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lewelma

Memorizing math facts

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I have a student who is 14 and really can't master his multiplication facts.  He is in school and will be marching lockstep with his classmates, so I can't change his curriculum.  He is a somewhat below average math student in integrated math of 9th grade Algebra/Statistics/Geometry. Without knowing his multiplication facts, his fractions and algebra are starting to be a problem. Next year he has a no-calculator algebra exam, so I have about a year to get them in his head.  Last year, he spent about 4 months with flashcards, but that just didn't do it.  I can sit with him and drill just 4 cards for 10 minutes and he still can't remember them. That is FOUR cards in TEN minutes, over and over and over.  Clearly, I need a better way.  My thought at this point is that I will need to link them through a joke, image, story, etc. I don't like having to do this as it will slow him way down in the future, but at this point I think that memorizing random number patterns is a no go. Open to suggestions.

Ruth in NZ

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Just curious — does he know his 10s?  His 0s or 1s?  His 2s or 5s?  

What about his addition facts?  His subtractions facts?

I would wonder if he knows his addition facts, or where he is on them?  

I think I would want to go back to addition facts, if that seemed like it might be fruitful.

 

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He has addition and subtraction facts, slow but there.  But I will ask him if he is actually counting up, or if they are from memory. Yes, he has 10, 0, 1, 2, but still struggles with 5s. 10s, 0s, 1s have obvious patter with nothing to memorize.  2s he does by adding.  5s require memory.

My kids used to play some video game with kill the monster and multiplication facts. Is that still around?  I don't know its name.

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I have done Reflex Math for math facts.  It has not been a full solution here but has definitely been helpful.  

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Times Attack is just flash cards in a video game format.  What you want is Times Tales and skip counting songs.  

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9 minutes ago, Terabith said:

Times Attack is just flash cards in a video game format.  What you want is Times Tales and skip counting songs.  

Yes! That is what I want.  But I think I will give Times Attack a go for a week and see if he is more motivated to practice.  I was never completely convinced that he was doing them daily at home.

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Worth a shot.  I have one kid who absolutely could NOT learn by memory work.  She still doesn't know her months of the year at 14.  She was also terrified of the background music in Times Attack.  But that would certainly be an easy fix if it works!  (Although, I have to say, Cat learned all her multiplication facts in 30 minutes with Times Tales.  But she's kinda weird in that she has an awesome memory for stories and songs and no memory for what she sees as random facts.)

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Both of my kids have good memories but don't really absorb their math facts super well, but they seem to do best encountering them in a meaningful problem...eventually. 

If he's visual, maybe cuisinaire rods with math fact games from Education Unboxed? http://www.educationunboxed.com/math-games-and-activities/

Is he good with quantities in general, or do you think he needs something like Ronit Bird?

I think factoring, factoring, factoring, factoring all kinds of numbers down to their primes is also really good for this--it's been one of our best ways to do facts here. You can do it all kinds of ways--with rods (video below), tree diagrams, etc. You do have to be more intentional about using numbers that break down to sevens and such, but that's not terribly hard. You can recombine the primes of a given number to find all their factors. Then you can write out the multiplication and division facts that go with the number you factored. 

My favorite thing about using factoring is that it associates a group of facts with a specific number. So, you can easily bring to mind a whole series of numbers that go with 48, for instance. Then, eventually you can make those associations for multiples of the larger numbers too. 

 

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I showed him Times Attack today, and got him to play it a bit.  He was very pleased and thought it would really help. So we will give it a go and see where we are at in a few weeks and whether we should switch to Times Tales.

I love the factoring idea. I've done some of that, but we are also on a school schedule to keep up with the class. So it is a balance of remediation and pre-set class work.  He is a slowish learner but very motivated, so is making steady progress.

 

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If he is 14 and can't keep the 5s multiplication facts in his head after significant studying, maybe you're looking at an LD of some sort.  Could he possibly get an accommodation for this?  It seems like a silly thing to hold up math advancement through algebra/geometry/alg2/etc.

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Oh, I definitely think there is some serious working memory problems with straight memorization of numbers, but he can memorize the geometry theorems so it is not across the board. But doubtful on getting accommodations.  He is only a little below average in maths so not nearly as needy as others.  But so far it is not holding him back in a major way.  Here in NZ, he can switch to qualitative statistics in 11th grade even if he fails the algebra portion of 10th grade math because he will pass the geometry, numeracy, and statistics portions. The qualitative stats program here is excellent, so that is my goal for him and I have already begun talking it up.

