Week 2: Misunderstood Minds

When the WGHB Educational Foundation describes key components in helping us identify students with math disabilities; they argue that one of the focal points is the cumulative nature of math. They state, “because math is so cumulative in nature, it is important to identify breakdowns as early as possible,” (WGBH Educational Foundation, 2002). This echoes the sentiments of RTI that has infiltrated the world of teaching mathematics, especially to lower level math students. The best models of RTI (Response to Intervention) target individual skill sets that a student is lacking, and customizes a plan to develop those skills. Many such plans are computer generated, thus each student response determines the next question or prompt that they will see. It is likely that no two students will be lacking the same exact skills, and this program will not likely generate two identical intervention programs. The program that we are piloting at my school is called Algebra Edge, and can be found at http://www.learningupgrade.com/algebraup/au_demo_lgl.htm. One of the greatest benefits to Algebra Edge that we have found over other similar RTI programs is that is it interactive. It doesn't just play videos or have students click a "next" button, they are required to move manipulatives to represent quantities, and change sliders to adjust parameters. Algebra Edge transforms learning from a passive to an active process, customizable for each learner.

One of the suggestions that WGBH offers for teaching students who have difficulty thinking with numbers really spoke to me. As WGBH suggests, “Teach basic concepts using concrete objects. Let children explore number concepts by adding and subtracting objects in the room (for example, add the legs of a chair to find the number four or subtract crayons from a box). Move from concrete materials to pictorial representations to numbers (abstract representations),” (WGBH Educational Foundation, 2002). Teaching from the concrete to the abstract make sense from Kindergarten all the way through Calculus. It seems intuitive if you are teaching basic arithmetic, in fact I cannot think of any other way to teach children how to add, subtract, multiply, and divide than with objects. So many teachers though, at the upper levels of mathematics struggle with this (and I understand why; sometimes it is very difficult to model complex phenomena in a concrete way). Many days of notes in upper level math begin with copying a formula, and then practice with inputting values and evaluating. Although this is traditional, and is actually what many learners and teachers prefer, I find that on the days that I let students develop formulas, notice patterns, and work from the concrete to the abstract; they are able to understand and retain so much more than when I use traditional formulaic and algorithmic methods.

References

WGBH Educational Foundation, 2002. Misunderstood Minds. Retrieved from  http://www.pbs.org/wgbh/misunderstoodminds/index.html on January 24, 2012.