Saturday, February 11, 2012

How do students understand functions?

When I was studying Multiple Intelligence, I read that people learn to understand by first visualizing what's going on - they want to see the big picture in simple terms that they can relate to.  The simpler, the better.  So with my students, I always think of how I can help them see the big picture.  I think of it as concept building.

So with functions it was the use of lines and a ruler and being able to deciper whether a graph is a function or not.  They did okay, but I think that next time, I will make them create a 1-string guitar in a 5 x 8 notecard.  Make sure you prepare a bunch of lines - diagonal, horizontal, vertical and a combination of these lines in mini-xy plane.  You can 6 in a regular white sheet of paper - have the students cut each one and have them insert it through the 1-string guitar.  During this activity, students will describe the # of points touched by the string and make conclusions about whether they are functions or not.  

After they are able to visualize the graph, then they need to see the numerical patterns of tables of functions and non-functions. 

Another good example is the use of mappings.  This will also help them understand the meaning of domain and range.

Examples are important.  So its always good to show examples of 1-1, 2-1 and 1-2 partnerships between domain and range whether they are points on a graph, tables or mappings.

Hey, if you have a strategy on teaching functions, please post.  Thanks.

Functions are basic all throughout algebra.  When I was teaching them quadratics, I went back to their vertical ruler test to show that parabolas opening to the left or right are not functions.  The same goes with absolute value functions and vertical step functions.

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