Edited by lewelma
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My DH (who double-majored in math and mechanical engineering in college) had trouble memorizing math facts as a child.  He said the facts gradually got memorized over the years through use.  Our eldest DD also had trouble memorizing math facts.  Before we started homeschooling, when she was required to take a standardized state test with no calculator, we did get one accommodation: she was allowed 10 minutes before test time to sit in front of the teacher and construct her own times table.  She was then allowed to use that times table for the test.  This let her do the adding to get to her times facts just once each, which sped up taking the test.

DD does have LDs, some not diagnosed until 5th grade, and some not diagnosed until age 17.  I recommend you get your teen assessed, as the information of what's going on with him/her can be invaluable.  Don't lose hope.  And tell your teen that there are plenty of mathy people in the world who have had trouble memorizing math facts.

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My husband has a bachelors degree in math and physics and a masters in physics.  He barely passed math every year until algebra, because he could NOT learn his math facts (addition, subtraction, multiplication, division).  I don't think he knows them to this day.  He knows some, but he pretty much calculates them all every single time he encounters them.  It's bizarre and inefficient, but his brain just doesn't retain math facts.  But he has absolutely no difficulties with higher level math.  Well, once he got to a couple courses in the final year of university, he found that level of theoretical math to be boring and tedious, since it wasn't applied to anything really.

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13 hours ago, lewelma said:

I love the factoring idea. I've done some of that, but we are also on a school schedule to keep up with the class. So it is a balance of remediation and pre-set class work. 

If you demonstrated, maybe he can do it on his own, particularly with rods. Then he could have a few "related" numbers to factor in between times you work with him (like one per day). If he doesn't know his facts that well, he might use a calculator to find all the factors and then write them down.

It's hard to balance, that's for sure! 

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The book Overcoming Difficulty with Number by Ronit Bird lays out all of the multiplication pre-skills, and I used that info to teach DS his math facts.  

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10 hours ago, AMJ said:

I recommend you get your teen assessed, as the information of what's going on with him/her can be invaluable.  Don't lose hope.  And tell your teen that there are plenty of mathy people in the world who have had trouble memorizing math facts.

 

Not my kid. He is a kid I tutor.  I doubt his parents will spend the money to get him assessed.  He is fine with a calculator, and can switch to qualitative statistics with the quantitative element using a calculator in about 1.25 years. So my goal is to keep him motivate in math, doing well in what he does best at, and remediate his facts. If he doesn't get them, and fails the algebra test, it doesn't matter.  NZ is not America.  NZ recognizes that all kids need math, but algebra is not the end all be all. He can fail algebra and still move forward in math in 11th and 12th grade because of the way the national curriculum is designed.  

I helped a discalculia kid through 12th grade statistics with a calculator. This kid at age 17 could not subtract 9-7 with a tally chart. And when she tried it took her 2 minutes to get 3. I got her through 12th grade math because we used the calculator as a tool.  So if this new kid I'm talking about can't get his multiplication facts down, I'm not worried.  I will make sure that he continues to see himself as a mathy kid who has analytical skills, and just needs a calculator to do algorithmic skills.  

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Have you tried having him sing the facts? Not every 14 year old boy would be game for that, but there are a variety of multiplication fact tunes out there or you could make your own.

Music is an excellent memory trigger for most people.

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Ds learned his math facts at 13. We hit it from every direction for years and years. Ronit Bird. Education unboxed. Drill games. Math families singapore math style.

The thing that worked was memorizing strings of numbers---for whatever reason 6x7 couldn't stick, but memorizing 6,12,18,24,30,36,42 did.....  We started with 10s, then did 5s, then 2s, and branched up.

My point is, it's possible to find something that works even when it's very difficult. 

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Did anyone mention Tang Math? He has charming workpages and they aren't too bad. He's doing a series of workshops on math intervention. I'm not sure his ideas are so lightning bolt, but the pages really are charming. Here's a link to his sample week pack 1, grade 4, and scroll down to Kakooma. See how a child could look at those numbers and make friends with them, give identity and mass and sense to them. https://tangmath.com/products/subscription  Changed mind, here's the overall link. Try the sample for Tangy Tuesda page 1 and look at Kakooma. Several of the Tangy Tuesday pack 2 pages would be good. 

So I'm using Tang stuff with ds and like it a lot. It's kind of different, interesting, makes him think. I bought all the packs for multiple grades and honestly I just toss the pages that can't work due to his other disabilities. Like I'm not going to slave over word searches and crosswords with him, no matter how witty they are, lol. Ok pack 3 has some of my FAVS, my absolute favs. And I don't know your student, but maybe you can ease him into these pack 3 pages, backing up if necessary, and get them to work, kwim? You really have to think and make friends with the numbers. 

