Northwest Indiana Postsecondary Regional Partnership
Mathematics: Content Knowledge
The Math Working Group analyzed content knowledge possessed by college ready students. This was categorized into four areas:
- Courses. This concerns the courses the student has taken in college.
- Standardized Tests. This concerns the student's scores on tests such as the SAT or ACT.
- Conceptual Understanding. This concerns the depth of a student's understanding of a topic and their ability to apply it or relate it to other topics.
- Content Knowledge. This concerns the student's competence with particular topics in high school mathematics.
Below is a complete list of our findings concerning these four areas.
Course Preparation
Marginally Prepared for Finite Math/College Algebra
- 8 credits of college bound level math & statistics
- Algebra I, Algebra II, Geometry (or Integrated) & Finite/Discrete & Statistics (1 Semester)
- Success Trend: 75%-85%
Prepared for Finite Math/College Algebra
- 8 credits of college bound level math & statistics w/o repeating a course
- Algebra I, Algebra II, Geometry (or Integrated) & Finite/Discrete & Statistics (1 Semester)
- Success Trend: 80%-90%
Marginally Prepared for Calculus
- 8 credits of college bound level math & statistics w/o repeating a course
- Algebra I, Algebra II, Geometry (or Integrated), Pre-Calculus (1 Semester of Statistics Recommended)
- Success Trend: 80%-90%
Prepared for Calculus
- 8 credits of college bound level math & statistics w/o repeating a course
- Algebra I, Algebra II, Geometry (or Integrated), Pre-Calculus and Calculus AB/BC
- Statistics Recommended (2 semesters)
- Success Trend: >90%
Standardized Tests
Marginally Prepared for Finite Math/College Algebra
- SAT composite score: 800-999
- ACT composite score: 20-25
- PASS ECA Core 40
Prepared for Finite Math/College Algebra
- SAT composite score: 1000-1199
- ACT composite score: 26-30
- PASS ECA Core 40
Marginally Prepared for Calculus
- SAT composite score: 1000-1199
- ACT composite score: 26-30
- PASS ECA Core 40
Prepared for Calculus
- SAT composite score: 1200+
- ACT composite score: 30+
- PASS ECA Core 40
Conceptual Understanding
Marginally Prepared for Finite Math/College Algebra
- Knowledge of facts and some understanding
Prepared for Finite Math/College Algebra OR Marginally Prepared for Calculus
- Knowledge of facts, understanding, and the ability to apply results.
- They can clearly explain their solutions to others.
Prepared for Calculus
- Knowledge of facts, understanding, and the ability to apply results.
- They can view the same topic from several points of view, therefore they can solve a variety of problems related to a topic.
- They can analyze problems and recognize pertinent concepts even when no reference to those concepts are mentioned in the problem.
- They are mathematically autonomous.
- They can clearly explain their solutions to others. Furthermore, they can analyze the mathematical arguments of their peers.
