Algebra that explores why and not just how, please!

[zarabellesmom]

My daughter is 12 and the hormones are hitting hard at our house. She's so easily frustrated lately and then starts crying and then yelling at me and our relationship is starting to suffer from the daily battles over math. The thing is, she's a good math student. She's done BA 3-5 and moved in AoPS prealgebra. We are through Chapter 11 out of 15 and she's done well aside from the drama. Part of it is that she's a perfectionist and is really angry if she can't get the answer right and pretty quickly too. Obviously AoPS is not designed to be that kind of program and we've talked about that too. But you know, hormones and perfectionism and just... She's so angry and I think she's starting to feel like maybe she's not so good at math which is soooo not true. I suggested maybe we take a break from AoPS and we try something else for a little while and she likes the idea. But...

 

I can't find anything I like. I had a copy of Lials Basic College Mathematics that I thought we'd just fill in the remainder of prealgebra with and move onto algebra. I opened it up to the Chapter on Geometry and we worked a few problems and it is not a good fit for us. This kid wants to know WHY something works and HOW it works which is why Beast Academy and AoPS were a decent fit (thought less so right this moment). We opened it to the chapter on geometry and the lesson for figuring out the area of a Trapezoid can be summarized as: here's the formula. Plug in these numbers and you'll have the area. Here are some problems for you to do. I'm NOT ok with that. And honestly, she's not either. She's not great at memorizing things, even if I were ok with it. That's just not a skill for her and it's never been the way we do math.

 

So... I own Jousting Armadillos and I gave her all of the chapter tests as a sort of placement and she passed them all 90% or better. I purchased a copy of Foerster's Algebra 1 and I don't like it. It also feels more like memorize this formula, and now plug these numbers in kind of thing, so I'm sending it back. I've already looked at Lials BCM and if the Algebra 1 book follows a similar teaching method, that's out as well. I have Jacob's Algebra and I'm getting ready to take a closer look at it.

 

I need AoPS but less stressful--Like AoPS light. Does that exist? Please help me. Selling her to the gypsies is out and I can't afford the counseling I'm going to need to get through this as things stand right now.

 

If you've made it this far, thank you!

 

Teresa

[almondbutterandjelly]

Mathusee is great for explaining the whys.

[serendipitous journey]

I don't know if I have any helpful ideas, but I do have two questions (one is really a tiny idea):

1.  Would you consider taking her off the traditional path for the rest of the year?  (no judgment on your answer here -- just trying to feel out what range of solutions you think will suit your family)

2.  Have you talked to the folks at Rainbow Resource?  They are awesome.  They often help me think things through more clearly even if I don't follow one of their specific suggestions. 

 

One idea: Math U See Algebra.  This totally explains the why.  My older is working through AoPS Algebra right now, after he did MUS (for reasons similar, I think, to your daughter's -- he needed to mature on the frustration front and to experience success).  I like a lot about MUS.  It, Singapore, MEP, AoPS are my favorite programs. 

 

She is young enough that you can stay with Math U See for as long as it works for her (my son is the one who wanted to try switching) and then, if she wishes, do some really challenging stuff.  If you get to their Calculus, you are well set up for some higher math or maybe a more in-depth run through Calculus with something like AoPS. 

 

ETA: The "Key to" series is also great, esp. for sticking points of any sort and clear, do-able problems.  There is a Key to Algebra set at Rainbow Resource.

Edited February 1, 2018 by serendipitous journey

[Christy Walters]

I've uploaded to my website a copy of two pages from my Geometry book that might help you.

http://www.aplusses.com/documents/Area_of_Trapezoid_and_Kite.pdf

This document references the Mdisegment of a Trapezoid Theorem, which was discussed earlier in the book.  Hopefully, you've seen that in AoPS, but if not, you need to know that the midsegment of a trapezoid (also sometimes called the median of the trapezoid) connects the midpoints of the two sides that are not parallel.  This segment is parallel to the bases, and its length is equal to half the average of the lengths of the other two bases. 

 

Also, you might also find the following videos on my website helpful:

http://www.aplusses.com/zencart/index.php?main_page=page_4

They probably won't help you a lot with Chapters 12-15 of AoPS Pre-Algebra, but they might help fill in a few gaps from the earlier chapters.  And they're free.

