Motion from IMACC (Illinois Mathematics
Association of Community Colleges
Spring 2013
The following provides important information regarding the motion to be voted on at our annual meeting.
What is being proposed?
The curriculum committee of IMACC is proposing a new pre-transfer (developmental) mathematics course titled "Preparatory Mathematics for Developmental Education" or PMGE.
Which students will study this course?
This course is designed for students who will complete their studies of mathematics with a general education mathematics class (general education mathematics, general education statistics, quantitative literacy, elementary mathematical modeling).
How is PMGE different from the course students usually study?
Intermediate algebra is a skill-based course designed to prepare students for pre-calculus mathematics course. Intermediate algebra includes the following topics: operations with algebraic fractions; solving equations with the algebraic fractions and radicals; solving quadratic equations; solving equations and inequalities involving absolute value; graphing functions, inverse functions.
PMGE examines similar mathematical content in context. It is a course focused on problem solving. The three major strands are algebraic reasoning with variables, functions, and modeling. Additional topics can include geometry, proportional reasoning, systems, and probability/statistics.
An additional benefit is that PMGE was designed to meet the new Common Core Standards of Mathematical Practice. The standards will be used to define "college readiness" in mathematics. More information is available at www.corestandards.org.
Will this course discourage students from choosing majors in mathematics, science, technology and engineering?
Many believe that the traditional intermediate algebra course with its procedural focus does more to discourage students from future study. We hope that PMGE will inspire some students to consider choosing such majors. A student who completes PMGE would need to complete intermediate algebra before proceeding to pre-calculus mathematics. Many colleges are considering self-paced intermediate algebra courses to enable PMGE students to qualify for pre-calculus more quickly.
Will two-year colleges continue to offer intermediate algebra?
Absolutely. Pre-transfer students who plan to study calculus will continue to study intermediate algebra.
Why do ISMAA and IMACC need to vote on the proposed course?
Illinois has had a mathematics articulation guide since 1973. In 1993, with the development of the Illinois Articulation Initiative (IAI), it became necessary to formalize the process. Since then, any changes to the joint articulation guide must be approved by the memberships of both ISMAA and IMACC. The IAI general education panel uses the joint articulation guide to determine whether or not courses will transfer among colleges that have adopted IAI. The joint articulation guide can be downloaded at www.imacc.org.
PMGE is not a transfer-level course but the proposal is that it be used as a prerequisite for four transfer courses.
Will PMGE be an approved prerequisite for the "Mathematics for Elementary School Teachers" course?
That is not a part of this proposal. Our early discussions indicate that many believe that PMGE would be a preferred prerequisite. IMACC will consider a future proposal. One challenge with this is that the standard preparation for elementary teachers will evolve due to the changing requirements from the Common Core standards.
Must all colleges offer the proposed course?
No. Each college will determine whether or not to offer the course. Some two-year colleges are not planning to do so. Most universities and four-year colleges do not offer pre-transfer courses so those schools will not offer PMGE.
Concluding Comments
Illinois has been a national leader in general education mathematics/quantitative literacy. The following statement appears in the articulation guide.
While College Algebra and Precalculus courses are taught at post-secondary institutions where needed, these courses should not fulfill general education or quantitative literacy requirements.
The traditional intermediate algebra course is designed to prepare students for college algebra and precalculus courses. Since most pre-transfer mathematics students at two-year colleges do not intend to study these courses, it is necessary to re-examine the pre-transfer (developmental) mathematics curriculum. PMGE should meet the needs of many of these students.
ISMAA/IMACC Curriculum Ballot - April 2013
________________________________________________________________________
Preparatory Mathematics for General Education shall be included as a pre-transfer (developmental) mathematics course in the Joint Articulation Guide.
YES NO
________________________________________________________________________
The prerequisites for General Education Statistics shall be Geometry and Intermediate Algebra both with a grade of C or better
OR Geometry and Preparatory Mathematics for General Education both with a grade of C or better.
YES NO
________________________________________________________________________
The prerequisites for General Education Mathematics shall be Geometry and Intermediate Algebra both with a grade of C or better
OR Geometry and Preparatory Mathematics for General Education both with a grade of C or better.
