Today’s Doonesbury cartoon (pictured below) deals with Wall Street executives and their high levels of compensation:
I don’t follow the financial world as closely as perhaps I should, so this is the first time I’ve heard of Joe Price and Sallie Krawcheck. I Googled “Sally Crawcheck Severance” and found this article from Bloomberg Businessweek. The headline and first few paragraphs of the article are below:
So let’s see here — we have 30,000 jobs being cut. And we have a target of $5,000,000,000 to save. I wonder what the average salary would be if those 30,000 jobs accounted for the full $5 billion in savings…
That would be an average salary of $166,666. Is that the average salary at Bank of America, I wonder?
What is the average salary for workers in the United States?
Some quick research tells me it’s around $45,000 per household — but in the chart below I learned what the median is rather than the average (or mean):
The way we usually teach mean and median and mode is to lump them together as terms students should memorize. There’s no context, and once the students answer the quiz question, they tend to forget the difference.
Here’s a fine summary of mean, median and mode from a website designed to help students prepare for the end-of-year exams in New York:
The premise behind the math curriculum I want to develop is that we’d have it in mind that at some point during the year we’d cover the idea of mean, median and mode. But we’d wait for there to be student interest in a real world situation.
By trying to gain some context for today’s Doonesbury cartoon, we’ve come to see that the median salary differs from the mean (or average) salary.
We’ve also learned that there were about 119 million households in the US, as of 2010. The US population today is about 312 million people (according to the U.S. Census Bureau)
So if we divide 312 million by 119 million, we learn that the average household size in the U.S. is about 2.62. Can I find a statistic that corroborates that?
I just ran a quick Google search
and found this article from May in USA Today.
This is math that Dan Meyer would like, I think — it’s acknowledging that the real world is messy and that we never know all the information in a problem the way math is usually presented in a textbook — as Meyer puts it in his terrific 12-minute TED Talk,
… ask yourself, what problem have you solved, ever, that was worth solving, where you knew all of the given information in advance, or where you didn’t have a surplus of information and you had to filter it out, or where you didn’t have sufficient information and you had to go find some. I’m sure we all agree that no problem worth solving is like that. And the textbook, I think, knows how it’s hamstringing students.
Here, what we’ve done is to use math to start to think about average and median salaries. We’ve also made students more comfortable with the terms million and billion, by using those terms in a real-world context. And we’ve started to think about the size of families in the United States.
We can also cycle back to the Doonesbury cartoon and think about what it means that some people are making so much money that their severance packages are $5 and $6 million dollars. And for middle school students, we can introduce the idea of a severance package.
So thanks, Gary Trudeau, for framing some math in an interesting (albeit left-wing) way. When we do math for an hour every day (which we will at the school I plan to open in 2013), this might take up most of our hour of thinking about math. It’s engaging and fun, and it’s something students will remember more than a rote lesson about mean, median and mode.
That’s not to say that students don’t need to know those three terms — they do. But we can and should make math more engaging.
Math is everywhere — even in the comics
P.S. I just tried to get global perspective on the size of households, to see how the US compares:
The result I clicked on looked odd to me — I was expecting the US to be reasonably low, relative to the rest of the world, but it came up fourth:
So then I looked more closely at the page, and I learned that this graph is just looking at North America and Europe:
This is a great way to show students that they need to think about statistics rather than just jump to the conclusion that family sizes in the US are the fourth largest in the world.
The world is bigger than that. Part of the reason I know that is because I visited Ethiopia in 2006, where families are much larger — on average more than five people per household. Here’s a screen clipping from a web page I found about Ethiopia’s population.
I corroborated that source with this other source that gives a more global context:
Average household size in Asia is around 4 persons per households. This is the second highest after Africa where the average size is about 6 persons per household. This trend is expected to continue in the next millennium.
The role of a
teacher learning facilitator in my school will be to help students slow down and be thoughtful about everything they do. In this case, it would be thinking about the scope of a statistic, but throughout the year it would extend to all sorts of areas of learning.