One thing I've never understood with homeschooling: How come parents think they have the competence to be a teacher? Just because you are educated doesn't mean you are a good (pedagogical) educator.
This applies equally to paid teachers, along with numerous downsides that don't apply to parents (i.e. being able to tailor education to a single individual, developing a relationship that lasts close to two decades, ability to slow down and speed up course material where necessary, and more). Paid teachers, contrary to semi-popular mythology, are not special and don't do anything that an average person couldn't do (they are not extra-"competent"). In the natural course of being a parent you learn how to interact, guide, and teach your children.
This argument also fails in many concrete situations. For example, where I grew up there is a decent homeschooling community made up of people with average levels of education, low to average income, and yet the kids perform very well academically and are well socialized. Saying that these parents are not competent because didn't get a badge (education-related degree) is absurd considering they do as well as the people who did get that badge.
Go spend some time in a classroom and get a fucking clue how much more there is to teaching than what your layman's view entails. You, and this disrespect for our educators and the potential of what we could be offering in our public schools is why we are the laughing stock of the developed world.
Yes, there are educators who are so great they can teach all 20 kids amazingly well, but those are super rare. Most likely kids who are learn much faster or much slower than the rest will be left behind. If you child is in this group, it's better off to stay away from public school.
(It could have been much better if there were advanced classes, "magnet" schools, etc.. but in many states those programs are being cancelled and everyone is being forced into rigid programs.)
At a minimum you need to use your judgement to vet good from bad practitioners in those fields.
Also "disrespect our educators" is so funny. Sorry, they're not that serious, mostly dumb. And we're not the laughingstock of the developed world, we are the rulers of the developed and undeveloped world
How, by the lack of it?
A lot of people bet for home schooling because, not despite of, their perspective from inside a classroom.
There's a lot of competence necessary to teach two dozen kids with different backgrounds and mastery levels, even in the rare moments when 2-4 of them aren't actively trying to derail the entire class.
The base level of competence necessary to go through a curriculum with one/a few of your own children is much, much lower. Could I do better with one/a few of your children given as much time and attention? Pretty definitely. Can I do better if your kid is in my classroom? In most cases, no.
Sure, there are things I could explain or guide a kid through because of my background and skills that homeschooling parents can't (though it mostly just takes more time and effort), but there's a huge amount they can do because of their relationship, access, and ability to devote time and attention that I couldn't hope to. And with modern homeschooling resources, tutors/group microschooling, online courses and group study, etc., the deficits have never been easier to overcome.
Also, two underdiscussed points: 1. An untrained, literate adult probably needs less than two hours to help a kid through what they'd learn in an eight-hour day at school. That time can go to other things. If they're productive, great. If they're not, no huge loss.
2. People significantly overestimate the level of care and competence average teachers have. You remember some fantastic ones. If fantastic and caring was the norm, you were quite lucky.
HOWEVER... remember that "home schooled" doesn't mean "as a parent you are the only teacher" right? You can hire tutors, you can form teaching groups with other parents, you can use online resources, etc. If done WELL and with a sense of one's own limitations, and the need to socialize your child, homeschooling can work.
It's just unfortunate that so often homeschooling is used as a way to ensure that no outside influences interrupt a parent's particular brand of ideological indoctrination... although in the narrow case of tech parents, I suspect that's less of a driving force.
I love that phrasing! I think I'm going to use it – thank you.
100%. But this also applies to people with degrees in education, teaching certs, and employment at your local school.
How do parents judge the ability of local teachers to be a good (pedagogical) teacher? If they discover a bad teacher, what is their recourse?
Sufficient erosion in the meaning and value of 3rd party teaching credentials then diminishes the relative value of outsourcing the process vs. doing it in-house: literally.
We think we have a relationship with our own child that allows us to understand what they need and how to communicate with them in a way that works for them. We think we have the time (assuming one parent is full time parenting) to give our child the attention they need to excel. And we believe that a combination of relationship and individual attention goes further in K–12 than any amount of formal training in education.
