Function is inherently an extraordinarily simple idea. Like a machine, a function has an input, an output, and a rule that connects every input to its unique output. Functions are powerful because they are patterns that can represent causes (inputs) and effects (outputs) in our world. Functions are building blocks that can easily be combined into models to represent even the most complex objects and processes.
We call this building process, functional thinking. When we apply functional thinking to problem solving, especially problem solving in the digital age, we find that a few fundamental models give use the tools to creatively solve quantitative problems. Think of functions as LEGOs, add columns using new rules, use outputs as new inputs, combine simple functions in new and creative ways.
Steps in Functional Thinking
Start by visualizing the problem. When you tackle a new problem, slow down, think about what you are being asked to do, picture the problem, and imagine the result you are looking for. Design thinkers call this part, empathize, put the problem in context, explore it, understand it.
Organize key data by first building a parameter table to enable you to easily change starting x0 values and incremental Δx values (or in this case t0 and Δt) of their inputs (independent variables), as well as the values of any “constants” that could be explored. Parameter tables make models and coding flexible, easy to change to ask valuable questions, and make spreadsheets transparent to others.
Build the model starting with an input discrete variable (x). Link its start value to x0 and use iteration to add the incremental value Δx to each cell in turn by copying the rule from either a column or row to create a numberline. Add an output column by using a rule to transform inputs.
Test and iterate your model to get the feedback to improve it and solve the problem. At this step you may want to add graphs, conditional formatting, or other data representations to design the output to do more than solve the problem or handle new data, but to communicate your results.
With the model in hand in a well-structured spreadsheet, you are ready to ask the most powerful business and STEM question, “What if…” I change this assumption, change the model, or input different data? When we solve problems in the digital age, we are expected to think out-of-the-box, to apply what we built to new situations and new problems.