I don’t really know if or how this’ll work, but I figure it’s worth a try. While you’re all locked at home in your individual countries/cities/houses/rooms, you may request help here on *any* maths problem, of *any* level: just ask your question in a comment on this post.

God knows what will happen, but I will do my best to give you some guidance in a reasonably prompt manner (within a day-ish).* Others are of course free to offer help, and if they do so then I will try to ensure any subsequent discussion progresses naturally and helpfully.

A couple quick points:

- Do your best to ask the question briefly but clearly, and indicate why you’re asking it.
*Hopefully*LaTeX works in the comments (try $ latex*[Your LaTeX code]*$ ).- If the question is small and easily resolved then the discussion can stay on this page; for more involved questions, I’ll create a separate post for the discussion.
- Please ask new (unrelated) questions in new comments, rather than replies to existing comments.
- My approach to this kind of teaching is to be pretty Socratic, to try lead a student to the answer, rather than just providing the answer. So, don’t be surprised if you’re asked to go away and ponder some specific aspect of the question.
- I don’t particularly care if the question comes from an assignment or whatever, though I prefer honesty on this point. (And, the more I suspect the question is somehow officially assigned work, the more Socratic I’m likely to be.)
- No CAS garbage, in either the questions or the replies. This will be ruthlessly enforced.

Ask away.

*) The Riemann hypothesis may take a little longer.

**UPDATE (25/03/20) **Here is MitPY 2 (change of base for logarithms).

**UPDATE (28/03/20)** MitPY 2 is done and dusted. Any offerings for MitPY 3?

I’m happy to lend a hand too. I’ll put on notifications for this post.

What is CAS?? Computer Aided Something?

Complete Anti-intellectual Shit. Thanks, Glen. It could be an explosion of questions coming, or none.

Ah. Handy abbreviation, that one.

I’m happy to lend a hand too. Am currently exploring the great unknown of remote teaching …. (This will be the silver lining that many educational bureaucrats see in all this mess – the potential saving of huge amounts of money. Because it will

appearthat 2 teachers can do the job of 8 ….)Latex check: .

Marti,

Good initiative . I am a great believer in teaching someone to fish .

One example on Pythagoras and inscribed circles below

https://www.newscientist.com/article/mg24532691-200-new-scientist-puzzle-46-pi-thagoras/

No CAS needed

Steve R

Or, you can teach a computer to say “fish”.

Generous offer, Marty.

I hope we can all see the questions asked and your solutions.

You never know, we may learn something. 🙂

Thanks, Geoff. The idea is that it’s all public. As it happens I help all manner of people privately on occasion, plenty of whom I’ve never met. I generally never refuse any good faith request for help. But I can’t make a public offering of private help for all and sundry.

Are questions about

teachingmaths considered on-topic? If so, I have plenty of those…Hi, SRK. I’m not sure whether you’re being facetious, but the basic answer is “yes”. If the question is along the lines of “What is going on with this topic/example?”, that is definitely on-topic. Many of the posts on this blog were inspired by some teacher (or student) asking such a question. If you’re talking about how one should teach a topic, for me that’s the same question. I think pretty much you can teach anything well if and only if you (really) understand what’s going on with it.

No facetiousness intended. I guess I was not merely wondering about questions about teaching a specific topic, but broader questions about teaching certain courses (given that one must comply with certain requirements) or – and this seems especially pertinent at the moment – how one might effectively deliver a course remotely.

Whoops. I thought I replied to this. SRK, I’m more than happy for you, or anyone, to post any such questions. I won’t be of any help whatsoever, but I’m happy for this blog to be a forum for these issues.

For what can happen if one does not understand what one is talking about, go take a squiz at the Absolute Zero post…

For instance.

I don’t know whether it’s a problem just with my computer, but the font on these posts is very small and very faint, which makes it very hard to read particularly in dulllish light.

Any chance of increasing the font size and brightness please?

Hi Geoff, the font looks ok to me, but if others agree with you I’m happy to look into it, or into anything people think will improve the appearance or function of the blog. (The LaTex equations are fuzzy, but I have no idea what to do about that.) I took a quick look and it seems one can alter the blog “Theme”, but I’m pretty sure I’m not smart enough to go tramping around there.

In last millennium C that would require some typing just to print fish or hello world…

#include <studio.h>

int main() {

printf (“fish”) ;

return 0;

}

Then you could experiment with the soundex algorithm

Steve R

OK. I’ll try to get a specific ball rolling and perhaps one that is slightly relevant at the moment and not really that well understood by my teacher colleagues (even some that teach mathematics classes) – how would you (Marty or anyone) go about teaching the change of base rule for logarithms to (say) a mainstream year 10 or extension year 9 class?

