Please note that this is "a work in progress." At present, what you see below is our goal, we are modifying things, and we are open to suggestions. Very little of this is "set in stone," nor has it been completely approved by Western Illinois University. This is a cooperative project.
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Description ~ What's this all about?
Training - Helping teachers develop such a course for their own high school ~ How do I develop one of these courses? Approval Process for High Schools ~ How can our high school seniors get automatic math placement into W.I.U. mathematics courses?
Possible textbooks ~ What textbook might I use? Possible course titles ~ What do I call it? |
The problem:
Many high school seniors have completed their minimum math requirement by the end of their junior year. Often the available options, PreCalculus or Calculus, seem unattractive, unapplied, and too demanding for many seniors. Too often then, they elect to not take a mathematics course their senior year. (Reasons vary: "I don't think I need any more math," "The next course is PreCalculus and I'm not interested--and my counselor said I didn't need PreCalculus for my intended major," "I want my senior year to be easy.") The problem is that with no mathematics course for a full year, the student's skills atrophy. Upon graduation their mathematics skills have become weak. In the freshmen year of college the student often must take a remedial course (often a repeat of their last math course from their junior year of high school). This is frustrating to students and parents, costs time and money, and compounded by that fact that remedial courses usually do not count toward college graduation. The student who goes directly into the workforce does not not have the necessary skills needed in today's work place.
This current project is part of ongoing "P-16" efforts by the Regional Office of Education #26 and Western Illinois University to improve the transition through the levels of education from Pre-School through College. This is a cooperative project involving Western Illinois University, seven Illinois Regional Offices of Education (ROE's), and Illinois teachers from these Roe's.
One Solution: A New Course
We recommend that high schools offer an alternative course for seniors who have successfully completed Algebra II. In this course, titled Mathematical Modeling for the Real World course, students learn to use mathematics in problem solving, modeling, and drawing inferences, through a study of diverse examples of real-world problems.
Mathematical Modeling for the Real World is:
- a course for high school seniors who plan to go to college and for those who plan to enter the work force.
- an applied course. The focus is on real-world applications.
- a study of mathematical concepts and procedures that students will encounter in life, the work force, or in college course work.
- a broad preparation for dealing with quantitative information and decision-making in a wide range of situations, and not a prerequisite for a particular course.
- designed to help students achieve the Late High School benchmarks in the Illinois Learning Standards.
- a highly attractive course for high school seniors who would otherwise not take a mathematics course their senior year.
As indicated, the focus and purpose of Mathematical Modeling for the Real World is student understanding of how mathematics is used in the real-world. Applications are studied daily. The course does not attempt to introduce new mathematical content beyond the Algebra II level. The emphasis is to understand how the concepts of Algebra II are used to solve real-world applications.
Mathematical Modeling for the Real World is similar to, and shares the same basic philosophy as, Western Illinois University's course Core Competency in Mathematics (Math 100). However, it is not the expectation that the high school Mathematical Modeling for the Real World course be equivalent to W.I.U.'s Math 100. If fact, the high school course will be better in many ways than the college course, and it is also better situated to help students become broadly mathematically competent. Topics for the Mathematical Modeling for the Real World courses at various high schools will vary. Teachers are afforded the opportunity to design their own course to fit their own interests, student needs, and district goals.
Alternative titles for the Mathematical Modeling for the Real World course include "Core Competency in Mathematics for Life," "Functions, Statistics, and Trigonometry," "Transition to Mathematics in College and Life."
Extra incentives for seniors to take the course
- Students taking an approved Mathematical Modeling for the Real World course their senior year, earning a C or higher, who attend Western Illinois University, will receive automatic mathematics placement into the general education mathematics courses during the first semester of their freshman year. This means students will be able to enroll in a math course that does count toward graduation and count toward mathematics general education requirements. This means students will not have to spend time and money to take remedial mathematics courses. Details of how a high school can get their course approved by Western Illinois University are below. We hope to also establish automatic mathematics placement options for other colleges and universities.
- Our goal is to award dual credit for students taking an approved Mathematical Modeling for the Real World course and earning a C or higher. College credit (3 SH) would be awarded for Western Illinois University's Math 100: Core Competency in Mathematics. It should be noted that all the details have not been finalized for this dual credit, but we hope to get all the procedures in place in the future.
Overall goals
The goal of Mathematical Modeling for the Real World is to make high school seniors (who are not prepared for, or interested in, a senior Pre-Calculus course) mathematically competent. Western Illinois University defines Mathematics Competency (in the Undergraduate Catalog) as follows.
"Competency in baccalaureate level mathematics enables students to successfully engage in the mathematical thinking encountered in undergraduate studies and in daily living. Central to this competency is the ability to solve problems, to use mathematical modeling, and to evaluate mathematical calculations and reasoning. Students are expected to express and interpret mathematical information in written and oral forms and to use technology (calculators, computers, etc.) appropriately.
