For the first example, it sounds to me that they are talking to designers, and their message is that, hey, look, pick better notational infrastructures so that it's easier for kids to learn math. The overall activity doesn't change for kids, i.e. they are using some kinds of notations to answer some kinds of problems. Not all notational infrastructures are the same, e.g. graphical representations have many affordances that symbolic representations do not), and thus more students may successfully answer those questions if they have access to graphical representations as opposed to only algebraic representations. However, unless I am missing something very important, I don't see how what it means to do mathematics has changed from doing the same with algebra. I still don't see any support to help students understand how (already-made) representations connect to the phenomenon they are investigating.
The second example is videogame making. I don't quite understand how that is doing mathematics either. The authors anticipated my question. They wrote, "It might be that some readers will be wondering what this has to do with mathematics. Our reply is that it is about rules expressed formally and their implications, and that—as we have argued earlier—this is a central aspect of what it means to think mathematically in the computational era." I hardly think so. I agree that if what they mean is that by doing these things you might get to use some math and to learn some math along the way. But I still don't see how that is doing mathematics.
If you see the connections, please help me see that!
Hello Fai,
ReplyDeleteRegarding the second example, I think the point that they are trying to make is that computer systems now require a different way of approaching mathematics since the execution of (complicated) processes has been devolved to computers. Accordingly, the knowledge that is now required is being able to understand how computational models work and the "mathematical mechanisms" that underlie them.
In the video game example, students understand that models are constructed based on certain algorithms and are able to explore deeper levels of objects. They are also able to manipulate the different functions that are performed by the objects. I see this activity as one that supports "syntonic" learning (a learning the establishes the building blocks of more complicated concepts in the future) for understanding how computational models are constructed and how they should be manipulated to serve our purposes.
But I approve, I don't believe this translates to mathematical knowledge as we understand it.