## Sunday, March 30, 2014

### Retests.

I agree, mostly, which is why I have retests.

However, many students need incentive to study now; instead of "I'll wait til after the first try at test. Then, I'll know what's on it." That's test-prep that won't last, not understanding.

Additionally, I do have other things to work on. Take algebra. Section 3 is writing and graphing linear equations. Section 4 is systems of linear equations.  Johnny can't do 4 if he truly doesn't understand 3.

I get the idea that students take different amounts of time to master material, but at some point, it is better to tell him that retaking the course would be a better option than retaking every test.  I don't mind if he completes algebra I in two years.

That image is being very disingenuous, though. Those exams don't lead to more learning ... they're the end-of-course exit exam, the final exam, the high-stakes test that so many reformers hate.

### Common Core math thing, round two ... a mathematician.

I was floating around the Internet and came across The Mindful Mathematician's A Letter to Frustrated Parents
I was never taught to make sense of numbers, I was taught one way to solve every problem, every problem had ONE way, memorize these steps and you will be able to solve this problem.  Sorry if you can't remember the steps.  This is how we do it.  I was robbed.  I was not taught to persevere and try to make sense of the problem... who cares what it means, here's how you do it, just do this.
I would feel sorry for you, but I cannot accept that this is truly what happened to you in school. As much as I get irritated by some of what I hear about elementary school teachers, I cannot believe that anyone took this approach.

You are flat-out misrepresenting what the "traditional" approach was in order to bolster support for the New way of doing things - to the exclusion of the algorithm. "I call Shenanigans."
Hold on, why am I crossing out this number and changing that one?
Because you don't have enough to take away.  Just do it!
But wait, I have 453 and I'm just trying to take away 17. I think there is more than enough to take away.
No you can't take 7 away from 3... Just cross out the 5. Just do it!
But wouldn't 3 take away 7 be negative...
NO! You can't take a bigger number from a smaller number, sit down, JUST DO IT MY WAY!
Bullshit. Or, to put it more kindly, IF this is a true and accurate transcript of the conversation, this teacher is not very good and probably would teach everything in the same tyrannical fashion. Rather, it sounds like the kid with a poor understanding and this is the "excuse" for why.
"Hold on, why do I have to have common denominators? "Because you can't add apples and oranges! Just do it"
"I was wondering... why do I have to flip the fraction upside down if I'm dividing?" "It's not your place to reason why, just invert and multiply!  JUST DO IT!"
Elementary teachers have enough problems teaching math, without your strawman argument and fairly obvious projection.

Second, isn't it interesting that you claim this fictional teaching method is the reason that all of our students hate math, yet you are the first counterexample among many ... most math teachers included. If you are looking for a cause-effect relationship, you've disproved it.

The probable causes for the lowered "love of mathematics" are the lack of enjoyment of the subject by those teachers, the nervousness and trepidation with which they approach math, and the over-reliance on discovery methods of teaching and the "Guide on the Side, not a Sage on the Stage."
The "new" methods you're seeing are not being taught.  They are methods that students naturally invent.  Just the way that mathematicians invented them before our formal mathematics system existed.
That is the crux of the problem. Too much of teaching now is centered around letting the kids "discover" a way of their own. Having the kids to "discover" their own way does not create "better understanding", it merely forces them to re-invent the wheel ... and then go through the trouble of learning. (I guess this is the next post.)

But I digress.

Students find comfort in tried and true methods that work without major thinking. They'll accept the  struggle with any method at first, because it is new. Once learned, there is a sense of pride of ownership, of knowing that they've got something to call their own, something that eliminates the need to count by ones on their fingers. They could subtract 37 from 63 by counting but it's slow, so we give them new methods. One in which you count up like a shopkeeper making change and the other, the "algorithm."

The algorithm, originally developed for simplicity, required the student subtracting 37 from 63 to "borrow 1 ten from the tens place to make 13, and 13-7 is 6. Then 5-3 is 2. Ah, 26." That requires understanding of place-value. That's very important.

