We’ll go through this in detail when we update this WitCH (scheduled for sometime in 2023). The problem with that is, unless the vectors and are appropriately related, the scenario simply cannot occur, meaning  cannot exist. As John Friend notes, it is at least a small step along the way to indicating the question is not all hunky-dory. Commenter has SRK has flagged a related video (and will pay dearly for it): 156 Comments on WitCH 41: Zero Understanding, algebra, Eddie Woo, index laws, infinity, teaching, WitCH, This is way unimportant in comparison to the current idiocy of the neoliberal nutjobs. (John Stillwell has written a beautiful book, in fact two beautiful books, on the history of mathematics from this perspective.) Is this sufficient to argue for introducing these infinities into the classroom? Cloudflare Ray ID: 5e5f68578b2ad6c1 That’s all pretty awful, but we believe there is worse here. So in the given order, according to BODMAS rule, we do multiplication before addition.

It is the closing summary of Chapter 21A, Estimating the area under a graph. It could easily be its own WitCH, but it fits in naturally here (and also with this WitCH). The real question is, can one define 1/0 in a meaningful manner? Why is 1/0 = 2/0, and why should it lead to 1 = 2? 37 Comments on WitCH 40: The Primary Struggle. How Many Rabbits Do You See Riddle ANSWER, Solve A Terror Case Puzzle Answers [SOLVED].

Jerry in the comments has located a draft version of the article, available here. (It is followed by 21B, Finding the exact area: the definite integral.). Ninety-three early-years Australian elementary teachers completed a questionnaire about their understanding of the role of struggle in the mathematics classroom. We’ll go with “Good luck”.

Thanks to Damo for pointing out the problem, and thanks to the commenters for figuring out the nonsense. Many of the remaining teachers (16 %) held what constituted conditionally positive beliefs about struggle, emphasising that the level of challenge provided needed to be suitable for a given student and adequately scaffolded. Now, as it happens, Mathematica’s/VCAA’s screw-up could have been avoided by using the function Reduce instead of Solve.

This WitCH is from Cambridge’s 2020 textbook, Mathematical Methods, Unit 1 & 2.It is the closing summary of Chapter 21A, Estimating the area under a graph. As commenters have noted, the Examination Report has finally appeared. And, as predicted, answer A was deemed correct, with the Report noting. Math comes naturally to some, but even simple equations remain baffling brainteasers to others. But, in the end, the thing will still be there and we’ll still have to come back to polish it off.

The examination report provides answers, identical to those in the Mathematica solutions, but indicates nothing further. The article is by (mostly) Monash University academics, and a relevant disclosure: we’ve previously had significant run-ins with two of the paper’s authors. But, as they say in the theatre, the shitshow must go on.*. This one comes courtesy of Simon the Likeable, who suggested we watch the following, and who will pay dearly for it.

Partly, the explanation can go down to this being a question from NHT, about which, as far as we can tell, no one really gives a stuff. The full article is available here, but is paywalled (Update: draft here).

Yes, we can. Cardinality is not relevant here, but the Riemann sphere and projective line definitely are; they are both capturing 1/0 as an infinity thing, in contexts very close to standard school mathematics. Next, suppose we lucked out and began with perpendicular to .

2020 BAD MATHEMATICS It is a multiple choice question from the 2009 Mathematical Methods, Exam 2; the Examination Report indicates, without comment, that the correct answer is D. We’re really, really trying to avoid new WitCHes right now, but people keep throwing them at us. You want to throw or or at us? She obliged, but the following morning she presented him with a gift. calculus, integration, Mathematical Methods, textbooks, VCAA, VCE, WitCH, This WitCH is from Cambridge’s 2020 textbook, Mathematical Methods, Unit 1 & 2. Option A gives the set of equations that can be used to obtain the values of m, n and p. Explicit solution would result in a null set as it is not possible for a result of a vector to be of greater magnitude than the vector itself. so 1 wand = 7. It looks like it would probably be easy, but it isn’t. For the NHT problem above, the massive elephant not in the room is an expression for the derivative function: What do you see? Take a guess.

The question is stuffed. Although teacher beliefs about, and attitudes towards, reform-oriented pedagogies have been a focus of previous research (e.g., Anderson, White, & Sullivan, 2005; Leikin, Levav-Waynberg, Gurevich, & Mednikov, 2006), teacher beliefs about the specific role of student struggle has only been considered tangentially. And, here is the first part of the introduction: Productive struggle has been framed as a meta-cognitive ability connected to student perseverance (Pasquale, 2016). Brooms Value – There are 4 Brooms, so 12/4 is 3. Dick. A viral math problem has taken the Internet by storm: 8÷2(2+2). Well, it’s something. You want us to think of division as “how many”, then fine, but don’t deliver a kindergarten-level speech on it. UPDATE (11/05) Steve C’s comment below has inspired an addition: The third greatest issue with the exam question is that it is wrong: none of the available answers is correct. How, then, do we find ?

You can watch a significantly younger, and significantly hairier, Marty discussing the notions here. exams, Mathematical Methods, transformations, trigonometry, VCA, VCAA, WitCH. On the other hand, it implies that the teacher is helping to orchestrate a challenging, student-centred, learning environment characterised by a supportive classroom culture. Plugin the known values, witch + 7 + 3 = 15. Of course taken literally, Eddie’s claim is silly; as we suggested in the comments, we can define 1/0 to be 37. How can we do this without using electricity? The fourth and final thing to note is that, as we will now argue, we can indeed make sense of 1/0 as an infinity thing. Those are the elephants stomping through the room but, as commenters as have noted, there is plenty more awfulness in this question: calculus, Cambridge, integration, Specialist Mathematics, textbooks, WitCH. But as soon as the teacher, perhaps in hushed and secretive tones, is suggesting or , then maybe they should also think about this in a less Commandments From God manner, and let come properly out of the closet. Which shows that the mess in the intended solution, Answer A, is ridiculous. Finally, what about 1/0 in the Extended Real Line? In particular, the “repeated addition” nonsense is excruciating, and entirely unnecessary.

Then, if we assume that the normal (field) rules of algebra apply to V, it is not hard to prove that 1 = 2. The Internet, though, is completely divided over the correct answer. Ideally, we’d just write a straight post but we just have no time at the moment, and so we’ll WitCH it, hoping some loyal commenters will do some of the hard work. If you are on a personal connection, like at home, you can run an anti-virus scan on your device to make sure it is not infected with malware.

Well, the positive or negative thing is definitely an issue. Now we have (Broom = 3 + witch = 5) x (2 x wand = 14). After a bit of trig and unit vectors, we have (in must useful form). This world is called the Extended Real Line. What about the two-pronged infinity, the version that kids naturally try to imagine, with a monster thing at the plus end and another monster thing at the minus end? This WitCH, which fits perfectly with the discussion on this post, is an article (paywalled – Update: draft here) in the Journal of Mathematical Behaviour, titled, Elementary teachers’ beliefs on the role of struggle in the mathematics classroom. Once Upon A Pandemic Anna and Andy ANSWER (Solved), Who Did The Farmer Buy The Well From?

We were working on an update to polish off this one, when Simon the Likeable pointed out to us the video below. Another way to prevent getting this page in the future is to use Privacy Pass. Your IP:

Readers will be learning more about Sai in the very near future.

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