Transcript 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
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......