In Christine Moynihan's 2013 Fall NCSM Newsletter article "Leadership Tips", she focuses on how “Learning is not attained by chance. It must be sought for with ardor and attended to with diligence.”
Too many words and phrases used in mathematics classrooms promote misconceptions and are barriers to students attaining conceptual understanding. Identifying and eradicating them from use can provide stronger pathways to understanding. Just a few of the offenders include:
- Borrow—When one borrows something, there is an expectation it will be returned; that does not happen when we “borrow” a ten.
- Carry—There is no “carrying” going on in the action of regrouping.
- Add a 0—How many of us were taught that you just add a 0 to the number when you multiply by 10? This flies in the face of 0 being the additive identity—any number with 0 added to it is the same number!
- Multiplying by 10 (or 10^1) is increasing the value by one power of 10.
- “Guzinta”—You know: 6 “goes into” 24 … instead of, how many 6s are there in 24, or how many are in each of the 6 groups if there are 24?
- Reduce—When something is reduced, it becomes smaller; 2/3 is not smaller than 4/6—it is just in simpler form.
- Altogether, etc.—This and a few others are taught as “key words”—altogether means that the problem should be solved by adding. Providing counterexamples allows students to see that they must analyze a problem carefully: There are 22 students altogether in Mrs. Sullivan’s class. Twelve are girls, how many are boys?
- Digit, number, numeral—These are often used interchangeably, yet have different meanings.
- Less or fewer—These are also often used interchangeably and should not be; less refers to continuous variables, while fewer indicates things that are discrete.
- Tricks and magic—There are NO tricks nor magic in mathematics! There is a valid reason for everything.
- Yours is not to reason why—just invert and multiply. Of course, we want our students to reason.