I work on homework with my kid every day and after all those things it's not like we have time (or she has energy) to fill in holes in her at-school learning
Next time you're in the car, try teaching your kid about solving systems of equations where both are linear vs one is linear and the other is parabolic. It's a lot easier to sketch it out on scratch paper than to pontificate from the driver's seat.
Sure those things (history/philosphy/etc) matter but in our society you still have to do well on math tests to do well in life.
As a parent you can teach them directly (homeschool) or augment a public school education, but the augmentation route needs to be done in slack time, which is tough.
And what would be the point? If we're right that their mom is better equipped to teach them than a teacher is (because of time to dedicate to them and a personal relationship and understanding) then what do we gain by having a teacher do it too?
(This isn't the thread for the socializing argument, because OP started with teacher qualifications. I'll just add that we are aware of that concern and have strong mitigations in place.)
While this is a good and rational awareness of one's own capabilities, as someone who grew up in Bible-belt homeschooling circles and saw a wide variance in approaches and effectiveness, the "homeschool co-op"/"homeschool group" model where one parent teaches one subject to many kids, classroom-style, is super common. See, for example, "Classical Conversations" [1], a pretty common one in my area, that leans on "parent as classroom teacher to many kids", without much in the way of prerequisite qualifications.
As an example i once lost a mark on a math test because when rounding to the nearest whole number, i put 3.0 as the answer. Wrong. 3 is a whole number, 3.0 is not i was told, and threatened with suspension on protest. That kind of thing sticks with you.
I agree with your sentiment however, i just dont think its a powerful retort.
You also shouldn't try to mention INT_MAX, negative zero, rounding error, or other computer science topics which do not exist in mathematics.
negative zero isn't in any math I know of. It is only in obsolete computer science though.
> The right answer they were looking for was 3, not 3.0. Adding that .0 implies a precision which is not correct.
In contemporary mathematics, 3 is 3.0 . Both 3 and 3.0 belong to the set of integers. There is no additional precision being demonstrated by adding a 0 at the end of the 3. This is simple notation, not refering to a new concept.
We definitely spent more time discussing different kinds of infinity than we did discussing rounding error!
I can believe that the situation might be different in "applied mathematics" or definitely in "engineering mathematics" - but at least at Berkeley, the latter degree is in the College of Engineering, not under the Math Department at all.
>>> a = 3.0
>>> b = 3
>>> type(a) == type(b)
False
For example, 10 / 3 = 3.333... right? We're then asked to round to the nearest whole number, and the answer should be 10 / 3 = 3. It is not correct to then say 10 / 3 = 3.0, because that is just wrong.
I'd end up siding with the teacher on this one. Just acknowledge you didn't understand what they were looking for and do better next time.
If you round 3.05 down to 3, 3.00 is not arbitrary precision, its explicit precision that's reflective of the rounding operation you did. I wasn't claiming that `type(3.0) == type(3)`. I was claiming that:
>>> round(3.0) == 3
True
10 / 3 != 3.000000000000000000000000 no matter how many times you refute it. You should really learn to accept it and continue on and look deeper inside yourself into this. It's sad you still haven't learned this lesson from elementary education. Maybe they should have suspended you.
In no world does 10 / 3 = 3.0. This is just a falsehood as much as 2 + 2. = 5. I don't care about your large values of 2.
Teachers not having the time to muse about such ideas and instead needing to package everything into a presentation appropriate for an entire room full of children is one of the more obvious failure modes of industrialized education.
Math terms like "whole number" are not defined in terms of the behavior of computer programming languages.
In math, not only are 3.0 and 3 the same thing, but also, so is 2.9999999...
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> They weren't looking to see if you knew the arithmetic with that question, they wanted you to show you understood what they meant by "whole number" and understand you can't just leave arbitrary precision after rounding.
Can you show any math reference that supports this viewpoint? This goes against my college mathematics training.
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> You didn't give the right answer
According to mathematics, 3.0 and 3 are the same thing (and so is the Roman numeral III, and so on.) So is 6/2.
