Choose-your-own-adventure

Today during advanced algebra, the students were given a really interesting task.  To cement their understanding of piece-wise functions, they were asked to create a poster to display two functions.  For the first function, the students were supposed to create a graph and then figure out the function from there.  On the second, they were supposed to generate a function and then graph it.

Some of the groups chose to do “easy” functions using equations such as y = -5 or y = 2x + 6.  Most groups, though, chose to do something more interesting.  They used absolute value functions and quadratics to create images such as faces or patterns that looked more like art than math.  These images then presented a real challenge when the students needed to generate the equations that make up the function.  The mathematics often worked out to be more challenging than anything they had done in class, but the students did not hesitate to tackle the difficulty.

Watching students work in this way makes me think that we sometimes do students a real disservice.  It seems pretty clear that we regularly underestimate the mathematics that they are capable of.  Today the students were motivated.  We did not tie the problem to any deeply meaningful real-life context to get this to happen, either.  The students were simply given an opportunity to express themselves creatively.  It is important to note that while not all students took the opportunity to really extend themselves, all students were engaged in the exercise.  I am looking forward to the chance to try developing tasks of my own.  Seeing so many people enjoying mathematics was really inspiring.

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