:baby_symbol: Parenting advice - you're gonna get hit

LaoC

@BernieTheBernie https://www.youtube.com/watch?v=JRRksyGCjoE

boomzilla

homoBalkanus

Benjamin Hall

Mason_Wheeler

dcon

PotatoEngineer

@PotatoEngineer said in Parenting advice - you're gonna get hit:

There's a post in my HOA's Facebook about some middle-aged dude letting his toddler get too close to the road. That would be me. The post vexed both me and my wife. My toddler currently loves watching cars go by, and the busy corner at the main street gives her lots to watch. There are a couple of intersections further away from that busy corner that have decent traffic for a housing area, but my toddler is, of course, not entertained by the idea that an entire minute might go by without a car.

But in the end, I decided to simply ignore the post, because I just couldn't imagine a discussion with such a busybody turning out to be productive in any way, shape, or form. Two of the replies to the post were reasonably positive, three others were negative, and I'm happy having not fed a ~~troll~~ busybody.

The bastard who thinks I'm parenting my kids wrong by sitting on the sidewalk and watching traffic... strikes again!

This time with a police report. Uniformed officers showed up at my house to tell me that someone had reported me lying (...unconscious?) on the sidewalk. I showed them I was fine, the kid was fine, and they left.

But not without traumatizing my wife, of course. The last time we had uniformed officers in the house, my older daughter had just died of flu. So I am not happy with our bastard neighbor. The police showed up at my house and asked for me by name, so the person who requested that fraudulent well-check was clearly someone from the neighborhood. (I don't necessarily know them, but I'm clearly not that hard to research.)

My wife posted on Facebook about it, and received support from almost everyone... except for one person who posted "but you should just move back from the street five feet." So I have a pretty good idea of who called the police. (Though, of course, perhaps there are multiple busybodies in my neighborhood...)

dcon

@PotatoEngineer This makes me think of those Facebook links with stories of stuff like that. (which are all just scrapes of reddit).

:evil_thought: Purposefully do that but make sure you talk with the officers when they come so they know why. Maybe that will end up being enough to get nosy-neighbor in trouble for file false reports.

PotatoEngineer

@dcon It's nearly impossible to actually get someone in trouble for false reports, last I heard. The police don't want people to fear getting charged if they call in an ambiguous situation. You kinda need to do your own legwork and prove that the reports are malicious, because the police won't.

That said, I'll definitely mention the pattern of behavior if the police show up again. Once is chance, twice is coincidence, three times is enemy action, and all that. (Though I suppose the second time was enemy action in this case.)

Polygeekery

@dcon said in Parenting advice - you're gonna get hit:

That's the trouble with tribbles.

Polygeekery

@izzion said in Putting the world on hyper-welfare:

And most of them have been taught the new math that doesn't prepare them for the results of doubling zero.

As a father of a 2nd and 6th grader, I fucking hate the "new math" with a passion. The other night I was helping our oldest with math homework and it was over ratios and something else and some of the problems were using unit costs as the story problems. Which really could not be any more in my wheelhouse if they tried. My son was trying to be way too clever about it in an effort to be lazy and it was annoying me. Not that I have anything against laziness so long as it leads to efficiency. In his case his laziness was causing him to do more work, which is counterproductive to laziness and efficiency.

I still remember the crux of the story problem that he got hung up on.

Mary bought 6 widgets and paid $47.94. What did each widget cost?

He got hung up on some stupid new math way of doing things and kept saying something about:

"94 is twice 47 so (whatever bullshit they have taught him)."

and was arguing with me about how the way he was trying to do it was the easiest way. Which I easily debunked by pointing out that he was wrong because he was struggling with the problem. I will give him credit that he was at least trying to sort it out from the opposite direction, which is clever and frequently works, but I have NFC what he was saying about how he was trying to do it. Finally in an appeal to his laziness I told him:

"The answer is $7.99 and I did that in my head via the absolute laziest way possible."
-checks my answer with a calculator- "How did you do that?"
"The total cost is $47.94, which is very close to 48, which is evenly divisible by 6. Divide 48 by 6 and you get 8. The difference between $48.00 and $47.94 is six cents, six cents divided by 6 is one cent, so subtract a penny from $8.00 and you get $7.99. I did all of that in my head and I knew the answer the moment that I read the problem just by seeing the relationship between the numbers and simplifying the process to something I can easily work out mentally."

Although, to be fair, when he started learning long division a couple of years ago I literally had to Google how to do it because it has been so long since I had to do it.

Rhywden

@Polygeekery He probably needs to learn a bit more about approximations. Though for that you really need to learn the multiplication tables by rote (preferrably up to 20*20) so he recognizes the breakpoints to approximate to.