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Old topic, but out of curiosity, how many "shortcuts" does he know? Like, if he doesn't remember, does he freeze up, or does he have ways to figure it out without just skip counting all the way up (which is terribly inefficient)? 

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Well, this kid can't really remember *anything*. Just a really really poor memory. He is fine with a calculator, so we are focusing on using it as a tool so that he can move forward in maths.  There is one national exam he has to take that is no calculator, but if he fails it, he can still move up in qualitative stats.  So not the end of the world. 

I've seen it all in my many years of tutoring. Some times it is just not worth the fight. He is currently playing Timez attack, so we will see if it will help.

I will also say that my older boy had a *terrible* time memorizing his multiplication facts.  We worked on it for 3 full years. He was still learning them when he was working independently through AoPS algebra doing ALL the problems, as in every single one. The solution was 3 times per day - breakfast, lunch, and dinner -- for 4 months. He just needed a LOT of repetition. There is NO connection between math facts and mathematical thinking. None.

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4 hours ago, lewelma said:

Well, this kid can't really remember *anything*. Just a really really poor memory. He is fine with a calculator, so we are focusing on using it as a tool so that he can move forward in maths.  There is one national exam he has to take that is no calculator, but if he fails it, he can still move up in qualitative stats.  So not the end of the world. 

I've seen it all in my many years of tutoring. Some times it is just not worth the fight. He is currently playing Timez attack, so we will see if it will help.

I will also say that my older boy had a *terrible* time memorizing his multiplication facts.  We worked on it for 3 full years. He was still learning them when he was working independently through AoPS algebra doing ALL the problems, as in every single one. The solution was 3 times per day - breakfast, lunch, and dinner -- for 4 months. He just needed a LOT of repetition. There is NO connection between math facts and mathematical thinking. None.

 

Yeah, I wasn’t arguing there was. I was just wondering if there’s a much smaller set of facts he could memorize and then use, say, the distributive and associative properties, assuming he’s fluent with them. That seems to be how my daughter manages, although she has a good enough memory that I’m sure she’ll actually successfully memorize it soon enough. 

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16 minutes ago, square_25 said:

I was just wondering if there’s a much smaller set of facts he could memorize and then use, say, the distributive and associative properties, assuming he’s fluent with them.

Yes, this is what RB does with scaling. You're not crazy, but odds are he's already figured that out.

And no, it's no guarantee the memory will come. Didn't for my dd. She stayed crunchy a LONG time. I went to college not knowing some of the upper facts and I was taking calculus, organic chemistry, etc., lol.

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10 minutes ago, PeterPan said:

Yes, this is what RB does with scaling. You're not crazy, but odds are he's already figured that out.

And no, it's no guarantee the memory will come. Didn't for my dd. She stayed crunchy a LONG time. I went to college not knowing some of the upper facts and I was taking calculus, organic chemistry, etc., lol.

Yeah, I was just wondering if that could get him adequately fast without as much memorization. But maybe not. 

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35 minutes ago, square_25 said:

Yeah, I was just wondering if that could get him adequately fast without as much memorization. But maybe not. 

Maybe the problem is the "fast" haha. At some point, low processing speed is still low, even when something is in there. And my dd had poor word retrieval scores. So to pull out words (talk about her math) while processing while using working memory while learning something was just horrible. It was fatiguing, slow. With my ds, his language drops, like dd's did, sigh, but at least I recognize it now and know what is happening. 

Well that's a discouraging, non-optimistic thought, lol. I've just been on the sucky, this isn't going to fix and only gets harder because that's how it really is end. That's where accommodations kick in. Lower work load, more calculators, medication, medication, etc.

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Just now, PeterPan said:

Maybe the problem is the "fast" haha. At some point, low processing speed is still low, even when something is in there. And my dd had poor word retrieval scores. So to pull out words (talk about her math) while processing while using working memory while learning something was just horrible. It was fatiguing, slow. With my ds, his language drops, like dd's did, sigh, but at least I recognize it now and know what is happening. 

Well that's a discouraging, non-optimistic thought, lol. I've just been on the sucky, this isn't going to fix and only gets harder because that's how it really is end. That's where accommodations kick in. Lower work load, more calculators, medication, medication, etc.

Yeah, maybe I don’t have enough experience with this. For the kids I’ve worked with so far, hooking ideas to things they can verbalize helps.

You can also access those properties visually, though. I have no idea if that’s doable or not here. Just brainstorming: only so much I can say without being able to experiment with a specific kid :-).