 

Finally, please feel free to send me a private message if you want to ask a specific question about why we do something else.

 

ETA:  I'm not sure why the link for the area of a trapezoid and kite didn't work, but I'm trying again....

http://www.aplusses.com/documents/Area_of_Trapezoid_and_Kite.pdf

 

Christy Walters

Edited February 1, 2018 by Christy Walters

[Farrar]

She sounds a good bit like my Mushroom. He really thrived doing some of Jacobs's Mathematics: A Human Endeavor before we fully dove in with Jacobs's Algebra. He does not always love math - but he also did really well with Beast Academy. He's also a perfectionist. M:AHE worked well for him because it was all grounded in the why and the applications and was outside the box. Jacobs's Algebra is working well for him (we're about 2/3 finished) because of the way the sets guide you through easier to harder questions. They're very well constructed problem sets.

[zarabellesmom]

I've uploaded to my website a copy of two pages from my Geometry book that might help you.

http://www.aplusses.com/documents/Area_of_Trapezoid_and_Kite.pdf

This document references the Mdisegment of a Trapezoid Theorem, which was discussed earlier in the book.  Hopefully, you've seen that in AoPS, but if not, you need to know that the midsegment of a trapezoid (also sometimes called the median of the trapezoid) connects the midpoints of the two sides that are not parallel.  This segment is parallel to the bases, and its length is equal to half the average of the lengths of the other two bases. 

 

Also, you might also find the following videos on my website helpful:

http://www.aplusses.com/zencart/index.php?main_page=page_4

They probably won't help you a lot with Chapters 12-15 of AoPS Pre-Algebra, but they might help fill in a few gaps from the earlier chapters.  And they're free.

 

Finally, please feel free to send me a private message if you want to ask a specific question about why we do something else.

 

ETA:  I'm not sure why the link for the area of a trapezoid and kite didn't work, but I'm trying again....

http://www.aplusses.com/documents/Area_of_Trapezoid_and_Kite.pdf

 

Christy Walters

Thank you, Christy. The information for finding the area of a trapezoid is found a little while later in AoPS prealgebra. We ended up pulling up one of their (AoPS's) free videos on trapezoid area and it was no problem. I'm more frustrated that the teaching in the particular book we were looking at (Lials BCM) was basically, "Here's a trapezoid. The formula is blah blah blah. Now calculate the area of these three basic trapezoids." That's just lame. I wouldn't count that as instruction at all. We're used to playing with things. We discover the formulas for ourselves usually because of how well laid out the AoPS book is, and failing that, we watch the short video and boom! Then there's no memorization needed at all because to can derive the formula itself using information you already know. It's exactly what we need/love, but we just need a slightly less challenging version while we deal with these other physical changes that are altering brain chemistry.  :) 

 

I'll check out your videos. Thanks.

 

Teresa

[serendipitous journey]

Why not start with the AoPS video and/or work the grey sections using the worked explanations (a perfectly AoPS-approved way to use the books for children who benefit from direct instruction) and perhaps slow down your pace -- maybe cut it in half or something like that? 

[zarabellesmom]

I don't know if I have any helpful ideas, but I do have two questions (one is really a tiny idea):

1.  Would you consider taking her off the traditional path for the rest of the year?  (no judgment on your answer here -- just trying to feel out what range of solutions you think will suit your family)

2.  Have you talked to the folks at Rainbow Resource?  They are awesome.  They often help me think things through more clearly even if I don't follow one of their specific suggestions. 

 

One idea: Math U See Algebra.  This totally explains the why.  My older is working through AoPS Algebra right now, after he did MUS (for reasons similar, I think, to your daughter's -- he needed to mature on the frustration front and to experience success).  I like a lot about MUS.  It, Singapore, MEP, AoPS are my favorite programs. 

 

She is young enough that you can stay with Math U See for as long as it works for her (my son is the one who wanted to try switching) and then, if she wishes, do some really challenging stuff.  If you get to their Calculus, you are well set up for some higher math or maybe a more in-depth run through Calculus with something like AoPS. 

 

ETA: The "Key to" series is also great, esp. for sticking points of any sort and clear, do-able problems.  There is a Key to Algebra set at Rainbow Resource.

