Coming to terms with the uses of literal symbols and variables in school mathematics Adapted from R A Philipp 1992 The many uses of algebraic variables The Mathematics Teacher 85 7 Reston VA NCTM Which of the following are equations of quadratic functions of one variable If you answer it depends please elaborate on the dependent conditions 1 y 7x2 5x 2 2 y 5r2 r 4 3 y ax2 bx c 4 y 5x 9 5 y mx b 6 y 1 2 rd 8 E mc2 What s the role of literal symbols in school math How is that role determined shaped by context What contextual knowledge might students possess and how might that knowledge interact with their understanding of literal symbols Example A Pekt gives the amount of money one would have after time t if P dollars were compound continuously at interest rate of k per unit time A Pekt How are literal symbols used in this equation 1 Which symbols denote constants quantities that don t change 2 Which symbols denote variables quantities that change 3 Which symbols denote parameters generalized constants Some Different Uses of Literal Symbols Labels yard f y in 3f 1y 3 feet in 1 Constants e c Unknowns x in 5x 9 91 Generalized numbers a b in a b b a Varying quantities x y in y 9x 2 Parameters Abstract symbols m b in y mx b e x in e x x There are six times as many students as professors at this university Write an equation to represent this statement Use the letter S to denote the number of students and the letter P to denote the number of professors Here is a response typical of many students seen across a wide range of grade levels Ok so that s 6 times as many students so that s 6S P Write an equation that can be used to calculate the number of feet in a measurement given the number of yards Use the letters F to represent the number of feet and Y to represent the number of yards What s the difference between the two equations F 3Y and 1 yd 3 ft I purchased the same number of books as records Books cost 2 each and records cost 6 each I spent 40 altogether What does the equation the equation 2B 6R 40 represent Here is a line of reasoning is there is anything wrong with it 2B 6R 40 Since B R I can write 2B 6B 40 8B 40 This last equation says that 8 books is equal to 40 So one book must cost 5 What would YOU say is the punch line of this story
View Full Document
Unlocking...