The "new method" takes a different kind of thinking. "Add 3 to get to 40. Add 23 to get to 63. Ah, 26." This thinking is also very important.

These two methods are not mutually exclusive in a student.

For 63-37, method 2 works better. For 8569 - 6325, the first one is superior because there's no cancelling and because the numbers are larger.
When people say that "borrowing" is unnatural, I present the addition to the right. Go.

Did anyone add 3 to one of the 27s to get to 30, then add 24 to get to 54? Probably not. That's the method for subtraction, done in reverse.

Did you add the twenties and then add the sevens? 20+20 = 40 and 7+7=14. Ah, 54." Maybe. Depends on how old you are. For 27+27, it's the most efficient.

More likely, you added 7+7 = 14, carry the 1; 1+2+2 = 5; Ah, 54.

If we're okay with "carry the one" why are we so all-fired-up about "borrow a 1" when subtracting?
Should kids be able to do it all three ways? Yes. It's math, and math is fun.

I'll leave you with this final example, from our intrepid mathematician -- right at the top of the page -- that exemplifies the best time to use the old algorithm.

Students must be able to do both. (or all three, or four).
Which they choose is up to them.

Why do we have so much trouble with that?

## Wednesday, March 26, 2014

### The Subtraction MathWars

I'm sure everyone has seen this "letter" from a"frustrated parent" who claims that despite having a degree in "electronics engineering", can't figure out the child's homework.

I call "Shenanigans", both on the letter and on the responses.

First, we must accept that the "parent" can't read instructions, is pre-disposed to being an asshole over the ways in which our children are taught math, and is probably not all that capable of understanding basic principles.

In addition, when claiming that "simplification is valued over complication", he failed to note that , in business, "Completing the Assigned Task" is given far more weight than "Over-simplification and pedantry."

... but I digress.

In the "Bad Old Days", I recall many instances in which people browbeat math teachers with the anecdote, "I went to the store and bought \$13.82 of stuff and the kid behind the counter couldn't make change for a \$20. You teachers need to teach them the basics."

The standard algorithm vs. The New Way (which isn't so new; it's "Making Change") - look at that problem up there. Pretend you just bought something worth \$111 dollars and you handed the clerk a \$427 check. How much money do you get back? Follow the little jumps and imagine someone slapping bills into your hand. Makes a lot of sense now, doesn't it?

So here's what needs to happen: Kids need both.

Sorry, Reforministas, the standard algorithm is more useful and easier sometimes.
Sorry, Ostrich-Headed Blowhards, the "New Way" is more useful and easier sometimes.

Let's face facts.
```  427
- 316
```
is much easier when done vertically. No borrowing, no hassle.

Even a problem that contains a "borrowing" is often easier done with the standard algorithm. It's more compact and it's cleaner. 492 - 327, for example. On the other hand, the "Counting Up or Down" is easier when you are close to certain values, such as the infamous 30001 - 29999 question.

A professor suggests that anything that can't be done with the New Way should be done with a calculator or WolframAlpha, but I disagree completely. He provides research that states teaching algorithms to young elementary students is harmful. I read the studies but I don't agree that we should NEVER teach the standard algorithm and borrowing; I just feel we should be more intelligent about it.
1. Kids should eventually be comfortable with both ways.
2. Timing is critical. Maybe the New Way should be taught before the Standard Algorithm.
3. Also, be more willing to MAKE kids learn the SA, even if it's temporarily painful. If they understand place value and the counting up and down, they can learn the SA.
4. Be less anal-retentive about the size of the problems and the difficulty of the subtractions (7 digit from 8-digit is extreme).
5. Stop insisting that the calculator is the Deus Ex Machina of mathematics. It is a tool and should be used to make already-understood work easier, but not if it replaces the understanding with No-Think Monkey Push-Button
Teach them both and then let them choose. Each method has advantages and each has disadvantages.

