This second posting on the topic of number sense highlights some things I learned or realized since writing the first one. This post emphasizes some new thinking on education and more of my ideas on how to develop and apply this sense, especially the overlooked importance of the number used to represents nothing.
A recent podcast from Freakonomics focused on math education in the US. Steve Levitt advocates that math teachers should focus on “data fluency”. At about minute 27, there is a discussion of what instructors at US “colleges” (i.e. universities) expect students to know vs. what high school teachers teach students. The instructors argue for three things:
- Mechanics: +, -, *, /, and especially fractions (personally, I think that memorizing the times tables up to 12 x 12 is not a waste of time)
- Data analysis and problem solving: ratios, growth rates over time, proportions, interaction effects
- The algebra of linear equations
With that solid foundation, everything else can be taught at a university. Part of the problem is that high school teachers think differently: i.e. they try to teach everything.
For people who advocate for the importance of data analytics, it is important to note that the tests are changing. In the US, doing well on the SAT exam is seen as key to being accepted at a preferred university. Intended as a general test of intelligence, the SAT test now has a section on evidence-based reading and writing where test-takers are asked to interpret a section of text which contains some numbers. These questions are a response to the claim that “I won’t use math in everyday life.” which was always false.
Even journalists are learning this lesson and media are responding by hiring journalists who can work with numbers to uncover and make sense of issues hiding in plain sight. For example, the huge number of sexual assault cases deemed to be “unfounded” even before going to trial. It is becoming less common to hear a journalist admit that they like their job because “they are not good with numbers”.
The challenge remains: how to develop a good sense of numbers without taking a class in arithmetic? I think that there are many ways to gain experience.
First, if you know nothing about a situation then everything must be a matter of calculation. So, read widely to know more. It only requires a bit of curiosity. For example,
Or follow the news: e.g. https://renx.ca/ or https://www.bisnow.com/toronto and ask, does that combination of numbers makes sense (or is something being hidden from you)?
It also seems to me that the number 0 does not get the respect it deserves. If you think that 0 means an absence of something then you have a problem. It is more accurate to say that zero is the line between positive numbers and negative numbers.
Understanding the line between profit and loss is critical in the real estate industry since the line can seem to move. People estimate price trends all of the time and the most common example of a failure to think critically in this industry may be the claim that “prices of property will always rise”. While the claim may seem right based on the moving target called “recent history”, older history offers many examples where the rate of growth in price is less than 0.
Experience with data fluency would help when learning from figures. If the word “graphing” were replaced by “data visualization” then it is a cool new skill. The Economist and Scientific American magazines show what is possible. Data visualization is central to a lot of discussions in the real estate industry because so much depends on location and spatial relationships.
Mostly, number sense helps with the informal work that occurs before the formal work begins. For example, a short article in the Economist applies this skill: how much would it cost the US government to build a moat at its southern border and fill it with alligators? Their answer is US$30,000,000,000. Knowing where to find some defensible numbers and being able to do back of the envelope calculations (in your head?) can make you appear authoritative.