Retention and internalization

[ScholarlyP]

DD will be in 5th grade. She seems to grasp ELA and math concepts well when we go over them. For instance, after watching a Khan Academy video on exponents, I pause it to ask her questions and then she does the practice problems accurately. However, the next day, when she encounters similar problems in a different textbook like AoPS, she might struggle and need hints to proceed. Even after receiving hints, she sometimes needs help again a few days or a week later with similar problems. I’m unsure if she fully understands the concepts or how to help her retain them better. Although she can explain her answers well when I ask her, she often still needs hints and review. This makes me hesitate to move on to the next topics. Has anyone experienced something similar?

[Rosie_0801]

Has this been a problem all along? Or is it fairly new?

[8filltheheart]

How many practice problems and how many days for a new concept?

There is a Montessori 3 stage concept for little children and learning: naming, recognition, and recall. (Naming is when you teach them what something is. Think about when you would pt to an object and say the word when your dd was a baby.  Recognition is when they can select out of a group but can't name it themselves. Recall is when they can recognize and name it independently.) It helps to think in similar terms even with older kids. Mastering a concept at the "recall" level doesn't happen after 1 exposure. Depending on the child, it might take multiple repeated practice sessions to master recall independently.

AoPS is not an approach that fits all learners. I have one child for whom it was a perfect fit. My other 7, no. It could be as simple as your child needs a program with lots of reinforcement of concepts for mastery.

Also, a 5th grader using AoPS is advanced. The lowest level AoPS bk is prealg. Many 5th graders are not ready for that level of abstract concepts. It has nothing to do with anything other than natural brain development. 

You might try some different approaches. My AoPS loving ds completed MUS's alg and geometry bks at age 10. They were accessible. Several of my kids completed them (both in a single yr) in 5th or 6th.  I use them as pre-alg and pre-geo. They gave them time to mature into algebraic thinking. But only ds thrived with AoPS. My others used more traditional direct teaching textbooks. (Foerster is my favorite algebra author.)

Edited July 28 by 8filltheheart

[HomeAgain]

Khan to AoPS is like going from learning to make a sandwich to expecting a fabulous souffle.  That's just an evil level of discrepancy between the two.  Khan is straightforward, simple, and direct.  AoPS is meant to make a student think about vocabulary and intent and puzzle out a solution.

Don't use Khan.  Use Alcumus if you're using AoPS.  But you should be doing the problems with your child as well so you can see where the issues might be.

[daijobu]

16 hours ago, ScholarlyP said:

 

However, the next day, when she encounters similar problems in a different textbook like AoPS, she might struggle and need hints to proceed. Even after receiving hints, she sometimes needs help again a few days or a week later with similar problems. I’m unsure if she fully understands the concepts or how to help her retain them better. Although she can explain her answers well when I ask her, she often still needs hints and review. This makes me hesitate to move on to the next topics. Has anyone experienced something similar?

We did not experience anything similar, but we did not use Khan, and both my kids and I are mathy.   I was very hands on with my teaching, working closely with them every step of the way.  (I know others students on this board worked through AoPS more independently than we did.) 

When you use AoPS, I recommend you (as teacher):

1. Work through the introductory problems together with your student.  (Prepare them in advance if you need review.)
2. Assign the Exercises at the end of each section as homework, and immediately upon completion explain any problems she could not solve independently.  If you need to do this one problem at a time, so be it; I did this only after my students attempted all the problems.
3. Set aside 1-3 days for end of chapter Review Problems and 1-3 days for end of chapter Challenge Problems.  She should attempt all of them; there are few enough routine problems in AoPS that she needs all the practice she can get.  At the end of each day's math work, review and explain any problems she could not solve.  

Immediate feedback is critical for novices, and exponents can be so confusing.  It's much more difficult to correct a student's misunderstanding than to learn it correctly in the first place.    

I see that in the AoPS pre-algebra text, the following chapter covers NT which will be light on exponents.  You can finish chapter 3 then return to the Review and Challenge Problems for chapter 2 and have her try those again.  

I agree alcumus is another good source of practice problems.  

As others have mentioned AoPS isn't everyone's cup of tea, so if it isn't working, consider an alternative math curriculum.  

[Tanager]

Nm

Edited July 29 by Tanager
Sleep deprived, must of misunderstood the qu.

[ScholarlyP]

In the spring, we were too busy to work with her one-on-one, and she had completed Beast Academy Level 4. Based on her request and after passing a placement test, we allowed her to start the AoPS Pre-Algebra 1 online class directly. She enjoyed gathering pins, which indicates she is quite young. 🙂 

We observed that it took her some time to complete Alcumus and the assigned homework. Despite this, she managed to finish her work by reviewing the textbook, asking questions during office hours, and receiving some help from us. 

We are taking a break this summer, but she plans to take Pre-Algebra 2. To prepare, we asked her to take the placement test for pre-algebra 2 and noticed that she has forgotten several topics from Pre-Algebra 1. We believe that if she can refer to the textbook, she would answer more questions correctly. However, to move on to Pre-Algebra 2, we think that she needs to demonstrate accurate and independent problem-solving skills. 

We are now reviewing each chapter with her, including both review and challenging problems. Indeed, her performance on Chapter 3 is better than on Chapter 2, which covered exponents.

Based on the suggestion, I am considering having her use Alcumus as well, but the issue is that I cannot track which problems she has completed especially those incorrect ones. Any alternatives? IXL?

 

 

 

[8filltheheart]

I suspect her struggles are gaps. Jumping from BA 4 to AoPS pre-alg and allowing her to use the book to complete work while continuing to advance forward is only going to weaken her abilities.