Through mathematics competency courses, students will:
- use basic mathematics in problem solving and modeling strategies as needed for college course work and for living in today's and tomorrow's world;
- clearly express mathematical ideas and calculations in writing; and
- make valid inferences from mathematical formulas, graphs, tables, and data."
Important Notes
- This new course is not for everyone. It is our belief that a Precalculus course is still a better college-prepatory course than Mathematical Modeling for the Real World. Mathematical Modeling for the Real World is designed for students who would otherwise elect to not take a math course their senior year (that is, they elect to not take precalculus, due to poor preparation or lack of interest). School counselors should continue to encourage students to take precalculus.
- The prerequisite for Mathematical Modeling for the Real World is Algebra II (also termed "Intermediate Algebra" or "Advanced Algebra"). It is assumed students have also had one year of geometry.
During the Spring 2003 semester we are holding a series of workshops and online activities to help teachers develop a Mathematical Modeling for the Real World (or whatever they wish to call it) course for their own high school.
• Thurs., Jan. 23, 2003, 5 - 8:30 p.m.
• Sat., Feb. 15, 9 a.m. - 4:30 p.m.
• Thurs., March 20, 5 - 8:30 p.m.
• Sat. April 5, 9 a.m. - 4:30 p.m.
• Thurs., May 15, 5 - 8:30 p.m.
With the broad goal of making the transition for students from high school to college as smooth as possible, it is a goal of this project to help high school teachers develop a Mathematical Modeling for the Real World course that is somewhat consistent from school to school, but which also affords teachers and schools the opportunity to design courses to fit their own interests, student needs, and district goals. We would like the core content, modeling emphasis, and course philosophy to be consistent and allow for additional topics to be added as teachers see fit.
Western Illinois University is establishing an approval process where high schools can have their Mathematical Modeling for the Real World (or whatever they wish to call it) course "approved." What this means is that seniors at their high school who take the approved course, and earn a grade of 'C' or higher, will receive automatic mathematics placement into the general education mathematics courses at Western Illinois University during the first semester of their freshman year. The financial and time benefits of such a placement are detailed above. We hope to also establish automatic mathematics placement options with other colleges and universities as well.
Requirements
The following is a list of elements that we feel should be present in any Mathematical Modeling for the Real World course. Teachers wishing to have their Mathematical Modeling for the Real World (other course titles may be used) course approved by Western Illinois University should submit a course description and sample course materials which demonstrate that their course has the following elements:
- Prerequisite and Structure - The prerequisite is Algebra II. The course is a two semester course for seniors.
- Content and Philosophy -
- Philosophy - The course should be taught with the expectation of preparing students to either step directly into college courses (math, science, humanities, or social science) and successfully comprehend the quantitative information and academic rigors, or into the workplace and successfully comprehend the quantitative information and expectations of world of work.
- Emphasis - The course should emphasize mathematical modeling as a means of solving real-world problems.
- Content - The course should include use of:
- Linear, quadratic, and polynomial models,
- Exponential and logarithmic models,
- Geometric models, including transition to algebraic models,
- Interpreting data and choosing an algebraic model to represent it,
- Right-triangle trigonometry,
- Basic statistics.
Models should be included from natural and social sciences, optimization, and finance.
- Use of technology - In the 21st Century, students need to learn to use available technology appropriately. Students in this course regularly use graphics calculators to analyze and solve real-world problems. While graphics calculators will be used extensively, it is also very appropriate to have non-calculator learning activities and non-calculator assessment activities.
- Assessment - The course contains an assessment plan which includes
- Assessment activities are included in the course that are used to verify that students earning a C grade are reaching a minimum level of mathematical competence. That is, it should not be possible for a student in this course to earn a C grade by just completing homework, group projects, extra credit, and the like, without demonstrating competence on individual assessments.
- A comprehensive semester final exam should be given each semester. One of the purposes of this course is to prepare the students for success in college courses--where there will be comprehensive final exams.
- Teaching - The teaching of a course of this nature is challenging for a number of reasons. It is not a standard mathematics course, methodologies need to involve hand-on learning, the students may have weak mathematics backgrounds, and the "perfect textbook" does not exist, to list a few. For a course to be approved it needs to be taught by a teacher who has either
- attended workshops on curriculum, teaching, and assessment for this course, or
- taught the course on an experimental basis for a year and developed their own course materials.
Schools will choose their own title for this course. Possibilities include:
Mathematical Modeling for the Real World
College and Life Mathematics Skills
Mathematics Foundation for Transition to College
College Competency in MathematicsCompetency in Mathematics for College
Mathematics Competency for College
Mathematics Competency for Transition to College
Mathematics Foundation for Transition to College
This project is sponsored by Western Illinois University and the following (7) Illinois Regional Offices of Education (Roe's):
| ROE 1, Adams/Pike counties ROE 22, Fulton/Schuyler counties ROE 26, Hancock/McDonough counties ROE 27, Henderson/Mercer/Warren counties |
ROE 38, Logan/Mason/Menard counties ROE 49, Rock Island county ROE 53, Tazewell county |