Make Math Great Again
As I reflect on my positionality as a math educator, I realize more and more that in every day contexts, math seeps into my life even when I am not trying to think mathematically. When my low fuel light turns on, I estimate about how many more miles I can go without having to be saved by a tow truck; when I plan my meals, I think about the number of calories I am consuming and compare it to my basal metabolic rate (BMR) to ensure I am in a calorie deficit if I am trying to lose weight; and most recently, during the State of the Union address delivered by President Trump, I listened intently as he described his accomplishments, quantitatively.
Note: My thoughts in this blog do not reflect my position politically; but rather, highlight the dire need for math educators to push their students to think critically, logically, and prove the correctness of a mathematical assertion, as math only describes what the context reveals.
Trump was convincing in his State of The Union address, I will admit. He tore at heartstrings, using evidence to justify his thinking, but his math may be out of context. For example, he opened by stating that since his election, America has “created 2.4 million new jobs, including 200,000 new jobs in manufacturing alone.” It’s easy to hear 2.4 million and think, “Wow! That’s a big number!” But, size is only relative, right? Mathematical thinkers around the nation were probably wondering, “how many jobs were created annually over the past five years? Is the change proportional? How does it compare to the ‘typical’ figures?” Well, the good news about the Internet is that data is easily available. According to the Bureau of Labor Statistics, this year actually represents a drop in the average number of jobs per month since 2012.
Looking at the data from another perspective, graphically, you can also see that there is actually a decline in the 12-month net change as Trump took office.
Moreover, it is important to see that the 2.4 million jobs President Trump claims have been created since his election is not representative of his actual time served as President. He took office on January 20, 2017; this means for the majority of January 2017, Obama’s administration was still in charge. If we look at February 2017 — January 2018, the actual time served thus far, the number of jobs created was only 2,114,000 (2.1 million). Even if we attribute all of January 2017 to Trump, then the calculation from January 2017 — January 2018 total comes out to be 2,373,000 jobs (27,000 fewer jobs than 2.4 million).
It is critical to remind students that humans can misrepresent data to make it say whatever you want, especially if you fail to put the data back into context. Here are some other great examples of data inaccurately represented.
This is exactly why the Standards for Mathematical Practice exist. The practices are a summary of the habits of mind educators believe all mathematical thinkers use on a regular basis. Encourage students to construct viable arguments and critique the reasoning of others (Standard for Mathematical Practice #3), just as I am doing here. If they hear a statement that they aren’t sure is accurate, they should analyze it and develop a rationale to support their thinking. These processes support the content that students learn and help them make sense of the math in front of them.
As you can see from my daily interactions with math, I embody a mathematical thinker as I make sense of the problems around me, justify my thinking, predict using evidence, and more. Don’t get me wrong — this doesn’t mean you have to be right. It just means you have a productive disposition, which enables you to see value in the math that you do.
I was definitely reasoning abstractly and quantitatively (Standard for Mathematical Practice #2) as I analyzed President Trump’s abstractions (the numbers he stated) and contextualized them (put them back into the context they belong). This helped me realize two things: a) 2.4 million isn’t the number that represents one full year in office; and b) in comparison to the past five calendar years, the number doesn’t represent an increase, though it sounded like it the way he said it. What else in his speech could be true, yet misleading as it was presented? Can you identify any other statistics or data in which the number sounds dramatic, but may not actually be? Alternatively, what data presented was correct and accurate with the context?
I encourage you to challenge your students to think mathematically, adapt their reasoning based on evidence and data, and use real-life applications to make sense of mathematics. Most importantly, don’t take abstract math at face value… be sure to understand the context!