[Enrollment Cliff ???]

Another source of revenue for colleges in need is international students.  These guys are paying full freight.    

[Round Table format about Sold a Story, put on by Learning Ally starting tomorrow]

Thank you!  

[Math after Calculus BC]

I vote for any of the AoPS classes, especially NT and CP.  You can definitely put WOOT on his transcript; I think it's very impressive if he can keep up with that class.  

Is he close to solving 10 problems on the AIME?  If he can grab an USAMO, he's in an elite group.  

The other options are also solid if that's what he prefers.  

[Favorite Lessons/Explanation for Average in Math.]

I like these explanations of the value of mode and median over the mean.

Mode  (this was taught to me by my teacher...in high school!)

Imagine you run a shoe store in a community with 2 types of people:  those with very small shoe sizes (say size 3) and those with very large shoe sizes (like size 11).  Say you are placing an order for new shoes for your inventory.  If you order based on the average shoe size, you will end up with a bunch of shoes of size 7, and no one to buy them.  

Median  (this is just what we see from the local realtors)

Median home prices are used a lot in our area because while most of the homes will be within a tight range of sales prices, there may be 1-2  homes that are way more massive and more expensive than is typical.  Those sales (maybe 100x the typical price) will skew the average home price and suggest that the average house has a higher value than the reality.  

[Charter schools for homeschooling]

43 minutes ago, Malam said:

What's stopping someone from joining the charter at the beginning of the year, spending the stipend (on approved curriculum of course), and then leaving, only to repeat the process next year?

It's a good question and as others have mentioned, non-consumables are the property of the school and must be returned.  I'm not sure how they'd enforce that if a family just made off with it.  Call the police?  They could make re-enrollment contingent on returning the stolen stuff or reimbursement.  

In our case, our ES was another local homeschooling parent, and everyone knows everyone in the homeschooling community, so word would probably get around if you stole stuff.  

In actual practice I don't think this happens much, but you do raise a good point.  

[Question about being a bigger fish at a smaller school]

I don't agree that "a degree is a degree."  I suspect quality varies, not only of teaching, but of a student's peer group at the school.  

If you think his peers aren't at his level, or maybe the classes will be too easy, try to arrange to have him accompany a current business major to classes.  

[AP Physics C or DE]

5 hours ago, Alice said:

My son really liked the PA Homeschoolers Physics. He did the AP Physics C Mech one semester and the AP Physics C E&M the second semester with Dr. Kernion. 

My dd also liked Kernion at PAH.  She started first semester with Lanctot and then switched to Kernion for E&M, and was glad she did.  

[Charter schools for homeschooling]

18 hours ago, Momof3sweetgirls said:

Pro: Stipend (1-2k) can be used for zoo/museum memberships, some sports, and learning subscriptions.

Con:  I thought we'd homeschool year round and take lots of breaks but you have to demonstrate attendance during the typical school year. 

Any insight on this kind of program?

I'll address these with the caveat that each charter has its own policies.  

My charter had a long, long list of approved vendors from which we could order materials.  These included the Singapore Math website, our local ballet school, and American Girl (for books, not toys), and tutors and music teachers.  For elementary it was still a chore to spend all my money by the end of the year.  

If the materials are considered consumable (like workbooks that you write in) you can keep it forever.  for materials that aren't consumable (science equipment that can be reused, textbooks, etc.) you need to return it to the charter before you disenroll.  

Mostly I'm glad I didn't leave money on the table, money I paid in taxes that I could recoup with little effort.  There weren't any conventions in my area, so I was buying curriculum materials sight unseen, so I liked being able to spend someone else's money.  It also allowed me to buy science equipment that I would use once and be done, and the charter was great because they would take it back, and I didn't need to worry about arranging to sell it or give it away, such a time saver!  

I schooled year round, despite being enrolled in the charter.  I could keep all my materials, even the non-consumables, over the summer, because I was planning to continue enrollment the following year, and they trusted me and were just generally very cool that way.  

I met with an Education Specialist, also a homeschooling parents, once a month and our meetings were efficient and delightful for my kids who got to brag to her about what they did all month.  It truly was lovely.  I had to do some photocopying of work samples, but this was before smartphones; I imagine parents can just take pictures using their phones.  This amounted to roughly an hour every month.  ES meetings were when the materials I ordered were delivered to me.  

