A calculator that teaches number sense

I had a tool that was similar to this (in a much more basic way) when I was a kid. It didn’t do what this one does (prompt you to estimate the answer, and it’ll tell you if your answer is close). You could do simple arithmetic with it. It didn’t have a digital display. Instead all it would do was tell you if your answer was right or not. I found it really helpful.

I’ve heard from mathematicians that a skill that’s really important in learning mathematics is the ability to estimate. It would seem this would be a good educational tool for that.

Originally shared by Timothy Gowers on Google+

I’ve just been told about a calculator that refuses to give you the answer unless you first give it a reasonable estimate. Apparently, it has had remarkable and positive effects on the willingness of young people to engage with mathematics. Designing it was difficult, because what constitutes a “reasonable estimate” is much subtler than just a tolerance for being out by a certain percentage. For example, the calculator does not consider 102 to be a reasonable estimate for 10 times 10, but it would consider 2.2 to be a reasonable estimate for the square root of 5.

I don’t know whether it lives up to its hype, but it’s an ingenious idea and I wouldn’t mind getting my hands on one.


Why it’s dark at night…I wonder…

Hmm. I feel like I want to see a more detailed analysis of the radiation from the distant stars (like, what would it be in Lumens if it were in the visible light spectrum as compared to the Sun) before I’d give more credibility to this notion. This makes it sound like we would be in daylight all the time if the light from the more distant stars weren’t red-shifted. I could buy the idea that the stars would look yellow-ish if not for this, but the “daylight all the time” notion feels like a stretch to me. I like the idea nevertheless. Interesting theory.

Originally shared by Daniel Dulitz on Google+

It turns out this is not a simple question. It’s dark at night because of the Doppler effect — what??!

Re. Windows 8

From Google+

A good demo about what’s different with Windows 8, and why it’s troubling to existing Windows users, and probably to developers. This video is from May 2012.

The thing that’s emphasized here is that W8 is made for a touch interface. It’s compatible with a mouse, but the UI mouse actions only emulate someone touching the screen where the mouse pointer is. All of the gestures operate from a touch interface metaphor. So it’s frustrating to someone who’s used to using a mouse.

What really struck home for me was the ending of this video, because it’s something that I sensed just from reading about W8. The guy who made this video said that what you notice almost immediately is “how much you’ve lost.” Microsoft has tried to simplify, simplify, simplify with W8, and I imagine a lot of people will like that on a tablet form factor. What MS has neglected is what this does to desktop users. The person who made this video said that you can “feel almost trapped” by the interface, that you can’t do what you used to do with Windows, or you can do it, but it’s all unfamiliar, and so feels frustrating.

Support for Windows 7 is going to be around for years to come, though my guess is MS is going to push W8 as much as possible by making it the default OS on new PCs when it comes out. It just seems to me MS is pushing this idea too fast and too hard, and it’s going to cause server/desktop/laptop users to seek an alternative.

What has Apple really invented?

From Google+

I already knew that Apple didn’t invent very much, but this video really adds specificity to that notion. They get into some popular Apple technology, and then talk about who they deem to have invented it. They seem to have a good basis for what they say, as they talk about how they’ve reviewed the patent record for this stuff.

Just to be clear, I’m not posting this because I hate Apple. I use a Macbook Pro as my primary computer. What I really like about this is they identify what Apple’s basic philosophy is, and then they illustrate it through some examples. They say that Apple is not a technology invention company. They’re a “technology recipe” company. They’re basically saying that Apple is a really good “kitchen.” They don’t usually grow the basic ingredients that go into what they create. They may do some processing and “prep” for the ingredients. They may invent a recipe to make out of those ingredients from time to time. I think most of what they do in this context is enhance existing recipes, but most of what they do in general is create “a very tasty meal” out of it, and that isn’t all bad. The issue is they often get more credit than they deserve (people thinking that they grow the ingredients in addition to making the “tasty meal”), and these guys are just trying to set the record straight.