How Accurate are the AOPS Placement Tests?

[wendyroo]

Peter (8.5) just finished Math Mammoth 6b, and my plan was to have him do a few chapters out of MM7.  Most of it looks like easy review (which he doesn't particularly need), but I thought it might be good for him to cruise through the chapters on Inequalities, Statistics, Probability, and Polynomials.

 

On a whim, I gave him the AOPS placement test for Pre-Algebra.  The instructions say to give the student one chance at the problems, then to mark any they got incorrect and give them a second chance.  To score: "A student who is ready for Prealgebra should be able to answer at least 22 of the 26 problems below correctly (after the second chance)."

 

Well, Peter got 24 of the 26 correct on his first try (he misaligned his columns when he calculated 51 × 319 and he misread one of the word problems), and 26 of 26 correct on his second try.

 

On one hand, I feel like any hesitation I am feeling about moving onward and upward has more to do with me not being ready rather than him.  He aced that placement test, and any new information MM7 may touch on in those chapters will be covered in more depth in AOPS. 

 

On the other hand, AOPS pre-algebra is a serious step up from MM6.  Maybe piddling around with MM7 for another few months will let him mature just a little bit more even if he doesn't really learn anything new.

 

Thoughts?  Encouragement?

 

Wendy

[Black-eyed Suzan]

The other indicator of success with AOPS is willingness to work through difficult problems. How comfortable is he doing that? If he's not comfortable, you might take time and do problems (like Math Kangaroo or AMC8 practice exams or Zaccaro) to practice that skill.

 

My ODS started AOPS PreA about about your son's age (I can't remember exactly). We worked through the book together. I would read silently and summarize the wordy descriptions. He worked the problems, then we went over the solutions. It was a slow process, but it worked.

 

Here are a couple of recent threads on the Accelerated Board on that topic. :) It is discussed often and at length there, so you may be able to find other threads by searching.

 

http://forums.welltrainedmind.com/topic/661600-9yo-dislikes-aops-prealgebra/

 

http://forums.welltrainedmind.com/topic/661631-so-disliking-aops-pre-alg-what-else-to-do-first/

[serendipitous journey]

Quick thought -- try working through one (or more, if he can) of the excerpts?  They are on the AoPS Prealgebra book page. 

 

Suzan's comments are very insightful. 

 

Also, of course, AoPS gets somewhat hairy after prealgebra and given some of the special concerns I see in your siggie (esp. the anxiety) you might want to proceed very carefully at the algebra + level. 

Edited November 10, 2017 by serendipitous journey

[silver]

MM 7 is pre-algebra, so it would make sense that if he's finished MM6b, that he'd be ready for pre-algebra in another curriculum. 

 

My son went from MM 6 to AoPS PreA (currently doing PreA this year). I did have him do some of the negative number sections in MM7 first, since there isn't much coverage of negative numbers in MM and AoPS PreA starts out with them. 

 

 

Edited to add:

There is a little bit of overlap between AoPS PreA and levels 4+5 of BA. If you don't think he has the maturity to do AoPS PreA just yet, or if he would balk at the wordiness of it, you could do level 5 of BA first.

Edited November 10, 2017 by silver

[wapiti]

The placement test reflects the prerequisite math skills needed but does not reflect the difficulty of the text.  It is *not at all* surprising to me that a kid who completed MM6 would be ready for AoPS Prealgebra, at least as far as math skills.

 

As for the other personal qualities, I don't think there's anything wrong with starting out with AoPS as buddy math on a white board and/or used socratically or whatever other combination works for the two of you.  My caution would be that many gifted kids that age are not going to find it a great fit for using independently, but there's no law saying that's the only way to use this fantastic text.

[GeoKitty]

In our experience, the placement tests are quite easy. I would consider starting it, but letting him also do Beast Academy for fun.

[wendyroo]

The other indicator of success with AOPS is willingness to work through difficult problems. How comfortable is he doing that? If he's not comfortable, you might take time and do problems (like Math Kangaroo or AMC8 practice exams or Zaccaro) to practice that skill.

 

He has been working through the Hands on Equations word problem book to practice that skill (and having to write out problems rather than work in a workbook).  So far he is flying through the easier problems in HOE, and being slightly challenged by the more difficult ones.  As he has worked through the book, I have seen him become a more resilient problem solver, though these are clearly not AOPS level problems.

 

Quick thought -- try working through one (or more, if he can) of the excerpts?  They are on the AoPS Prealgebra book page. 

 

Suzan's comments are very insightful. 

 

Also, of course, AoPS gets somewhat hairy after prealgebra and given some of the special concerns I see in your siggie (esp. the anxiety) you might want to proceed very carefully at the algebra + level. 

 

We own the prealgebra book (I have been working through it so I can gauge its level and be prepared to help as required), so I had considered having Peter work through one subsection a week (whether it took one day or two or three) and then finishing out the week with MM if he needs a break.

 

Peter is such an asynchronous kid.  He rarely shows any anxiety about math (even when working through some of the University of Waterloo Math Circles), but the other day an episode of Magic School Bus left him cowering under his bed.  That said, I am really hoping to stretch out the pre-algebra book for 18+ months.  I'm planning to have him do quite a bit of alcumus along the way, so he will have hopefully been introduced to a lot of the algebra topics before we get there.

 

MM 7 is pre-algebra, so it would make sense that if he's finished MM6b, that he'd be ready for pre-algebra in another curriculum. 

 

My son went from MM 6 to AoPS PreA (currently doing PreA this year). I did have him do some of the negative number sections in MM7 first, since there isn't much coverage of negative numbers in MM and AoPS PreA starts out with them. 

