Mathematical Notation and Schools: The Series
Here’s a summary of the series (thus far) of posts on mathematical notation, with links. This allows you to read them in order, from oldest to most recent.
In this series, I’m investigating variations of standard mathematical notation, with an eye on its use in schools.
1 – In the first installment, I look at the raised minus sign you see in American schools, to indicate a negative number. You see ⁻7 to indicate negative seven, distinct from the normal minus sign used in e.g. 10 – 7 to indicate subtraction. How is that useful, and if so, why do people stop using it after a certain grade?
2 – In the second installment, I look at notations for multiplication, and the way that “×” tends to be phased out in secondary school. You see “•” used in middle school, but both “×” and “•” are too easily confused with common symbols in middle school: “x”, the variable, and “.”, the decimal point. The secondary school (and later) convention of simply juxtaposing things to indicate multiplication (where 4ac means 4 times a times c) works, but makes it necessary to write 3(4) to mean 3×4. I suggest an alternative in using “*” as a variant for “×” from about fifth grade on.
3 – In the third installment, I look at notations for sequencing and nesting of operations, and suggest an alternative notation for parentheses which I call bags. These bags are easy to draw, but hard to type on a keyboard. On a keyboard, these bags naturally devolve into ordinary parentheses. Bags are easy to nest, and they look just as natural for terms as they do for factors.
4 – In the fourth installment, I started a look at the many uses of the equals sign, confusing if not conflicting, and looked at a common non-symmetric use of it, the one you see on many calculators: “do this now”. What alternative notations might help disambiguate this?
5 – In the fifth installment, the use of “=” for equivalence, e.g. is highlighted. The “=” is used here to assert that left side and right side will evaluate to the same value regardless of the value chosen for x. Is this use of “=” worth differentiating from the use of “=” in equations, and if so, what notation would help student learning?