There are annual testing requirements, which were minimal in elementary but by middle school, were such a chore and inconvenient and time-consuming and took away too much time from actual school.  Since I could see that we wouldn't use the charter for high school anyway, we dropped it in middle.  

Overall my experience was positive, and I have fond memories of the charter. 

 

[Charter schools for homeschooling]

As others have pointed out each charter has its own policies and pros and cons.  The best thing you can do is speak with other parents who have their kids enrolled at the school or used to be enrolled at the school and ask them what it's like.  

Know that you can always enroll and if it isn't your cup of tea, you can return to private homeschooling.  Or vice versa.  

In my case, we did a charter for elementary.  This school did not provide any classes or field trips or anything except some light oversight and a lot of money.  I hung out with my local homeschoolers who were a mix of charter and private.  I organized book clubs, math clubs, field trips for all homeschoolers.  It didn't matter at all who was doing what, we were all homeschooling.  

In our particular county, there was only one charter available to us, and I learned that the charter was a nightmare for high school students.  I was feeling the pain of hoop-jumping when my kids were in middle school, so we dropped the charter and seamlessly moved to private homeschooling, albeit without the money, but with the independence that I needed to prep them for college admissions.  

I came to learn that in So Cal, they seem to have a surfeit of charter schools and it seems consequently their charters are more flexible and offer more services than mine did.  

But the best thing you can do is talk to actual families who have experience with your particular charter school, or barring that, just enroll and try it out for as long as you like it.  

[AP Precalculus]

6 hours ago, EKS said:

I suspect it's a way to deal with the dumbing down of the high school math sequence by making precalculus seem like a college course.  Ridiculous.

I don't know.  In the absence of any national standards, I welcome the attempt to impose some order on high school curriculum.  Students will find out earlier in their high school career whether they are adequately prepared for calculus and so on.  I would love to see an AP algebra, with appropriate standards.

Honestly, I would not call any AP course, not AP chem, not AP bio, not AP calculus, college level material.  

["Show your work"]

My rule of thumb is they are getting the correct answer, I don't change anything.  If they are making mistakes, then they need to include additional steps to prevent errors.  

[AoPS self paced Intro to Algebra questions??]

1 hour ago, Kezia said:

Have you found the self paced to be easier for the student to complete than doing it with just you at home? 

In other words, do you make them read through the section first? 

Working with a parent at home using just the textbook is more time-consuming then letting them work independently online.  The self-paced online option wasn't available to me at the time, so we used the textbooks at home.  My dd's attempted every single problem in the textbooks.  They never did alcumus and never watched the videos.  If there were any problems they couldn't figure out we worked through them together.  

I'm sure there are some students who can read the textbook independently, but I think it's a big ask for most students, even in high school.  I read the textbook out loud with my student next to me.  I had a pad of paper and wrote through their example problems line by line (hence all the time required).  

We spent one day on each section of a chapter and then 1-3 days on Review Problems and 1-3 days on Challenge Problems.  

If you want to salve the Give Up buttons, you can present the problem to him, on paper, once again.  If he can solve it, then move on.  If he can't, review the solution with him.  The problem sets are so short as it is, you want your student attempting as many as possible.  

[I have a multi-layered college question]

On 1/24/2023 at 10:39 AM, ShepCarlin said:

So my questions are:

Are there universities in the southeast that offer outstanding teaching degrees? Or a chance to get a degree in a particular subject with an emphasis on teaching?

What should he look for as either an education major or majoring in a different subject but with the intent to teach that subject?

 

There is a subreddit for teachers that might be able to provide some career advice.  Warning, though, the unhappy teachers tend to post a lot.  And boy are they unhappy.  

[AoPS Calculus after Saxon Advanced Math]

Since you are planning to take the AP exam, I would get yourself audited by the College Board as an AP teacher.  (Should take 10-15 minutes if you select one of their pre-approved syllabi.)  You'll then have access to their calculus Question Bank so you can create practice worksheets with actual calculus exam questions.  