My most fun shortcut is utilizing commutation, i.e. 6% of 50 gives the same result as 50% of 6. Regularly blows the minds of my pupils.

remi

@Polygeekery said in Parenting advice - you're gonna get hit:

I fucking hate the "new math" with a passion.

Can you ~~show us on the doll where new math touched you~~tell us (me?) what "new math" is in this context?

I have heard about it, but around here "new maths" is so old that I was supposedly taught with it. I don't think I actually was, but whether this is because it had already died by that time, or because it wasn't uniformly adopted by all schools (teachers?), I can't say. Plus of course I've only got a hazy recollection of how I was taught, since ~~my is kicking in~~I was obviously very young. But it's definitely not very "new" anymore.

"New math" here was something about learning ensembles and relationships between stuff and figuring out things rather than rote memorisation of e.g. multiplication tables. Is it the same for you? Have you got specific examples of "new maths" things? The problem you're giving looks very much like a problem I might have had to do, so not very "new."

remi

Btw I was overall good to very good in primary school, but one thing I absolutely remember struggling with was long division. There, um, may have been a couple of tamper tantrums while my mother tried to get me to understand how to do it.

izzion

@remi said in Parenting advice - you're gonna get hit:

"New math" here was something about learning ensembles and relationships between stuff and figuring out things rather than rote memorisation of e.g. multiplication tables.

https://www.usnews.com/education/k12/articles/understanding-the-new-math-your-children-are-learning

That article seems to suggest a similar approach here. It's pretty common for people to lampoon "new math" though because it's so much more word problem heavy than just numbers on a page and times (multiplication) tables. The main problem I've seen getting memed on is when a parent who isn't very good with word problems has to try to help the kid with the homework, and the work sheet's questions just looks like a giant blob of Greek to the parent.

Also, the general more complaints about the US Education system's shift from hard facts to student feelings.

remi

@izzion thanks.

But it really looks like the US is at least 30 years behind, well, I won't say the rest of the world since I don't really know, but at least France. What TFA describes sounds so obvious to me that what baffles me is not that the US is now using that but rather why they were not already using that! I wasn't explicitly taught about "friendly numbers" or the like, but I definitely was taught to do what is described -- and in fact, so is @Polygeekery when explaining to his son.

Now of course I'm sure there's plenty of jargon and and people , as ever when a new thing is introduced (and especially in education). And all that is irregardless of the overall state of (US) education. But, again based on TFA, I find hard to criticise the idea (other than "it's not how I was taught!11!").

remi

@izzion said in Parenting advice - you're gonna get hit:

The main problem I've seen getting memed on is when a parent who isn't very good with word problems has to try to help the kid with the homework

Re-reading your post (after having posted my answer, of course, what else did you expect? ), there's one thing that comes to mind: aren't most US exams (even for lower levels?) mostly made of multiple-choice questions? If so, switching to word problems would probably be a significant change.

Around here I don't think we ever did much multiple-choice, so much so that when once in a while an exam did use them, the teacher had to remind us how that worked. We've always done word problems, and in fact one very old school meme is the "tap problem" which is something like "a tap is flowing at a rate of x L/min into a bathtub which empties itself at the rate of y L/min, compute [something that makes sense... or, more often in the memes, something that does not makes sense!]."

Dragoon

@remi

The approach is also known as common core math and it hasn't been a raging success:

The NCES Fast Facts Tool provides quick answers to many education questions (National Center for Education Statistics)

Common core was officially adopted in 2010.

Here are a few reasons that many people dislike it: https://www.institute4learning.com/2018/04/26/12-reasons-the-common-core-is-bad-for-americas-schools

izzion

@remi said in Parenting advice - you're gonna get hit:

@izzion said in Parenting advice - you're gonna get hit:

The main problem I've seen getting memed on is when a parent who isn't very good with word problems has to try to help the kid with the homework

Re-reading your post (after having posted my answer, of course, what else did you expect? ), there's one thing that comes to mind: aren't most US exams (even for lower levels?) mostly made of multiple-choice questions? If so, switching to word problems would probably be a significant change.

Around here I don't think we ever did much multiple-choice, so much so that when once in a while an exam did use them, the teacher had to remind us how that worked. We've always done word problems, and in fact one very old school meme is the "tap problem" which is something like "a tap is flowing at a rate of x L/min into a bathtub which empties itself at the rate of y L/min, compute [something that makes sense... or, more often in the memes, something that does not makes sense!]."

Standardized (state/national) testing is almost exclusively multiple choice for "hard" subjects and largely multiple choice for language too (literature stuff is always multiple choice, though there have been essay / writing sections on those exams as well, that kind of wax and wane in frequency and proportion of the test).

