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Below are lists of the most important math
proficiencies needed in Introductory Statistics...
General
Proficiencies
Post-secondary instructors insist that the general
proficiencies in the table below are extremely important for anyone wishing to
succeed in an Introductory Statistics course. In many ways they are
more valuable proficiencies for the student entering a post-secondary Intro Stats 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 Intro Stats course is difficult to over-emphasise.
General
Proficiencies Essential For Introductory Statistics |
General
Proficiency |
Related Proficiencies |
Comments |
| Thinking Skills |
Critical, Logical Thinking |
Orderly, analytical, inquiring thought processes. |
| Solving Word Problems |
|
Experience and comfort in setting up, solving and writing up word
problems. |
| 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. |
| Language Skills |
Reading, Writing |
Reading with comprehension and writing clearly. |
| 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 INTRODUCTORY
STATISTICS |
| M |
Understand and use Straight Line and Linear
Functions. |
Essential |
| J |
Understand and use Data Analysis. |
Important |
| E |
Solve Equations and Inequalities. |
Important |
| A |
Understand and use Polynomial Expressions. |
Important |
| D |
Understand and use Radical Expressions. |
Important |
| C |
Understand and use Exponential Expressions. |
Important |
| L |
Understand and use the Function Concept. |
Important |
| K |
Understand and use Sequences and Series. |
Important |
| N |
Understand and use the Quadratic Function. |
Important |
| B |
Understand and use Rational Expressions. |
Nice to Know |
| R |
Understand and use the Logarithmic Function. |
Nice to Know |
| F |
Understand and use the Geometry of Lines and
Points. |
Nice to Know |
| T |
Understand and use some Concepts of the
Calculus. |
Nice to Know |
| Q |
Understand and use Polynomial Functions. |
Nice to Know |
| P |
Understand and use Quadratic Relations. |
Nice to Know |
| H |
Understand and use Triangle Trigonometry. |
Not Important |
| G |
Understand and use the Geometry of Circles. |
Not Important |
| S |
Understand and use Circular Trigonometric
Functions. |
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 Introductory Statistics courses are given below:
THE
TOP 20 MATH PROFICIENCIES FOR INTRO STATS - IN ORDER OF IMPORTANCE |
| Code |
Mathematics Proficiency |
Rating |
| M2 |
Understand and use the slope of a line. |
Essential |
| M1 |
Graph and write the equations for linear
functions. |
Essential |
| U1 |
Find and write up solutions to word problems
connected to specific math/stats topics being studied. |
Very Important |
| U5 |
Use the set operations: union, intersection. |
Very Important |
| U4 |
Understand and apply the concept of set,
subset and complement of a set. |
Very Important |
| U6 |
Graph set interrelations using a Venn Diagram. |
Very Important |
| U7 |
Use a scientific calculator. |
Very Important |
| E1 |
Solve linear equations. |
Very Important |
| J1 |
Organise and graph data from an experiment. |
Important |
| J2 |
Obtain, organise and graph sample data. |
Important |
| U2 |
Engage in the completion of extended projects
involving multiple, varied areas of mathematics/statistics. |
Important |
| J3 |
Apply sample information to population
information. |
Important |
| M3 |
Write direct variations as equations. |
Important |
| J5 |
Select appropriate sampling methods. |
Important |
| J4 |
Determine 90% confidence intervals. |
Important |
| A1 |
Simplify polynomial expressions. |
Important |
| E2 |
Solve linear inequalities. |
Important |
| K3 |
Understand and use sigma notation. |
Important |
| L1 |
Understand and use function notation. |
Important |
| A2 |
Add and subtract polynomial expressions. |
Important |
Although the above specific proficiencies have been rated highly for success in an
Intro Stats course, there are others. For example, the 21st proficiency is "Use
a statistical software package like MiniTab or SPSS". 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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