need advice about reviewing alg 1 before moving on...

[Noreen Claire]

DS12 (just turned 12 last week) is in 6th grade and is finishing up chapter 9 of AoPS Intro to Algebra book. I'm guessing that he will be done with the "algebra 1" part of the book (chapters 1-13) sometime in August/September. This is the first time that he's ever really had to *work* at math. I'm fairly sure that it has to do with growing/sleeping/hormones, as he suddenly has a man-sized body. He's done a really good job with the book, on his own with help from me as needed, but I don't feel like it is as solid as it could be before we move on (to either the NT, C&P, or geometry books, we haven't decided yet). So, I have several different ideas for solidifying the algebra before we move on, and I was hoping someone else could give input into the choices.

Choice #1: enroll in an online AoPS Alg 1 course right now. (He previously took their pre-alg2 course.) This would review/reinforce the topics he's already worked in chapters 1-9, and then bring him through the final few chapters. We could then spend August and September (and maybe October?) working the challenge problems in the book for chapters 10-13, before moving on to the next thing. 

Choice #2: enroll in an online AoPS Alg 1 course after he's finished chapters 1-13 on his own. (This will put us into December.)

Choice #3: work through a secondary algebra 1 text after he finishes chapter 13 in the AoPS text. I have several algebra 1 textbooks on the shelf (Jacobs, Pearson, etc), and we could just do the chapter reviews, dipping into the chapters as-needed.

Choice #4: Move on to whatever subject book he wants to do next, and throw in algebra reviews, either as they come up or in parallel.

other choices? There is always the option to just finish the Intro to Algebra book through chapter 22 for his 7th grade year...

Edited April 9, 2021 by Noreen Claire

[mathnerd]

Here is how I approached this:

We did not move on completely from Alg1 after DS had done about 14 chapters in the AOPS Intro to Alg book mainly because I was worried that he had not done enough review problems, though I had no basis for this feeling. To convince myself that he had mastered all the topics, I pulled out extra problems per topic from other texts, problem books (Posamentier's problem books: https://www.amazon.com/Challenging-Problems-Algebra-Dover-Mathematics/dp/0486691489 ), AMC contests etc. I also set the difficulty level of his Alcumus to "Insanely Hard" and had him turn all of the topics to blue.

He was doing other math meanwhile as well: he started on Geometry while still working on the above, so, no complaints from him about stagnating.

When he finished Alg2, we followed your Choice #2 (again for my own comfort) because I did not have the time at that point to keep spreadsheets and follow his progress and mastery per subtopic and to me Alg2 was the gateway to higher math and I did not want to leave it to self study. It turned out that doing the AOPS class online after finishing the book was a overkill for him. He did greatly enjoy the class as the instructor knew that he was capable and pulled him aside to give him more deeper insights (like a private chat room/whisper ... don't know what the term is) into topics and also the Written Proofs were graded meticulously.

[Not_a_Number]

So... I'd be curious which parts you thought weren't solid, as that would change my answer 🙂 . What do you think he might still not be totally proficient at? 

[Noreen Claire]

50 minutes ago, mathnerd said:

Here is how I approached this:

We did not move on completely from Alg1 after DS had done about 14 chapters in the AOPS Intro to Alg book mainly because I was worried that he had not done enough review problems, though I had no basis for this feeling. To convince myself that he had mastered all the topics, I pulled out extra problems per topic from other texts, problem books (Posamentier's problem books: https://www.amazon.com/Challenging-Problems-Algebra-Dover-Mathematics/dp/0486691489 ), AMC contests etc. I also set the difficulty level of his Alcumus to "Insanely Hard" and had him turn all of the topics to blue.

He was doing other math meanwhile as well: he started on Geometry while still working on the above, so, no complaints from him about stagnating.

When he finished Alg2, we followed your Choice #2 (again for my own comfort) because I did not have the time at that point to keep spreadsheets and follow his progress and mastery per subtopic and to me Alg2 was the gateway to higher math and I did not want to leave it to self study. It turned out that doing the AOPS class online after finishing the book was a overkill for him. He did greatly enjoy the class as the instructor knew that he was capable and pulled him aside to give him more deeper insights (like a private chat room/whisper ... don't know what the term is) into topics and also the Written Proofs were graded meticulously.

Thank you for your response! I had forgotten that I could tweak the difficulty on Alcumus. That is an option - to add in Alcumus review parallel to whatever book we do next. (He's currently working it at the 'regular' setting, turning everything blue.)

[Noreen Claire]

2 minutes ago, Not_a_Number said:

So... I'd be curious which parts you thought weren't solid, as that would change my answer 🙂 . What do you think he might still not be totally proficient at? 

Overall, he's just been much slower. It comes and goes, though. He just flew right through the chapter on optimization problems. Other chapters were just a long slog.

At a finer level, some things don't feel as .... I don't quite have the words to explain it. For example, he always solves equations so that the X is on the left-hand side, even if it would be easier mathematically to have it on the RHS. I don't know if that is his tendency toward OCD/rigid thinking, or if he just doesn't yet have enough practice to see the easier way. Does that make sense?

[Not_a_Number]

6 minutes ago, Noreen Claire said:

Overall, he's just been much slower. It comes and goes, though. He just flew right through the chapter on optimization problems. Other chapters were just a long slog.