Content Knowledge
Marginally Prepared for Finite Math
Confident Knowledge of:
- Operations with Fractions
- Like terms; polynomial operations
- Exponent rules
- Problem Solving
- Solving Equations; Linear and Systems of Equations (2X2 & 3X3)
- Plane Graphing; Linear Equations Systems
Familiarity With:
- Venn Diagrams/Set Theory/Combinations/Permutations
- Calculate Mean and Variance
- Epsilon symbol recognition
- Sequences and Series
Prepared for Finite Math
Confident Knowledge of:
- Fractional operations calculator
- Like terms; polynomial operations
- Exponent rules
- Problem Solving
- Solving Equations; Linear and Systems of Equations (2X2 & 3X3)
- Plane Graphing; Linear Equations Systems
Confident Knowledge of Half of These Topics and Familiarity of the Rest:
- Venn Diagrams/Set Theory
- Combinations/permutations
- Calculate Mean and Variance
- Epsilon symbols and use
- Sequences and Series
Marginally Prepared for College Algebra
Confident Knowledge of:
- Operations with Fractions
- Like terms; polynomial operations
- Exponent rules
- Basic Problem Solving
- Solving Linear Equations; Solving 2x2 Systems of Linear Equations
- Graphing Linear Equations
Familiarity With:
- Logarithms
- Simplifying radicals
- Factoring
- Exponent Rules-Basic operations
- Special Triangles
- Pythagorean Theorem
- Determination of the Domain and Range of a Function
- Solving Equations
- Quadratic, Exponential
- Systems of equations (2X2 and 3X3)
- More Advanced Problem Solving
- Plane graphing
- Inequalities
- Systems (with obtaining solution)
- Even/Odd Functions; End behavior/asymptotes
- Standard Forms of Special Cases of the Following Classes of Functions:
- Absolute Value
- Conics
- Exponential
- Logarithmic
- Quadratic
- Radical
- Cubic
- Rational
Prepared for College Algebra
Confident Knowledge of:
- Fractional operations calculator
- Like terms; polynomial operations
- Exponent rules
- Problem Solving
- Solving Equations; Linear and Systems of Equations (2X2 & 3X3)
- Plane Graphing; Linear Equations Systems
Confident Knowledge of Half of These Topics and Familiarity of the Rest:
- Logarithms
- Simplifying radicals
- Factoring
- Exponent Rules-Basic operations
- Special Triangles
- Pythagorean Theorem
- Determination of the Domain and Range of a Function
- Solving Equations
- Quadratic, Exponential
- Systems of equations (2X2 and 3X3)
- More Advanced Problem Solving
- Plane graphing
- Inequalities
- Systems (with obtaining solution)
- Even/Odd Functions; End behavior/asymptotes
- Standard Forms of Special Cases of the Following Classes of Functions:
- Absolute Value
- Conics
- Exponential
- Logarithmic
- Quadratic
- Radical
- Cubic
- Rational
Marginally Prepared for Calculus
Confident Knowledge of:
- Fractional operations calculator
- Like terms; polynomial operations
- Exponent rules
- Problem Solving
- Solving Equations; Linear and Systems of Equations (2X2 & 3X3)
- Plane Graphing; Linear Equations Systems
Confident Knowledge of Half of These Topics and Familiarity of the Rest:
- Logarithms
- Simplifying radicals
- Factoring
- Exponent Rules-Basic operations
- Special Triangles
- Pythagorean Theorem
- Unit Circle Trigonometry, Including Trigonometric Identities and Solving Trigonometric Equations.
- Determination of the Domain and Range of a Function
- Solving Equations
- Quadratic, Exponential
- Systems of equations (2X2 and 3X3)
- More Advanced Problem Solving
- Plane graphing
- Inequalities
- Systems (with obtaining solution)
- Even/Odd Functions; End behavior/asymptotes
- Standard Forms of Special Cases of the Following Classes of Functions:
- Absolute Value
- Conics
- Exponential
- Logarithmic
- Quadratic
- Radical
- Cubic
- Rational
Prepared for Calculus
Confident Knowledge of Almost All of the Following Topics:
- Fractional operations calculator
- Like terms; polynomial operations
- Exponent rules
- Problem Solving
- Solving Equations; Linear and Systems of Equations (2X2 & 3X3)
- Plane Graphing; Linear Equations Systems
- Logarithms
- Simplifying radicals
- Factoring
- Exponent Rules-Basic operations
- Special Triangles
- Pythagorean Theorem
- Unit Circle Trigonometry, Including Trigonometric Identities and Solving Trigonometric Equations.
- Determination of the Domain and Range of a Function
- Solving Equations
- Quadratic, Exponential
- Systems of equations (2X2 and 3X3)
- More Advanced Problem Solving
- Plane graphing
- Inequalities
- Systems (with obtaining solution)
- Even/Odd Functions; End behavior/asymptotes
- Standard Forms of Special Cases of the Following Classes of Functions:
- Absolute Value
- Conics
- Exponential
- Logarithmic
- Quadratic
- Radical
- Cubic
- Rational