# Quantification

The amazing science podcast, Radiolab, recently did a show titled “Worth.”  Andrew Stadel, over at Divisble by 3, blogged about some math problems this podcast made him think of.  The podcast didn’t necessarily make me think about math problems, instead it made me consider reasoning about value and quantity.  More specifically, is everything quantifiable?

Google defines “quantify” in this way:

Which makes me wonder can everything be expressed or measured in a quantity?  Can everything be quantified?

Radiolab gives three instances in which things are given a dollar amount that would not normally be thought of in this way.  It gives worth to things that are normally thought of as “priceless.”

Does everything have a price?

The first example is, “how much is one year of life worth?” In the story a reporter goes to Times Square and reluctantly asks passersby this question.  She quickly realizes that people are not freaked out when asked, which she thought they might be.  People just generally had many, many clarifying questions before giving this existential question an honest go.

The second example is, “how much is the life of a deceased loved one worth?”  The United States has a history of paying families if their loved ones are killed because of military actions not directly connected to war procedures.  Yes, this means if a soldier runs over a person in the street after a night out, that person’s family can get reimbursed, but how much?  How much is this worth to the families and also to the US government?  Is it the same or different? If different, how can the difference be reconciled?

The third example (and in my opinion this most interesting) is, “how much is the Earth worth?”  From the Radiolab blurb:

This idea of quantifying the “work” that is done by bees pollinating flowers on Chinese farms, in order to compare it to the work done by humans who have replaced the bees after being displaced by pesticides is amazing to think about.  Is nature priceless? Is anything priceless?

I wonder what other things in our lives are quantifiable.  Love? Death? Happiness? All have in-roads to investigating their worth, but do we want to go down those roads?

Having students think about and ask these questions is where mathematics education is heading.  Standard for Mathematical Practice #2 Reason abstractly and quantitatively is clearly addressed here.  “Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.”

If this is where we are headed as math teachers, I ask “how much is a night off from homework worth to you?”

## 1 thought on “Quantification”

1. Does everything have a price?
Great question. It’s interesting how this question can be both subjective and objectively viewed, making it extremely challenging and quite possibly unanswerable in an absolute way of thinking. However, I think the value is in asking the question and simply reflecting on the magnitude of it.

As for your question, “how much is a night off from homework worth to you?”
Sadly, not much in my opinion. Homework isn’t worth that much to me so even if students value it more than me, it’s a losing proposition to me. What if we asked questions where we place a greater emphasis on the inclusion (or addition) as opposed to the subtraction. That’s definitely a message I was reminded of from the podcast. I highly doubt you’d get the same response if you asked someone, “How much is a year subtracted from your life worth?” versus “How much is an additional year of life worth?”
How much is this engaging activity worth to you?
How much is the activity that will perplex you worth?
These are much more difficult questions to formulate, but I think they’re more meaningful than the alternative.

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