The Meaning of And
Word problems become harder when the definitions change. In this case it was a simple conjunction. My daughter was stumped on her 8th grade pre-Algebra homework when the formulas did not work the way she thought they should for the problem pictured.
She was trying her best to convert the text into a single complex algebraic expression such as D=(13+W)+(9-R). She was adamant that the word "and" represented addition while I argued it meant equals. My formulas were D=13+W and D=9-R, or 13+W=9-R but these did not seem complex enough for her. It is of course Algebra, and that requires complex expressions - right?
I would argue that the use of "and" in this case is grammatical and not a mathematical usage. Does this mean the problem is poorly worded? In fact, the entire word problem is rife with couplets: more than Wes AND less than Ross, write AND solve, scores for Damon AND Wes.
I'm not even sure how my mind interprets the context to reach my own conclusion and this may be too philosophical of a debate. But I believe it is important to realize where a student struggles in their understanding.
Once she understood there is more than one definition to the word "and" she was able to move on with the problem. But that leads to a more intriguing thought, how do we understand the contextual definitions of words in math problems? Is there a cross correlation between grammar and math? Imagine, we could be teaching math in English class and grammar in math class!
Extra thought: Who remembers comparative measurements but not hard figures? My bill is more than yours and less than his, but for the life of me I cannot remember how much my bill is. Come on people, this isn't even a realistic problem! Comparisons are drawn from concrete values.