Comments on: The Math I Learned After I Thought Had Already Learned Math /2015/the-math-i-learned-after-i-thought-had-already-learned-math/ less helpful Thu, 04 Feb 2016 16:56:32 +0000 hourly 1 https://wordpress.org/?v=6.8.2 By: Russell /2015/the-math-i-learned-after-i-thought-had-already-learned-math/#comment-2417307 Thu, 04 Feb 2016 16:56:32 +0000 /?p=23591#comment-2417307 I’m starting a probabilty unit with my 7th graders. After reading this post, particularly Jason Dyer’s comment, I started wondering what the graph of possible dice combinations would look like. I jumped on desmos, and tried it out. Really cool stuff. For two 6-sided dice the number with the highest probability is seven. The cool thing about graphing it, is that number is along the diagonal of the square, always. Blew my mind.

https://www.desmos.com/calculator/qdonee4lof

]]> By: David Jones /2015/the-math-i-learned-after-i-thought-had-already-learned-math/#comment-2416420 Sat, 09 Jan 2016 18:09:49 +0000 /?p=23591#comment-2416420 Area of a parallelogram. I had always taught the formula – ie average length x perp distance or TWO triangles. About 6 yrs ago after having taught for near to 20yrs. I was shown that if you draw a rotated SECOND trapezium and put it with the first, you will get a parallelogram ie (a+b)xh then half it! This was a humbling moment for someone who think they are quite good at maths.
Also if you teach parallelogram straight after rectangle, trianlges become easier. Any triangle is half a parallelogram. I think the usual order for teaching is rectangle, triangle, then papallelogram.
Non right angled triangles are then more difficult to understand using only the rectangle idea.
In my first yr of teaching, I was shown by HOD the way of generating pythagorean triples, something I had not been taught. Rule is easier to express as two rules depending on a being odd or even
eg 13, go for two numbers which are one apart but sum to 13squared….13,84,85
eg 14 go for two numbers which are two apart but sum to HALF of 14squared….14,48,50 (which happens to be a repeat of 7,24,25 I know)

]]> By: dy/dan » Blog Archive » 2015 Remainders /2015/the-math-i-learned-after-i-thought-had-already-learned-math/#comment-2416208 Mon, 04 Jan 2016 16:24:42 +0000 /?p=23591#comment-2416208 […] The Math I Learned After I Thought Had Already Learned Math […]

]]> By: Alex /2015/the-math-i-learned-after-i-thought-had-already-learned-math/#comment-2411587 Mon, 14 Sep 2015 00:51:09 +0000 /?p=23591#comment-2411587 I’ve seen a couple of posts about the .5 versus 0.5 on the line slope exercise. The real question is why present this as a decimal? Ask for all points along a line of slope 1/2 gets the “5” completely out of the picture.

It’s a minor point compared to some of the other nice replies. I remember being in an honors physics class in high school and being increasingly surprised by trigonometry – and effectively circles – appearing all over the place in the math for periodic motion. The idea that the linear acceleration due to springs was a simple (1 dimensional) case of what we’d see later in circular orbits and so forth becomes sort of an open question in what circles even *are*, which I found fascinating.

]]> By: PhasmaFelis /2015/the-math-i-learned-after-i-thought-had-already-learned-math/#comment-2411579 Sun, 13 Sep 2015 20:20:55 +0000 /?p=23591#comment-2411579 That last one looks less like misconceptions and more like a lot of students missed the decimal point and described a slope of 5 instead of .5. It’s an easy mistake to make, and not reflective of actual understanding; you should generally use a leading 0 (“0.5”) to avoid that.

Speaking of confusing punctuation, the checkboxes under the Submit Comment button include both of these:

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Are they different in some way?

]]> By: Reader /2015/the-math-i-learned-after-i-thought-had-already-learned-math/#comment-2411567 Sun, 13 Sep 2015 06:31:06 +0000 /?p=23591#comment-2411567 You might have had better results with the slope question by writing the slope as 0.5 rather than .5.

Unless maybe you were trying to prove a point about leading zeroes?

]]> By: Eric /2015/the-math-i-learned-after-i-thought-had-already-learned-math/#comment-2411561 Sun, 13 Sep 2015 02:10:04 +0000 /?p=23591#comment-2411561 Some of the problems are easier than others. One leads to a parabola, but that’s kind of hard to see when just dragging and placing a single point. What if the students could place multiple points?

]]> By: Kara /2015/the-math-i-learned-after-i-thought-had-already-learned-math/#comment-2411534 Fri, 11 Sep 2015 21:26:08 +0000 /?p=23591#comment-2411534 Somehow I made it through an entire engineering degree without figuring out how the sine and cosine graphs relate to the unit circle. Wasn’t until I subbed for a high school math teacher and had to teach it myself. Brilliant.

]]> By: Karen /2015/the-math-i-learned-after-i-thought-had-already-learned-math/#comment-2410231 Wed, 19 Aug 2015 20:44:21 +0000 /?p=23591#comment-2410231 Thank you Dan! I was that kid that flew through math in high school, giving me this false sense that I was good at math, when in fact, all I was really good at was following what the teacher did. Nothing came together for, as I saw all math as disjointed. I still remember the day graphs started making more sense…freshman year take 2 (after an 11 year break) in my Calculus class and my prof says, “a graph is simply a set of inputs generating a set of outputs.” What??? My whole world was shattered, I finally started to see the fluidity between everything in math. I am still having “aha” moments after 5 years of teaching and I am not afraid to tell my students when they occur. I think it is helpful because I explain what I thought I knew and tell them what I know now…it’s almost a shared “aha” moment.

]]> By: Denis /2015/the-math-i-learned-after-i-thought-had-already-learned-math/#comment-2410118 Sun, 16 Aug 2015 23:30:10 +0000 /?p=23591#comment-2410118 It was only after grad school that I learned (from Lockhart’s book Mathematician’s Lament) to consider natural numbers as stones that can be arranged in various patterns that illustrate the different properties of a number. For example, evens are piles of stones that can be arranged into two equal rows, and square numbers have just the right number of stones to make a square! It’s really fun thinking about various operations in this way, and there are some beautiful proofs based on this technique. For example, why the sum of the odd numbers 1 + 3 + 5… Is always a square.

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