# Technology, Algorithms, and the Creativity Conundrum

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Educational theorists often distinguish between algorithmic thinking and creative thinking. Algorithmic thinking involves applying a formalized series of steps to solve a problem, while creative thinking usually refers to the genesis of a completely new piece of work. Creative thinkers invent and build things, while algorithmic thinkers apply formulaic solutions to situations that they recognize as belonging to a particular category of problem.

This is not to say that there is no crossover between these ways of thinking. The thought process involved in evaluating a situation and choosing which algorithm to apply can sometimes be a very creative process. Most often, however, we educators tend to deal with these thought processes as separate and distinct from one another.

The memorization and application of algorithms is a key component of learning in subjects such as math and science. Chemistry students follow algorithms when they balance chemical equations. Algebra students follow algorithms when they factor polynomials or solve for a variable in an equation. Memorizing these algorithms and knowing how and when to apply them are essential factors to student success in these courses.

However, the tendency to label these subjects as primarily algorithmic often has a negative impact on students' perceptions of the creativity involved in these subjects. Some students comment that these subjects are boring and lack creativity. Teachers struggle to get students to learn and correctly apply algorithms because they believe that once a student has mastered the algorithms involved in the basic concepts of the course, the doors will be open for more creativity and experimentation.

Understanding Algorithms by Playing with Them!

I can remember trying to memorize various formulas and steps in science and math when I was a student, and I can also remember some of my better teachers insisting that we not only memorize the algorithms, but that we understand the logic behind them Many of my teachers took extra time to explain why these algorithms worked in the hopes that knowing more of this logic would lead to a deeper understanding of the algorithms and therefore, a deeper understanding of the mathematic or scientific concepts in general.

This, of course, seems like common sense. We strive to move beyond basic understanding and recitation of material to reach higher-order thinking However, as most of my former teachers would report, it's easier said than done. I can remember tuning out during long explanations of why the quadratic formula works to give you the X intercepts of a quadratic function. By the time the teacher was halfway through a mind-numbing explanation of some algebraic equation I was just as happy to accept the fact that it worked and to plug my numbers into it the next time I needed to without giving the whole concept much more thought.

While the intentions of these teachers were in the right place, their mistake was in trying to achieve a goal that was essentially constructivist in nature through teaching methodologies that rejected constructivist theory Rather than giving us opportunities to experiment with these algorithms, these teachers were telling us the theory behind them. They were trying to transplant their understanding of them into our brains rather than creating opportunities for us to construct our own understanding.

In order to truly internalize them, students need the opportunity to play with the algorithms--to make changes and see the results. They need to be able to break down algorithms, identify their components, and put them back together again.

Modeling via Technology

Fortunately, in today's high-tech world, there are many computer programs that can model algorithmic behavior and allow students to manipulate the effects of different algorithms on complex systems. Programs such as Geometer's Sketchpad and Interactive Physics allow students to build complex models and then to manipulate them to see how their changes affect the system as a whole. …