On Aug 27, 2013, at 10:46 AM, Richard Strausz <Richard.Strausz@farmington.k12.mi.us> wrote:
> Let's talk specifics. Here is the most recent post from Meyer. > > http://blog.mrmeyer.com/?p=17153 > > Please share briefly what you like and what you don't about the pedagogy. It does seem to fit nicely into Algebra.
There is no algebra here Richard. And the original text isn't any better. I don't like anything about this particular example.
To fix this lesson into an algebra lesson one would have to determine analytically what the area is of the circle the pennies occupy and what is left over. They would have to determine the diameters of circles that circumscribe pennies arranged in groups of 1, 2, 3, 4, etc. I am not asking for a general exact solution of "n" pennies, but I am asking for exact solutions of specific cases. And we would explore a little with pennies and a compass. It is very important to get the spatial model right. But then it becomes geometry and expressions. Is what I am suggesting too advanced? Maybe for an average class, but then again, that is why I really dislike this example of a problem. You don't use problems like this in an algebra class if the algebra of the problem completely escapes the classes ability. And avoiding the algebra altogether as Dan (and the book) does it not a solution.
Algebra is not about predicting and measuring. It is about symbolic reasoning, period. These "busy work" examples are no substitute for building symbolic reasoning. I am open to an amount of operational stuff in the class. But not to the point where there isn't any symbolic reasoning left. I think my rule of thumb where 25% of the class can be operational while the other 75% should be symbolic reasoning is a pretty fair and decent standard.