We can't be doing this:
DC: "Go ahead, use your standard algorithm to compute: 4,000,002 - 3,999,999"
Me: "This problem is better solved by counting up. 41036 - 28569 is easier solved by subtraction algorithm.
DC: "That is better solved with a calculator. #justsayin"

No. NO. Goddamn it, NO.

 "There's no longer a reason to memorize a mindless math algorithm." What if it's NOT meaningless?
Jumping to the calculator the instant the problem gets slightly weird can only lead to disaster for students. If I gave the student four hundred of these, I'd expect him to cut and paste into a spreadsheet or WolframAlpha, but one problem and he gives up and reaches for a calculator?

"There's no longer a reason to memorize a mindless math algorithm. There's plenty of reasons to understand thinking behind them." I agree with that. Proper teaching starts with understanding ... but then, once you understand the method, the algorithm is no longer meaningless; memorization occurs organically. The algorithm NEEDS understanding of place value.

When I reply that "Algebra, messes it up for many: 410x - 36y - 285x + 69y, as does calculator madness" (see the madness) and the response is, "Thankfully WolframAlpha", well that's when you know someone is not dealing from the top of the deck.

Yeah, Wolfram gives you the answer, coupled with

How in the bloody blue blazes of hell is that useful to someone who can't subtract?

## Friday, March 21, 2014

### CK-12 Stealing Images Again

NPR.org's Planet Money ran "74,476 Reasons You Should Always Get The Larger Pizza" and graphed things out pretty nicely.

Then CK-12 took it, converted the format to a lossy jpg, branded it with their own logo and has been reposting it as if they had done the work and owned it:

If you're going to use an image on a webpage, very few people will mind. If you go to the trouble of taking the picture and changing it and then claiming it as your own ... that's not cool.

## Thursday, March 20, 2014

### Leveling the Playing Field for the SAT.

I got the email the other day:
Exciting news: Khan Academy is partnering with the College Board so that all students who want to go to college can prepare for the SAT at their own pace, at no cost. The College Board just announced that they’re redesigning the SAT for 2016, and we’re partnering with them to make free, world-class prep materials.
I'm underwhelmed. There are thousands of SAT practice sites around the Internet, some good and some not-so-good. There are thousands of SAT practice videos on YouTube, you just have to look. In my mind, the one thing that Khan is providing is a moderately well-organized list of boring-ass videos.

By spring 2015, you’ll have access to state-of-the-art, interactive learning tools that give you deep practice and help you diagnose your gaps. All of this will be created through a close collaboration with the College Board specifically for the redesigned SAT.
So they will need at least 12 months to put this together. Seems like a lot of time spent on a test, but maybe it will be worth it. Screw you if you need anything before our planned roll-out date, of course, but Khan Academy isn't about the student.
Our goal is nothing short of leveling the playing field for every student taking the SAT, so please help us reach as many people as possible.
There's the rub. You can't level the playing field with a test-prep course. If test-prep could do that (and it doesn't), it would indicate that a few hours of knowledge-blitz is enough and would validate all those thousands of dollars spent on Kaplan and Princeton Review and everyone else in this test-prep sucker's game.

But test-prep helps, right? No, not really.  What 10 weeks of 4 hours a week test-prep will do is ease student tensions, help them focus, warn them of some of the obvious pitfalls, advise the students of "tricks" the test makers tend to play. This amounts to about 50 points "improvement" over untrained students ... which sounds like a lot, but it's well within one standard deviation, and about what happens when the student takes the test A SECOND TIME. That's right, test-prep eliminates some basic errors in test-taking, not in subject ability and knowledge.

"But the guarantee?" Yep, they have a guarantee. "Do 100 points better or we'll let you retake the course for free."  First off, 100 points better than what score if you haven't taken it? Second, if you don't improve by that amount, what kid is going to sit through another 10 weeks of this course, even if it is free?

