What are some of your favorite basic math hacks?
borovik.net
borovik.net
I would have to agree with the article.
I tried to learn the Trachtenberg system [1] a while back. I thought it would be a simple and fun thing to do. Maybe it's just my brain but I couldn't wrap my head around all the different rules for simple multiplication. Rather than speeding up my mental arithmatic it slowed it down considerably. In the end I gave up, feeling a little bit more stupid than when I started.
So for 4545, you do 45, which is 20 and add 25 to the end, giving 2025.
That's a fun one because it's quicker to do it in your head than it is to type it into a calculator.
So you mean:
"So for 45x45, you do 4x5, which is 20 and add 25 to the end, giving 2025."*
And while that's interesting, it does feel like you're simply responding to the question/title, rather than reading and responding to the actual article.
I did read your article but I felt that it buckets all hacks together as an unnecessary evil in education.
I think it's quite a nice confidence booster to know a method that would speed them up (usually in basic arithmetic). It also provides a future learning opportunity when trying to derive why a hack works.
I agree with the article, but I would really be interested in some in-depth examples of what the alternative to tricks/hacks are? I don't ever remember a case where I was only taught the hack, for example. We learn it the long way and then the teacher/lecturer might show us a quick version in passing. Is this not the case all of the time?
You're welcome.
> Yes, formatting messaged up.
Do you mean "messed up"? I can't make sense of "messaged up" but I'm guessing it doesn't matter.
> I did read your article ...
I didn't write it, so it's not really "my" article.
> ... I felt that it buckets all hacks together as an unnecessary evil in education.
I think in this case and this context, "hack" refers to "doing something a quick and dirty way without necessarily knowing how or why it works."
> I don't ever remember a case where I was only taught the hack, for example. We learn it the long way and then the teacher/lecturer might show us a quick version in passing. Is this not the case all of the time?
Then you are lucky, and no, it's not the case all the time. There are many cases of students being taught "Tricks" to get a result without them having any real understanding of what's going on. You don't need to spend very long talking to students about how they're solving exam problems to realise that in many (but not all!) cases they're just applying hacks, tricks, and processes without knowing why they work.