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AoPS and "review" or lack thereof


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Yeah another AoPS thread lol

 

On another thread I read last night someone said that AoPS didn't really review, it was more of a mastery method, assuming the child masterered the previous material and expecting them to use it properly without any review.

 

For those using AoPS how true is this? My son is currently using Saxon. We did one of the sample Pre-Algebra lessons yesterday. It seems like it would be a good fit and after watching the videos, my son thinks so as well. By I am concerned about lack of review. The discovery method and videos look like they will be great for him, but after being in the Saxon mindset, I am afraid that lack of review will not be good for him.

 

What say you AoPS users? Is there enough review? If not, do you supplement with anything to review?

 

Thanks!

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We have used AoPS Intro to Algebra, geometry, Intermediate Algebra and now Precalculus.

We found the problems provided in the book sufficient to achieve mastery and find little need for additional review. You are correct that the book does not have built in review chapters or sections, but that does not mean you can not review as needed. We give comprehensive final exams at the end of each semester and spend a few days reviewing the semester's material using the problems from the sections of the book when the material was taught.

Of course, techniques that are not used continuously will be forgotten, but the important techniques and concepts that are continuously used are retained well if properly mastered the first time..

To illustrate what I mean: you do not need review to solve linear equations, or systems or quadratics if you have mastered them the first time around; you will still be able to do all these things years later, because the need to apply them recurs throughout math. OTOH, the formula for sums and differences of cubes is used rarely and will eventually be forgotten by almost every student -BUT the student will remember that there was something and will be able to reactivate this knowledge when needed.

I do not realistically expect my students to remember every single detail of the books years later, but I do expect them to master the important concepts to such an extent that they can derive for themselves the details they may have forgotten. Up to this point, the mastery approach of AoPS has met this goal.

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We have begun term exams based on Regentrude's suggestion. This forces your child to review as preparation for the exam. It has also given me a chance to teach my ds some study skills.

 

Compared to Saxon, AoPS has no review of previous chapters. Each chapter is self-contained.

 

Ruth in NZ

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Yeah another AoPS thread lol

 

On another thread I read last night someone said that AoPS didn't really review, it was more of a mastery method, assuming the child masterered the previous material and expecting them to use it properly without any review.

 

For those using AoPS how true is this? My son is currently using Saxon. We did one of the sample Pre-Algebra lessons yesterday. It seems like it would be a good fit and after watching the videos, my son thinks so as well. By I am concerned about lack of review. The discovery method and videos look like they will be great for him, but after being in the Saxon mindset, I am afraid that lack of review will not be good for him.

 

What say you AoPS users? Is there enough review? If not, do you supplement with anything to review?

 

Thanks!

 

I would say that I've seen three approaches in different math programs.

 

1. Spiral and review so that there are frequent review problems, but fewer and less deep of any given topic in a given lesson.

 

2. Mastery where a concept is learned and then the student moves on and doesn't address that topic again for a long time. (This was something I saw in a school I did practicum in. The teacher told the kids they were done with fractions and they could throw away the pages from those lessons.)

 

3. Mastery where the concepts learned are then applied frequently.

 

I would argue that AoPS falls under #3. We're about half way through the Intro to Algebra book. There are frequently problems that require my kids to apply their understanding of manipulating equations, simplifying fractions, multiplying or dividing fractions, using exponents, etc in order to solve the problem that is the focus of the lesson. For example, a recent graphing chapter problem had them using the pythagorean theorem as well as cross multiplication and simplifying an equation with exponents in order to find the value for the variable.

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Now if I can just put aside my box-checker, worry wart mentality enough to go out on a limb and use something that looks like it will work for my son but won't have clear cut, check-the-box type review

 

You can easily create a review scheme: at the end of each semester, spend a week working problems from the review section at the end of each chapter - something like a day for each chapter, for example. (It does not matter that your kid has seen the problems a few weeks before; he won't have memorized the answers). This way, you can be sure that periodic review is done, if you don't trust the built-in review through application of the previously learned concepts in the new material.

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The problems are so hard ds won't recognize them later:) I plan to go back and give him a selection of previously done problems halfway through the book. We also don't always get to all the challenge problems at the end of the chapter so we can go back and do those as review.

 

Brownie

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I would say that I've seen three approaches in different math programs.

 

1. Spiral and review so that there are frequent review problems, but fewer and less deep of any given topic in a given lesson.

 

2. Mastery where a concept is learned and then the student moves on and doesn't address that topic again for a long time. (This was something I saw in a school I did practicum in. The teacher told the kids they were done with fractions and they could throw away the pages from those lessons.)

 

3. Mastery where the concepts learned are then applied frequently.

 

I would argue that AoPS falls under #3. We're about half way through the Intro to Algebra book. There are frequently problems that require my kids to apply their understanding of manipulating equations, simplifying fractions, multiplying or dividing fractions, using exponents, etc in order to solve the problem that is the focus of the lesson. For example, a recent graphing chapter problem had them using the pythagorean theorem as well as cross multiplication and simplifying an equation with exponents in order to find the value for the variable.

:iagree:

 

In addition, we (or I should say my husband) tries to create review questions or exams at the end of every chapter that also cover or incorporate prior concepts.

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:iagree:

 

In addition, we (or I should say my husband) tries to create review questions or exams at the end of every chapter that also cover or incorporate prior concepts.

 

And don't forget that you can use the Alcumus problems to identify weak spots, provide review or even give you some questions that could be woven into test sets.

 

When my kids are either struggling with lessons or have completed a chapter's problems but don't seem to have the necessary fluency in the topic, I will assign them a couple of days of doing problems from Alcumus.

 

I've even been known to pull tough problems out of the older AMC 8 exams.

 

I want them to understand that tough math problems don't have to be scary because you just whittle them down one bite at a time.

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