Functional Thinking

Functions based on inputs, outputs, and the rules connecting them are the heart of spreadsheets and the creative problem solving process we call “functional thinking.” Learn to visualize a problem using functions, organize data and ideas as functions, build a model by connecting functions, iterate it to test, revise, and solve the problem, and finally to ask “What if…” These are the skills and strategies to use mathematics for problem solving in the digital age.

1. Visualize Begin your problem-solving process by visualizing the problem, picturing it in context, looking for its key elements, recognizing its connections, and focusing on its constraints. Design thinking* labels this first step as empathize, for before we try to solve a problem, we need to understand it, to see it through the eyes of those who have the problem, imagine a solution, and therefore visualize it.
2. Organize Your second step is to organize the data and layout tables related to the problem by defining the parameters (those quantities we may want to control), and choosing the variable quantities that will be the inputs to produce the outputs to solve the problem. When we build spreadsheets to solve problems, as in all coding, flexibility is key. Define as many parameters as you can so that you can change them.
3. Build The third step is to create functions using unique rules to connect outputs to inputs, and then to build models by linking those functions together to represent the problem and its solution. Functions are the perfect model-building tool, because they can be composed by using the output of one function as the input of another or combined by adding, subtracting, multiplying, or dividing them.
4. Iterate The fourth step, iterate, uses one of the great powers of spreadsheets and digital thinking, the representation of discrete functions. Using digital (discrete) functions makes mathematics and problem solving concrete for students, enabling them to focus on iteration, on making a series of small changes to the model to both understand its behavior, to test it, revise it, and use it to solve the problem.
5. “What if…” The last step in the modelling process asks the creative question, “What if…” If the model is a good one, then it enables students to explore new areas and to find new and unexpected connections. “What if…” is the power of spreadsheets to consider a model in a broader context, to use it in new ways, to extend it, and to perhaps even revisit the functional thinking problem solving process to reach novel conclusions.

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*”Design thinking is a deeply human process that taps into abilities we all have but get overlooked by more conventional problem-solving practices. It relies on our ability to be intuitive, to recognize patterns, to construct ideas that are emotionally meaningful as well as functional, and to express ourselves through means beyond words or symbols.”        Tim Brown, CEO, IDEO