Math Proficiencies Required for Success in First Year
Math for Elementary Education

Below are lists of the most important math proficiencies needed in first-year Math for Elementary Education courses...

General Proficiencies

Post-secondary 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 post-secondary 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 over-emphasise.

General Proficiencies Essential For Math for Elementary Education

General Proficiency

Related Proficiencies


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
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 more-specific sub-proficiencies.  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.


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.


A Understand and use Polynomial Expressions.


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 Sub-Proficiencies - THE TOP 20

Each Specific Proficiency Category contains several, individual sub-proficiencies.  The twenty individual proficiencies rated highest for entry to university/college Math for Elementary Education (MFEE) are given below:


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 Post-Secondary Mathematics/Statistics Courses Project Report may be freely quoted when the source is credited.

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