It is deeply and profoundly incorrect to treat an answer as incorrect because the mantissa was written out.
The teacher is simply incorrect, as are you.
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> Just acknowledge you didn't understand what they were looking for and do better next time.
If a teacher asks "what is the country north of Austria," in an English speaking school, and you write "Germany," and the teacher says "no, it's Allemande," they're just incorrect. It doesn't matter if the teacher is French. There are only two ways to look at this: either the correct answer is in the language of the school, or any international answer is acceptable.
A normal person would say "oh, ha ha, Germany and Allemande are the same place, let's just move forwards."
A person interested in defeating and winning, instead of teaching, might demand that the answer come in in some arbitrary incorrect format that they expected. That's a bad teacher who doesn't need to be listened to.
Yes, we know there's also some kid who is explaining to just do as teacher instructs, but no, we're there to learn information, not to learn to obey.
> The word integer comes from the Latin integer meaning "whole" or (literally) "untouched", from in ("not") plus tangere ("to touch"). "Entire" derives from the same origin via the French word entier, which means both entire and integer.[9] Historically the term was used for a number that was a multiple of 1,[10][11] or to the whole part of a mixed number.
https://en.m.wikipedia.org/wiki/Integer
The question was to understand the idea of a "whole number" aka an integer.
The takeaway from trying to really nail down a definition of "integers" (or anything, really) is going to be something along the lines of "if it quacks like a duck up to unique isomorphism, it's a duck". The encoding is not important and one frequently swaps among encodings when convenient. In any case, no one who knows any math is going to say to a child that 3 and 3.0 aren't interchangable outside of some extremely specific contexts. In fact that's not even encoding: it's notation. They can be literally equal, not just equivalent. Those particular contexts aren't ordained, and e.g. propagation of uncertainty is "better" than significant figures if you're doing engineering anyway.
Writing something like '10/3=3' is likely to trigger the mathematicians because lots of people get confused about what '=' is supposed to mean (and often use it to mean something like "next step indicator"). '3=3.0' not so much.
The exact context was given. They wanted only whole numbers.
> Writing something like '10/3=3' is likely to trigger the mathematicians
Sure, when lacking the context of all answers should be rounded to the nearest whole number. But that was the context, and it's astounding so many people with alleged math backgrounds arguing things like intergers aren't a thing to understand.
Being equal to 3, 2.9999... is also a whole number.
Teaching to use '=' in a statement like '10/3=3' is an example of where teachers don't know math in depth and make errors about details that are actually important/later cause confusion. 10/3 is not equal to 3. '=' doesn't mean "answer". Then not accepting 3.0 which is equal to 3 just layers on that confusion. '=' is transitive. If a=b and b=c, then a=c.
Saying 3.0≠3 is a subtlety you really only get into in math when defining these things, and then you immediately redefine them so that 3.0=3 and you don't have to think about it again.
But the question wasn't testing that you knew how to divide and round. The question was testing if you understood what the teacher was trying to teach about whole numbers, integers, rational numbers, real numbers, etc.
6/2 as written is not an integer. It is not a whole number. The value it represents can be written as a whole number, I fully agree, but as written it itself is not a whole number. Whole numbers are the set of numbers Z including -3, -2, -1, 0, 1, 2, 3, 4,... I doubt any math teacher, upon teaching "what is a whole number", draws a number line and proceeds to label it -3.999, -6/2, -12/6, -5/5, 0, 5/5, 12/6, 6/2, 3.999..., and on.
The notation was the key part of the question and was a key part of the answer.
The teacher wasn't looking for a value (which is what you're so focused on looking at), they were looking for a notation, a format.
6/2 is a whole number. 6/2 = 3. 3 is a whole number. They are equal. Usually, they are the exact same mathematical object. It is not merely that they share properties. They are literally definitionally the exact same thing (the same set in ZFC). "n is a whole number" is a proposition. It is true for n=6/2.
