AoPS Pre-Algebra question

[Embassy]

I had a look at the pre-test for AoPS Pre-Algebra. My son is almost finished with 3B in Singapore and part-way through LOF Fractions so I figured he had a ways to go before he was ready. But I'm pretty sure he could pass that test right now. How is that possible? Should I look into this sooner than I expected?

[Julie Smith]

We recently had a thread about this. The conclusion was many people go from Singapore 5bto AOPS per algebra.

[Momling]

I understand that the pre-test is deceptively easy. The book isn't.

[Haiku]

There are three sample chapters of AoPS Pre-Algebra available. I put them on my Kindle and read through them. The placement test for AoPS is extremely misleading. I also thought, "Wow, my dd in 4th grade could pass this test." But the material in AoPS would be too advanced for her.

 

Incidentally, while I liked how AoPS teaches kids how to think about what they are doing in solving the problems, I found there to be no context in the three sample chapters I read. There was no, "This is how you might end up with information configured in this equation." It was just, "Do this equation. Now do this one. Now do this one. Ok, here's how they are solved."

 

If I'm missing something, please feel free to clue me in.

 

Tara

[Deniseibase]

Agree that the placement test for AoPS books tends to be off the mark. The sample chapters were, for us, a much better indicator of level. This is our second year of pre-algebra, because AoPS pre-algebra is SO much more in depth than our previous work. However, even if AoPS Pre-Algebra HAD been out last year, there is NO WAY my DD would have had the maturity to handle the 'wordiness' of AoPS before this year, she would have kicked and whined and ended up hating it. So that's something to keep in mind too - the pre-test makes it look like 'if your child has mastered these procedures, they can handle this course' and there is WAY more to it than the procedures.

 

Especially look at excerpt 1 from the pre-algebra - http://www.artofproblemsolving.com/Store/products/prealgebra/exc1.pdf The actual PROCEDURES being discussed for the example problems are ridiculously easy, my kindergartener could answer them. But the pages and PAGES of abstract discussion of the properties involved are the heart of the lesson here, and essential to work the rest of the chapter.

 

Also agree with the previous poster that AoPS is not a 'context-heavy' program. The focus with AoPS is much more on 'math for math's sake' and the enjoyment of solving puzzles. The practical child who needs real-world connections to make math important to them would not do well with this. There is a little context in some of the word problems, but honestly even those tend to be fairly 'un-practical' problems like 'There are 17 cars and bikes in a garage and a total of 56 wheels. How many cars are there?' or 'Three years ago, I was two-thirds as old as I will be eight years from now. How old am I now?' Not exactly the same as some other programs that give you real problems from construction or the sciences to illustrate a concept.

[Haiku]

Thanks, Denise! I learned a lot from your post!

 

Tara

[Embassy]

Thanks for the responses! It has been very helpful. It sounds like a better indication of readiness is a completion of strong 5th grade level material.

[MBM]

Incidentally, while I liked how AoPS teaches kids how to think about what they are doing in solving the problems, I found there to be no context in the three sample chapters I read. There was no, "This is how you might end up with information configured in this equation." It was just, "Do this equation. Now do this one. Now do this one. Ok, here's how they are solved."

 

Yes, AoPS wants students to try to solve the problems before reading the section. Students should always read the section even if they can do all of the problems because they might learn an easier, more elegant ways to solve the problems.

 

For those of you who don't have an AoPS text, here is a little blurb from the book that explains the reason why they suggest doing problems first (my son tries but usually can't do them without reading the section):

 

This book is probably very different from most of the math books that you have read before. We believe that the best way to learn mathematics is by solving problems. Lots and lots of problems. In fact, we believe that the best way to learn mathematics is to try to solve problems that you don't know how to do. When you discover something on your own, you'll understand it much better than if someone just tells it to you.

 

When our son first started AoPS Algebra (no Prealgebra back then), he struggled with the first half of the book even after doing NEM Algebra. Actually, he still struggles with some/many of the problems, but he knows this is normal. So, if your student is finding it difficult, that is probably not unusual.