 

I have never actually looked at Math U See. I've heard people talking about the younger grades and the non-traditional sequence and it just didn't seem like the right material for us. I took a look at the Algebra samples on the Rainbow Resource website and it looked intriguing. I'm going to look at them again this evening. I haven't talked to Rainbow Resource. I usually count on the hive here.   :lol:

 

I don't mind taking her off the traditional path for a little while. We do a little school over the summer as well, so we aren't really in danger of falling behind. 

 

As for the Key to series. Is there anywhere that anyone knows of to see a sample of the inside of these? I've been curious about them before but I hate buying sight unseen.

 

Thanks,

Teresa

[serendipitous journey]

...

 

As for the Key to series. Is there anywhere that anyone knows of to see a sample of the inside of these? I've been curious about them before but I hate buying sight unseen.

...

 

... found a nice sample at Christianbooks.  Has bits from several (maybe all?) of the individual booklets. 

[zarabellesmom]

Why not start with the AoPS video and/or work the grey sections using the worked explanations (a perfectly AoPS-approved way to use the books for children who benefit from direct instruction) and perhaps slow down your pace -- maybe cut it in half or something like that? 

 

It's worth a shot. We've thought about watching the videos first, but haven't done it. Don't ask me why. I really don't know. My first instinct is always to jump ship. (Maybe because I like shopping. Ha!)

[zarabellesmom]

She sounds a good bit like my Mushroom. He really thrived doing some of Jacobs's Mathematics: A Human Endeavor before we fully dove in with Jacobs's Algebra. He does not always love math - but he also did really well with Beast Academy. He's also a perfectionist. M:AHE worked well for him because it was all grounded in the why and the applications and was outside the box. Jacobs's Algebra is working well for him (we're about 2/3 finished) because of the way the sets guide you through easier to harder questions. They're very well constructed problem sets.

 

Since you have both of these, can you help me compare a bit? I have the Elementary Algebra book. I'm looking at the TOC of AHE. Some of the topics in the Human Endeavor book look really intriguing. Do you feel like the Elementary Algebra book is different enough that it's worth doing both? I mean, is there a lot of overlap? The tessellations on the cover are almost enough to sell it. Which edition do you have? I'm thinking I'd like to buy used. They haven't made many changes across the different editions, I don't think. I could be totally misinformed though. 

 

Also, I'm sending you a PM.

 

Thanks,

Teresa 

[Farrar]

Since you have both of these, can you help me compare a bit? I have the Elementary Algebra book. I'm looking at the TOC of AHE. Some of the topics in the Human Endeavor book look really intriguing. Do you feel like the Elementary Algebra book is different enough that it's worth doing both? I mean, is there a lot of overlap? The tessellations on the cover are almost enough to sell it. Which edition do you have? I'm thinking I'd like to buy used. They haven't made many changes across the different editions, I don't think. I could be totally misinformed though. 

 

Also, I'm sending you a PM.

 

Thanks,

Teresa 

 

 

There's some overlap between AHE and Jacob's Algebra. The chapters on functions, IIRC, really overlap. But there's a TON of stuff in AHE that isn't covered in Algebra at all. Some of it is more geometry and probability. But there's also other topics. Mostly, it's just approached in a very fun way. It's a lot of useless math from the perspective of the sequence of traditional math and math standardized testing. But it's engaging math. The whole first chapter is all billiard balls and cards and so forth. There was a chapter that was music and waves and so forth. It's interesting stuff.

 

I don't know offhand which edition I have. The cheapest? It's OOP, so you have to get it used. The Teacher's Guide is worth it if you can find it at a decent price. It resells well since there are so few. I keep thinking that I should scan and post the answers from my teacher's guide. The problems aren't hard per se, but, like with pre-A and algebra, some of them are multi-step enough that I really wanted the answer key and a few of them were tricky enough that I liked being able to be sure we had it right.

 

ETA: There are several TG's on Amazon for well under $100. I would consider that to be pretty much the going rate and worth the price IF you can swing it. Since the text goes for $10 or less much of the time, the price altogether being less than $100 seems reasonable to me overall. However, if you can't swing it, most people find they can do it without the TG. And certainly you can get it and see how it goes.

