In my earlier note I suggested that learning problems might arise from lack of explicitness in writing some expressions:
> 1 Dropping the sign for multiplication (*) between two numerical > expressions or between a number and a variable name and depending on a > space or juxtaposition or a fence (parens, brackets, braces, etc) as an
> implicit indicator of multiplication. We don't do this with +, -, or /. > Of course once we understand the math we can abbreviate, depend on rules > of precedence, etc to make our expressions as short as possible -- but > should we do this for students while they're learning the maths? > Tad pointed to another example:
Actually, in a mixed number, we add the whole number part and the fractional part to get the actual quantity. Technically this may not be an operation case, but I have heard that some students were confused about this.
And Terry confirmed the hypothesis:
You've heard right, Ted. Tho we think of a mixed number as a natural sort of thing, many students in my experience DO get confused about the juxtaposition of a whole number and a fraction, esp. after beginning a study of algebra when juxtaposition DOES imply multiplication. And I think a case could be made for a mixed number being "operational".
There's also the tendency to interpret the expression "3a" incorrectly when evaluating it, for example, when "a = 5". Many of my students simply write "35" and think of it as "thirty-five". They just take the easy way out and don't think. Terry Trotter ***************************************************
Case closed; the problem exists, the solution is obvious, let's declare victory and get on with it. I suspect that the group is ready to vote unanimously in favor of a no-holds-barred campaign to get all school textbook publishers to henceforth write all mixed fractions with a plus, as in 3+1/7, and to always put in the multiplication sign, as in 16*timesec^2 and 3.5*b*c. But first a question, has this experiment been tried before?
Ladnor Geissinger Math Prof at UNC Chapel Hill & Math Chair at IAT email: firstname.lastname@example.org or email@example.com phone: 919-405-1925 address: Institute for Academic Technology 2525 Meridian Parkway, Suite 400 Durham NC 27713 USA IAT phone: 919-560-5031 IAT fax: 919-560-5047 IAT web home page: www.iat.unc.edu LEARN NC home page: www.learnnc.org Mathwright Library: ike.engr.washington.edu/mathwright/