I've convinced my school to allow me to offer SAT prep as an elective. Am I being hypocritical? Nope. What I do daily is work on math or English. I do the test-prep, too, but mostly I focus on filling all those little gaps in their knowledge and then we have time to practice them. It's a tutorial.

I'm looking to improve the math knowledge and understanding, not just talk about tricks. Sure, I'll focus on only certain parts of Algebra I, but they've already taken algebra I ... I'm filling many of the gaps. Not all, but it's an improvement.

I'm looking to improve vocabulary and grammar and I have the time to do it. It's often surprising to me how much students can appreciate grammar ... about five years after they've learned it. (Or after they've taken a language.)

I'm looking to have them write the stilted and boring essays that get scored well, while telling them all of the ways they can deviate from the stilted and boring pattern if they want to, for the English teacher or for their own personal writing.

Perfect Practice is not poison. Perfect Practice is not drill and kill. Perfect Practice leads to Automaticity, which allows the student time to think and gives her a knowledge base to work with.

Fallon is right, but I'll talk about why, next time.

## Tuesday, March 11, 2014

### Paranoiacs in Charge

Don't you just love it?

We have Google Apps on our domain and I guess I should be thankful for that but it really sucks when they tell you that "Hey! There are some really cool add-ons" but fail to mention that the ability to add add-ons has been disabled by the domain administrator .... the same one who sent the email.

Things like: Track Changes, EasyBib Bibliography creator and much more.
Now I'm excited ... maybe there are trendlines in sheets ...

Hopes are rising ...

Well, damn.

## Wednesday, March 5, 2014

### A Response to the Income Gap Question and Comments.

Bumped to the top from 2009 ...

Let's recap the last few posts, shall we? I've come to the conclusion that the income-scores correlation that shows up in every testing situation is actually rooted in the parents and their attitudes about school and education.

The smarter, motivated, dedicated parent who is demanding of a good education is also likely to have passed similar traits to his child which, while not being a guarantee certainly shows a strong correlation to that child's success. Show me a bored, unmotivated, or stupid child and I'll bet that you've got a bored, unmotivated or stupid parent. We just had open house and all that I saw reinforced my feelings on that - all of the visitors but one was the parent of a hard-working kid.

Yeah, yeah, I know. There are exceptions and everyone can point to the kid who breaks the mold. But averages don't care about your exceptions.

How else to explain that persistent gap between the rich and the poor? There's the racial gap, but that disappears when you control for income. Likewise for the gender gap, or the city-size gap. Examine the increases for repeat test-takers and you can see that even here, the differences aren't as great as that for income.

It's not a simple A-B correlation: More money does not make a kid smarter. The cause-effect isn't there. We need the confounding factor that causes both effects, sort of like the correlation between the amount of "Bling" and the low death rate in cars. Does "Bling" prevent deaths? No, but the ability to afford it means that you can also afford a safer car.
Jonathan asks "If I can paraphrase: Smart adults --> high income, Smart adults --> smart kids. If I have this right (and please correct me if I do not) I think it is bunk."
He then goes on to describe the exact things that do allow a wealthier parent to raise better students (and those traits invariably show up as "being smarter"):
"intellectually enriched environment, ... more expensive towns ... schools maybe not better, but at least better-funded. ... stimulating things around ... babysat by a reader ...more likely to be exposed to culturally enriching stuff. Plays ... the library ...travel ... fewer stresses from neighborhood, hunger, family ... depends on the parents' wealth, not on the parents' smarts."
And I agree. But what affects the wealth? I would maintain that any person can rise in this world, though for many it is harder than it is for others (racism, classism, sexism, and bigotry are alive and well -- the situation is improving but.) Being smart and motivated is a good start. Lazy and stupid are starting well behind the stagger.