In-class testing in my math classes (pre-Common Core) was very "show your work" problems heavy, though not necessarily very word problem heavy, more toward just an explicit "solve this" or "do that" type exposition that didn't require you to figure out what they were asking in order to answer it. I don't have real world experience with what current math tests look like, as I neither have kids nor am dating ~~a teacher~~:sadpanda:

Dragoon

@remi said in Parenting advice - you're gonna get hit:

And all that is irregardless of the overall state of (US) education.

Yet despite all of the problems that we have, we still do a pretty damn good job at it:

https://www.imo-official.org/results.aspx

remi

@Dragoon said in Parenting advice - you're gonna get hit:

Yet despite all of the problems that we have, we still do a pretty damn good job at it:

There would be (and probably has been!) a book to write on the gap between how people perceive their schools vs. how they actually perform.

For a long time (this is now starting to change, but very slowly), France thought that they had (some of) the best school in the world, especially in how it was "the great equaliser" of social divides (everyone likes to trot out stories of great people whose parents were middle class and grand parents working class). In reality, France is... well, definitely not bad, but not really good either -- and schools in France pretty much do nothing about equalising things. Higher education is disproportionately for rich kids, like in every country in the world. So this is sort of the opposite of the US perception/situation.

Polygeekery

@Rhywden said in Parenting advice - you're gonna get hit:

My most fun shortcut is utilizing commutation, i.e. 6% of 50 gives the same result as 50% of 6. Regularly blows the minds of my pupils.

That's one that I try to drill into him in all contexts of addition and multiplication but works exceptionally well in the context of percentages. I always tell him that he can reorder the numbers in multiplication and addition however he wants to as you will get the same result (assuming that the problem is sufficiently simple, order of operations can screw you on more complex problems).

As an example, let's take the earlier problem and switch it up.

$7.99 * 6 to many people would be harder to calculate in their head than 6 * $7.99 but both problems lead to the same result and in the second one you can do 6 * $8 and then subtract $0.06 to get the result.

Of course this all leads to him mentally misplacing the decimal point when applicable so I try to get him to work with approximations to double check his answers, but laziness.

Speaking of decimal points I also find that in his mind 6 * 7.99 is a vastly more difficult problem to solve than 6 * 799, even though they are essentially the exact same math problem so I usually tell him to forget about the decimal point and bring it back in at the end. Which is what you are doing anyway, but I have him discard it right at the beginning to get over that mental block.

@Rhywden said in Parenting advice - you're gonna get hit:

Though for that you really need to learn the multiplication tables by rote (preferrably up to 20*20) so he recognizes the breakpoints to approximate to.

Absolutely. And his laziness has him doing more work because he thinks that he is too clever to learn the fundamentals.

Another mental math trick that I love, but is only infrequently applicable, is that any number X squared is equal to ((X +1) * (X -1)) + 1) and you can apply that the other way if you have two numbers with a difference of 2 such that X * (X - 2) = X² + 1.

So a simple example might be that 19 * 19 may not an easy problem for some people to work out in their head, but 18 * 20 and then adding one to the result should be easier. Alternatively, if the problem is 29 * 31 then an easy way to think about it is that it will be one less than 30 * 30, or 899.

Another math trick that I've used a lot over the years is a property of 3 and 9 and works really well for double checking answers. For any number that has 3 as a factor you can add up all of the digits and the result will be divisible by 3. For any number that has 9 as a factor you can add up all of the digits and the result will be divisible by 9. This is only applicable when working with 3 or 9, and by extension also works with 6 and 18 if the number is even, 12, 24, 36 and 72 by seeing if the last two digits are divisible by 4 or 8. If you want to go a little farther you can even work it out for 48 and 144. by determining if the last 4 digits are divisible by 16, which is not very difficult to do if you know how numbers correlate with certain factors. Hell, it isn't even that difficult to do in your head for 32.

Also by extension if you add up all of the digits and the result is not divisible by 3 or 9, then whatever remainder you have will be the remainder when you are done with your division.

I used to feel like they should spend more time teaching how numbers correlate with certain factors, but then I came to realize that most people would never get it and it would have limited applicability, but once you start to get it you can break down math into simpler chunks and do the work in your head.

An examples I have used to illustrate my point to the oldest:

1,496 / 3

I immediately add up 1 + 4 + 9 +6 in my head and get 14 as a result so I know that is not evenly divisible by 3 and has a remainder of 2. Okay, so I know that 1,500 is divisible by 3 and is 500. I need 4 to get from 1,496 to 1,500 so that takes two 3's, so the answer is 498 with a remainder of 2 or 498.66666667.

Rhywden

@Polygeekery Yeah, those are all nice ones.

I usually make my pupils' heads explode by (seemingly) doing calculations of huge numbers in my head. When in reality I'm just exploiting the scientific notation, commutation and basic principles behind multiplication of exponents.

