Harvard's attack on Home Schooling

2,793 Views | 52 Replies | Last: 3 yr ago by TexasAggie81
Ulrich
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If I were designing a curriculum for a K-8 private school, I wouldn't diverge too much from what is normally taught. There's too much momentum on it and one school that feeds into high school and college can't diverge too far without leaving gaps.

One thing I would do is take a look at the curricula of the two or three high schools that your students are most likely to attend, and make sure that whatever you come up with fits into that - does it fill gaps those schools will leave, and does it prepare them for those schools. For the most part, the K-8 track seems like it has to be pretty set because of all the constraints around it.

However, I like the idea of working in a few classes that intentionally introduce students to some important ideas; some for immediate practical implementation, others to give a non-threatening introduction. A lot of this is probably covered in some form or fashion so sometimes the best tack might just be making sure that they are emphasized when they come up in existing classes. Not everyone probably has time for four extra classes, so maybe they are electives or replace/are subsumed by similar classes.

Introduction to Life Skills
Basic personal finance and the value of having a job, the idea of owning your mindset, introduction to philosophy, introduction to economics, psychology, and behavioral econ/psych (biases and heuristics). Eighth graders are close to getting their first jobs and having their own money, seeing depression and anxiety crop up in themselves and their peers, and starting to engage with the political and economic ideas they will likely follow for the rest of their lives. Equip their minds for self-determination.

Quantitative Literacy
How to do simple math problems in your head, how to estimate things, high level descriptions of different fields of mathematics with fun problems (I think Strogatz has some interesting material here). The idea is to show how to use math day-to-day in a non-threatening way, and start developing an intuitive idea of how to how attack certain problems or when something is really wrong. Show the power of math before teaching them to write proofs.

Introduction to Software
A programming assignment that goes from defining and diagramming a business or personal problem to writing and testing the code. It's not necessarily about learning the language, it's about learning how to think through a problem and know whether you have solved it. Abstract from reality, translate into the language of logic, and then check the answer against reality.

Nonfiction Writing
This is really for critical thinking, conveying ideas well and simply, and being as brief as possible (no word counts). Each assignment is probably several weeks long. Write a journalistic article - research, present both sides with a neutral tone, think about the purpose of what you are writing and journalism in general. Write a technical article - clearly express complex concepts in a logical order, make dry things interesting, think about format and audience. Write a case for a controversial issue - how to lay out an argument and be persuasive without getting emotional or committing fallacies.
Ulrich
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Ping! Reminder of this thread.
Quad Dog
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AG
A big idea I've heard before that I like is to replace calculus as the higher level math taught with statistics. Statistics is much more useful to the majority of people.
Edit to add that the "new math" that everyone hates is much more focused on quantitative literacy than the memorization method we all learned. My young kids are much better at number sense and mental math than I am even now.
commando2004
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AG
Quad Dog said:

A big idea I've heard before that I like is to replace calculus as the higher level math taught with statistics. Statistics is much more useful to the majority of people.
High schools do offer statistics courses. I took one.
powerbelly
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AG
Quad Dog said:

A big idea I've heard before that I like is to replace calculus as the higher level math taught with statistics. Statistics is much more useful to the majority of people.
Edit to add that the "new math" that everyone hates is much more focused on quantitative literacy than the memorization method we all learned. My young kids are much better at number sense and mental math than I am even now.
Yep. The new math is good stuff.

I agree that stats is more useful than calculus for almost every person.
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Beer Baron
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AG

Quote:

Edit to add that the "new math" that everyone hates is much more focused on quantitative literacy than the memorization method we all learned. My young kids are much better at number sense and mental math than I am even now.

Can someone explain the hate for the "new math" thing for someone who isn't that familiar with it? My understanding is that it's basically just formal instruction on all the mental "tricks" you do without thinking about it much. Like, for 47+34, you'd do 47+30 = 77, then do 77+4 to get the 81.