To truly improve the students' performance, you can't just give them money. You can feed them and eliminate some stresses and move them into a wealthier town ... and get nowhere because that's not the cause in this relationship. You can't just move into a better neighborhood and suddenly improve your scores.

But the better neighborhood DOES have better schools and better students. What is cause and what the effect? We need to look at the acquisition of wealth. On average, which type of person will acquire wealth, a boorish lout or a diligent, studious worker?

Over the population, which group of people will stay in a company and rise in the corporate ladder, the smart and driven ones or the unmotivated slackers? Which type will job-hop (or be fired) and remain at the lowest levels of the many companies' pay-scales? Which type will recover from a major setback or rise from the slum and make something of himself? Which will read books, learn math, and practice speaking without an accent that labels him as uneducated? Which type of person will motivate his kids and provide a richer environment than that of his neighbors? Which single mothers will rise at 4:30am to tutor their children -- the alcoholic or the mother of a future President?
Pissed Off Teacher asks "How about all the money rich parents spend on SAT prep classes and private tutors? Lower income kids cannot get this extra help."
They don't get that help and that's a shame. I'd like to see ALL schools offer a half-credit SAT prep course, basically a review of math and English. Now that they've had a taste of what they'll need it for, they might be prepared to pay better attention and break out of the bad habits that they started school with.

I should also mention that the most-advertised grade bump that Kaplan Test Prep and others provide is simply the elimination of the common mistakes. Meeting once or twice a week for ten weeks is not enough time for more than test-taking strategies and gimmickry. Their "guarantee" of 100-point gains are backed by an offer to retake the course free. If the offer was for your original money back, then I'd listen.

Darren, who's obviously been hearing waaaaay tooo much tax-raising talk from his Governator said...
I know what let's do! Let's tax the rich, and if that doesn't work, let's tax them some more! Then, when there's no rich left, there will be none of this gap between rich and poor!
We'll have to cut him some slack. His "Republican" governor has been sounding like a tax-and-spend liberal Democrat lately.  That and those deficits would make anyone cranky.

So what do we do now?

I'm not entirely sure, to be honest. I'm not sure that the income-gap problem CAN be solved because it has already happened; what we are seeing in our classrooms is the fallout.

We already offer free-or-reduced lunch and breakfast. We already introduce them to the things that make intelligent, well-rounded, and educated people and try to help them break whatever mold they're in. We already offer extra help in the corridors because Packemin HS doesn't have any extra rooms.

What we really need to do is to stop agonizing over scores. We should look for improvement in each student and try not to worry so much about improvement from year to year and from cohort to cohort. We certainly should ignore the idea that 100% will achieve proficiency in four years.

Spending more money on the schools might or might not be the answer -- it really depends on whether you've been spending the right amount in the first place. If you've been undermining the system for years, cutting back further certainly won't help. If you're at the right level of funding, spending more won't help either.

Teach the ones in front of you. Do what you can. Don't try to save the world.

There, I said it.

### SAT scores are linked to Family income. So what?

Bumped to the top from 2009

Just a warning ... I'm going there.

Flypaper, the edExcellence Blog, has commentary on the SAT scores that refuse to go up.
"Gaps widening a bit by race, income, parental education. Indeed, the tidiest relationships and smoothest curves are those that continue—as they have for as long as anyone can remember—to show the steady upward progression of average SAT scores (pdf) as family incomes and parents’ education rise."
Chester then goes on to show some details and to say,
What does this say about 26 years of education reforming since A Nation at Risk? For starters, it says the reform efforts haven’t seriously penetrated our high schools. Then it says that current moves (e.g., the “Common Core” national standards project of the governors and chiefs) to align high-school exit expectations to college and workforce readiness are urgently needed, indeed long overdue.
That's an interesting take. If you can't get results in 26 years of trying reform after reform, let's try another reform! (Insert sound of Bells and Whistles). Then there is the sentiment that "Reforms are obviously urgently needed."

