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Concepts and College Math Do students and faculty speak the same mathematical language? What’s wrong with this? When I say ‘variable’ students hear and think about... Variable A variable is a symbol on whose value a function, polynomial, etc., depends. For example, the variables in the function f (x,y) are x and y . A function having a single variable is said to be univariate, one having two variables is said to be bivariate, and one having two or more variables is said to be multivariate. In a polynomial, the variables correspond to the base symbols themselves stripped of coefficients and any powers or products. Weisstein, Eric W. "Variable." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Variable.html When I say ‘equation’ students hear and think about... Equation An equation is a mathematical expression stating that two or more quantities are the same as one another, also called an equality, formula, or identity. Weisstein, Eric W. "Equation." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Equation.html Well, maybe not quite... But I was wondering and decided to find out. I asked all my students on the first day of class to provide definitions for some common math words; terms that I knew I would be using throughout the semester, not knowing really whether my students understood these in the way that I would imagine/intend them to be understood... Ad-hoc Survey? Define the following mathematical terms in your own words: A variable is a... A constant is a ... An unknown is a ... A known is a ... A formula is a ... An equation is a ... An expression is a ... An equality is a ... An algorithm is a ... An inequality is a ... A solution is a ... What am I learning? Variable – student definitions 1 (9) blank 2 (1)value 3 (1)a component in an equation that is used to represent a certain amount; variables can change and represent different things depending on what it is set as 4 (2) a letter used instead of a number 5 (1) value that can change 6 (1) letter and number mix 7 (3) a letter in a (math) problem 8 (2) a letter that stands in place of something (substitute) 9 (3) number 10 (1) a whole number Variable continued 11 (1) sum of two numbers 12 (1) single digit 13 (1) a number that is substituted by a letter 14 (1) a number or a letter used in math problems 15 (20) letters to represent/replace the numbers 16 (1) term that is represented by something in an equation 17 (2) a letter that stands for a number that has to be solved 18 (1) a symbol placed in the place of a number 19 (1) a letter that may or may not stand for something Variable continued 20 (1) something that is unknown 21 ( 2) a letter that goes after/with the number 22 (1) letter 23 (1) a letter that is unknown 24 (1) a letter used to find a number in an equation 25 (1) a term that needs to be found and/or solved for 26 (1) a number that varies 27 ( 2) letter used to represent an unknown number 28 (1) a letter that reflects a number 29 (1) a part of a math problem that can be changed 30 (1) example: 3x, the 'x' is a variable Equation – student definitions 1 (9) blank 2 (2)a statement asserting the equality of two expressions 3 (1) a math sentence stating that two expressions are equal 4 (2) something that you solve 5 (22) a (math/algebra) problem 6 (1) a problem that is solved using variables 7 (1) mathematical sentence with an equals sign 8 (2) a problem that has to be solved 9 (1) is where the numbers on the right side of the equal sign are the sum of the numbers on the left side of the equal sign 10 (1) another word for a problem Equation continued 11 (1) a problem with letters and numbers 12 (1) something that helps solve the problem 13 (1) a formula of numbers that leads to an answer 14 (1) a group of numbers or variable coming together to solve and balance out a problem 15 (1) formula 16 (1) a mathematical question that needs a solution to answer 17 (1) a problem set up where things are equivalent 18 (1) expression 19 (1) when the left side of an equals sign is equal to the right 20 (1) something that is constant like a + b = c Equation continued 21 (1) an un-simplified problem, numerical phrase, or expression 22 (1) a solution which contains two math problems on both sides of the equals sign 23 (1) a way to figure out answers such as addition equations, x, y equations 24 9 ) steps you take when finding a solution to a problem, a formula 25 (2) an expression that you are trying to find a solution for 26 (1) two or more variables or constant that is either added, subtracted, multiplied, or divided 27 (1) has an equals sign 28 (1) what you are solving: ex. 7x+3x=10x Some things to notice Variable as number Equation as action Context A2 – B2 = (A + B)(A – B) equation?, formula?, expression? variables?, unknowns?, something to solve? Y2 – X2 = (X + Y)(X – Y) same?, different? (m2 – n2)2 – (m2 + 42)2 = {(m2 – n2) + (m2 + 42)}{(m2 – n2) – (m2 + 42)} same?, different? Silly example Dog: (Canis lupus familiaris) is a domesticated subspecies of the wolf, a mammal of the Canidae family of the order Carnivora. The term encompasses both feral and pet varieties and is also sometimes used to describe wild canids of other subspecies or species. I saw you with that girl last night. What a dog! You dating both girls? You’re a dog! To be continued......