If a teacher is teaching that 6/2 is not an integer, unless they are in the middle of constructing the rationals and need to make a distinction between integers and equivalence classes of pairs of integers, then they are wrong. The very first thing you do after you're forced to make that distinction is you make it go away. They shouldn't be teaching the student to hyperfocus on a specific notation or format. That's a bad lesson to teach, and is something a real teacher will need to fix later. Actual mathematics professors are happy to let you write "let <christmas tree>∈ℝ". An intro proofs professor will definitely put something like "-3.999..., -6/2, -12/6, -5/5, 0, 5/5, 12/6, 6/2, 3.999..." on a number line to illustrate the point that these are just different ways to write the same thing. Fluidity in switching through and following different notations without getting distracted is a centrally important mathematical skill.
Finally, you're starting to understand the context of the question at hand.
I'm also happy you're starting to show you do understand there's a notational difference between 6/2 and 3. That the values are the same the notation is quite different, thus there are some differences. Not functionally, true, but notationally.
The notational difference was the point of this lesson. You may think it'll only be a barrier in the future to point it out like that (maybe it is!), but the notational difference was the lesson.
> Fluidity in switching through and following different notations
If you don't really have an understanding of the notations, you're going to have a hard time being fluid switching between them.
> An intro proofs professor
An intro proofs professor wasn't leading the lesson, it was probably an elementary or middle school math teacher. The point of the lesson is different, the context of the lesson is different.
In any context that a child is working in, 6/2 and 3.0 are a whole numbers. If the teacher says otherwise, they are wrong. Just because the teacher wants to teach a lesson doesn't mean that lesson is actually correct. The teacher is just confused.
If they weren't confused, it would be highly inappropriate to go into that level of detail with anyone other than a curious gifted kid that's asking questions that are years ahead of a normal curriculum. So much so that it's beyond the level of knowledge expected of a schoolteacher.
You also wouldn't mark it wrong because the entire point is to define things in a way that makes the distinction go away. Even after that distinction has been presented and is front-of-mind, you still generally write down whatever representative is convenient.
It's either literally wrong, philosophically/pedagogically wrong, or both.
Pretty sure all teachers I had even in elementary school studied at least high school level algebra. In middle school and above they all had masters or better in mathematics.
> the distinction is not relevant
> I highly doubt that the teacher was making that distinction, or even aware it exists
> the teacher was making a distinction that does not exist
The distinction both exists and does not exist. Incredible.
> it would be highly inappropriate to go into that level of detail
The detail of a thing that does not exist, right?
> it's beyond the level of knowledge expected of a schoolteacher.
Right, the teacher is wrong because you wouldn't expect the schoolteacher to be smart enough to be right about it.
There's similar logical snags when trying to define real numbers because technically you'll need distances which have to be rational because you don't have real numbers yet, but really you'd like distances to be real. It's not actually an issue though, and as far as everyone is concerned, distances are real.
Or you define things only up to unique isomorphism by their properties and wash your hands of the whole ordeal. The construction is merely to show that some object with those properties exists.
The teacher is wrong because if they are being pedantic about it to a child, they're a bad teacher. And they're missing the point.
I got threatened with suspension on protest once. It was about the meaning of a word, but still.
Luckily, I'm a university brat, so I just waited a couple days until my dad was keeping me at his office, then I wandered down the hall, and I asked some professors for a detailed and referenced way to push back. I brought candy and tums, because that's what professors want from children who can't bring beer.
About a week later, I went in with a 30 page computer printed essay. As a nine year old. It had six phone numbers in the back, four to PhDs, which could be called for further detail if needed. It was addressed to both the teacher and the principal.
An opening note was "please look into how Marilyn vos Savant was treated when she explained the Monty Hall problem, when considering whether teachers are permitted to threaten students for disagreeing politely. Are you really so afraid of being incorrect?," written by an internationally renowned mathematician.
I was carrying an etymological breakdown that to this day I can barely read, stretching all the way back to the hypothetical proto-indo-european roots.