As you probably know, the AoPS problems are challenging, and your student will learn a lot, but in order to do well on the exam, she'll want to be familiar with the idiosyncracies of the AP exam specifically.  You don't want her parsing problems she's unfamiliar with for the first time on the exam.  

As long as you are prepared to spend some time doing dedicated AP practice, you should be good.  

[Common App basics -- help?]

Another overlooked resource is the Common App tech support.  I find that when I ask a question of their own online support, I get a response very quickly and I was paired with someone on one ticket so I could keep the conversation going with that person about my issue.  For every CA question, I would post to WTM and also ask them directly.  

[Common App basics -- help?]

@blue plaid You are in good shape if you are planning to apply next year.  As other's have said, you've totally got this and we are here for you if you have specific questions.  For now, do you have a list of courses your student has taken the past 3 years, course descriptions, grades, textbooks, etc?  If not, that might be your homework this month.  

[Ap computer science options]

FYI, I would skip CS Principles and just do CS A.  I don't think there is much to be gained by taking the easier CS course.

Since your student is already solid on python and just needs to get the gist of Java, I would look for ways to self-study if he has the EF skills to manage it.  It won't be a lot of new material.    

[College student seeks to transfer after freshman year - what do we need to know?]

3 hours ago, Grace Hopper said:

Oh man, it got a D. 😳

And yeah, we should have looked more closely. 

 

Thanks for the report back.  And to be clear, I do not blame you.  College financial bankruptcy is a relatively recent phenomenon, and that the Forbes list in only a few years old is one manifestation. 

I was just reading about some free speech controversy at Hamline College in Minnesota (also a D on the Forbes list), and incidentally the journalist mentioned that many of these small colleges are hanging on for dear life and can ill afford any negative publicity impacting their enrollment.  

[College student seeks to transfer after freshman year - what do we need to know?]

18 hours ago, Grace Hopper said:

Rumor is that the uni is actually financially struggling which is obviously not apparent in recruitment and orientation materials, but is obvious in maintenance failures.

This is going to become a key issue for many college applicants:  is their university on solid financial ground, and will it still exist when they are seniors.  You say this was not obviously apparent when your student was applying, but looking back now, were there any warning signs?  

Forbes assigns a financial grade (A-F) to schools based on their endowment, admissions yield, and other factors.  When you search for your student's old college, what was its financial grade?  (I'm curious how valid is Forbes' assessment.)  

[Online Python courses]

Before my kids took the AoPS beginning Python class, I had them do some work out of Python Programming for the Absolute Beginner by Michael Dawson.  I'm sure having python experience before taking the class isn't necessary for many kids, but I know that AoPS courses tend to be fast-paced anc challenging and I wanted compensate for that a bit.

I think they took it somewhere around grade 6.  

[Grammar]

20 hours ago, Clarita said:

Why did you skip level 1? 

We didn't skip it.  I just really, really like CE 1 and 2.  WWW in the subsequent levels was a disappointment, but I'm not sure if they've updated it since I used them.  

[Grammar]

We didn't have Poodle level when my kids were little.  The 4 level sentence analysis practice books were absolutely key.  The grammar lessons stuck with them through high school.  I also enjoyed the Caesar's English vocabulary lessons, in Levels 2 and 3.  

[What is your favorite tools or curriculum for teaching math?]

Singapore Math (US edition) was solid for elementary for us.  I'm kind of glad Beast wasn't around when my kids were younger because I don't think that would have been a good fit.  

Also, we used MOEMS books like once a week which was excellent preparation for math contests later on, like MathCounts and AMC 8.  

[What do we know about the science of teaching math?]

On 1/3/2023 at 5:05 AM, EmilyGF said:

I came across this website: The Science of Math that has some short, research-based rebuttals to some math questions, but it isn't as deep as I'd like.

 

 

Thank you for linking this; I hadn't heard of it before.  I was able to find a few podcast interviews, and I'm learning that the miseducation we see with reading is also happening in math.  

[What do we know about the science of teaching math?]

I stumbled on this article about Australian math education, and I see a lot of similarity with US education.  The big difference is they seem to have systems that operate province-wide, so one uninformed bureaucrat can have a big impact.  The US system is highly fragmented, so you never know what you are going to get.  