Like, 4 * Pi² * 3.5E7 / 2E6 - which I'd first approximate by doing Pi² is roughly 10, then rearranging 10 * 4/2 * 3.5 * 1E7/1E6 which then yields 10 * 2 * 3.5 * 10 and you get 700.

Usually I'm done before the first pupil even begins typing on a calculator.

Polygeekery

@remi said in Parenting advice - you're gonna get hit:

Have you got specific examples of "new maths" things?

Not offhand. I cannot remember the ways that they have taught him because they all seem so foreign and abstract to me. You could probably find examples of it by Googling "united states common core math".

I understand why they are doing this. They are trying to teach a myriad of different ways to do math so as to have a higher likelihood of teaching each child a way that works for them. The problem I see is that I think they did a study of the different ways that brains might process numbers and math and created curriculum to cast a wide net but I wonder if those methodologies came from those who are inclined to be good at math and therefore the curriculum suffers from a sort of "Survivorship Bias" at the expense of adequately teaching the fundamentals.

One of the fundamentals that really helped our oldest was explaining to him how everything is just addition. This really helped him grasp multiplication and therefore division. They also either did not explain to him, or did a poor job of explaining to him, that multiplying large numbers is the exact same as adding up the products of each of the places. He had no concept that:

6 * 1,472 is the exact same as (6 * 2) + (6 * 70) + (6 * 400) + (6 * 1,000) and until you understand that I do not see how you could possibly grasp what multiplication actually is. Sure, students should figure it out on their own but how many will get frustrated in the process and how long will that take?

Children also get hung up on numbers being "large". I remember well my kids getting stuck on problems like 7 * 2,000 because multiplying such large numbers seemed insurmountable at the time, even though the problem is the exact same as (7 * 2) * 1,000. Break it down into manageable chunks.

How do you eat an elephant? One bite at a time.

Rhywden

@Polygeekery said in Parenting advice - you're gonna get hit:

How do you eat an elephant? One bite at a time.

Oh God, the Elephant jokes.

How do you fit an elephant into the fridge?

remi

@Polygeekery I'm still a bit puzzled because I was taught like you describe "new maths" and the "tricks" you describe seem to fit overall the description of "new maths" as well (i.e. learning to see the underlying patterns, that numbers are not just arbitrary squiggles but have clear relationships that can be exploited to make maths easier).

What I mean, is that I'm surprised to hear that teaching of maths in the US has not been like that for more than 10 years or so (common core is 2010 if I read correctly?). Since this has been the case here for longer than I was taught (), I assumed it was the same everywhere. Then again, assume, ass, you, me etc.

Then there's the implementation and I can't remember any change of programs in school that did not bring its share of and people complaining. Even for changes that, a few years later, everyone praises. Also there's so much that depends on individual teachers and everything else in and around the school. And bad examples stick much more than good ones, so every parent will remember the one dumb thing a teacher did and forgot all the rest...

Dragoon

@remi

Common core math:

Benjamin Hall

The thing with all of those "mental tricks" is that they rely on having fast (ideally completely not conscious) access to the basic "math facts". AKA times tables for small numbers (etc). Which really only come by intensive drilling until they're etched into the brain.

And the "new math" says that drilling is anathema. And that facts are superfluous. And worse, it's being taught (in the US anyway) by people who, in the main, went into their particular career in large part because they were bad at and did not like math. AKA elementary teachers.

I had many students who literally had difficulty dividing 100 by 10. Or dealing with multiplication by 2. They had no "number sense" at all. So things like pulling apart numbers and rearranging? Panic attack. It'd take them forever just to see that you could even do that, let alone figure out which parts were easy to combine.

PleegWat

I got 'story problems' back in elementary during the early nineties, but they were in a minority. When my sister did nurse school they had a real problem in their math class because they were only teaching story problems, and that led to pupils being unable to solve the problem if it didn't match one of the stories they were taught.

Polygeekery

@Rhywden said in Parenting advice - you're gonna get hit:

I usually make my pupils' heads explode by (seemingly) doing calculations of huge numbers in my head. When in reality I'm just exploiting the scientific notation, commutation and basic principles behind multiplication of exponents.

You should have seen the reaction when I would do the same in construction contexts. Like when calculating what percentage fall to set a pipe laser to in my head, on the fly, for arbitrary numbers. But I was doing it all via approximations and keeping us on the correct side of the constraints that we had to work with.

The general rules, for sanitary sewer as an example, were:

You have a minimum slope of 0.4%
As a result, all pipe has to have slope towards the outflow
No pipe can have more than 0.02' of backfall in it, but do your absolute best to make certain that all pipe have correct fall on them or at worst be level
You want to stay reasonably low because you can always raise pipe up to gain elevation, but you have a limited ability to lose elevation because of your first two constraints

So let's say that we are at or above planned elevation (pipe lasers are fairly precise but the farther the run and the greater the temperature differential between ground temperature at grade and ambient air temperature the more your laser beam would "wander" due to heat lensing or the mirage effect) and we have a 328' run of pipe to setup on. Per the blueprints that run calls for a fall of 0.52% which equals 1.71'. This is all on the blueprints already.

