Friday, February 13, 2015

Math Links for Week Ending Feb 13th, 2015

On the Math with Bad Drawings blog there has been a series of posts on over reliance on using algorithms in place of conceptual understanding. The series was called How to Avoid Thinking in Math Class. We have had conversations similar to this at our end. The way that I have always framed it is that "we can teach monkeys to use the quadratic formula (but they won't understand what they are doing)". The last of the six posts is titled The Church of the Right Answer. And starts with an interesting thing a student said:
So, like, I don’t really understand anything you’re saying, but I can still get the right answer. Oh, you were talking about this extra stuff, like the ideas behind it and everything. I don’t… you know… do that. So is that okay? I mean, as long as I can get the right answer? - A. Student
The whole thing reminds me of the Phil Daro video I posted last year where he talks about our penchant in North America for "Answer Getting" (if you haven't seen this video then I strongly suggest you take the time to watch it). I think these are very good discussions to have and if you want to start then I suggest starting with this series of posts.
Curriculum Tags: All
Post 1, Post 2, Post 3, Post 4, Post 5, Post 6

I have mentioned before that I like performance tasks. I also like when teachers collaborate with each other via the Interwebs. Last year I mentioned Alex Overwijk's grade 10 performance task and this year Amy Lin used it as a model to create a performance task for her grade 9 and 10 applied students. She has posted the results (and the task) online on her blog. See the link below for the full report.
Curriculum Tags: MFM1P, MFM2P

Here's a nice 3Act task from Jon Orr. Watch the video below of Act 1 to see that the general purpose of the task is to figure out the model for how points are given out based on where Mario lands on the pole. You can make connections to all kids of functions including quadratic and exponential. He uses PearDeck as his technology of choice which has the nice feature of allowing students to drag points to secure their guesses for things. Depending on which course you are using this in will probably require some adjustment of the task but still it has a lot of places that it could be used.
Curriculum Tags: MBF3C, MCF3M, MCR3U, MHF4U, MAP4C

I like this simple investigation of sine law on Dave Lenovaz's Sine of the Times blog. It uses a Geogebra plugin that students interact with to complete the investigation. This would really save the time of actually having to measure all the angles and side lengths to let you get to the theory relatively quickly. Students get  the worksheet which has direct link to the Geogebra Sketch.
Curriculum Tags: MPM2D, MBF3C

I love kinetic sculptures. Especially ones that help me teach math. In this one there is all kinds of math going on. From the 3D graphing that could be linked to vectors to the moving functions that could be linked to advanced functions.
Curriculum Tags: MCV4U, MHF4U

And this one is a bit older but follows the same principles.
Curriculum Tags: MCV4U, MHF4U

Keeping in line with the featured link above, this video might give some insight as to what an extreme version of just applying an algorithm to get an answer might look like to someone who doesn't get it. This is from a British comedy show and it is a skit of a fictitious game show called Numberwang where the rules are nonsensical. Like having a function machine with no discernible pattern.
Curriculum Tags: All

I saw this at a workshop I was at yesterday. Surely there is some math that could be done here on patterning or series and sequence.
Curriculum Tags: Gr7, Gr8, MCR3U

I love this interactive infographic about how accurate the predictions of ground hogs are on Groundhog Day. For what ever reason our society has put the start of spring in the hands of small rodents. This data set is from 30 years of predictions of all the ground hogs in the US and whether they predicted when the weather would shift. When you look at the data you really get a sense that it is as accurate as flipping a coin. So that is why I think, beyond the data, this is a great example of probability in real life.
Curriculum Tags: Gr7, Gr8, MBF3C, MDM4U

Taking pictures of real things and then bringing them into the classroom is a nice way to make something abstract seem real. In this case it is the idea of "what is the angle for any vertex of a regular heptagon". Fairly abstract question until you come upon this park bench. Check the site out for more images and the connection that in real life things don't always turn out as expected. 
Curriculum Tags: MFM1P, MPM1D

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