That makes sense and it's faster than mentally carrying the 1 for a lot of people. When I was a kid and they were teaching the carry the 1 thing I never understood why I was doing it, I just knew that's how you got the answer. My mom showed me the whole "find easier numbers to add" trick and it made a lot more sense to me.
Ulrich
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A version of statistics and probability (different than what is taught most of the time) would be a high school requirements in the world where I'm a more-or-less benevolent dictator. We live in a statistical world, and most people have absolutely no sense of how probabilities rule our everyday lives. Even if they master the domain of selecting red and yellow balls from an urn, it results in no sense of how statistics work in real life. I think it would be beyond most 8th graders to understand though, it's a much more subtle and pervasive thing.

Even most college-educated adults who passed STAT 211 are completely inept on this stuff.

Calculus is an elective, most people will never encounter calculus after graduation or have any particular need to understand what it is.
Quad Dog
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AG
Because it's not the way they know how to do math. Some of the more vocal haters can only do math by lining up the two numbers vertically, carrying the one, etc. The concept of breaking apart numbers and putting them together in different ways is completely foreign to them.
The way the kids learn now is they learn all these different methods to add or multiply numbers and they have different names. All the names and methods can get confusing to the kids and parents. My son struggled with all the options because he would mix them up halfway through until I pointed out that they were teaching many methods and he just had to pick the one that made the most sense to him.
Ulrich
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IMO knowing both ways is fine. The ones we were brought up with are faster for calculating the correct answer on paper. The new math stuff fits into a bucket of tricks and methods for understanding what the math is really doing and being able to work it faster in your head. Which method you use depends on what you're doing at the time.
commando2004
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AG
Ulrich said:

The ones we were brought up with are faster for calculating the correct answer on paper.
Thing is, pencil-and-paper arithmetic just isn't that useful of a life skill anymore. Back in the 1990's, our teachers justified it by saying "you won't always have a calculator with you", but these days virtually everybody does: It's a built-in app on even the cheapest cell phone.

Now, estimation is still a good thing to know. A person should be able to see an expression like "57913 / 314", quickly approximate it to 60000 / 300 = 200, and realize they made a typo if the calculation shows something around 20 instead. But actually doing the exact long division to get "184 remainder 137" or "184.4363057..." is just busy work.
Ulrich
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commando2004 said:

Ulrich said:

The ones we were brought up with are faster for calculating the correct answer on paper.
Thing is, pencil-and-paper arithmetic just isn't that useful of a life skill anymore. Back in the 1990's, our teachers justified it by saying "you won't always have a calculator with you", but these days virtually everybody does: It's a built-in app on even the cheapest cell phone.

Now, estimation is still a good thing to know. A person should be able to see an expression like "57913 / 314", quickly approximate it to 60000 / 300 = 200, and realize they made a typo if the calculation shows something around 20 instead. But actually doing the exact long division to get "184 remainder 137" or "184.4363057..." is just busy work.

That's exactly the sort of thing I would want to teach.
Star Wars Memes Only
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AstroAg17 said:

Yeah the way they do it now is perfect. Both calculus and statistics are elective, and nobody picks statistics because that would be a poor choice.
But you'd have to take statistics to prove that, and therein lies the conundrum.
Star Wars Memes Only
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I think there are important ideas a statistics class could expose people to. I don't really know what they teach in high-school level statistics, but things like conditional probabilities (which I think everyone thinks they understand, but really are terribly understood), counting and combinatorics and a feel for how quickly numbers grow in those situations, the law of large numbers, the fact that from very simple and easily satisfied conditions groups of random variables will often follow distribution laws, and properties of those distribution laws are all examples of things I think could be taught at a high-school level. Though people may not be looking at p-values, they should be able to understand the concept of standard deviations. All of these things I think could be important at some point or another in real life, and simple exposure to those concepts, even if one doesn't remember them precisely, could go a long way.
Ulrich
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To me, the key is approaching it through real life situations or even games rather than through math (not beans in a vase). Once you understand what is really going on, the math follows and typically isn't all that hard.

The typical person rounds 49% to 0% and 51% to 100%, even in pretty abstracted situations. Understanding that you're probably wrong at least 10% of the time even when you're really sure of something is a really important thing to know (in my book).

I hated stat classes, but I love figuring out how to apply probabilities, confidence intervals, Bayesian probability, risk/expected value, and so on in real life.
TexasAggie81
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James Dwyer (at Harvard)? The same guy who got a PhD in "Moral Philosophy" from Stanford?
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