Below are lists of the most important math
proficiencies needed in firstyear Math for Elementary Education courses...
General
Proficiencies
Postsecondary instructors insist that the general
proficiencies in the table below are extremely important for anyone wishing to
succeed in a Mathematics for Elementary Education (MFEE) course. In
many ways they are more valuable proficiencies for the student entering a postsecondary
Math for Elementary Ed course than are even a large number of individual, specific
mathematics skills. Although general proficiencies are difficult to measure, the
effects of these qualities and attitudes towards success in any MFEE course is difficult
to overemphasise.
General
Proficiencies Essential For Math for Elementary Education 
General
Proficiency 
Related Proficiencies 
Comments 
Thinking Skills 
Critical, Logical Thinking 
Orderly, analytical, inquiring thought processes. 
Modelling 

Finding appropriate constructs or methods to solve a problem.
Example: writing a function that captures the components of a problem. 
Integration of Topics 
Combining concepts
Synthesising 
Using two or more concepts in combination. Example: the
concept of perpendicularity with the concept of the equations of such lines. 
Symbolism 
Symbol Manipulation 
Familiarity and comfort with mathematical symbols. 
Positive Attitude towards Math 
Little or no Math Anxiety; Comfort with Numbers 
A willingness to try; a comfort with numbers and number operations.
Build on success and enjoyment. 
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Specific Proficiency Categories
The survey completed by college/university instructors listed broad
proficiency categories containing morespecific subproficiencies. These
main proficiency categories of specific mathematics topics that students typically
encounter in senior secondary courses are ranked in the table below. Each category
has also been given an importance rating of: Essential, Very
Important, Important, Nice to Know or
Not Important, in accordance with the survey results.
Code 
Mathematics Proficiency Categories Rated for Math for Elementary
Education 
E 
Solve Equations and Inequalities. 
Very Important 
M 
Understand and use Straight Line and Linear
Functions. 
Important 
A 
Understand and use Polynomial Expressions. 
Important 
C 
Understand and use Exponential Expressions. 
Important 
D 
Understand and use Radical Expressions. 
Important 
F 
Understand and use the Geometry of Lines and
Points. 
Important 
B 
Understand and use Rational Expressions. 
Important 
L 
Understand and use the Function Concept. 
Important 
J 
Understand and use Data Analysis. 
Nice to Know 
G 
Understand and use the Geometry of Circles. 
Nice to Know 
N 
Understand and use the Quadratic Function. 
Nice to Know 
K 
Understand and use Sequences and Series. 
Nice to Know 
H 
Understand and use Triangle Trigonometry. 
Nice to Know 
R 
Understand and use the Logarithmic Function. 
Nice to Know 
P 
Understand and use Quadratic Relations. 
Nice to Know 
Q 
Understand and use Polynomial Functions. 
Not Important 
S 
Understand and use Circular Trigonometric
Functions. 
Not Important 
T 
Understand and use some Concepts of the
Calculus. 
Not Important 
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Specific SubProficiencies  THE TOP 20
Each Specific Proficiency Category contains several, individual
subproficiencies. The twenty individual proficiencies rated highest
for entry to university/college Math for Elementary Education (MFEE) are given below:
THE
TOP 20 MATH PROFICIENCIES FOR MFEE  IN ORDER OF IMPORTANCE 
Code 
Mathematics Proficiency 
Rating 
E1 
Solve linear equations. 
Very Important 
E2 
Solve linear inequalities. 
Very Important 
U1 
Find and write up solutions to word problems
connected to specific math/stats topics being studied. 
Very Important 
A2 
Add and subtract polynomial expressions. 
Very Important 
F3 
Understand and use the Pythagorean Theorem. 
Very Important 
U5 
Use the set operations: union, intersection. 
Important 
A1 
Simplify polynomial expressions. 
Important 
C1 
Use the Laws of Exponents to simplify
expressions. 
Important 
D1 
Simplify radical expressions with index 2. 
Important 
U6 
Graph set interrelations using a Venn Diagram. 
Important 
A3 
Multiply and simplify polynomial expressions. 
Important 
M1 
Graph and write the equations for linear
functions. 
Important 
M2 
Understand and use the slope of a line. 
Important 
U4 
Understand and apply the concept of set,
subset and complement of a set. 
Important 
E8 
Solve systems of linear equations in two
variables. 
Important 
F1 
Understand and apply the angle relations
resulting from two intersecting lines and from parallel lines cut by a transversal. 
Important 
B2 
Multiply and divide simple rational
expressions. 
Important 
B3 
Add and subtract rational expressions. 
Important 
D2 
Apply the four basic operations to radical
expressions with index 2. 
Important 
L1 
Understand and use function notation. 
Important 
Although the above specific proficiencies have been rated highly for success in a Math
for Elementary Education course, there are many others. To view the specific ratings and
the entire list of topics, including ones not specifically mentioned in the survey, you
may use a pdf
reader to download the entire Mathematics Proficiencies
Report from HERE.
The Mathematics Proficiencies for PostSecondary Mathematics/Statistics Courses
Project Report may be freely quoted when the source is credited.
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