 

Our son does AoPS as well as his school's math, and the two are definitely different in their approach.

[Haiku]

Yes, AoPS wants students to try to solve the problems before reading the section. Students should always read the section even if they can do all of the problems because they might learn an easier, more elegant ways to solve the problems.

 

I think you misunderstood what I meant. I wasn't talking about arriving at solutions. I was talking about arriving at the equations themselves. It's great that 5 1/4 - y = 19 3/4, but in what circumstance would someone need to configure the information in that? What type of actual problem would one need to solve in such a way other than a problem on the page of a math book? AoPS seemed, to me, lacking in practical application (the dreaded "When will I ever use this??"), whereas something like Lial's Prealgebra (which I previewed today) has a lot of.

 

Tara

[Roadrunner]

 

Also agree with the previous poster that AoPS is not a 'context-heavy' program. The focus with AoPS is much more on 'math for math's sake' and the enjoyment of solving puzzles. The practical child who needs real-world connections to make math important to them would not do well with this. There is a little context in some of the word problems, but honestly even those tend to be fairly 'un-practical' problems like 'There are 17 cars and bikes in a garage and a total of 56 wheels. How many cars are there?' or 'Three years ago, I was two-thirds as old as I will be eight years from now. How old am I now?' Not exactly the same as some other programs that give you real problems from construction or the sciences to illustrate a concept.

Have you seen any math programs that use real problems like you mentioned? I would be so interested (mostly for me at this point).

[Capt_Uhura]

I plan to use Forester's to get more of the real-world problems. I also have some workbooks from Math Mammoth website that are real-world problems such as how to figure out which cell phone plan is the cheapest depending on your usage....although now I guess most cell phone plans are unlimited. :lol:

[Deniseibase]

Have you seen any math programs that use real problems like you mentioned? I would be so interested (mostly for me at this point).

 

Foerster and Dolciani both have some of those kinds of problems. Saxon 4th Edition actually has the most of those sorts of problems of any program I know of, but I'm not familiar with a lot of the common ones like BJU, Lial's, TT, and Chalkdust. Saxon 4th Edition is what I use for ME to get myself up to speed on procedures so that I can keep up with my DD on AoPS Pre-Algebra - she's the mathy one, the discovery method for math does NOT work for ME at ALL :001_smile: I get way too confused!!

[ErinE]

I think you misunderstood what I meant. I wasn't talking about arriving at solutions. I was talking about arriving at the equations themselves. It's great that 5 1/4 - y = 19 3/4, but in what circumstance would someone need to configure the information in that? What type of actual problem would one need to solve in such a way other than a problem on the page of a math book? AoPS seemed, to me, lacking in practical application (the dreaded "When will I ever use this??"), whereas something like Lial's Prealgebra (which I previewed today) has a lot of.

 

Tara

 

Although I haven't seen AoPS pre-algebra (waiting for my, I mean, my son's book), I like the discovery approach. I use it in my career and I want to encourage the skill in my kids.

 

I build financial models for a living and I'm often confronted with situations where I don't know the equation, but I know the solution. Or I have a financial structure that is time dependent so I need to create an equation to solve for value. I joke with my clients that half my time spent modeling is actually thinking about the formulas before I write them. Algebra encourages elegance in equations and finding the simplest form.

 

Although you may never see the specific method shown in real life, the thinking skills algebra develops are very important. There will be many unknowns my kids will confront and it's important that they think about the solution and the process to get there.

[Roadrunner]

Foerster and Dolciani both have some of those kinds of problems. Saxon 4th Edition actually has the most of those sorts of problems of any program I know of, but I'm not familiar with a lot of the common ones like BJU, Lial's, TT, and Chalkdust. Saxon 4th Edition is what I use for ME to get myself up to speed on procedures so that I can keep up with my DD on AoPS Pre-Algebra - she's the mathy one, the discovery method for math does NOT work for ME at ALL :001_smile: I get way too confused!!

