Tackling the Staircase Problem with Coding and Math
During his TED talk , Conrad Wolfram describes computer programming as a means of recording procedures and processes and he offers that it is a great way to fully engage students and to check that they truly understand the concept being explored. He says that students gain intuition and experience in far greater quantities through programming and are able to tackle more challenging problems. Thus, they are “able to play with the math, interact with it, feel it. We want people who can feel the math instinctively. That's what computers allow us to do.” In other words, programming is an opportunity to do and understand mathematics! With this in mind, let's take a look at the following problem: How many different ways are there to climb a staircase with n steps (for example, 100 steps) if you are allowed to skip steps but not more than one at a time? A programming approach to this problem was discussed by Maria Litvin during a panel discussion at the 2011 PyCon Con