It's true. The only correlated data that ETS has with an R-value greater than 0.1 or so is between scores and family income. The NYTimes has this:
Everyone, of course, dismisses that income-scores correlation as silly, saying "You can't just give the family more money and raise the scores, ha, ha." That's right, but I don't think that money causes good scores, although there is a lot to be said for SAT prep courses, which are really a total review of math and basic grammar and that's good no matter what.

I think the problem is an incorrect correlation, a confounding factor. It's not that A (money) causes B (scores). It's that C causes D which affects B. Simultaneously D causes A.

Parents are the confounding factor.

As I see it, smart parents are likely to have smart children. More importantly, motivated, dedicated, educated and intelligent parents are likely to have M, D, E, and I children. They are also more likely to have money because they work harder for it and are more capable of holding the job and moving up the ladder to the big bucks and higher family income. Simultaneously, their M,D,I, and E children are more likely to have better scores.

Children whose parents were poor because of misfortune or some other external factor don't tend to fit this pattern. They're the Horatio Algers of the world, the kid who worked his way up from the mailroom to CEO. There's no reason to assume the black or Hispanic kid can't be doctor, lawyer, etc. In fact, the kids of those successful (and higher income) blacks and Hispanics are likewise high-scoring and successful. The single mother who instills dedication, motivation, and a healthy respect for education into her kids might not have money but her kids will.

Children whose parents were not motivated, etc., always fit the income-score correlation. Race has rarely been a factor in determining motivation and dedication (simply look at KIPP schools to see that), but it has been an indicator of income due to longstanding segregation and migration patterns. Money doesn't seem to drive scores, but it does correlate.

The constant desire for improvement and reform and reform and change and reform again is doomed to repeat its cycle of failure.

Are reforms necessary? Sure, if you can point to a definitive improvement that will result. I'd appreciate it if you'd define "improvement," first. Improve what and by how much? Student satisfaction, tech-toys, test scores, athletic titles, graduation rates, future wages? Fundamentally, is "success" as defined by "average scores increasing yearly" or "adequate yearly progress" possible? I don't believe so.

I think we should stop looking for the perfect reform because it doesn't exist. We should instead focus our attention on doing the best we can each year with those we have in front of us.

Just sayin'.

### SAT scores are dropping.

 Everyone will succeed at something.
Bumped to the top from 2012

So everyone is worried (screaming, whining, carrying on, using for cheap political gain) about the fact that SAT scores have been dropping since 1972. Causes from aliens to the dumbing down of the curriculum are thrown out there.
Reading scores on the SAT for the high school class of 2012 reached a four-decade low, putting a punctuation mark on a gradual decline in the ability of college-bound teens to read passages and answer questions about sentence structure, vocabulary and meaning on the college entrance exam. Many experts attribute the continued decline to record numbers of students taking the test, including about one-quarter from low-income backgrounds. There are many factors that can affect how well a student scores on the SAT, but few are as strongly correlated as family income.
And there you have the real reason. More students are taking the thing and many of those people are unqualified.  You can blame the schools (and me) if you want but you really need to look at the overall picture ... through a cleaner piece of glass.

 \$150,000 debt. \$20/hour. Obviously not a math major.
The simple fact is that you have more people being conned into thinking they need to go to college in order to be successful, and since the SAT is a big piece of that process, you have more people taking the SAT who probably shouldn't expect to do particularly well. Add in the guidance counselors who convince their charges to take the test so their participation numbers look good.  Add in the athletes who need SAT scores for the national clearinghouse.

Repeat after me:
You don't need to go to college to be successful.

You need to be self-motivated, hard-working, and not a jerk. If your chosen road leads through college, fine, but don't assume that you'll be successful merely because you attended college and racked up a huge debt.

Something that not everyone understands.

