The Psychology in Numbers
Finding patterns (and wisdom) in numbers
Posted Jun 24, 2018
How did you learn the mathematical formula for pi? It was likely the way I learned it. I was told to commit the value pi = 3.14 to memory along with the formula to calculate the area of a circle. Savvy math teachers today encourage students to learn math by the discovery process, rather than by memorization. In a process that is a lot more productive, fruitful, and fun, they coach students to learn pi the way it was discovered. Students measure the circumference of any circular object, from a tire to a Frisbee, and divide by its diameter. They discover that the number 3.14, the ratio of a circle’s circumference to its diameter, recurs repeatedly. Students unwittingly rediscover the number pattern the Babylonians and Egyptians discovered centuries ago.
Pi was always there, a pattern just waiting to be discovered. Teaching and learning become a win-win proposition when teachers see the “aha” look of discovery on student faces. More and more of today’s students learn that math is more than plugging numbers in formulas.
Math is the search for patterns in numbers to reveal an underlying rule or concept. Like many of today’s students who are coached to search for patterns in numbers, numbers persons understand, practice, and even enjoy that.
Finding, describing, explaining, and using patterns to make predictions are among the most important skills in mathematics. When perceiving a graph for example, the first step is pattern recognition (Shah, 1997). Pattern recognition includes whether there is a straight or jagged line, if there are multiple lines, and whether lines are parallel, converging, or intersecting. If the graph depicts a trend, one can predict with some confidence where the next data points will be plotted.
For years, my home energy supplier informed my family how many kilowatts of energy we used each month. I had little interest in the number data until about three years ago. Instead of reporting just the numbers, the report graphed how efficient we were conserving energy compared with our neighbors. This kind of feedback grabbed our attention.
The graph showed that we were ranked 15th out of 100 homes in our neighborhood. That placed us in to top 20 percent of energy users, for which we received kudos and a smiley face. My wife and I now are keenly aware of how much electricity we use and work to conserve it by shutting off lights and reducing heat when not needed.
The company behind these reports is Opower, a utilities customer engagement platform and subsidiary of Oracle Corporation founded in 2007. Opower’s data has shown that highlighting patterns in consumers’ energy usage translates to measurable energy savings. Some of these data-driven patterns that are used on reports include a single period neighbor comparison, a neighbor comparison over the past year, a comparison to the customer’s own energy usage from the previous year, breakdowns of home energy usage by appliance, and more. Opower helps customers save energy and money just by highlighting these energy usage patterns and presenting tips for how customers can reduce their energy usage. Savings are consistent across all income levels (Bend, 2014).
Dave Bend, Principal of Opower, told me that the report was inspired by a psychological experiment done several years ago by two California graduate students. The premise behind the experiment was to explore how to get people to start paying more attention to the energy they’re using, and how to motivate people to waste less energy. The behavioral science experiment was designed by the two graduate students in 2003. The graduate students put signs on every door in a neighborhood in San Marcos, California, asking people to turn off their air conditioning and turn on their fans (Bend, 2014).
They used door-hangers with a different messaging tactic for each of their four experimental groups. The first technique was a money-saving message, the second was an environmental message, the third told people they should be good citizens and help prevent blackouts, and the fourth said, “When surveyed, 77 percent of your neighbors said that they turned off their air conditioning and turned on their fans. Please join them.” (Bend, 2014)
The only messaging tactic that had any impact on energy consumption was the fourth message. The people who received this message showed a marked decrease in energy consumption simply by being told what their neighbors were doing. This idea that social pressure can motivate people to save energy prompted these two graduate students, Alex Laskey and Dan Yates, to found Opower, and it is still the ideology behind Opower’s reports today. Opower can receive feedback from customers through the web portal, which allows customers to share their story about their experience with the program (Bend, 2014).
Are you numbers smart? Determine the number of these questions to which you can answer “yes.’
- Can you spot trends from scattered data points plotted on a graph?
- Are you able to predict from a series of numbers what the next number will be?
- Can you predict from reading an account of a company’s assets and liabilities whether it is financially healthy or not?
- Are you able to perceive the relationship between two groups of data, like someone’s height and weight?
- Can you accurately estimate the number of open seats in a movie theater or the number of people in a crowded meeting?
- Are you able to see the big picture while playing Sudoku to easily figure out the missing numbers that you can plug into the right places?
- Can you organize a random group of different numbers into groups of similar properties?
You be the judge of how number smart you are.
Shah, P. (1997). A Model of the Cognitive and Perceptual Processes in Graphical Display Comprehension. Palo Alto : AAAI Technical Report FS-97-0.
Bend, D. (2014, July 17). Principal, Opower. (R. Barkman, Interviewer)