An Educational Conjecture

OK, time for a competition (And, no, we haven’t forgotten our previous competition, which we shall revive at some stage.)

Here is a conjecture:

Every new idea in modern mathematics education is either trivial or false.

Can we prove this conjecture? Of course not. Not, at least, if we do not Learn More about it and without reading thousands of pages of educational gobbledegook. (Which. We. Will. Not. Do.) Is the conjecture true? We don’t know. But we are not aware of any counterexample.

The competition, then, is to attempt to prove the conjecture false. The winner is the commenter(s) who comes up with and argues most persuasively for a counterexample: the new idea in modern mathematics education that is true and the least trivial. The winner(s) will receive a signed copy of the number one best seller,* A Dingo Ate My Math Book.

Just a few notes on the parameters:

• By “idea”, we mean any claim about or approach to teaching or learning mathematics.
• By “new” we mean something other than dressing up a traditional idea in new clothing.
• By “modern”, we mean from the last fifty years or so, back to about 1970.
• By ”least trivial”, we mean something of genuine value, least trivial to mathematics education. So, deep ideas in neuroscience, for example, will score little if the subsequent application to mathematics education is trivial.
• By “true” we mean true.
• Suggestions, which can be made in the comments below, need not be long, specific or heavily documented. We will reply politely to any suggestion (and other are welcome to reply), querying and critiquing. Further argument and evidence can then be provided.
• Will we be fair? Probably not. But, we’ll honestly try.
• Multiple entries are permitted, and there may be multiple winners.

Go for it. We’re genuinely curious about what the responses may be.

*) In Polster and Ross households.

UPDATE (17/4)

The competition is, of course, a challenge: put up or shut up. If a reader cannot propose and defend one single idea of modern mathematics education then that reader should perhaps stop imagining that any such idea exists. And, if such an idea does not appear to exist, the reader should consider what that suggests about the mountains of Wow produced by the maths education industry, and what it suggests of the shovelers creating these mountains.

Now, what could or should one expect the response to be to such a challenge on an aggressively antiestablishment blog such as this? This blog has a decently large (but not huge) readership, although we can only determine the nature of the readership from the minority who comment, which is obviously a very biased sample. Still, it is probably reasonable to place readers of this blog into three camps:

1. There are the fellow travellers: like thinkers and “Marty fans”.
2. There are puzzled and/or annoyed teachers, who smell that there is something wrong with their teaching world, while still maintaining some faith in the orthodoxy. They may appreciate some of the specific critiques on this blog, while not buying the overall message of contempt.
3. There are the Marty haters, people who are convinced that Marty is an asshole or a nutcase,** who loathe this “nasty” blog, but who visit occasionally in order to feel superior.

This competition is primarily directed at members of Group 3, those who create and promote and value modern maths education. Again, it is a challenge: put up or shut up. If such a person cannot defend such ideas outside of the comfort of their cult, then there is no reason for anyone else to take them seriously.

Do we expect responses from members of Group 3? No, of course not. They regard debating on a blog such as this as beneath them. But the challenge is there, and it will remain there.

What about Group 2? Here, we’re guessing there are some thoughts of possibly defensible ideas, but there is probably some nervousness in proposing them. Such ideas will of course be critiqued (that’s the whole point), and strongly. So, we totally understand any such trepidation, although it is misguided. This blog is scathing of bad ideas, but it is respectful to all good faith commenters, which has been pretty much everyone.

Group 1 can take care of itself, of course, although its members could be more actively critical of this blog …

**) Both are true.

UPDATE (12/05)

OK, it seems like a good time to begin rounding this off. So, who is the winner? We’re not convinced anybody “won” in the sense that anyone has suggested a significant counterexample to our conjecture. None of the suggestions compares, for example, to the elephant truth that mathematics teachers need to understand mathematics a hell of a lot better than they do. None of the suggestions deals with the fundamental flaws of modern education, with, in particular, the deification of technology and the demonisation of discipline. We’re convinced as much as ever that modern educational “research” is fundamentally useless, when it is not actively destructive.

Still, if the suggestions below are minor in effect, some are good and sensible. We have thoughts on a winner, but we thought to let readers have a shot at it first. So, if you have an opinion on the best response to our challenge, please indicate below. We’ll consider, and we’ll announce our winner later in the week.

Update (29/07/21)

We’ve finally ended this. The winner is student-teacher (wst). See here for details.

Don’t Go West, Young Man

No, Burkard’s and my new book has nothing to do with going West. A signed copy of our book is, however, first prize in our new Spot the Exam Error(s) Competition. (Some information on our previous exam competition can be found here.)

We spend a fair amount of our blog time hammering Victoria’s school curriculum authority and their silly exams. Earlier this year, a colleague indicated that there were perhaps similar issues out West. We then had a long email exchange with the semi-anonymous Charlie, who pointed out many issues with the 2017 West Australian Mathematics Applications Exam. (Here is part 1 and part 2. WA’s Applications corresponds to Victoria’s Further Mathematics.)

Following our discussion with Charlie, we sent a short but strong letter to WA’s School Curriculum Standards Authority, criticising one specific question and suggesting our (and some others’) general concerns. Their polite fobbing off indicated that our comments regarding the particular question “will be looked into”. Generally on the exam, they responded: “Feedback from teachers and candidates indicates the examination was well received and that the examination was fair, valid and based on the syllabus.” The reader can make of that what they will.

The Competition

Determine the errors, ambiguities and sillinesses in the 2017 WA Applications Exam, Part 1 and Part 2(Here, also, is the Summary Exam Report. Unfortunately, and ridiculously, the full report and the grading scheme are not made public, and so cannot be part of the competition.)

Post any identified issues in the comments below (anonymously, if you wish). You may post more than once, particularly on different questions, but please don’t edit on the run with post updates and comments to your own posts. You may (politely) comment on and seek to clarify others’ comments.

This post will be updated below, as the issues (or lack thereof) with particular questions are sorted out.

The Rules

• Entry is of course free (though you could always donate to Tenderfeet).
• First prize, a signed copy of A Dingo Ate My Math Book, goes to the person who makes the most original and most valuable contributions.
• Consolation prizes of Burkard’s QED will be awarded as deemed appropriate.
• Rushed and self-appended contributions will be marked down!
• This is obviously subjective as all Hell, and Marty’s decision will be final.
• Charlie, Paul, Burkard, Anthony, Joseph, David and other fellow travellers are ineligible to enter.
• Employees of SCSA are eligible to enter, since there’s no indication they have any chance of winning.
• All correspondence will be entered into.

Good Luck!