 

Thanks!!! I really need to go back and refresh all the math before my kids hit middle school years. :001_huh:

[MBM]

I think you misunderstood what I meant. I wasn't talking about arriving at solutions. I was talking about arriving at the equations themselves. It's great that 5 1/4 - y = 19 3/4, but in what circumstance would someone need to configure the information in that? What type of actual problem would one need to solve in such a way other than a problem on the page of a math book? AoPS seemed, to me, lacking in practical application (the dreaded "When will I ever use this??"), whereas something like Lial's Prealgebra (which I previewed today) has a lot of.

 

Tara

 

Aha. I see now. I think what you are asking about is application. To answer the bolded part, most likely, different fields of science and finance (like Erin mentioned) -- or math, of course!

 

Here are two short, interesting articles written by Richard Rusczyk that explain the reasons behind AoPS's methods:

 

http://www.artofproblemsolving.com/Resources/articles.php?page=problemsolving'>http://www.artofproblemsolving.com/Resources/articles.php?page=problemsolving

 

http://www.artofproblemsolving.com/Resources/Files/problemsolving.pdf

 

Both are from here in case you might want to look through some more: http://www.artofproblemsolving.com/Resources/articles.php)

 

HTH. :)

[Haiku]

To answer the bolded part, most likely, different fields of science and finance (like Erin mentioned) -- or math, of course!

 

 

Yes, I know. But what I'm getting at is that this is not shown to the kids (at least not in the samples I looked at). It's just a bunch of problems, with discussion on how to solve them, but no discussion of what they would actually mean in the real world or what might happen in the real world that would make you need to solve a problem algebraically.

 

Although you may never see the specific method shown in real life, the thinking skills algebra develops are very important. There will be many unknowns my kids will confront and it's important that they think about the solution and the process to get there.

 

I understand this. In fact, when my dd9 asked me last night what algebra was, I told her it was a way of thinking through problems in order to solve them. I know that algebra is important; I use it even as a SAHM. But my point is that AoPS seems only to focus on solving problems with no indication to the student when these skills that they are learning would be useful. As someone previously mentioned, it seems like the focus is just math for math's sake. While I can appreciate that as an adult, as a student I wanted to know "What will I ever use this for?" AoPS doesn't seem to show any of that.

 

Tara

[NittanyJen]

Add in a little Life of Fred! Most of the problems there are directed at solving 'real-world' problems.

[Scuff]

So, what currics would you say provide real-world examples. That's the one thing I see lacking from my own education. I could do the work, bu it was all playing with numbers to me.

[8filltheheart]

So, what currics would you say provide real-world examples. That's the one thing I see lacking from my own education. I could do the work, bu it was all playing with numbers to me.

 

Foersters is very heavy in real world application problems. That said, I completely disagree with the contention that AoPS is not going to provide students w/understanding of how concepts apply to the real world. If anything, AoPS only strengthens the understanding by having students fully prove the concepts which in turn do apply to the real world.

[Haiku]

Can you give examples of when or how AoPS demonstrates real-world application to the students? I have nothing against AoPS, it was just my impression from reading their (extensive, which is nice) samples that there wasn't discussion of practical application. I seem to have gotten conflicting information in this thread about that.

 

Tara

[8filltheheart]

Can you give examples of when or how AoPS demonstrates real-world application to the students? I have nothing against AoPS, it was just my impression from reading their (extensive, which is nice) samples that there wasn't discussion of practical application. I seem to have gotten conflicting information in this thread about that.

 

Tara

 

Just b/c AoPS does not include numerous real world application problems does not mean that students will be missing how concepts apply to the real world. B/c students solve the math problems via proofs, they develop greater understanding of the concepts. It is the level of complexity behind the development of the concepts that easily translates into understanding how they apply to the real world.

 

The exception to "few" real world application problems is their calculus course; it is very application problem "heavy."

 

I have kids that have gone both routes.......Foerster and AoPS. My "Foerster" only route ds is now a chemical engineer that graduated Cum Laude (never made anything below an A in any math course). My 10th grader is taking AoPS cal. My AoPS ds has a far better conceptual understanding of math than his engineering brother. AoPS is the reason why. Both are fabulous math students, but AoPS does develop an understanding that is lacking in traditional approaches like Foerster.