Professors don't like kids being threatened.
I did not hear about that teacher doing that again while I was in that school.
Definitely not a great school! both my brother and I ended up going to college and getting engineering degrees, and had zero issues with academics in high school. My mom did a pretty okay job but it was absolute hell on her, I entered high school ahead on mathematics/history but pretty behind on writing and science. The science I dont blame my mom for, all the curriculum at the time was insanely religious, so the ones we could find were very dry.
Multiple members of my wife's family are teachers in the local public school system. From what they have told me: they don't want to be in that place. Parents demand it of them, despite their strong attempts to push back and say "hey this one is your job as the parent to solve". So that's the reason in at least some cases, although probably not all.
Anecdotally, if I were to stack rank my education in k-12 based on quality of teacher, it would essentially be all professors followed by k-12 teachers, with those receiving more teacher instruction being lower on the list. I was once instructed by a history teacher, to not use examples on a history essay that we didn't learn in class, because she had to look them up.
I find it incredibly easy to believe that I can teach my children better than the average teacher.
The fact is that in many places school standards have been so low and social promotion has been going on for so long that we now have people coming out of high school and college that have never achieved anything academically. Many of these people go into teaching (even when schools were academically rigorous, majoring in education was always regarded as one of the least challenging areas of study).
That isn't to say that there aren't good teachers, or that there aren't smart teachers - there certainly are. It is to say that having an education degree or a teacher's certificate does not mean that one is qualified to do anything.
Does this mean every parent is smart enough or cut out to properly home school their child? Of course not! What it means is that (many) schools have effectively failed as institutions and until they are improved many people are going to look for alternatives.
It absolutely does in Finland. It absolutely carried meaning when I was educated in my (non Finnish, non US) country.
What is revealed here is that a New York State teachers certificate doesn't mean much.
1. Teachers develop skills in managing rooms of ~30 kids. I believe this is completely different from tutoring someone 1:1 and likely has very little overlap.
2. Part of my day job is already mentoring/teaching. I enjoy that part of my work. I've received feedback that I'm good at it. Actually when I was younger I thought I'd switch into teaching after building up some savings with programming. I've since heard/read enough about the realities of being a teacher that I can't imagine doing that job (especially with public school). Homeschooling or teaching a homeschool pod seems like the best way to actually be able to teach if that's your inclination.
3. The k-12 curriculum is not really much to cover. Schools move at a pace appropriate for the slower kids in the room. It doesn't seem like a high bar to beat, and most of what I've found looking into it indicates that homeschool parents generally do outperform schools with a fraction of the time spent.
3a. I've already been teaching my 3 year old phonics and reading when she's in the mood. She doesn't really have the attention to sit and focus for more than ~5 minutes, but that's okay, and it's still going alright. I expect she'll already be years ahead of the school curriculum before it's even time to start. So initial results have been promising and suggest I am indeed capable of teaching a child.
4. When it comes to more advanced/in-depth understanding, I don't expect teachers to have the background. Like just looking at the math education program at my alma mater, there's no requirement for real analysis or algebra. There's no requirement for science courses (physics, chemistry, etc.). All of the options in the math department except education require at least a minor in another STEM subject. It's no surprise that a common trope is that teachers (particularly math) don't know how to answer how something gets used in the real world, but that's insane to me as a status quo. There are tons of applications of pretty much any math you might learn before graduate level in pretty much any field you examine (conic sections stand out to me as a niche thing that we covered in high school. Not that they don't have applications to e.g. orbits, but they don't seem to apply to other fields, and I don't believe the connection to physics was made in my high school class anyway (presumably because math teachers where I grew up aren't required to learn physics)).
Honestly I think school is mostly more useful for socializing and something like arts/crafts that entail mess and require a bunch of energy to do at home, especially before high school/AP classes. The academic part seems trivial. Once you've reached that conclusion, it makes sense to ask whether there are alternatives that are better suited/are more aware of and aligned to their purpose as enrichment.