So my thought process would be:

4 * 328 is 1,312
Either move the decimal point 3 places or just realize that I need to be fairly close to 1.something
Minimum fall of 0.4% would be 1.31'
That is 4 tenths difference

Then depending on whether or not that was too much or not, and how close we are to an end of run I might roll with minimum fall. But let's say that seems like too much. We are putting pipe in the ground, not doing rocket surgery.

The plans call for 0.52%, minimum fall is 0.4%, the difference between those two percentages is 0.12% and the difference in outcome is 4 tenths, so each change of 0.03% makes 1 tenth of difference in elevation. From there I make a judgment call on what to do.

Now keep in mind that I literally pulled all of these numbers (except the minimum slope) out of my ass and did not cherrypick them to make the mental math easier but generally speaking you can usually break things down in a similar manner. I could do all of this in my head in seconds, while sitting on an excavator digging out to set the boxes for our next run. So someone would come to me with the elevation shots and numbers from the plan.

"Hey, the laser drifted on that last run so we're a tenth over the prints."

Keep in mind that depending on circumstances this could be really bad.

"This next run has decent fall on it, what's the elevation difference, slope and run?"
-looks at notes- "1.71 feet, point five two and 328 feet."
-quick math in head- "Set the laser to point four three and that will bring us in two tenths low to the next manhole and give us some breathing room again."

When we would get ready to set boxes for the next run:

"How do you do that sort of math in your head and so quickly?

I would try to explain it to them but it was like deer in headlights. They looked at me like I was some sort of mutant. It was even worse when a run would be planned for something like 0.42% and we needed to lose elevation and I would almost instantly know that on that same 328' run from earlier that running at minimum fall would only gain us 6-7 hundredths of a foot.

They're all just numbers, whether they seem very large or very small. Break it down to manageable pieces, forget about the decimal point and approximate where appropriate, when you get an answer give it a quick sanity check based upon the other numbers at hand, double check yourself when failures will be catastrophic.

Polygeekery

@Rhywden said in Parenting advice - you're gonna get hit:

How do you fit an elephant into the fridge?

Depends. Is there currently a giraffe in there?

Polygeekery

@remi said in Parenting advice - you're gonna get hit:

I'm still a bit puzzled because I was taught like you describe "new maths" and the "tricks" you describe seem to fit overall the description of "new maths" as well (i.e. learning to see the underlying patterns, that numbers are not just arbitrary squiggles but have clear relationships that can be exploited to make maths easier).

You're not wrong, but the difference is that they start with the "tricks" and skip the fundamentals. The tricks don't make sense unless you have a foundation of fundamentals. They teach the "What" before the "Why" and "Why" is the foundation that the "What" is built on.

remi

@Dragoon sounds pretty much like the memes we had in France in the 70s/80s about our new maths, except it was more about making everything into "sets." But in the end, as I said, I was taught with this and never saw any "sets" nor any of the memes being made about them. I assume the same here, from the couple of articles linked.

On the whole, I'm rating all this as a big nothingburger combined with parents whining that "I wasn't taught like that" and a sprinkling of generic politics .

So yeah, as @Benjamin-Hall and @Polygeekery are pointing out, some people grok numbers easily, some don't. Some "tricks" will only ever remain "tricks" to some people, because they just don't get (or don't make the effort to, which amounts to the same in the end) how numbers work. These people might have gotten better grades under "old maths" because some of them might have managed to wing it by rote memory (or pure luck) but that wouldn't have made them better at maths in Real Life. And saying that "new maths" is bad because children are being taught the underlying relationships between numbers rather than having to work it out themselves... let's just say that doesn't make a very convincing argument.

Also, "word problems," well, welcome to Real Life. You will encounter stuff like "each item is $x, there's a 3-for-2 deal, how much will I pay?" You will not encounter stuff like "what is x*y?"

Polygeekery

@remi said in Parenting advice - you're gonna get hit:

Also, "word problems," well, welcome to Real Life. You will encounter stuff like "each item is $x, there's a 3-for-2 deal, how much will I pay?" You will not encounter stuff like "what is x*y?"

When you go to the grocery and you need 6 oranges and they cost $17.23 each (because inflation), that problem is the same as:

@remi said in Parenting advice - you're gonna get hit:

"what is x*y?"

Benjamin Hall

@remi said in Parenting advice - you're gonna get hit:

@Dragoon sounds pretty much like the memes we had in France in the 70s/80s about our new maths, except it was more about making everything into "sets." But in the end, as I said, I was taught with this and never saw any "sets" nor any of the memes being made about them. I assume the same here, from the couple of articles linked.

