## Arithmetic for Human Beings

Review of Arithmetic for Human Beings by Robert Froman

Arithmetic for Human Beings: An Anti-Textbook for People Who Loathe Arithmetic by Robert Froman.

I read this book in two sittings and recommend it to everyone, even those who *don't* loathe arithimetic. It was preaching to the choir to me, because it described what I did day in and day out in my CPA career, and what I do now in my everyday life with math. People say I am good with math, but what I really am good at doing is knowing how to judge how much math I need to use given an individual set of circumstances. It is this skill the author believes is not being taught to kids today.

The author has an excellent point that the way arithmetic is typically taught in school, most people do not learn how to use math unless it is modeled for them, or they figure it out on their own. The closest I've seen an author describe this is Marilyn Burns' Math: Facing an American Phobia (her "Thanksgiving dinner" example in particular), but I think this author does a better job of addressing the problem.

I found the book searching on the author, whose contributions to the Young Math series I was really impressed with. In particular, Froman's "A Game Of Functions " introduces functions to children and is really well written. He also wrote a very accessible book on topology for children. I've gleaned many ideas on how to introduce what I would have thought of as more complex math ideas to younger children through these books.

This book is called an "anti-textbook" because Froman demonstrates how blindly applying textbook arithmetic to math problems we encounter in real life will often actually produce the *wrong* answer. To demonstrate, he spends a whole chapter on applications of multiplying 979 by 743. There are many different situations wherein we might need to do this in real life - and in not one of these situation is it helpful at all to calculate the exact answer. In some situations, thinking "It's a little less than a quarter of a million" is the right answer, if, say, you are trying to rack up a million flying miles and want to know how far you have to go. A more exact answer only muddies the picture and keeps you from understanding that you are about 3/4s of the way there and have 1/4 to go.

Froman brings up another real life situation involving a business decision regarding whether or not to buy a gadget based on a buy and sell price, and sales projections. He makes the excellent point that in situations like this, exact calculations can actually do more harm than good. As he puts it, the time and effort to make exact calculations imbues in the calculations themselves an incorrect meaning. The fact is, the answer itself is an estimate, all you are trying to do in the given situation is determine whether it is good business to make the purchase. By calculating your risk of potential loss using exact dollars and cents, it implies this is an exact loss, when in fact, the entire situation is tentative.

Froman says you *should* use tentative numbers if the situation is tentative - that diving into exact calculations actually short circuits your brain and keeps you from using your intuition. In the end, he stops using arithmetic when he gets his answer - in this scenario, that the risk is worth taking, because even if the businessman cannot sell the at-risk inventory and takes a total loss on it, he will still make an overall profit. He does not calculate the exact profit because a) that wasn't the question and b)it is too tentative to bother doing the math, it won't be the right answer.

The entire time that I was reading this I was remembering my personal experience in business, and how in every business situation I was in, my ability to *not* resort to exact calculation and apply only the arithmetic that was appropriate to each situation was key to success. Employees or professionals who could not do this were let go, or sent to a department where their inability to let go of arithmetic details would not be a liability.

Froman makes the point that exact and accurate calculations are very important for higher math, and there are some (infrequent) situations in life that an exact calculation is necessary. But his problem is that young children are taught to apply math this way many years before they will need it for higher level math, and in reality many may never need it. All of us need practical math, which is highly reliant on these skills that are not in the curriculum.