YES NO
________________________________________________________________________
The prerequisites for Quantitative Literacy shall be Geometry and Intermediate Algebra both with a grade of C or better
OR Geometry and Preparatory Mathematics for General Education both with a grade of C or better.
YES NO
________________________________________________________________________
The prerequisites for Elementary Mathematical Modeling shall be Geometry and Intermediate Algebra both with a grade of C or better
OR Geometry and Preparatory Mathematics for General Education both with a grade of C or better.
YES NO
The goals of teaching and learning mathematics must emphasize conceptual understanding and problem solving.
“But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from.” (Common Core p. 4)
Specific characteristics of a problem-solving teaching approach include the following (from Margaret Taplin - Institute of Sathya Sai Education, Hong Kong)
The Common Core Standards for Mathematical Practice are: (Common Core p. 7)
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
6 Attend to precision.
7 Look for and make use of structure.
8 Look for and express regularity in repeated reasoning.
Preparatory Mathematics for General Education (PMGE)
3-4 semester hours
Prerequisite: Basic Algebra with a “C” or better or appropriate placement
This course is designed to help students develop conceptual understanding and problem solving ability. In particular this course must satisfy the Common Core Standards for Mathematical Practice.
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
5 Use appropriate tools strategically.
6 Attend to precision.
7 Look for and make use of structure.
8 Look for and express regularity in repeated reasoning.
Purpose: This course is designed to be a second course in algebra and serves as a prerequisite for General Education Statistics, General Education Mathematics, Quantitative Literacy, or Elementary Mathematical Modeling. Students wishing to enroll in courses other than these courses should take Intermediate Algebra. Students may also take Intermediate Algebra upon completion of this course if they choose to pursue courses beyond general education mathematics.
The primary goal of this course is to enable students to develop conceptual understanding and problem solving competence at the intermediate algebra level. This course differs from traditional courses in that it does not focus solely on procedures. However certain procedures are essential to the study of algebra and they will be included.
There must be some flexibility in this course in order to meet the unique needs of colleges. Colleges must determine how to best prepare their students for future study.
Modalities
Course Description: This course focuses on developing mathematical maturity through problem solving, critical thinking, data analysis, and the writing and communication of mathematics. Students will develop conceptual and procedural tools that support the use of key mathematical concepts in a variety of contexts. The instruction should emphasize the connections between verbal, numerical, symbolic and graphical representation of the concepts being taught whenever possible. Emphasis should be placed on modeling and problem solving, with techniques and manipulations covered in context. The appropriate use of technology, such as a graphing calculator, is strongly encouraged.
Note: The three strands of the course are Algebra, Functions, and Modeling. Each strand must be covered but colleges are free to determine the amount of time spent on each strand. The strands together with their descriptions are taken from the Core Standards.
Algebra Overview
Seeing Structure in Expressions
• Interpret the structure of expressions
• Write expressions in equivalent forms to solve problems
Arithmetic with Polynomials and Rational Expressions
• Perform arithmetic operations on polynomials
• Understand the relationship between zeros and factors of polynomials
• Use polynomial identities to solve problems
• Rewrite rational expressions
Creating Equations
• Create equations that describe numbers or relationships
Reasoning with Equations and Inequalities
• Understand solving equations as a process of reasoning and explain the reasoning
• Solve equations and inequalities in one variable
• Solve systems of equations
• Represent and solve equations and inequalities graphically
Functions Overview
Interpreting Functions
• Understand the concept of a function and use function notation
• Interpret functions that arise in applications in terms of the context
• Analyze functions using different representations
Building Functions
• Build a function that models a relationship between two quantities
• Build new functions from existing functions
Linear, Quadratic, and Exponential Models
• Construct and compare linear, quadratic, and exponential models and solve problems
• Interpret expressions for functions in terms of the situation they model
Modeling Overview
Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Quantities and their relationships in physical, economic, public policy, social, and everyday situations can be modeled using mathematical and statistical methods. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data.
Course Objectives:
Topics must include the following:
Topics must also include at least two of the following: