Math Proficiencies Required for Success in First Year Introductory Statistics

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. 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 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.