## Tuesday, March 4, 2014

### Should Math Really Be A Required Subject?

I recently got an email:
And as a homeschooling father to a nine-year-old who puts two hours-plus of serious math instruction into each day I find myself in complete agreement with your approach to teaching the subject.  BUT...

I'm curious, do you find anything to agree with in Nicholson Baker's famous critical essay on Algebra II?  I do, and I make up for time that would be spent on the subject with an excess of number theory.  Any opinion greatly appreciated!  Best,
Oooh, boy.

Good evening,

I haven't read it, and it's behind a paywall, but what little I can see of or about it leads me to think "Just another whiny English Major and writer railing against algebra." "I don't DO math. Hee, hee."

I agree with the idea that students who have absolutely no interest in a mathematical major in college should probably be able to take a good statistics course instead of what alg2 has become under CCSS, but I hesitate to let all of them off the hook so quickly. I've found that most students can get SOMETHING out of my algebra class, and I hate to see them quitting on themselves after Geometry. I also believe that many kids vastly overestimate the difficulties they will have.

I think putting an elective as the third year and allowing kids to take alg2 as seniors is often a good compromise.
I guess for me the biggest complaint is this idea that every kid must take it and do well.  Why is A the only acceptable result? Why can't a kid struggle with it, get a D and move on? (And by D, I mean the kinda-gift, 'thanks for trying, but you really don't know this well enough for me to say Alg2 on a transcript') At least then he's been exposed to some things, has a partial idea of what logs are and how they apply to pH, and some pretty functions and so on.

The next time, if there is a next time, he'll do better. If there isn't a next time, well ... there's that small fraction he did understand.

If we look at a common complaint, "I'll never get this in a million years!" and tone down the exaggeration to "I'll never get this in one year!", it should become apparent that some kids may only get parts of alg2 this year. But they can always revisit it later in college or as the parent of student.

It does develop abstract thinking and the concepts are critical in most of the modern world. Yes, I understand that everyone thinks they "didn't use algebra in the RealWorld today" but they are wrong.  Algebra in its pure form never appears ... but the concepts, ideas, and behaviors show up everywhere.
Finally, I ask this one question .... If I said "Your son is too stupid to take algebra." "Your daughter is incapable of such abstract thought; have her take something more girly." "Your black child can't understand that." "Your daughter shouldn't fill her head with difficult math."  What would you do?

Well, I think you'd be calling for my head.

You know your kid best and even you don't think that you can predict his future; neither of you have any idea what he'll need or desire to do. You aren't really sure whether his difficulties are due to bad teaching or a lack of ability. You've read that girls learn their math-phobia from their mothers/ kindergarten teachers/ peers/ MyLittlePony and you do not want to limit her in any way before she's had a chance.
So why do we all have this mindset to "Let them admit defeat so early"? Me, I'd rather have them try again.

I tell kids "You have no idea what you'll do tomorrow. How can you predict what you'll be good at in ten years?  Algebra is difficult, but lots of things are difficult -- besides, you're 16 ... what else do you have in mind to take? What else can you do while the education is FREE? Do you want to put this off until college and pay \$1200 per credit for it?

I was good at math and physics in HS, but I really hated history (BOOOOOORING). I got my degree in engineering and I spend hours during my vacations solving math puzzles .... but my passion is medieval reenactment. I can hold my own with the history department on anything older than 1600, pre-Renaissance. I have complete sets of armor that I wear in full-combat martial arts ... and the people I fight against are teaching me techniques they've researched from centuries old fechtbuch (in the original German). Last summer, we were camped around the fire, period canvas pavilions in a big circle, and we spent spent hours discussing the accuracy of the story of Bayeaux Tapestry as compared to and checked by contemporary sources.  Who would have predicted that?

Should every child take history? Yes. Math? Yes, including all the algebra they can stand, and then some. Art? Science? Languages? English? Yes.
No, I don't when you'll use it.
But I do know you'll do very little without it.

I've gotta get back to work. Thanks for reading.