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Concepts and College Math

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

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Concepts and College Math

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  1. Concepts and College Math Do students and faculty speak the same mathematical language?

  2. What’s wrong with this?

  3. 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

  4. 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

  5. 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...

  6. 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 ...

  7. What am I learning?

  8. Variable continued

  9. Variable continued

  10. Equation – student definitions

  11. Equation continued

  12. Equation continued

  13. Some things to notice • Variable as number • Equation as action

  14. 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?

  15. Silly example • Dog: (Canis lupus familiaris) is a domesticatedsubspecies 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......

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