[Scuff]

Thank you. That kinda reinforces the decisions I've made for my dc.

[melmichigan]

Can you give examples of when or how AoPS demonstrates real-world application to the students? I have nothing against AoPS, it was just my impression from reading their (extensive, which is nice) samples that there wasn't discussion of practical application. I seem to have gotten conflicting information in this thread about that.

 

Tara

 

I have never gotten the impression that AoPS does not lead to real world application or is math just for the sake of math. If anything, applying math makes that much more sense to my DD now than it ever did before. When I asked her about it she answered that she learns how to apply the problems using all of the book, videos, and her online class interaction.

[Deniseibase]

Just to clarify my earlier remarks, in case I am the source of confusion here (which, ya know, I wouldn't rule out, seein' as I know how I am :lol: ) - I DO think AoPS students will definitely be able to apply their knowledge to the real world in applied situations, otherwise I would not bother to be using it with my DD! :D But, I do think that for the student who wants to see real-world applications incorporated right into the text, AoPS does not provide much of that kind of problem. One question is about later applicability - AoPS has that. One is about addressing a certain kind of student's learning style - AoPS does not have that. Hope that helps!

[MBM]

Yes, I know. But what I'm getting at is that this is not shown to the kids (at least not in the samples I looked at). It's just a bunch of problems, with discussion on how to solve them, but no discussion of what they would actually mean in the real world or what might happen in the real world that would make you need to solve a problem algebraically.

 

I understand this. In fact, when my dd9 asked me last night what algebra was, I told her it was a way of thinking through problems in order to solve them. I know that algebra is important; I use it even as a SAHM. But my point is that AoPS seems only to focus on solving problems with no indication to the student when these skills that they are learning would be useful. As someone previously mentioned, it seems like the focus is just math for math's sake. While I can appreciate that as an adult, as a student I wanted to know "What will I ever use this for?" AoPS doesn't seem to show any of that.

 

Tara

 

Tara, I have not seen the prealgebra book, but the beginning algebra book has real-life problems. Could it be that the sample chapters you're looking at just don't contain those types of problems? Maybe someone reading this thread who has the prealgebra book could look through for you.

[Capt_Uhura]

Thank you for posting your experience 8FilltheHeart!!! DS used to fly through MM but AoPS pre-alg really makes him think. It is work for him. But I think that's a good thing!!

 

Just b/c AoPS does not include numerous real world application problems does not mean that students will be missing how concepts apply to the real world. B/c students solve the math problems via proofs, they develop greater understanding of the concepts. It is the level of complexity behind the development of the concepts that easily translates into understanding how they apply to the real world.

 

The exception to "few" real world application problems is their calculus course; it is very application problem "heavy."

 

I have kids that have gone both routes.......Foerster and AoPS. My "Foerster" only route ds is now a chemical engineer that graduated Cum Laude (never made anything below an A in any math course). My 10th grader is taking AoPS cal. My AoPS ds has a far better conceptual understanding of math than his engineering brother. AoPS is the reason why. Both are fabulous math students, but AoPS does develop an understanding that is lacking in traditional approaches like Foerster.

[letsplaymath]

... As someone previously mentioned, it seems like the focus is just math for math's sake. While I can appreciate that as an adult, as a student I wanted to know "What will I ever use this for?" AoPS doesn't seem to show any of that.

I think of AoPS more as "math for puzzle's sake." The idea that a challenging math puzzle can be fun on its own, without needing any "real world" application, seems to be one of the driving forces behind the site.

[Haiku]

I think of AoPS more as "math for puzzle's sake." The idea that a challenging math puzzle can be fun on its own, without needing any "real world" application, seems to be one of the driving forces behind the site.

 

I definitely think my dd would appreciate some of that. She's mathy and likes math. It would never work for ds. He's a "just the facts, ma'am" kinda kid when it comes to math.

 

Tara