On the whole, I'm rating all this as a big nothingburger combined with parents whining that "I wasn't taught like that" and a sprinkling of generic politics .

So yeah, as @Benjamin-Hall and @Polygeekery are pointing out, some people grok numbers easily, some don't. Some "tricks" will only ever remain "tricks" to some people, because they just don't get (or don't make the effort to, which amounts to the same in the end) how numbers work. These people might have gotten better grades under "old maths" because some of them might have managed to wing it by rote memory (or pure luck) but that wouldn't have made them better at maths in Real Life. And saying that "new maths" is bad because children are being taught the underlying relationships between numbers rather than having to work it out themselves... let's just say that doesn't make a very convincing argument.

Also, "word problems," well, welcome to Real Life. You will encounter stuff like "each item is $x, there's a 3-for-2 deal, how much will I pay?" You will not encounter stuff like "what is x*y?"

I'm all for word problems. But to do word problems effectively, you need to have the core facts cold. In fact, to understand the underlying relationships and not get lost, you need those facts cold.

So it's not memorize vs real understanding. It's "if you don't memorize, you will never have a real understanding, no matter how. you're taught." The memory work is a necessary and essential precondition. And it's not only not done in "new math", it's actively denigrated and rejected.

Benjamin Hall

@Polygeekery

But...to recognize that (true fact), you need to have the pattern matching experience. Both are necessary. The failing of the "new math" is that it tries to go all the way to the other end of the spectrum before the kids have any kind of grounding in the (much simpler) patterns and facts.

The only way to teach this is

Extensive, exhaustive drilling in math facts starting early. Like...1st grade or before. Keep this up until those facts are instinct level.
Once one set of facts (say addition) is instinct level, start teaching algorithms and "tricks" for that one set of facts. Such as the distributive/associative property of addition.
Keep drilling as you add more and more types of facts that build on each other. And keep building algorithms as you go. So once you have negation as a concept that's understood at the core level, you can do "subtraction is just negative addition". Etc.
Once you have a large enough "library" of core facts and algorithms, start assembling them into word problems.
Keep going for as long as necessary.

remi

@Polygeekery said in Parenting advice - you're gonna get hit:

When you go to the grocery and you need 6 oranges and they cost $17.23 each (because inflation), that problem is the same as [x*y]

Well, duh. But have you ever seen how difficult it can be for people who know you to do "x*y" to do "6 oranges at $17.23 each?" Well you probably do, but still.

When I was young, I did some tutoring (and my mother did a lot, and tbh most of my stories come from her). Perhaps the most common, and hardest thing to get pupils to understand was, "read the problem." Like:
: Oh it's about oranges and, uh, what do I need to do with oranges?
: Read the problem.
: Oh, right, 6 oranges. So what do I do with that?
: Read the problem.
: Uh, each orange is $17.23. What now?
: Read the problem.
: Ah, I want to know how much 6 oranges cost. So that... and this is the point where maths kick in ...

So frankly, a math course that teaches that and not just x*y... I don't even see how that's contentious.

dcon

@Polygeekery said in Parenting advice - you're gonna get hit:

When you go to the grocery and you need 6 oranges and they cost $17.23 each (because inflation), that problem is the same as:

Nah. Just buy the 5 pound bag. No math required!

remi

@Benjamin-Hall it's funny (in a non-ironic way!) how I can see exactly the same arguments every time I hear about a school reform, in the few countries where I've heard about them (I make no claim of exhaustivity here!). It's always about how "we learnt fact and how to think, now it's all dumbed-down and wishy-washy vague ideas" and "you need to learn to walk before running" and similar tropes.

Which, I'm not saying that this makes your comments invalid. But my experience is that these things are always said, regardless of whether the changes turn out to be good or not (which usually takes quite some years to work out, for a variety of more or less reasons). So again, I'm not saying you're wrong, but... this is not very convincing by itself.

Benjamin Hall

@remi said in Parenting advice - you're gonna get hit:

@Benjamin-Hall it's funny (in a non-ironic way!) how I can see exactly the same arguments every time I hear about a school reform, in the few countries where I've heard about them (I make no claim of exhaustivity here!). It's always about how "we learnt fact and how to think, now it's all dumbed-down and wishy-washy vague ideas" and "you need to learn to walk before running" and similar tropes.

Which, I'm not saying that this makes your comments invalid. But my experience is that these things are always said, regardless of whether the changes turn out to be good or not (which usually takes quite some years to work out, for a variety of more or less reasons). So again, I'm not saying you're wrong, but... this is not very convincing by itself.

