Getting to Art of Problem Solving Pre-Algebra

[Guest patticus]

Background info:

My wife and I are exploring homeschooling curricula. Our oldest is 2, so we have some time. I am a High School Math Teacher by education and a Camp Director by occupation. I taught HS Math from Remedial Algebra to College Calculus in a charter school in Syracuse for 6 years before leaving teaching. During that time I came across AoPS and bought all of the books to use for my math team in preparation for contests. I really love that curriculum and would love to use it with my kids eventually. My background does not include much knowledge of early childhood development. I do know that all children are different and I don't plan on forcing mine into my mold if it doesn't seem to suit them, but hypothetically speaking---.

 

Question:

What sequence would you recommend that would prepare my children for this curriculum and at what age I could/should feasibly start.

[maize]

If your oldest is 2 you may be able to use the AOPS elementary curriculum, Beast Academy, for grades 2-5, then jump into AOPS Prealgebra.

[Kiara.I]

Yes, Beast Academy.

Before that, you might consider looking at Righstart Math.

[waa510]

Do you mean 2 years old, or grade 2? 

 

I will mirror the previous posters and say Rigthstart for the child initially to build a strong foundation in place value and mental math ability. I would switch to Beast Academy as soon as possible, as that is Art of Problem Solving's elementary curriculum. If your child is 2, they may have more levels out by the time you need them so you may be able to go straight into their curriculum! 

[Pegs]

I have observed that kids who are heading for AoPS tend to use Beast Academy, Rightstart, Miquon, Singapore, or Math Mammoth, or a combination of these.

 

Not all children thrive on conceptual and discovery methods of instruction, though. And some children do better with very dry, explicit instruction early on, then surprise us all by diving into problem-solving once they mature a little.

 

I'm not sure whether AoPS is something you can plan for, so early. Of course it's great to know what your options are, but I encourage you to fit the mathematics curriculum to the child, rather than figuring out the best preparation for AoPS, and attempting to fit the child into that.

[Alice]

We used Singapore through 6B with my oldest and he had a very easy time transitioning to AOPS for 6th grade. We added in a bit of Beast Academy along the way but it came out too late and too slowly for us to use it as our primary curriculum. Singapore is not as experiential as BA but it has the same emphasis on understanding the concept, place value and mental math and problem solving. We used the Singapore Intensive Practice books as the main workbook and added in Challenging Word Problems and I think being used to struggling with problems is what helped the transition more than anything. 

 

I think being ready for AOPS probably has more to do with the personality of the kids and their style of leaner than the curriculum. If you are a math teacher, I would assume you'll give your kids a solid math foundation in the elementary years regardless of curriculum. 

[fourisenough]

RightStart AL Abacus/Activities for the Abacus (you could begin playing with it during the toddler/preschool years), followed on by Math Mammoth, Singapore Challenging Word Problems & Singapore Intensive Practice for 1st-3rd grade levels, then Beast Academy 3rd-5th grade (2nd grade if it's released by then).

[8filltheheart]

Well, I'll break the trend and say that I don't believe success in AoPS depends as much on curriculum used as solid foundation and whether or not the child enjoys approaching math that way. I have 2 children equally strong in math. 1 loved AoPS and regretted when he finished their offerings. ( he is now a physics and math major.) My dd, otoh, had no problems with the class, but she did not enjoy the approach and felt like it took too much and detracted from her other studies. She loves languages and she was taking 2 at that point and wanted to add a 3rd. She wanted a more straightforward math class.

 

Fwiw, they both used absolutely nothing but Horizons for elementary math.

[Mike in SA]

Tough, tough question to answer for a 2 year old. 

 

DS8 just finished AoPS Prealgebra, but it isn't because we hyper-parented.  He started showing interest in math during K, and began accelerating after his 7th birthday.  His Pre-K and K years were very ordinary, but he started getting interested in math and physics during first.  He taught himself his addition and multiplication tables, and we began exploring topics from abstract algebra and number theory together.  When he did well on those, we allowed him to jump to Pre-Algebra on the condition that he continued doing 5th grade and 6th grade math on the side (for reinforcement of the basics).

 

I guess the point is that it won't matter one bit before 6 or 7 years old.  Do whatever you are comfortable with before that.

[go_go_gadget]

As other have said, there's no one path to AoPS Pre-A. Common paths on these boards are Miquon/Mathematics Enhancement Programme (MEP)/Singapore Math (SM until third grade, when Beast Academy (BA) currently starts, but I couldn't begin to enumerate all the possible paths. BA's second grade level should be out by the time your child is about 4 or 5 so you'd be able to start earlier than third grade. One of mine did no formal academics until age 5 and started with RightStart (RS) B, which is an excellent, if expensive, program, followed by SM2 and part of SM3, then BA 3 came out and he switched to that. My daughter started formal academics earlier, and used some of RSB, some of SM2, and was happiest with Miquon until BA3.

 

You could start with Cuisinaire rods (c-rods) with or without Miquon when and as your child seems interested, and focus on building number sense in particular. Education Unboxed (by a fellow board member) has oodles of ideas for using the rods to play and learn, and AoPS's Kitchen Table Math series is excellent for this, as well (without c-rods). 

 

If you're really keen, this question has been asked of AoPS themselves quite often, and their BA page on Facebook is full of answered questions, including this one. If you don't have Facebook, they're also very responsive to email.

