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ASU MTE 494 - Symbols and variables in school mathematics

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Coming to terms with the uses of literal symbols and variables in school mathematics*Slide 2What’s the role of literal symbols in school math?A = PektLabels: f, y in 3f = 1y (3 feet in 1 yard)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. Slide 7Slide 8What would YOU say is the punch line of this story?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 + 22. y = 5r2 – r + 43. y = ax2 + bx + c4. y = 5x + 95. y = mx + b6. y = (1/2)πrd8. E = mc2What’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?Labels: f, y in 3f = 1y (3 feet in 1 yard)Constants: π, e, cUnknowns: x in 5x – 9 = 91Generalized numbers: a, b in a + b = b + aVarying quantities: x, y in y = 9x – 2Parameters: m, b in y = mx + bAbstract symbols: e, x in e*x = x Some Different Uses of Literal SymbolsWrite 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. “There are six times as many students as professors at this university” “Ok, so that’s 6 times as many students, so that’s 6S = P”Here is a response typical of many students’ (seen across a wide range of grade levels):•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 write2B + 6B = 40 8B = 40This 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


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ASU MTE 494 - Symbols and variables in school mathematics

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