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