At a finer level, some things don't feel as .... I don't quite have the words to explain it. For example, he always solves equations so that the X is on the left-hand side, even if it would be easier mathematically to have it on the RHS. I don't know if that is his tendency toward OCD/rigid thinking, or if he just doesn't yet have enough practice to see the easier way. Does that make sense?

Hm, interesting. I've seen the thing about wanting x's to be on the left before -- I think it sometimes comes from being very used to the equals sign as an "assignment" operator instead of a "balance" operator. I don't know if that's the case for him, though 🙂 . 

I would agree with you that lack of fluidity with algebraic manipulations would concern me and would prompt review. I'd probably do Choice 1 or Choice 4, since it doesn't sound like he's THAT shaky on it, and getting into reinforcement quicker is ultimately a good idea. 

For what it's worth, I think Algebra 1 is almost all about understanding both variables and equations well, as well as having the fundamentals you're building on down. And I do think you could easily integrate that with work on another subject, if you had the time to pay attention to it. Right now, I'm doing some sort of mishmash of algebra and geometry with DD8, and it's working well -- her algebra is definitely getting reinforced. 

Edited April 10, 2021 by Not_a_Number

[daijobu]

27 minutes ago, Noreen Claire said:

Overall, he's just been much slower. It comes and goes, though. He just flew right through the chapter on optimization problems. Other chapters were just a long slog.

At a finer level, some things don't feel as .... I don't quite have the words to explain it. For example, he always solves equations so that the X is on the left-hand side, even if it would be easier mathematically to have it on the RHS. I don't know if that is his tendency toward OCD/rigid thinking, or if he just doesn't yet have enough practice to see the easier way. Does that make sense?

I always put the x on the LHS.  I'm a little discombobulated to see it on the "wrong" side.  I also like my chain inequalities to be increasing...unless we're comparing a variable with a number, then--you guessed it--the variable goes on the LHS regardless of the direction of the inequality.

Can he solve most of the Review Problems and some or most of the Challenge Problems?  If so, then I think he's good to continue with the textbook.  Learning from a textbook, IMO, is an important skill to maintain.  If he's able to do it now, I'd have him keep at it.  

[Not_a_Number]

3 minutes ago, daijobu said:

I always put the x on the LHS.  I'm a little discombobulated to see it on the "wrong" side.

I'll cop to that, too, lol. But I wouldn't make my math harder to make it come out that way -- I might just flip the sides along the way. 

[SoCal_Bear]

I found myself in a similar place, I was not convinced that my son was as solid as he could be when we reached ch.13. We actually went back over Ch.10-13 before moving forward with the rest of the book. I used Alcumus as the basis for the second pass through. His grasp was much more solid after the second pass through the material. Having read about other people's experiences, this portion of the textbook just takes more effort and work so that helped him to know that.

Mine is around the same age and has a tendency to use LHS but I think that it is habit and not always stepping back to see what works easier. Sometimes he expands too early versus just leaving things expressed as factors because they easily simplify later. It's harder to see when you expanded something to a 6 digits.

[Noreen Claire]

8 hours ago, calbear said:

I found myself in a similar place, I was not convinced that my son was as solid as he could be when we reached ch.13. We actually went back over Ch.10-13 before moving forward with the rest of the book. I used Alcumus as the basis for the second pass through. His grasp was much more solid after the second pass through the material. Having read about other people's experiences, this portion of the textbook just takes more effort and work so that helped him to know that.

Mine is around the same age and has a tendency to use LHS but I think that it is habit and not always stepping back to see what works easier. Sometimes he expands too early versus just leaving things expressed as factors because they easily simplify later. It's harder to see when you expanded something to a 6 digits.

Thank you!

[gracefamilydoc]

I haven't read all the previous but we did Alcumus for review, also Dolciani if it was really shaky.  I wouldn't make a kid redo all of Algebra for a few shaky topics, especially if he's already done AOPS.  That would drive me nuts as a kid who was really good at math.  The only thing with Alcumus is you have to make sure you read the solutions in detail and not just do the ones you know and skip the ones you don't--that point was obvious to me, but not my kiddo.  I actually do them with my daughter (upon request).  That seems to help her to actually learn the material better than being fully independent.   Also, there is some reinforcement of skills as you move forward.

[kiwik]

On 4/10/2021 at 2:49 PM, daijobu said:

I always put the x on the LHS.  I'm a little discombobulated to see it on the "wrong" side.  I also like my chain inequalities to be increasing...unless we're comparing a variable with a number, then--you guessed it--the variable goes on the LHS regardless of the direction of the inequality.

Can he solve most of the Review Problems and some or most of the Challenge Problems?  If so, then I think he's good to continue with the textbook.  Learning from a textbook, IMO, is an important skill to maintain.  If he's able to do it now, I'd have him keep at it.  

I was taught to always have it on the left even if it means flipping the whole equation first.

[Not_a_Number]

14 hours ago, kiwik said:

I was taught to always have it on the left even if it means flipping the whole equation first.

That's kind of weird 😛 . 

[Drama Llama]

On 7/18/2021 at 7:14 PM, Not_a_Number said:

That's kind of weird 😛 . 

I don't know if I was taught that way, but it's what I always did.  When I'd copy out a problem to work it, I'd just copy it flipped if that's what made sense.  

[kiwik]

On 7/19/2021 at 11:14 AM, Not_a_Number said:

That's kind of weird 😛 . 

I think it is more about spacing on the page than anything else.  As an non student I do it however I want but as a student my instructors found it easier if everyone did the same.