Wednesday, May 23, 2012

Dynamic Geometry® - A Solution to Math Boredom

I have been writing a piece about dynamic geometry® software, and have had a really difficult time conveying the power of dynamic mathematics environments in the static environment of the written word.

Let me clarify what I mean by dynamic geometry software - I do NOT mean software that is just for geometry.  Dynamic geometry means the ability to take all sorts of mathematics visualizations (shapes, graphs, plots, functions) and drag and manipulate them to create infinite examples. These dynamic movements follow mathematical behaviors and allows for exploration, discovery of relationships and properties and allow students to interact directly with the mathematics because the mathematics is visual and tangible. Dynamic geometry software is specifically mentioned in the Common Core Standards of Mathematical Practice because of it's ability to be a tool that promotes reasoning, questioning, making conjectures, persevering, modeling, and communicating. Naturally, I have a strong bias towards specific dynamic geometry software: Sketchpad, Tinkerplots and Fathom.

Knowing that dynamic geometry software is all about movement, as I try to write about it for this piece I am doing, I realize it is almost impossible to convey the power of dynamic geometry with words or even with pictures.  I have been describing what students would be doing with the software and then supporting this description with a picture that steps through the process, but what I find is they are just pictures taken at one point in time.  And while the pictures show a progression of change, they do not capture, just as the words do not capture, the amazing change in the mathematics, the sense of wonderment, and the 'aha' moment that a student might encounter when working in a dynamic environment.

In a word - they are boring.

Which is probably why students who are exposed to only textbooks with words and pictures of math never get the sense of power, wonder and infinite possibilities of mathematics. Even students who are using technology (calculators or computers or apps) but only doing drill-and-practice type applications or calculations with these tools, are not getting the sense of movement, connectedness and variation that dynamic geometry software provides.

Here is an example of what I mean by boring and static:
Using TinkerPlots®, it's possible to explore relationships between attributes (i.e. variables) from data on which students have the heaviest backpacks. Grab an attribute from the card stack of data, say body weight, drag and drop it onto the horizontal axis of the plot, then grab a second attribute that might have a relationship, like pack weight, and drag and drop it on the vertical axis. Separate the data both vertically and horizontally to get a scatter plot, and determine if indeed there is a relationship. In this case, there is a positive correlation between body weight and pack weight.  Add a moveable line and create a line of best fit, which shows the equation of the line using the attributes from the problem, making the function fit the context of the situation. 

What?!!!

That's what I think a student might say if they read something like that in a textbook.  But - never fear - there are pictures that show what is happening:
 Are you getting the sense of movement? Do these pictures convey the relationships that exist between the variables? Do they convey the relationship between the data, attributes and graphs?

Now, look at the exact same problem done in the dynamic environment where you can actually do what was described and see the data change as you explore and manipulate:
 


I think my point is dynamic geometry software is a technology tool that makes mathematics come alive for students rather than be a static subject they read about, look at, but never interact with in a way that helps them see and make connections. My hope is that etextbooks and online assessments and other technology resources that will become more commonplace in this ed tech focused environment will consider doing things dynamically, rather than simply replicating the static words and images that currently exist. Giving students the ability to create, explore, change and manipulate on their own is powerful and exciting. It makes math engaging rather than boring, expanding rather than limiting.


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