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Lots of people worry that students are not learning enough mathematics or learning it well enough.  Lots of people are turned off by math in high school, and I am surprised at the number of business students who avoid math.  Some of the math stuff which I teach seems fancy to some people, but I teach it because it is useful and surprising.  Still, as an educator, I am shocked at what kinds of stuff people think is too fancy and find this debate distracting.

It seems to me that business life is dominated by two equations:

• Profit= Total Revenue minus Total Cost
• Total Revenue= Price times Quantity.

Number sense is also all about +, -, x, /.

To develop a sense of numbers, everybody should memorize the times tables at least up to 10x 10 or a bit higher.  It may not be exciting but it is a simple investment.  Smartphones may seem to make this skill obsolete but that perception is wrong.  Most people think of math classes as learning how to find a precise answer.  Unofficially, number sense is a softer skill learned as a by-product of problem-solving exercises.  It is used to know when to use a calculator and when to ask tough questions about unreasonable answers.

For example, consider an accountant who says that the selling price was 11.95 per unit and that 18.5 million units were sold last quarter and that total revenue was 157 million.  Without using a calculator, should you trust this accountant?  No!  (By focusing on only the first digit, it should be obvious that P is more than 10 and Q is less than 20 so, applying number sense should tell you that the correct answer is near 10x 20 or 200 (i.e. not 157).  By focusing on two digits: P is close to 12 and Q is somewhat less than 20 so, applying number sense should tell you that Px Q is somewhat less than 12x 20= 240.  The precise answer is 11.95x 18.5= 221.075.  So, something like 60 million in revenue disappeared somewhere. )

Asking some tough questions would show whether the accountant is stealing, incompetent or his/her calculator needs a new battery.  More commonly, lots of students make silly mechanical mistakes when answering questions on tests and assignments; without number sense, they cannot check if their answer is reasonable.

As another example, consider a common trick of journalists to use lots of numbers and a variety of scales to explain random outcomes perfectly: “With a profit margin of 15 percent and annual sales of \$10 million, last month’s rise in unit sales by 10,000 caused yesterday’s \$1 increase in the stock price.”  How do you begin to figure out what is missing if you do not know how to put the numbers together?  (Partial answer: you need to have built a library of facts and trivia as background knowledge.)

Or, compared to an amplifier with a volume scale which goes up to “10”, is an amplifier which goes up to “11” exactly 10 percent louder?

Some math stuff is hard, although not because Barbie says so.  Some ideas are subtle or complex and it is worth taking the time to learn because the situation is subtle or complex.  But some things are no brainers.  There should be no debate that everybody needs to know the basics, like number sense.

PA