Multiple Representations

In class this week, I learned how to show students positive and negative integers in different ways: using beans and a large number line down the middle of a classroom. I like the idea of getting the students out of their seats and doing math. Moving from concrete to abstract was a big idea I learned. Another fundamental understanding I learned to associate is the definition of subtraction - which is addition of the opposite. I never used algebra tiles and now at least I know what they look like. I learned it is important for teachers to understand different strategies and present students with different multiple representations of the same math problem. Just because I learn best one way does not mean my students will see the solution the same way. Lastly, I am also starting to see how technology is changing math - for instance today we took a look at the website: www.gapminder.com.

Using math manipulatives, talking about your thinking, asking questions, drawing pictures, using a number line, etc. should all be a part of the classroom norm. I remember math class consisting of being my math book, notes, and homework from the book and a worksheet. There was hardly any talking or discussion with my classmates. As a new teacher, I am going to have to play with algebra tiles, geometric shapes, and beans for example to be comfortable showing students how to use them as a strategy and discover mathematical rules and properties.

Questions: It seems inquiry based approach and students being able to discover their own genearlizatinos are good foundations for students before given them the formula or the "how to" but are students really doing better in math with this type of inquiry based approach? Will the attitudes about math change?