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Comment Proof that 1=2 is based on simplifying x/x (Score 1) 1067

I'm surprised no one has mentioned this yet, but allowing that x/x can be simplified when x=0 allows for strange equalities to emerge, basically that 0=1 or that 1=2. (This also serves as a proof by contradiction to the ability to simplify x/x for x=0) Consider the following reference: https://www.math.toronto.edu/m...

Comment Proof that 1=2 (Score 1) 1067

I'm surprised no one has mentioned this yet, but allowing that x/x can be simplified is dangerous ground because it allows us to prove equalities that are not true. (From another standpoint, then, we can prove by contradiction that x/x does not work for x=0.) For reference, consider the following site about the proof that 1=2. https://www.math.toronto.edu/m...

Comment Re:imagine that. (Score 1) 113

My biggest concerns with the introduction of technology into the classroom are that first, we don't really have any killer-app that justifies the expense,

Not entirely correct: As a math teacher I have found that Desmos (.com or app) is a remarkably good graphing calculator for mid-range algebra 2 students. When the alternative is an $80-120 graphing calculator, it has its appeal. Khanacademy.org has extreme value, when used for extra practice, and digital copies of texts are more prevalent, though current methods of DRM make them often more costly over time than the physical version, if not more up-to-date.

It's extremely easy to get off-task when you have the bulk of the Internet at your disposal, even if there's content filtering. General purpose computers give students almost unlimited choices in what to do, and only one of those choices is the intended one.

This is absolutely true, and the main reason that while I recognize the potential value of cell phones, I generally see greater problems in the classroom with their use.


One thing that hasn't been alluded to yet that I think is VITAL: my students exhibit high levels of technology dependence. Their every spare moment automatically drags them to their device. This is leading to a growing situation where they will entirely ignore a class-wide announcement unless they have been called to attention BY NAME. It's reaching greater levels of absurd every year.

Comment Re:Fast track (Score 1) 355

On the contrary: I teach in a public High School. These students most likely learned these habits at public school (or at home): Don't do your work most of the trimester? Turn it all in at the end! Don't want to be polite or act like a human being? Trash talk the teacher, they're paid to help you. This isn't always true: I've had many success stories with lower-level students, but there is no way that making the schools entirely state-funded will magically make it possible to just kick out poorly-behaved students. That said, there should be a process he should be able to go through. At least at the High School level there are options for the worst-behaved students to go through a behavior review process.

Comment Firefox vs Apple? (Score 1) 764

So the CEO of Firefox got fired for voting a certain way (I honestly don't remember the specifics, only that it had to deal with his vote on an sexuality issue), but the CEO of Apple is applauded for taking a stand on the other side of the issue in a way he believes is right. Is the only difference the public's opinion of whether the guy is a bigot or a hero? Or is there more to it than that?

Comment Re:Three times less = negative number! (Score 1) 171

While technically correct in a literal sense, the phrase is colloquially understood to also mean reduced (fractionally) by a factor of 3. When they say three times less, they are in fact trying to communicate a third, and it's generally understood.

You might as well argue the semi-anually vs bi-annually case. the semi and bi prefixes have lost meaning because of continued colloquial use.

Even one textbook I teach from defines semi-monthly as twice a month and semi-weekly as once every two weeks. The terms have less of a literal meaning and more of a context-specific meaning.

Comment Re:Every Inch of A Jail (Score 1) 643

Except that only those in possession of recordings are able to bring the truth to light. This means that bad things can still happen, but only those with the recordings get to do anything about it. I agree, though, that prisons should have pervasive recordings that are audited by an external source.

Comment What about MY rights? (Score 1) 643

Am I the only one worried by the fact that I'm not perfect? That is, the more cameras we have, the more likely someone will have a recording of us doing something that, though maybe not illegal, might be damaging to our reputation. As much as I like the idea of police having record of altercations, what happens when I do make a mistake and someone recorded it? There are so many rules and laws, that if a person is recorded constantly, their imperfections (real or perceived) can be recorded and then selectively used against them.

Comment The answer is... (Score 1) 663

D) 1. The test is clearly dealing with subtraction and parts missing vs the whole. That said, why they use the vocabulary they chose, not sure. Can't you teach the word 'equation' to first graders :P. #12 is lousy, though, since the solutions are not represented as equations that use subtraction. The test is TRYING to emulate different ways of saying and encountering subtraction, but still has room for improvement.

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