Author: Art Bardige

I am a digital learning pioneer who believes that technology can play a great role in enabling every child to learn efficiently, effectively, and economically. What if Math is my latest work and the most exciting I have ever been involved with. I hope you will give it a try.

Empathy

Empathy is an odd idea to discuss in math or even in STEM/STEAM education. It is usually thought of as an issue in psychology or sociology, perhaps in the humanities, a topic for English or history classes to consider in school. Yet, it is the first step in the Design Learning process where Stanford’s D School tells students to empathize “you observe, engage, watch and listen.” In short, you begin the creative problem-solving process by looking at problems in human terms, from the standpoint of the people who have the problem they need to solve. In the Functional Thinking problem solving process that mirrors Design Learning, we ask students to visualize the problem to make a problem real, see it in context, and picture the kind of answer they will be looking for. We believe that students who visualize a problem will naturally empathize with it.

There is an even greater role that empathy must play in our schools. For if we want our students to care about solving the problems we assign to them, then we must develop and assign those problems empathetically. An empathy-based curriculum may seek to find those few amazing problems that nearly every student empathizes with, or problems that have such a potent human emotion attached to them that students engage immediately. Those great projects are worthy targets. But there is another way.

Imagine instead a future STEM curriculum made up of thousands of creative problem-solving Labs so that students can, in large measure, choose those they want to work on, those they find interesting, those they have observed, those that engage them, those they already have established empathy with. If our goal is no longer the mere acquisition of knowledge, the development of personal libraries of information or techniques, because such libraries are available to all on the Web, then we can focus on practicing creative problem-solving, the skills they will need for the digital age. And they can build these skills because they have also developed the empathy to truly understand how to solve problems in the digital age. Those of us who create these Labs must thus hold empathy as our core vision and first step.

What if Math 2.0

Over the past year, we have been working to combine our spreadsheet math lessons (downloaded more than 20,000 times) into digital age problem solving Courses that promote readiness for school transitions and prepare students for STEM careers. We developed a new model for creatively solving digital age problems that we call Functional Thinking. And we built a new website to enable you and your students to flexibly use our Courses, Modules, and Labs.

Go to our FREE whatifmath.org and see:
Gallery: Over 100 Labs (problem-based-learning lessons)
Content: Courses to develop creative problem solving skills
About: A visual introduction to Functional Thinking
Blog: Our Tips for Digital Age Problem Solving.
• Or scroll down our home page to see the animated function machine and much more…

If you dream of students becoming creative digital age problem solvers who understand and effectively use math, spreadsheets, and coding to succeed in STEM jobs, then join us at whatifmath.org.

[email protected], [email protected]
A search for something magicalJohn Williams

Functional Thinking

We call our problem solving process, functional thinking. When we apply functional thinking to problem solving in the digital age, we find that a few fundamental models give us 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.

1

Visualize the problem and set up parameter table with starting value x0 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 changed.

2

Organize your data into functions with an input, an output, and a rule connecting them.

3

Build and complete the model by adding additional functions and functions of functions.

4

Test and iterate your model to improve it and solve the problem. Add graphs, conditional formatting, or other data representations to design the output to communicate the results.

5

Now ask “What if…” I change this assumption, change the model, or input different data? Think out-of-the-box. Apply what you built to new situations and new problems.

Documents

Our slideshow

Our White Paper

GDP

The GDP or Gross Domestic Product of a country is one measure of its wealth. What can this data tell us about the U.S. economy? Are we getting wealthier? Are each of us really wealthier after inflation? What else does this data tell you?

Parametric Equations

Parametric equations are powerful tools to model projectile motions and to graph things that are not functions like circle or ellipses. The x and y coordinates are defined as two separate functions with a common independent variable often labelled “t”.