Mathematical Modeling

I am currently teaching a week long summer class on mathematical modeling at Waterhouse Guild in El Segundo, with age ranges from 9-14 including a variety of mathematical abilities.  This concept was inspired by a former colleague and friend of mine, Nancy Butler Wolf, Ph.D.  She wrote the book Modeling with Mathematics and begins by sharing a story about teaching factors and how all the students understood how to factor, but when the context was changed to a real life problem they could not answer the question correctly. In the same way, some of the students in my class understand  slope and y-intercept and are comfortable with graphing, but when I presented the modeling activity, their understanding of these concepts did not give them an advantage over the rest of the students.

I started off with a simple block pattern with three figures on the board and I asked them to show that pattern using the blocks in front of them, and then to use those same blocks to create the next two figures.  I have students in groups of 3 or 4 so there is mathematical dialogue, which in my opinion is the best part of the activity -- students conversing about mathematics, what could be better?  I then asked them to describe in a sentence what was happening and a 9 year old said, "It {the pattern} is increasing by two."  Then an older student said, "It is increasing by adding two blocks on the bottom."

I do not want to bore you with the rest of the modeling activity, but a pattern of wood blocks were able to open the eyes of elementary students to physical modeling, seeing a pattern, coming up with a model, and then projecting what the 50th figure would look like.  Even though the algebra students I have know how to write equations and substitute, they had never before modeled mathematics, so they were just as engaged and challenged as the students with no algebra background.