I'm coming from having taught science in high school for 7 years and having worked closely with the math teachers. I've seen what's being taught and we had the less asinine curricula. I've seen this evolution away from "know the facts" to "talk about things in an arty-farty manner" personally. I've been to the conference talks where they tout this whole thing. So I'm not just talking .

As with all things educational, it's been a succession of fads. This attitude (in various guises) has come and gone at least twice during the adult lifetime of my parents. And was just as destructive both times.

Understanding word problems (which I like at the higher levels!) or anything more complex requires a firm understanding of the context and the underlying facts. Doesn't matter if it's literature, science, art, or anything. If you don't know the language, it doesn't matter how you ask the question, all you'll do is confuse people.

Coupled with this is the utter abysmal track record of US education with reading. Most kids I taught were reading well below grade level...and "grade level" is a joke. Seriously, it puts the Hobbit at high school level; something I read for myself starting at about age 7 (ok, I was an advanced reader, but really). And most of the kids I taught, even the smart ones would have struggled with that. Not just the language, but the underlying facts. To "get" any of it, you need tons of context, and that context needs to not take significant numbers of mental cycles to extract.

As for math, if it takes you 3 seconds to recognize that 4 is evenly divisible by 2 (not uncommon for the kids I taught), then a "trick" relying on rearranging things to make the numbers easy just won't happen. You've lost them--their mental cycles are entirely occupied just parsing the numbers.

Polygeekery

@remi said in Parenting advice - you're gonna get hit:

So frankly, a math course that teaches that and not just x*y... I don't even see how that's contentious.

I have no problem with story problems, if that is what you are asking. Those could, in theory anyway, show students how math can be applicable to everyday life. It probably doesn't, for reasons similar to what you just explained. But in theory......

Polygeekery

@Benjamin-Hall said in Parenting advice - you're gonna get hit:

I'm all for word problems. But to do word problems effectively, you need to have the core facts cold. In fact, to understand the underlying relationships and not get lost, you need those facts cold.

This is illustrated to me all the time with how people interact with percentages and they do not get how you cannot swap around the numbers willy nilly and get the correct answer. I am to blame for some of this because I have seen people trying to, as an example, change a number by 15%. So if they want to add 15% to a number they will multiply the number by 0.15 and then add that to the number. I suggest that they cut out the middle step and just multiply by 1.15. So then they later might need to reduce a number by 15% and try dividing it by 1.15. That does not work.

This gets even worse in that the closer the percentage is to zero the closer those two results will approximate each other. Reducing 100 by 15% gets you 85, but dividing by 1.15 is ~87. But as you get closer to 100% the results deviate even further such that reducing 100 by 95% should result in 5, but dividing by 1.95 gets you ~50. They do not understand that the more direct route to the answer is front loading the addition or subtraction operation into the calculation of the percentage change. If you want to do the same operation then you need to front load the subtraction and multiply by .85 or .05.

The other night while I was working on our golf cart our oldest was out there and brought up the batteries in it as a comparison to the one in their Power Wheels. Our golf cart has six 8V batteries and Power Wheels have 12V batteries. Trying to explain to him, without getting out a pencil and paper and going through the calculations, that 12 is 150% of 8 but 8 is 33% less than 12 just didn't sink in as quickly as it does for me.

Polygeekery

@Benjamin-Hall said in Parenting advice - you're gonna get hit:

I'm all for word problems. But to do word problems effectively, you need to have the core facts cold. In fact, to understand the underlying relationships and not get lost, you need those facts cold.

Additionally, and to make certain that this deceased equine is adequately bludgeoned, story problems are only the beginning. You have already defined the problem and led them in the correct direction to finding the solution. I wish that schools would do more to help students learn how to discover what the problem is and break it down into logical steps.

Back in the day I worked at companies where college graduates would get hired to help estimate jobs and I do not recall a single one of them having any concept of how to get started even though they would be given spreadsheets with all of the variables laid out for them and formatted in a logical manner. Plug and chug. Go over it with them multiple times, they would still falter. The variable costs were all very elementary math. It took handholding and some of them it would click for them and then they were good. Many would just get by with nothing more than memorization of the process and you could tell that they had no real understanding of why they were doing what they were doing.

HardwareGeek

@Polygeekery said in Parenting advice - you're gonna get hit:

Those could, in theory anyway, show students how math can be applicable to everyday life.

In fact, I've always understood that to be their purpose. But many people have a hard time extracting the math from the words — probably because they haven't really learned the math before being asked to convert the words. It's kind of like if you were to ask me to, say, extract the meaning of your post and convert it to Spanish. I know a little Spanish, but not enough to translate it fluently; I could do it, eventually, but I don't have all the vocabulary and I'd have to look up some words in a dictionary. The kids know a little math, but not well enough to recognize the relationships between the words and numbers.

