Math Week 8: Math + Philosophy = X

Today in math class I learned about different ways to teach geometry, how to think about graphing backwards, putting emotion into math, and having the right to fail.  Woah, that's a lot.

The backwards graphing caught most of us off guard.  We're so used to graphing with units in mind.  We've been trained and been marked down on tests for not labeling the units on the axes.  So today, when we had to plot data points to show the linear relationship in measurements, we felt like the earth had switched its rotation direction.  What makes present-day math teaching and learning so linear?  Why aren't more teachers allowing their students to explore different facets of math and offer different access points for learning?  Is it fear of failure?

This society also is very set in the mindset that we cannot let students fail.  We can see this on innumerable levels and understand why this is so ingrained in our culture.  I like what we talked about in class in terms of the lessons that we learn from failing.  Often, we have made our most life-changing choices when faced with these situations.  This is juxtaposed by the philosophy that in order for us to keep desiring learning, we need to be successful.  There is a balance between these philosophies; the question is where?  I suppose the answer is that it depends on the individual. 

Ahhh...refreshing!

Check out this clip by the talented Demetri Martin.  His comedy relates to attention span, percents, self-image, and obedience...everything we see in schools!

Jokes.com
Demetri Martin - Doors
comedians.comedycentral.com
Demetri Martin Stand-Up Demetri Martin Jokes Demetri Martin Person Videos

Math Week 7: Techie Transformations

Today, I learned how to use some of the basic features of Geometer's Sketchpad.  This is a great, simple program that allows you to draw shapes.  In the process, you learn how to informally prove that a shape is what it claims to be, as well as explore the concepts of definitions of shapes.  This is a tool that we can use in our classrooms, on the computer or Smartboard.  We can also setup example problems, like the one we did in class today, and have our students interact with the software, solve, and discuss concepts.  I wonder how this software could be used as a method of assessment also.  It reminds me of when I used Solidworks in a class I had and took tests by building models using the program.  I think this type of assessment would be yet another access point for different learners to demonstrate their knowledge.

We also learned about all the add-on gadgets for graphing calculators which can provide ways to collect data and analyze graphs.  I like how this interactive process is engaging for the whole class while also helping students turn abstract ideas into concrete understandings.  As we wondered in class, when do we think technology will transform cell phones into graphing calculators?  After all, why have a bunch of gadgets when they can all be combined into one?