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8 hours ago, square_25 said:

 

Yeah, I wasn’t arguing there was. I was just wondering if there’s a much smaller set of facts he could memorize and then use, say, the distributive and associative properties, assuming he’s fluent with them. That seems to be how my daughter manages, although she has a good enough memory that I’m sure she’ll actually successfully memorize it soon enough. 

Oh I know you weren't. Sorry that I made it sound like that! Clearly, I was too tired last night.   I was just writing for the bigger audience because there are lots of people who thing the multiplication facts = math.  

Basically, I have limited time with this kid. Just one hour per week, and he is 14 and about to go into 10th grade integrated math - algebra, geometry, statistics - with required national exams.  So from my point of view, if memorizing his facts is too time consuming for him, I'm going to hop ship and focus on what he can do.  If he fails that algebra exam (the only one without a calculator), he can still progress in qualitative statistics in 11th grade which is what I'm expecting to do. He doesn't have the brain power or interest to go into the calculus path, so my goal is to get him able to do basic algebra with a calculator. It will be enough.

I'll ask him in more detail next week what strategies he does use for circumventing recall.  I think it is a calculator. 🙂  

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2 hours ago, lewelma said:

Oh I know you weren't. Sorry that I made it sound like that! Clearly, I was too tired last night.   I was just writing for the bigger audience because there are lots of people who thing the multiplication facts = math.  

Basically, I have limited time with this kid. Just one hour per week, and he is 14 and about to go into 10th grade integrated math - algebra, geometry, statistics - with required national exams.  So from my point of view, if memorizing his facts is too time consuming for him, I'm going to hop ship and focus on what he can do.  If he fails that algebra exam (the only one without a calculator), he can still progress in qualitative statistics in 11th grade which is what I'm expecting to do. He doesn't have the brain power or interest to go into the calculus path, so my goal is to get him able to do basic algebra with a calculator. It will be enough.

I'll ask him in more detail next week what strategies he does use for circumventing recall.  I think it is a calculator. 🙂  

 

From my perspective, I'd say that the distributive and associative properties pay off in algebra, anyway, even they don't help him with recall. And they are the easiest to understand with integers (you have both verbal and visual access to them.)  So if I were tutoring him, I'd definitely try spending a bit of time on that. 

On the other hand, an hour a week is really not a lot, and I imagine there are lots of other things he needs help with as well. So i can see why you'd like him to work on this on his own time. I wonder if there'd be a way to get him to use these properties on his own time as well... Hmm.

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I just found out 2 weeks ago that even though I've been working with him on memorizing the facts for 8 months, he is using a calculator in class, so not reinforcing his memorizing.  I was kind of surprised, but perhaps I shouldn't have been.  Sometimes you don't know what questions to ask, and clearly I should have told him to stop using his calculator. oops. But since they were working on measurement unit, he needed it; but when he switched back to algebra, he should have stopped using it.  But the ok then, but not ok now can be confusing to a kid. 

The problem is that we are walking into the equivalent of Algebra 1 (2 exams), Geometry, Statistics, and Numeracy all in the same year.  So basically the culmination of 3 years of study tested in the last year.  He needs to pass for his belief in himself.  So it is probably a better use of my time to get him to pass the other 4 exams that allow a calculator, and keep him doing algebra but not expect to pass the non-calculator one.  Kind of a strategic choice.  

I should add that there is no grade inflation here, so 20% of all students fail any one exam.  These exams are HARD. 

Edited by lewelma
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1 minute ago, lewelma said:

I just found out 2 weeks ago that even though I've been working with him on memorizing the facts for 8 months, he is using a calculator in class, so not reinforcing his memorizing.  I was kind of surprised, but perhaps I shouldn't have been.  Sometimes you don't know what questions to ask, and clearly I should have told him to stop using his calculator. oops. But since they were working on measurement unit, he needed it; but when he switched back to algebra, he should have stopped using it.  But the ok then, but not ok now can be confusing to a kid. 

The problem is that we are walking into the equivalent of Algebra 1 (2 exams), Geometry, Statistics, and Numeracy all in the same year.  So basically the culmination of 3 years of study tested in the last year.  He needs to pass for his belief in himself.  So it is probably a better use of my time to get him to pass the other 4 exams that allow a calculator, and keep him doing algebra but not expect to pass the non-calculator one.  Kind of a strategic choice.  

I should add that there is no grade inflation here, so 20% of all students fail any one exam.  These exams are HARD.

 

Yeah, I totally get that "triage" feeling. On the one hand, you kind of wish you could start from scratch, on the other hand, you have finite time and you don't want anyone to fail their tests or exams.. 