 

As a side note, since you mentioned it above, I also have the Key to books. They are good for just get it done math. They're VERY simplified with really good, long practice sets that build understanding. We turn to them when anxiety is high and/or a concept just won't take. Both my boys think of them as the deadly boring math books. But, on the other hand, they breeze through them and gain confidence that's needed sometimes. Unless a kid is really a struggling student at heart, I don't think of them as a complete program. Supplemental, definitely. Or something for bridging a time period.

Edited February 2, 2018 by Farrar

[Penelope]

Have you looked at Dolciani?

 

The problems require more thinking than a more basic prealgebra or algebra. It doesn’t teach directly to the student, though. You may have to flesh it out some.

[Momto6inIN]

Video Text is fabulous at teaching the why behind the how and it worked for both my mathy DS (who eventually went on to AoPS when we found it) and my non-mathy DS. It's a bit pricy if you're just looking for a break from AoPS and it has a bit different S&S from most programs, but my mathy DS says it's great on concepts and he's glad he did it before going on to AoPS.

 

Sent from my Z988 using Tapatalk

[dancingmama]

My daughter did the same thing while during AoPs Pre-A (and now on Ch. 5 of the Algebra book). She needed a break. We took the book off the table for awhile, she did alcumus on line and a few worksheets and logic puzzles. (This go around we have added prodigy). I found when she was ready, she pulled the book back out on her own. she just needed to step away for awhile. We took longer to finish but that's ok.

 

Edited to add that I also found out she wasn't watching the videos in AoPs when she was stuck so I have to remind her to watch them every now and again.

Edited February 2, 2018 by dancingmama

[Jann in TX]

FYI-- the Geometry formula work in Lial's Basic College Math and in the Pre-Algebra text is just that-- teaching students how to plug into/use a formula and at the same time practicing the current topic (usually decimals). At this level the standards are not to teach how to derive the formulas (whys)-- it is just a demonstration of how formulas work and experience for the student with formulas before they enter high school (useful for science).  The 'whys' are taught in a high school Geometry class.

 

If you look at the other Lial levels (Pre-Algebra and beyond) you will see the whys written next to each step as the problem is worked out in the lesson.

 

Puberty does do a number on the brain-- it physically SLOWS down the logic center-- diverting the extra energy to growing other body parts...  this is one of the main reasons why middle school math is repetitive! 

[deerforest]

Been there, tried everything including all of Foerster’s algebra and still not being happy. Came back to AOPS Algebra this year (so a 2nd year of algebra) and everything suddenly is working for her now! She’s in 8th so we had time too to just do a 2nd year.

[J-rap]

I thought VideoText Algebra was great at really explaining everything.  My kids were a little older when we used it, but your dd might be ready for it.  It's pricy!

 

 

[La Condessa]

What about letting her finish up the year with WTM Academy AOPS Pre-Algebra?  (Do they let students transfer in mid-way?)  It's supposed to be slower and gentler than doing it through AOPS.

[daijobu]

Is she getting stuck on the starred problems or the challenge problems?  You can skip those, or perhaps don't have her do them independently, but maybe work through them together.  I also like the idea of slowing down your pace, if that works for your schedule.  I believe that sleeping after learning something new helps students to retain the info.  It also allows you to review a bit before plunging into the problem set.  (But that's just stuff I've heard on the internet.)

[zarabellesmom]

Today we watched the videos first. I went through all the teaching problems with her, which she found annoying because she kept saying, "I get it, OK?" I then cut her loose on the exercises and she did fine. We worked the challenge problem (in this case, there was only one) together. It actually went pretty well. We only had one moment when her eyes started to water and her voice started to creep up (I swear these hormones are going to be the end of me). I feel like I've looked through every book and watched quite a few videos and I'm just frustrated. AoPS needs to create a program specifically for overwrought preteen girls. 

Edited February 5, 2018 by ZaraBellesMom

[LEK]

AoPS needs to create a program specifically for overwrought preteen girls. 

 

I would buy that in a heartbeat! having similar issues here

 

[SoCal_Bear]

Have you looked at the second and third books after Jousting Armadillos? That would be what I would look at or Jacob's. 

 

http://www.arborcenterforteaching.org/publications/?category=Arbor+Algebra