[SilverMoon]

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Edited May 18 by SilverMoon

[The Governess]

My daughter used Singapore through level 5B and then switched to AoPS for pre-algebra. It was a great transition for her. We did use the challenging word problem and intensive practice workbooks, and I think that those helped with the transition.

 

That said, I think the best thing to do is choose a solid curriculum that fits your child. Beast Academy was not available at the right time for my daughter, but even if it had been I would have used it only as a supplement. It took her a while to warm up to the discovery method - she is very good at math but needed to mature a bit and gain some patience and problem-solving stamina. In her case, waiting until pre-A to try AoPS was a perfect fit.

[Jackie]

The path it looks like we'll be taking is RightStart Math levels A-C, then Beast Academy 3-5, then AOPS. We also do lots of math games, Highlights MathMania magazines, living math books, and may add in some Zaccaro.

 

However, there are many possible paths.

[Clear Creek]

I think that any math curriculum that provides a solid foundation will work. My oldest used Rod & Staff through the 7th grade book, then began AoPS pre-algebra in the middle of her 6th grade year. My youngest will probable use AoPS pre-algebra, but he is on a completely different path through arithmetic. He used Math-U-See through Gamma, and is currently flying through Math in Focus 3. I would like to transition him to Rod & Staff, but he really needs a workbook still at his age (8) and R&S is a textbook at his level.

[boscopup]

I agree that curriculum doesn't really matter. An AoPS kid probably picks up math easily with just about any curriculum. Plus you yourself are clearly mathy, so you would impart that naturally.

 

My child that has used AoPS did Saxon K-1, Math Mammoth 1-4, Singapore 4-5, then AoPS Prealgebra. My other kids are using CLE, and they'll likely use AoPS later. We sometimes play with Beast Academy, but for a main curriculum, I've found that I actually prefer a traditional elementary math. I really felt like Math Mammoth and Singapore pushed the different mental math techniques and such to the point that my oldest son wasn't coming up with his own as much anymore, whereas when he was bored in school using Saxon (at grade level), he would come up with his own methods and think more. So I kind of feel like some kids don't need all the explicit teaching of those things. I know I didn't get that stuff until math team in 6th grade, and I excelled at math into my college years, naturally thinking the way the Asian programs teach. So YMMV. :)

[Farrar]

I think curriculum matters, but I agree with everyone else that a huge part of it is the kid.

 

I think you'll probably something like...

 

Miquon OR Right Start A-C OR MEP 1-3 followed by Beast Academy, which is meant to lead right into AoPS's Pre-Algebra.

 

Or you'll do Singapore Primary Math 1-5 or 6.

 

However, if none of those turn out to be right and you end up using something else, it's okay. There are other paths to AoPS. And there are other paths to a good math education than AoPS.

[daijobu]

I agree with the above advice to provide a solid foundation in elementary math, whatever curriculum you use.  But I think if you want a smooth transition to AoPS, an important strategy is to avoid situations where you  and your students regularly expect to get 95-100% of the problems correct.  Always challenge them and make sure they are confronting problems they can't solve, at least not in the first 5-10 minutes.  You want your students to grow accustomed to solving hard problems without being sad.  

 

One way to accomplish this is to spend a regular amount of time on old MOEMS exams, especially volumes 2 and 3.  Start with the elementary level and when your student is regularly getting 4 or 5 correct, then switch up to middle school level.  (Don't wait until they are actually in middle school if the elementary level is already too easy.)  When middle school level MOEMS is too easy, then start doing old chapter level MathCounts problems or old AMC8 problems.  

 

Always keep them challenged!  

[Tranquility7]

We haven’t used AoPS yet but I plan to start DS9 on PreAlgebra in about a year. He is in Singapore Math 5B right now, and we may do 6A and 6B before going to PreA. We have *loved* Singapore Math (especially the Challenging Word Problems) and I have heard it is excellent prep for AoPS. We also supplement informally with Beast Academy (DS just reads it for fun, occasionally does the problems with me, lots of good discussion). He has also gone through all three levels of Hands On Equations, which I highly recommend as a great introduction to algebraic thinking. Like PPs have said, there are many paths to AoPS, but this has been ours… I’m optimistic that it will turn out well for DS (and so far DD5 is on the same path).

 

Btw, as a math teacher you might really enjoy reading Liping Ma’s book Knowing and Teaching Elementary Mathematics. While the ideas might be old hat to you, you might still find it professionally interesting given your background. Ma compares the teaching practices of typical math teachers in America and China and I think it really shows why there is such a disparity in our countries’ math achievement. It was a book that seemed to be widely circulated among homeschoolers years ago and seemed related to the surge of appreciation for conceptual programs such as Singapore, Right Start, Miquon, etc. as opposed to more algorithmic programs like Saxon.

 

All the best to you. Researching (and collecting! :thumbup: ) curriculum can be so fun and addicting, and even though it seemed ridiculously early when I started doing it when my eldest was only about 2, it really was a great time to start figuring out my philosophy, style, and options. So kudos to you and your wife!

[Guest patticus]

Thanks for the tips everyone. Much appreciated!

[Upennmama]

My struggling 12 year old did it in 7th grade after Saxon Math and then trying teaching textbooks.