Some excerpts:

One of its fundamental failings is the treatment of algebra, by which measure the new curriculum falls short by a country mile.

Algebra is the beating heart of mathematics. It is the naming of the quantity being hunted, setting the stage for its capture. It is how we signify pattern and how we express the relationship between quantities. You want to understand something else, probability or statistics or geometry? Algebra is essential. Algebra is how Descartes captured geometry, and how Newton and Leibniz captured calculus.

A fundamental insight is that algebra is simply arithmetic, just with numbers we don’t know. The current curriculum states this clearly, in a Year 7 instruction to ‘Extend and apply the laws and properties of arithmetic to algebraic terms and expressions’. By contrast, ACARA’s new curriculum instructs Year 7s to ‘generate tables of values from visually growing patterns or the rule of a function; describe and plot these relationships on the Cartesian plane’.

This is pointless, and it is not algebra, except in the most trivial sense. It is substituting data entry and graphical busywork for the critical practice of algebraic skills. The curriculum is choked with such nonsense, strangling the few stray instructions that might otherwise engender proper study. The term ‘algebra’ and the critical discipline of algebra have been distorted to meaninglessness.

**********************

There is, to recoin a phrase, no royal road to algebra. A mastery of algebra requires practice and memorisation and struggle. And preparation. Prior to the arithmetic of numbers we don’t know comes the arithmetic of numbers we do. In order to understand a/b = c/d, we must first understand 4/6 = 6/9. This is the work of primary school.

**********************

The treatment of mental skills is little better. Automatic recall of the multiplication tables is critical to all the arithmetic that follows: a student cannot apply 4 x 9 if they are struggling simultaneously to remember it or calculate it. The multiplication tables were mangled in the draft curriculum and then fixed, but only up to a point, where they are referred to as ‘multiplication facts’.9 This is weird and telling. Much worse, the tables (still) only reach 10 x 10, rather than the traditional 12 x 12. This matters. We have 60 minutes in an hour and 360 degrees in a circle for a reason. Having natural multiples and factors and fractions readily at hand is critical for the learning of arithmetic.

The ignorant decision to exclude 12 turns out to not matter, however, since few students even get to 10. The large majority of primary school students do not learn their multiplication tables. This is because, clear curriculum direction notwithstanding, the very large majority of primary school teachers do not consider the tables important, much less mandatory. Teachers have been fed other ideas.

**********************

ACARA’s new curriculum is a large but entirely predictable step down. Modern education is steeped in grandiose perversion, with innovative but misconceived practices working not to improve but to undermine fundamental processes of understanding. There is Higher Order Learning, and 21st Century Skills, and Flipped Classrooms, and Child-Centred Learning, and Discovery Learning, and Inquiry Learning, and Play Based Learning, and on and on and on. Underlying almost all of this is the philosophy of constructivism.

Built upon the tautology that we only understand what we understand, constructivism claims that students must construct this understanding through their own experience. Constructivist approaches are to be contrasted with the boring old practice of directly teaching students, and in particular the teaching of clear facts and skills. Always lurking is the boogieman of Rote Learning. This boogieman in particular has frightened teachers away from orderly ‘tables’ and into embracing isolated ‘facts’.

There is a proper and important role for mathematical exploration, but that role in primary education is limited. It took thousands of years for civilisation to come up with the crystal concepts and truths and techniques of ‘elementary’ mathematics. Constructivism is the slowest and most painful and least successful method of mastering these fundamentals.

Not everyone, however, sees this as a drawback. A teacher focused on students’ Higher Order Thinking may have little concern for the lowly basics. Mistakenly. Rather than basic facts and skills being opposed to deeper thinking, the basics are the foundation for deeper thinking. Before twenty-first century skills, whatever these might be, there must come a mastery of seventeenth-century skills.