Benjamin Hall

@Polygeekery said in Parenting advice - you're gonna get hit:

I wish that schools would do more to help students learn how to discover what the problem is and break it down into logical steps.

Yeah. But that kind of higher-order, meta-algorithmic (ie an algorithm to decide what the problem is and figure out the algorithm(s) that will be best suited) thinking requires a really really really firm foundation on the rest of stuff. And is exquisitely "topic" dependent. If just executing any algorithm requires max CPU, the kind of speculative execution and experience-based heuristics required to break down the problem causes overload and breakdown.

One thing I'm very much against is the idea of teaching "critical thinking" or "problem solving" as an isolated, context-free idea. Breaking down the problem and "thinking critically" or doing "problem solving" on it are so tied up in what you're working on that it doesn't really transfer over much except between very allied regimes. You need a huge fact (and algorithm) base to even begin to start to do it in multiple areas.

I had a reputation growing up as being "really smart" and "knows everything." But I'm not all that fast of a thinker; certainly not genius level. But what I do have, thanks to a family pattern of reading voraciously and arguing about it, is a huge vocabulary and knowledge base to draw on. That means I can interpolate between known facts to new facts really easily, and adding new facts and methods is much easier because I have a nice framework to hang them in. Most people don't have that. Or rather, they have narrow intellectual frameworks and lack the ready ability to generalize, preferring to silo information. The kid who knows everything about Minecraft, but can't reason outside of that (even when things are near analogies to things he does understand well). The kid who does well in Math class, but then when asked to apply those ideas in a new context (say physics), flounders because math class is math class. Etc.

izzion

@Polygeekery said in Parenting advice - you're gonna get hit:

So if they want to add 15% to a number they will multiply the number by 0.15 and then add that to the number. I suggest that they cut out the middle step and just multiply by 1.15. So then they later might need to reduce a number by 15% and try dividing it by 1.15. That does not work.

Funny story about 15% fudge factors and division.

I used to play a couple different online browser & real time "strategy" games (think Clash of Clans, before mobile phones or graphical UIs, and without the p2w). They both had the concept of one way to get information about the total number of troops the target had, which gave accurate information but only about the total number of troops for each classification, and a second way that gave more details about how many of each type of troop were at home, away, or in training but included a random fuzz factor of up to 15%. One guy maintained an online calculator for the first game that put the math for the two sets together, and always had people complaining that his numbers were too high because he'd adjust the fuzz number by /1.15 and then it was 1.18x the displayed number and by golly he was trying to make them send more of their troops out than necessary.

So when that guy wrote his own version of the genre (which was the second one that I played), he used the same fuzz factor but displayed "may be off by up to 18%" on the in game screens. But it was confirmed in official forum posts (but not in documentation) that he was using a 0.85-1.15x scalar in what you were shown. When I went to write a calculator tool for that game (my first foray into PHP ), I got a raft of shit from people about why am I not dividing by 1.18 and am I trying to make them fail their attacks.

Can't win for losing, I guess

Rhywden

@remi said in Parenting advice - you're gonna get hit:

@Benjamin-Hall it's funny (in a non-ironic way!) how I can see exactly the same arguments every time I hear about a school reform, in the few countries where I've heard about them (I make no claim of exhaustivity here!). It's always about how "we learnt fact and how to think, now it's all dumbed-down and wishy-washy vague ideas" and "you need to learn to walk before running" and similar tropes.

The thing is that Math is basically a language. You need to learn its grammar and its vocabulary.

And unless you're some kind of savant, learning a language requires learning both of those. Same for math.

Sure, you can add stuff to make it fun - but on a basic level, every skill you want to learn requires repetition and training. Want to do Karate? You better learn the basic movements, increase your flexibility and do strength and endurance training. Want to play the guitar? Learn the chords and repeat them until you don't need to think about where to put your fingers.

Same principles. No one ever has mastered a skill without having mastered the basics.

dcon

@Rhywden said in Parenting advice - you're gonna get hit:

Same principles. No one ever has mastered a skill without having mastered the basics.

ButButBut... <oh wait, wrong thread>

Zecc

@Polygeekery said in Parenting advice - you're gonna get hit:

Another math trick that I've used a lot over the years is a property of 3 and 9 and works really well for double checking answers. For any number that has 3 as a factor you can add up all of the digits and the result will be divisible by 3. For any number that has 9 as a factor you can add up all of the digits and the result will be divisible by 9.

This is called the digital root and even for numbers which aren't divisible by 3 it is preserved by addition and multiplication.

Casting out nines - Wikipedia

Zerosquare

All this talk about new math, and none of you have mentioned Tom Lehrer?
https://youtu.be/UIKGV2cTgqA

Guys, you disappoint me.

(: yes, the new math he's mentioning is probably not the same as today's new math.)