I've often wondered how others get the multiplication tables to stick. When I was in school and tasked with learning and being tested on them I remembered them - just about - for long enough to be tested (primarily from a quick reminder on the way to school) and then they were gone.
My overall experience was that they were a very boring song with terrible lyrics. I can't ever say that any meaning clicked especially. The teacher called out the first part of the verse and I "sang" it internally and hopefully got it right. Having gotten through that it was gone by lunchtime in time for a different set of words to the same song next week.
I tried again about 30 years later as a adult and had much the same experience. You might as well have been asking me to remember items on a tray.
To me it's like this:
chicken x tree = rock
brick x kangaroo = Susan
boat x walnut = dinosaur
Now imagine you have to remember 288 of those (because you might be asked to produce either side of the equals sign) and somebody asking you to recall one arbitrarily.
How do you get your students to get them to stick?
I do the dots thing too. I've never heard anybody else describe it and, to be honest, it's quite comforting to hear I'm not the only one. In fact I don't just imagine dots, I imagine die faces. This obviously gets problematic after six. I too feel limited by my working memory: it makes mental arithmetic of numbers with two digits very very hard without an external store like fingers.
> We start by finding a number that forms a perfect square that is close to 33. Here, let’s pick g=6, since 6^2=36.
As somebody who is numerically essentially blind I'm not only incredibly jealous and in awe of most of the comments in this thread but also utterly perplexed by the above. How does that even come to mind that 6 is a good starting value? Do you people just intuit this stuff or do you rapidly run through the options? If you're asking me to come up with something that when multiplied by itself is something near 33 then you're in for a long wait.
There's another comment in this thread:
>Everyone generally knows the perfect squares up to at least 12, and then for bigger values, you can use even powers of 2, which I assume people also know.
Having worked on the PL/1 and Assembler that formed the core accounting systems of a bank: yes.
Not only did I have source control I had flow diagrams of the entire system for all points in the chain. My code reviews had me doing line-by-line justifications. I wrote tests.
Just because the technology and practitioners are old it doesn't mean they don't know what they're doing.
Generally they invented whatever "you" are reinventing the first time around.
An availability zone (AZ) in AWS eu-west-2 was flooded by a fire protection system going off within the last year. It absolutely did affect workloads in that AZ. That shouldn't have had a large impact on their customers since AWS promote and make as trivial as is viable multi-AZ architectures.
Put another way: one is guided towards making operational good choices rather than being left to discover them yourself. This is a value proposition of public clouds since it commoditises that specialist knowledge.
Wavefront brings a number of things to the table that aren't core competencies we wish to maintain in-house.
I know it can scale to massive volumes without interaction from us.
I know it'll be available when our infrastructure isn't. By being a third party we can be confident that any action on our part (such as rolling an SCP out to an AWS org, despite unit tests) won't impact the observability we rely on to tell us we've screwed that up.
I can plug 100s of AWS accounts and 10s of payers into it and I don't have to think about that in terms of making self-hosted infrastructure available via PrivateLinks or some other such complication.
I pay mid six-figure sums annually for these things to "just work". If you folks believe I can achieve this functionality on a per-seat basis I'd be interested in saving those six figures.
My overall experience was that they were a very boring song with terrible lyrics. I can't ever say that any meaning clicked especially. The teacher called out the first part of the verse and I "sang" it internally and hopefully got it right. Having gotten through that it was gone by lunchtime in time for a different set of words to the same song next week.
I tried again about 30 years later as a adult and had much the same experience. You might as well have been asking me to remember items on a tray.
To me it's like this:
chicken x tree = rock
brick x kangaroo = Susan
boat x walnut = dinosaur
Now imagine you have to remember 288 of those (because you might be asked to produce either side of the equals sign) and somebody asking you to recall one arbitrarily.
How do you get your students to get them to stick?