**********************

Hand in hand with constructivism goes problem-solving, one of the great con jobs of mathematics education. Mathematicians love the idea of problem-solving, since it is a one-word definition of what they do. Mathematicians love to see children working on authentic, well-structured problems, with clear mathematical content and purpose. But school problems are different. School ‘problems’ are typically poorly defined, open-ended explorations with no measure of or concern for success, and with students ill-prepared for a venture of any significance. These problems are all the worse for almost invariably being about something other than mathematics, about a largely fictitious Real World. Thus, rather than a carefully crafted problem about prime numbers and factors, students ‘explore’ or ‘model’ the painting of walls and the graphing of mortgage rates. Students are presented with pseudo-problems that require little thought and inspire less.

ACARA and the education authorities regard the Real World as a great selling point. Hence the new curriculum has a stream on ‘Space’ rather than geometry. Hence NAPLAN has a test on ‘Numeracy’ rather than arithmetic. Hence the mandating of statistics way beyond its very limited pedagogical worth. Hence the unceasing focus on STEM, which reduces mathematics to an instrumentalist, utilitarian skill set. This all fits in well enough with the neoliberal notion of education as training, but it is otherwise reductive, and it erodes the basis for mathematical thinking. Real Worldness in school is almost invariably contrived, and thus as boring as dirt, because we simply need very little mathematics for our everyday lives.

Such Real Worlding also feeds back to devalue and to poison the teaching of mathematics. The critical point of mathematics, the source of its incredible power, is that it removes the distracting noise of the world. Mathematics abstracts from messy reality to create something much simpler, something that can be analysed and honed and generalised. And yes, mathematics then gives back, providing indispensable tools for the understanding of real-world phenomena. But the mastery of these tools is beyond the scope of school mathematics for any but the most banal of real-world situations. What results is simply the glorification of noise—the presentation of noise as the central topic of mathematics education. It is absurd, and disastrous.

**********************

Mathematics education wastes untold time and energy and goodwill on electronic media: students watch videos instead of reading; they ‘move’ shapes on screens instead of shifting physical blocks; they push calculator buttons instead of computing on paper; they ‘prove’ statements by pressing Solve or Graph on their handheld computers.

**********************

Plenty are fooled by constant references to ‘visual learners’ and ‘digital natives’, but there is no fooling reality. The perverting effect of these media is that students are not required to think or to reflect. They need never pay proper attention, to a teacher or even to their own thoughts. The electronic media stimulate and entertain, occupying the space where contemplation might have occurred. In his 1986 book Amusing Ourselves to Death, Neil Postman wrote on the effect of television on education: ‘The name we may properly give to an education without prerequisites, perplexity and exposition is entertainment’. That is where we are, except that now television, and much worse, are in and are intrinsic to the classroom.

**********************

THE PAST IS A FOREIGN COUNTRY
And the name of that country is Singapore. For instance.

Asian countries dominate TIMSS, the international test of school mathematics. Asia even dominates PISA, the anti-algebraic non-test created specifically so that Western countries would feel better about themselves. Even if one wishes to concentrate upon ACARA’s snake-oil games, it turns out that attention to the basics is the way to go.

Australia once did much better, although that was long ago and is largely forgotten. The powerful forces of entertainmenting have been at work for many decades. Moreover, there are two intertwined forces, one political and one philosophical, which have directly perverted mathematics education.

**********************

First, the political. Historically, for good and bad, Australian mathematics education was carefully controlled by education bureaucrats under the guidance of mathematicians.15 In the 1970s, teachers started to be given more autonomy.16 Also around that time, a fourth group, of education academics, was beginning to emerge as a force.17 Since then, and with varying overlaps and alliances, these four groups have tussled over the nature and control of mathematics education.18 All-out war broke out in the early 1990s, with the bureaucrats attempting to wrest control from the other three groups.19 The bureaucrats failed, but the downward slide was well underway. The power of education academics has continued to grow, and they are now much more closely wedded to the bureaucrats.

**********************

With mathematics education academics now in possession of their own world, they are generally much less connected than they once were to the world of mathematics; they are less adept at and less interested in it. This lack of mathematical expertise encourages and necessitates an emphasis on other, non-mathematical concerns, laying the fertile ground for constructivist obfuscation. Much more time is spent in apologising for and avoiding the difficulty of mathematics than is ever spent addressing that difficulty, or in demonstrating the beauty and the power that can result from proper effort.