The Plastic Brain


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Rewriting the didactic contract

More brilliant advice on changing the culture of the Mathematics classroom from Dan Meyer.

They may even resist you. They signed their “didactic contract” years and years ago. They signed it. Their math teachers signed it. The agreement says that the teacher comes into class, tells them what they’re going to learn, and shows them three examples of it. In return, the students take what their teacher showed them and reproduce it twenty times before leaving class. Then they go home with an assignment to reproduce it twenty more times.

Then here you come, Ms. I-Just-Got-Back-From-A-Workshop, and you want to change the agreement? Yeah, you’ll hear from their attorney.

I love this concept of a “didactic contract”. We need be aware of what has been metaphorically signed, especially if we are attempting to rewrite.

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Teachers’ Day with Martin Westwell – Follow up

This links to the post below, in which I reflected on some lesson from Teachers’ Day with Prof Westwell.

At the end of the day, he said that only 5% of us would put something we learned today into practice, and challenged us to commit to something in order to up that percentage.

Well, I took up that challenge in my next Maths class, teaching, of things, percentages. I chose to use principle 10 of Dan Meyer’s Ten Design Principles For Engaging Math Tasks

Highlight the limits of a student’s existing skills and knowledge. New mathematical tools are often developed to account for the limitations of the old ones. You can’t model the path of a basketball with linear equations — we need quadratics. You can’t model the growth of bacteria with a quadratic equations — we need exponentials. Offer students a challenge for which their old skills look useful but turn out to be ineffective. That moment of cognitive conflict can engage students in a discussion of new tools and counter the perception that math is a disjointed set of rules and procedures, each bearing no relationship to the one preceding it.

I used as my leading question: How can we order fractions with different denominators?

We came the position that it would be much easier if they had the same denominator. Hey presto, this is where I stepped in with the idea of percentages – A way of comparing fractional amounts, where the denominator is always 100.

I didn’t work perfectly, as these thing rarely do, but I got through to some of them, and it’s something I can build on.

At least I’m part of the 5%.

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Video images described as a series of mathematical equations. Vector graphics: another great application to inspire maths students.

prostheticknowledge:

British researchers claim they can kill the pixel within five years 

The familiar pixel could be on it’s way out, as developers are putting together a video codec which works with vectors, via Extreme Tech:

The humble pixel — the 2D picture element that has formed the foundation of just about every kind of digital media for the last 50 years — may soon meet its maker. Believe it or not, if a team of British researchers have their way, the pixel, within five short years, will be replaced with… vectors.

If you know about computer graphics, or if you’ve ever edited or drawn an image on your computer, you know that there are two primary ways of storing image data: As a bitmap, or as vectors. A bitmap is quite simply a giant grid of pixels, with the arrangement and color of the pixels dictating what the image looks like. Vectors are an entirely different beast: In vector graphics, the image is described as a series of mathematical equations. To draw a bitmap shape you just color in a block of pixels; with vector graphics, you would describe the shape in terms of height, width, radius, and so on.

These two methods are very different, and they fulfill very different needs. Vector graphics, because they’re made out of geometric primitives, are infinitely scalable, making them the ideal image format for illustrations, clipart, maps, typography, Flash animations, and so on. For everything else, we use pixel bitmaps. Streaming videos, digital cameras, movie editing, video game textures — all bitmaps. There might be different file formats involved (PNG, MOV, JPG), but they’re all ultimately converted into pixel bitmaps when it comes to displaying them on your monitor, TV, or cinema screen

Which finally leads us back to the innovation at hand: Philip Willis and John Patterson of the University of Bath in England have devised a video codec that replaces pixel bitmaps with vectors. In a conventional digital camera, images (or videos) are captured as pixel bitmaps and compressed using a codec such as JPEG or H.264. Willis and Patterson have devised a codec called Vectorized Streaming Video (VSV) that converts the bitmap image into vectors. This builds on their previous work with VPI — vectorized photographic images [PDF] — which deals with converting bitmap images into perfect, vectorized copies.

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I would not call it the inverse of art, but otherwise, I echo these sentiments.

themathkid:

❤ ❤ ❤

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