Have these students already been taught log laws?

Thanks, RF, for choosing a truly awful topic. It’s one I always dread when tutoring. The main issue with the topic is, who gives a shit? As presented in school it’s just a thing, with no purpose other than to test whether students know the thing. True idiocy. That purposelessness also makes it

reallyhard to teach, because there is no easy value in going into depth. Nothing in VCE hinges on understanding why the change of base works.I think this will be thorny enough to give it a separate post. So, I’ll do that now, and then come back with the link.

Hi, RF, and everyone. I’ve created a post for the logarithm query here.

Thanks Marty – I will elaborate on the other post.

SRK – I’m thinking of a hypothetical class (for now) but my thinking is that they would have been taught indices and logarithms and the change of base rule just sort of rounds off the topic in a nice way, provides an opportunity for some sort of learning by discovery and is well within the grasp of a student of reasonable ability to comprehend.

Except that all other logarithm laws have an index law “partner” so this one just sticks out a bit.

For me, this does have an index law counterpart:

*edit: LaTeX….

I’m not sure this partners with the change of base rule or of the log(a^b)=blog(a) rule.

RF: Perhaps I’m misunderstanding, but I think Glen’s point is that they are more or less the same, since the change of base rule follows very quickly from that log law. (Indeed, that’s more or less how I teach the change of base rule, just as an application of that log law).

Yep!

Thanks, all. Glen, and SRK, maybe post what you mean as comments on the dedicated MitPY2 post.

Sorry – I posted before I read your reply.

Teaching students the other day about log scales, I wondered out loud how I could do an experiment in measuring sound levels in the class. One student told me that we could do it on her watch. I shouted “Hey” and she recorded 70dB. Then I tried “HEY” and got to 75dB. Dick Tracy would be impressed.

y=log_{a}x MEANS x=a^y (1)

If you understand x=a^y then you understand y=log_{a}x .

(“Terry is Alice’s brother” MEANS “Alice is Terry’s sister”.)

Many high-school problems about logs, including the change of base formula, can be readily solved with (1).

One aspect of showing the change of base rule to students is that they see (1) in action.

Thanks Terry, I quite like this fundamental, reinforce the fundamental idea approach. If nothing else, as you say it gets students to keep seeing (1) before they hit VCE.

Red,

As a starting point the teacher could do worse than read how Feymann explained inverse operations to his undergraduate physics class in section 22-2 of his caltech series

https://www.feynmanlectures.caltech.edu/I_22.html

Steve R

Thanks, SR. I think you’ve pointed out that chapter before, and it’s great, from a masterpiece. Every maths teacher should read it and study it. But, it’s probably not direct enough for the specific question RF is asking.

Then if practice helps then Paul’s online notes from Lamar University provide plenty of worked examples

http://tutorial.math.lamar.edu/Classes/Alg/LogFunctions.aspx

Steve R

Now you’re aiming too low!

Thanks Steve, not looking for examples, just a way to get the big idea across in a meaningful way (which none of the school textbooks seem to be able to do without saying “here is the rule, now just use it”)

Marti,

sorry I am a statistician … so we may get closer to the right level by doing some of Paul’s practice questions using the change of base recipe whilst the teacher reviews sections 1 and 2 of Ch22 of the Feynmann lecture series.

BTW I can remember using log e 10^n conversions tables in a pre calculator era

Steve R

Well, SR, stats has never been my thing … More seriously, you are of course correct, that specific examples of how things work is helpful, if not essential to the understanding. But it doesn’t get to

whythe rule works. So, a more pertinent use of example is as suggested by Storyteller on MitPY2.I know you said no CAS but since there’s not much going on here I thought I’d try my luck… any idea what is going on with this? I don’t understand why they are different. https://i.imgur.com/GxkmOoE.png

Geez, that’s weird. Thanks for reminding me how much I hate CAS. Craig, maybe indicate what machine/platform you’re using, and others may be able to say why the second, pretend-complex answer is appearing. (I’ll loosen the “No CAS” rule to permit such questions here.)

I’d say your calculation mode is on some sort of complex number mode. If it’s set to real numbers only, then CAS just returns a warning of a non-real result when you enter the second expression.

SRK, I don’t think that’s it. The result is identical and real in both cases.