geometry, A Complete Course.

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My DD will be starting pre-Algebra next year.  We have been using Horizons from the beginning, and I had planned on using it through Algebra.  However, I've been rethinking that and now am leaning towards a different program.

 

I want to have DD learn math in a more sensible way.  I don't want to do the traditional Pre-Algebra, Algebra 1, Geometry, Algebra II dance.  For a while I've known that I would rather she learned all of Algebra together and then move on to Geometry.  However I've never found anything to use.

 

Well, recently I stumbled upon this curriculum: http://videotext.com/algebra-a-complete-course/

It's exactly what I've been looking for and, in it's teaching, stresses the "why" of math.  The only problem is that it's extremely expensive.  For that reason, I'm thinking of just trying the first module as an online class (Module A which is pre-Algebra) and see how it goes.  If the program is a hit and works, I'll progress by purchasing one module at a time.  While that ends up being more expensive in the long run, it's an incremental payment we can handle every now and then rather than the whole thing at one time.  Then we'll proceed with their Geometry, A Complete Course.

 

:thumbup:  for VideoText Algebra!

 

I initially purchased the first three Modules individually—used and with VHS tapes—at a great price through Amazon. Thankfully, I didn't have any trouble with the used VHS tapes. Once I discovered that VT was a hit and our path was set, then I invested in the rest of the modules—also used and with VHS Tapes. Fortunately, I came across a great deal at a local homeschool book shop and was able to pick up another used but complete set with DVDs, so I was able to sell my complete VHS set, via Homeschool Classifieds, and keep the DVD set. All that being said, if no other used options had presented themselves, I would've purchased them new.  :thumbup1: We love the conceptual teaching provided in VT.

 

On a side note, we continue to toss Singapore's CWP into the mix.

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So how does one do that if they themselves aren't strong with the concepts? I really wanted to make it work, but I couldn't make it work. I wish someone had warned me so I didn't waste money on it so I'm putting this out there.

 

I don't love Saxon, but there are a ton of support materials so it's working out well for us. I do wish I could find something else after Algebra 2 (that is where we are at now). We are using one of the AoPS math competition books as a supplement. It's kind of like their bigger books, but with less time spent on each concept.

Sorry, I just now saw this. If the parent goes through a chapter or even a couple of subsets ahead, then it can work quite well. The text is very explanatory as long as you do not approach it from the standpoint of algorithm mathematics. This is the reason the first chapter takes the reader all the way back to addition/subtraction/multiplication/division. You have to be willing to drop what you once learned to learn anew. Combined with the solutions manual, it steps you through every problem. In my experience the difficulty comes from wanting to combine algorithm math with AoPS. That can work if you can see the concept bridge, but it cannot if you are not strong in the concepts. It requires the mentor to start from zero, be okay starting from zero, and learn with the student.

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Yep, JA isn't super difficult until Ch 6, which is fairly challenging I think.  

 

DS breezed through JA until  middle of Chapter 5.  I don't know what it was exactly.  We stopped and did Real World Algebra for a while and came back to JA and easily went through the rest of Chapter 5 and Chapter 6.  I was nervous to push on to AoPS Algebra (which was my original plan) and am now waiting for my Jacobs Algebra book to arrive. 

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DS breezed through JA until  middle of Chapter 5.  I don't know what it was exactly.  We stopped and did Real World Algebra for a while and came back to JA and easily went through the rest of Chapter 5 and Chapter 6.  I was nervous to push on to AoPS Algebra (which was my original plan) and am now waiting for my Jacobs Algebra book to arrive. 

 

That's interesting - very similar to Shannon's experience.  And, FWIW, she breezed through the first 5 chapters of Jacobs, but has now slowed down on Ch. 6.  She is still doing fine, but is going much slower and really having to pay attention to both the brief lesson at the beginning of the section, and the discovery-based teaching process within the Set problems.

 

it's funny, I didn't realize how discovery-based Jacobs was at first.  Somebody here posts about this, I think maybe it's wapiti?  But because on these boards Discovery=AoPS in so many discussions, I had missed the subtle way that Jacobs leads the student to discovering the concept through carefully constructed incrementally stepped problems.  We continue to really like it!

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That's interesting - very similar to Shannon's experience.  And, FWIW, she breezed through the first 5 chapters of Jacobs, but has now slowed down on Ch. 6.  She is still doing fine, but is going much slower and really having to pay attention to both the brief lesson at the beginning of the section, and the discovery-based teaching process within the Set problems.

 

it's funny, I didn't realize how discovery-based Jacobs was at first.  Somebody here posts about this, I think maybe it's wapiti?  But because on these boards Discovery=AoPS in so many discussions, I had missed the subtle way that Jacobs leads the student to discovering the concept through carefully constructed incrementally stepped problems.  We continue to really like it!

 

That IS interesting!  I've been following your math journey since last spring so I'm interested to see how my ds does once we start Jacobs!  Yes, the whole "discovery method" idea finally scared me off from AoPS--at least for now!

 

Really, RWA was the life-saver for us.  We went back over some concepts again and their presentation was so much easier for him to get than JA for some reason!  

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it's funny, I didn't realize how discovery-based Jacobs was at first. Somebody here posts about this, I think maybe it's wapiti? But because on these boards Discovery=AoPS in so many discussions, I had missed the subtle way that Jacobs leads the student to discovering the concept through carefully constructed incrementally stepped problems. We continue to really like it!

You are not alone! I have recently been quite surprised by how much discovery I have started noticing in other programs. And good word problems, too. I had honestly started to believe AoPS was the only program that had either. It's not. Who knew? ;)
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