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1 hour ago, lewelma said:

he is using a calculator in class, so not reinforcing his memorizing. 

I wouldn't assume this. For my dd, the key was to ponder whether it was faster (or less fatiguing) to use the calculator or just as fast to pull it from her head. We would do her math together and I would ask that, which way is faster, just to see if she'd stop and think about it. But either way, her test scores on standardized testing still went up.

Does this dc have undiagnosed or unmedicated ADHD? The low processing speed can go with that. My dd's math scores on the ACT went up *significantly* when she started ADHD meds. 

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2 hours ago, lewelma said:

Story of my life. 

 

Yeah, you kind of do your best and cross your fingers, I know how it goes.

With my sister (who is my main remediation experience), it was super helpful to have the summer to work with her. That actually let us do extra stuff and build understanding. During the year it was almost always a dead loss. And the frustrating thing was that it really WAS a loss. She never remembered anything I told her from when we were studying for tests (even though I was clear and thorough and she seemed to kind of get it at the time), whereas the summer "extras" stuck. 

But hey, she did well on her SATs and got good math grades and is going to a good college. So it's worth it, really. Just frustrating. 

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4 hours ago, PeterPan said:

Does this dc have undiagnosed or unmedicated ADHD? The low processing speed can go with that. My dd's math scores on the ACT went up *significantly* when she started ADHD meds. 

No. This boy is the most calm, focused child I have probably ever taught. He does have dyslexia which can definitely impact facts memorization.

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5 hours ago, lewelma said:

dyslexia which can definitely impact facts memorization.

Maybe the brain structures could help you think of more ways to hit them? Supposedly (if you believe the Eides' tiny samples, snort) dyslexics should have widely spaced mini-columns in the brain, resulting in a circuitous path of learning that makes unusual connections. So my dd, who enjoyed circuitous learning and narrative, seemed to do well with math that brought in narrative. Like give the numbers meaning through stories. Winding side routes.

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8 hours ago, PeterPan said:

Maybe the brain structures could help you think of more ways to hit them? Supposedly (if you believe the Eides' tiny samples, snort) dyslexics should have widely spaced mini-columns in the brain, resulting in a circuitous path of learning that makes unusual connections. So my dd, who enjoyed circuitous learning and narrative, seemed to do well with math that brought in narrative. Like give the numbers meaning through stories. Winding side routes.

Definitely.  That is my next option if timez attack is a bust.  

We have time, the exam without a calculator is next September.

Edited by lewelma
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On 10/2/2019 at 8:14 AM, square_25 said:

Yeah, I was just wondering if that could get him adequately fast without as much memorization. But maybe not. 

It might if processing speed is reasonable. My one kiddo is quite fast with his circuitous workarounds. The other (dyslexic) tends to be fine with his workarounds but then either lose WM due to slower processing, or he writes it down wrong, sigh. But my non-dyslexic kid did get faster and faster, and he's solid with calculations even with his workarounds. He might have even eventually learned the facts. I haven't asked because he seems to be fine. 

On 10/2/2019 at 4:26 PM, lewelma said:

I'll ask him in more detail next week what strategies he does use for circumventing recall.  I think it is a calculator. 🙂  

So, does he have some muscle memory? I wonder if you could harness that on a paper calculator. You could give him a sheet that looks like his calculator, have him "enter" the numbers by pushing the fake buttons, and then still retrieve the math fact for practice. My DH is a big muscle memory person; if he retrieves a phone number, he does so by entering it into the air like he has a keypad in front of him. 

On 10/2/2019 at 10:09 PM, square_25 said:

With my sister (who is my main remediation experience), it was super helpful to have the summer to work with her. That actually let us do extra stuff and build understanding. During the year it was almost always a dead loss. And the frustrating thing was that it really WAS a loss. She never remembered anything I told her from when we were studying for tests (even though I was clear and thorough and she seemed to kind of get it at the time), whereas the summer "extras" stuck. 

I didn't have trouble with fact retrieval, but I had a year of totally worthless Algebra II instruction. The teacher had ONE way to do everything, and my brain didn't do it that way. Ever. I suspect the teacher couldn't do it another way vs. had a big preference about it. Even mathy kids often struggled in her class. Anyway, my friend's mom tutored me, and I pretty much lost everything she taught me; it was SO MUCH WORK to understand it one way and then turn around and somehow translate it back into a presentation that pleased the teacher. It was a total loss. I relearned some of my Algebra II concepts taking Trig-based physics later in high school (where the word problems made a heck of a lot more sense too, lol!).

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