 

 

Edited to add:

There is a little bit of overlap between AoPS PreA and levels 4+5 of BA. If you don't think he has the maturity to do AoPS PreA just yet, or if he would balk at the wordiness of it, you could do level 5 of BA first.

 

Yeah, we have already done the MM7 chapter on Integers as well.  He needed a firm grasp of negative numbers before he was ready for Hands on Equations.

 

He completed Beast Academy 4, but when I suggested buying 5, he just wanted to read through the guides, but said that the problems were too easy.  That is when I let him start on the HOE word problem book instead of BA 5.

 

The placement test reflects the prerequisite math skills needed but does not reflect the difficulty of the text.  It is *not at all* surprising to me that a kid who completed MM6 would be ready for AoPS Prealgebra, at least as far as math skills.

 

As for the other personal qualities, I don't think there's anything wrong with starting out with AoPS as buddy math on a white board and/or used socratically or whatever other combination works for the two of you.  My caution would be that many gifted kids that age are not going to find it a great fit for using independently, but there's no law saying that's the only way to use this fantastic text.

 

I'm not opposed to helping him through the book, but in general he doesn't like buddy math.  He just wants to work it out his own way and for me to tell him if he got it right or wrong.  He has a low tolerance for listening to me talk about how I thought about a problem or other ways he could have solved it.

 

My biggest concern is that he HATES writing any of his math down.  I've insisted that he show his work for Hands on Equations, but it is like pulling teeth.  I can see this easily leading to problems if he gets one of the AOPS problems wrong, but I can't really help him because he hasn't written anything down and he refuses/isn't capable of discussing how he came up with his answer.

 

Thank you all for your thoughts.

Wendy

[wapiti]

My biggest concern is that he HATES writing any of his math down.  I've insisted that he show his work for Hands on Equations, but it is like pulling teeth.  I can see this easily leading to problems if he gets one of the AOPS problems wrong, but I can't really help him because he hasn't written anything down and he refuses/isn't capable of discussing how he came up with his answer.

 

My kiddo who started the text at 9 y.o. was like this.  Handwriting issues, among others.  He would do occasional scratch work on the white board on the counter, but mostly would do it in his head such that several minutes would pass between reading the question and shouting out an answer to me a room away.  It got to where I thought maybe he was cheating and so I hid the answer key, but he wasn't.  The key was for me to not speak to him during those minutes because if I were to interrupt, he would then lose the whole problem in his head.

 

He didn't really write down math until somewhere in the middle of algebra, and it wasn't really until somewhere in the middle of alg 2 that he had to do it properly and officially for a teacher at school.  He then learned to do so quickly without issues.

Edited November 10, 2017 by wapiti

[Arcadia]

He has a low tolerance for listening to me talk about how I thought about a problem or other ways he could have solved it.

 

My biggest concern is that he HATES writing any of his math down. I've insisted that he show his work for Hands on Equations, but it is like pulling teeth. I can see this easily leading to problems if he gets one of the AOPS problems wrong, but I can't really help him because he hasn't written anything down and he refuses/isn't capable of discussing how he came up with his answer.

My younger boy is similar and it just means he takes double or triple the time that older boy takes. Now he ask for help from his brother because he realized that refusing help means less down time for him. He doesn’t like to write but he can talk your ear off. My very quiet older boy doesn’t talk and hate writing but would write out the working when he is stuck.

 

Both my boys started the prealgebra book when they were 8. Since my boys have plenty of time to reach Calculus in high school, younger boy can be as obstinate as he like about asking for help and take his time to puzzle through.

 

ETA:

My kids were too lazy to do the placement tests. They prefer to dive in and suffer.

Edited November 10, 2017 by Arcadia

[boscopup]

If he's done MM6, I would expect him to place well in AoPS Prealgebra. He's more than ready! My oldest did PreA after completing Singapore 5, and my middle started it after completing Math in Focus 5 and part of MM6 (he was sooooo bored that I decided to bump him up for the challenge - it worked!). So give it a try. Since he's young, work WITH him, holding his hand as much as necessary, discussing the problems, etc. Don't try to finish the book in any particular amount of time. Just work steadily at his pace. My oldest spent 2 years on the book, starting at age 9. He would have been about 1.5 years if we'd not had a complicated pregnancy mess up our school days that year. He's doing well in geometry this year in 8th grade.

[wendyroo]

Okay, you all talked me into it.  I'm going to offer him the choice of either finishing up the last few chapters of MM7 or starting on AOPS Pre-A.  I honestly don't know which he will choose, but I think either will go more smoothly if it is his decision.

 

When we tackle AOPS, either now or in a few months, we will take our time and just feel our way through to see how we can make it work for him.

 

Thanks!

[daijobu]

Another option if you want to delay AoPS Algebra, is to work through the AoPS Pre Algebra challenge problems at the end of each chapter only.  My kids spend 2-3 days per chapter on challenge problems.  

 

 

[Crimson Wife]

FWIW, my "mathy" kid is lukewarm about AOPS Pre-Algebra. He did a couple chapters after finishing Singapore 6 but he found it just "meh". Then I switched him to Elements of Mathematics and he LOVED that.

 

After finishing EoM 1-7 and the Pre-Algebra supplement, there were a few topics the AOPS Pre-Algebra book that he didn't know (square roots and the geometry chapters). So he's working through them now. He has been asking when can he go back to EoM so I'm undecided about what to use next semester. The charter we're in now will pay for AOPS but not EoM.