Here is an example. I can solve independently math through about the first 1/2 of alg 2. (I took math through cal way back in the 80s, but I definitely do not remember it.) But, I can successfully help my kids beyond that. (I have adult kids who majored in chemE, physics/math.) How? I can look at problems in the textbooks and solutions in the solutions manual, work backward to see the steps and then apply them to work forward. BUT,  in no way could I actually solve the problems myself. It is gaming the system....it is how so many kids manipulate online programs for grades without actually learning.

There is no bonus prize for rapid acceleration without mastery. (FWIW, I have 8 kids of widely varied abilities. One of my ds's graduated from high school having completed multivariable, diffeq 1&2, and either linear alg or real analysis (I can never remember without looking at his transcript.) But, he never skipped anything other 2nd grade math (and that was only bc he had taught himself all of his multiplication tables while playing with Legos.)

Gapping creates problems you are going to constantly have to go back and try to find and support.

ETA: AoPS placement tests are noted for being too easy to be fully representative.

Edited July 29 by 8filltheheart

[EKS]

My experience, both with my own students and myself, is that learning math is an iterative process that involves far more forgetting than it does remembering.  You're doing ok if when you encounter the thing again it takes less time to learn it, or, even better, you say "Oh yeah!" and that is that.

So, I would argue that this idea that there are gaps that once filled will make everything come together is not quite right.  There will always be gaps.  The great thing about homeschooling, the kind where there is a human in the room interacting with the student each step of the way, is that you can detect the gaps and fill them on the fly.  Eventually students can figure out how to fill their own gaps, but I would not expect this of anyone who isn't an advanced math student.  I certainly wouldn't expect it of a sixth grader.

 

 

 

[daijobu]

8 hours ago, ScholarlyP said:

In the spring, we were too busy to work with her one-on-one, and she had completed Beast Academy Level 4. Based on her request and after passing a placement test, we allowed her to start the AoPS Pre-Algebra 1 online class directly. She enjoyed gathering pins, which indicates she is quite young.

The one-on-one instruction is critical here.  Plenty of students can study AoPS independently (just search the WTM archives), but that is beyond the reach of many students including mine.  

9 hours ago, ScholarlyP said:

Based on the suggestion, I am considering having her use Alcumus as well, but the issue is that I cannot track which problems she has completed especially those incorrect ones. Any alternatives?

Maybe your student could return to BA Level 5?  If she's in grade 5, she has plenty of time to complete the elementary levels before continuing to the upper levels of AoPS.  There's a lot of overlap between BA level 5 and PreA, and in fact, the Level 5A book also covers exponents.  Also Level 5D.

One reason I don't recommend Alcumus as readily as other parents is that the problems are presented one at a time, and students are afford something like 2-3 attempts to solve, or give up.  The full solution is presented on screen, but I personally find screens full of numbers and text difficult to parse and there is the ever-present temptation to just move on to the next problem instead of learning from the experience.  

[BusyMom5]

8filltheheart is correct in her assessment- I think you jumped ahead too much.  Go back to BA 5.  Math isn't a race, it's more like building a skyscraper.   You need to build a strong foundation and complete each step thoroughly.   

[maize]

I'll add another voice for not approaching math as a race ahead and avoiding gaps.

I had very disconnected education growing up; my family made international moves frequently,  each time to a different country. Math is quite intuitive to me, but all the moving between school systems left significant gaps such that I really struggled by the time I got to high school. There were no similar problems with other subjects because they aren't as cumulative in progression as math.

Puberty also does strange things to kids' brains; for girls, 5th grade is well within the zone where brains and bodies are busy with growth and development and mental culling and rearrangement. I think some degree of brains acting like a sieve is pretty normal at that stage.

I'd pull back and do something else for math for now. Beast Academy 5, or a different program entirely. Math Mammoth is very solid and builds a good conceptual base.

[Clemsondana]

I've got a kid who also started AoPS pre-A in 5th grade, and trying to move through it at the normal 'one lesson/day' pace is probably my biggest homeschooling regret.  In some ways, using AoPS at all is a regret, although it ultimately turned out OK and the Number Theory and Probability books were my kid's favorite math.  We made the adjustment to move very slowly, taking 1.5 years each for pre-A and A, and not doing every challenge problem.  People say you miss the good stuff, but frustrating my kid is not good stuff so we made the choice that was right for us.  But, this kid also learned a lot with Life of Fred, and had I known about it sooner I probably would have gone the Arbor Press/Jousting Armadillos route, which involves exploration without as much challenge.  And, I tried the arbor press route with my younger in 6th and it turned out that kid made it through the preA in 6th but didn't understand A in 7th.  We made another pass using a traditional program in 8th that was successful.  AoPS and LOF were both good for older (and very different - kid really benefitted from the different presentations) but only because we did preA and algebra for such a long time.  And my younger would not have done well because both have so few practice problems.  

All of that is to say that the program may not be a good fit, or your student may need to move more slowly.  Or there could be a developmental gap.  I was in an accelerated program in school and really struggled to understand algebra (after finding pre-A to be easy).  When I hit algebra 2 after taking geometry, I once again found it easy.  I really think I was just not developmentally ready, or at least not ready to do it the way that it was being taught.  Maybe moving more slowly, or using a different program, would have made a difference.  Your student may have a gap, such as not being solid with fractions.  My younger used Life of Fred's Fractions and Decimals book at some point to help solidify those concepts.  And your student may just need more practice and would benefit from a program that has less complex problems and more frequent review.  AoPS problems can be so complicated that students lose sight of what they are supposed to be learning.