College of DuPage Transitional Math Course Pilot: Fall 2018 - Spring 2019 Course Description: This pilot course is designed to develop mathematical reasoning and maturity and to facilitate placement into college-level mathematics. This year-long course is designed for high school seniors who have taken or are taking a course comparable to Intermediate Algebra. The curriculum will be similar to that of COD s MATH 0465 course. Additional objectives may be added by the instructor, if desired. This course is a hybrid of two connected components. The first component is a project-based exploration of mathematical topics as they apply to real world examples. The second component is the use of an individualized, mastery-based learning system which allows students to move through material at their own pace and provides individualized remediation, thus moving towards the rigor of college mathematics. This aspect of the course is completed via ALEKS PPL. This course is intended to place students into General Education Mathematics (Math 1218) or Quantitative Literacy (Math 1220). However, this course incorporates flexibility to accommodate students who were unable to choose between the Quantitative Literacy and Technical Mathematics Pathways or for whom their desired pathway was not available at their school. In this single course, students can earn placement into the Quantitative Literacy Pathway, the Technical Mathematics Pathway (Technical Math, Math 1115 or Math for Health Sciences, Math 1102), or the Basic Math Pathway (Business Math, Math 1100). Furthermore, any proctored ALEKS assessment can also be used for placement into courses beyond Math 1218/1220, such as College Algebra (Math 1428), Math for Elementary School Teachers (Math 1321), Precalculus (Math 1431), Finite Mathematics (Math 1533), or Statistics (Math 1635). Advising is an essential part of this course. Many students have little to no knowledge of college courses and placement. Learning the benefits that successful completion of this course will bring can be an important motivating factor. In addition, students who previously did not anticipate attending college may reconsider their career path when learning of the wide variety of degrees and certificates available at COD. Visiting COD and meeting with college math faculty is highly recommended. Course Structure: The project-based exploration component of the course is divided into approximately 5-6 units. Each unit is designed to explore mathematical topics as they apply to real world examples. Students spend a portion of the time in class working together on problems and projects. Outside of class, students have regular homework sets. From the Statewide Panel s Transitional Math Overview: Although some content in the courses will not be new, the experience should be. Students should work on complex problems, not just complex procedures. The problems should be relevant to a senior in high school who will soon be an adult in society and as such will be a community member, an employee, and a college student. While the students have had some of the content before, they do not understand it well enough to show college readiness as measured by multiple means including standardized tests and course grades. Transitional math courses work to address the gaps in understanding by working on bigger problems, emphasizing problem-based learning and projects, communication, and integration of concepts, not just skill acquisition. Contexts used should be authentic whenever possible and apply to the
student s college or career path. This approach is motivating and engaging but also sets the stage for the types of problems a student will be exposed to when they reach college. Additionally, transitional courses will focus on a growth mindset, resilience, and perseverance as well as college knowledge and 21st century skills. These traits are essential to success in college for any student but particularly first-generation college students. At the beginning of their senior year or end of their junior year, students will take an initial assessment in ALEKS. This assessment determines the individualized learning plan which students will work on throughout the course. This initial assessment is considered an unproctored exam, but in order to obtain an accurate assessment, it should be administered as if it were a proctored exam. A second ALEKS assessment will be taken at the end of the first semester to help students determine the progress they have made. A final ALEKS assessment should be taken near the end of the second semester. Approximately 30 minutes of class time per week should be devoted to students working individually in ALEKS, with tutorial support available from the class instructor. Students are expected to spend at least 30-60 minutes per week outside of class working in ALEKS, in addition to other homework which may be assigned. Recommended Text: (Suggested for use as a textbook or as a resource for planning) Elementary and Intermediate Algebra by Jay Lehmann, Math Lit Second Edition by Kathleen Almy and Heather Foes Course Objectives: The following objectives should be taught using modeling and real world examples whenever possible. 1. Perform arithmetic operations with signed numbers 2. Perform arithmetic operations with decimals and fractions 3. Find powers, roots, and absolute values of real numbers 4. Use the order of operations to evaluate numerical expressions 5. Convert units of measure 6. Evaluate algebraic expressions 7. Find the prime factorization of an integer 8. Apply the rules of exponents to algebraic expressions 9. Use scientific notation 10. Solve linear equations 11. Solve linear inequalities in one variable and use interval notation 12. Solve systems of linear equations in two variables 13. Solve systems of linear inequalities in two variables, graphically, including applications with constrained variables. 14. Plot points in the Cartesian coordinate system 15. Create a scatterplot from a set of bi-variate data, given either as ordered pairs or in tabular form 16. Sketch a line of good fit for a scatterplot and use it to make projections 17. Graph a line given two points, and find its slope 18. Graph a line given its equation 19. Determine the equation of a line given two points 20. Perform arithmetic operations with polynomials 21. Factor polynomials with a leading coefficient other than 1 22. Solve equations using factoring and the zero-factor property
23. Identify relations and functions and use function notation 24. Identify the domain and range of relations and functions defined algebraically or graphically 25. Perform arithmetic operations with rational expressions 26. Simplify rational expressions 27. Solve equations containing rational expressions, recognizing any extraneous solutions 28. Convert radical expressions into exponential expressions and vice versa 29. Simplify radical expressions 30. Solve equations containing radicals, recognizing any extraneous solutions 31. Solve quadratic equations using factoring, completing the square, and the quadratic formula 32. Construct the graphs of quadratic, square root, and absolute value functions 33. Find the inverse of a non-constant linear function 34. Evaluate an exponential function* and construct its graph 35. Evaluate a logarithmic function* and construct its graph 36. Convert an exponential expression into logarithmic form and vice versa 37. Calculate the rate of change of a function between successive pairs of data, where the function is expressed in terms of ordered pairs or in tabular form * 38. Identify a set of ordered pairs as coming from a linear, quadratic, or exponential function * 39. Estimate trigonometric ratios by measuring the sides of similar right triangles 40. Use trigonometric ratios and the Pythagorean theorem with a basic scientific calculator to solve problems involving right triangles * 41. Develop relative frequency tables for discrete and continuous variable data *Indicates that technology may be useful in completing these objectives. Please see the policy on calculator use under the Additional Recommended Policies heading. Course Grading and Placement Policies: For the 2018-2019 pilot, the 2 nd semester course average is based on the following. 0-5% Notebook and Preparedness Students should bring a math notebook to class every day for taking notes and completing projects. Students should have a separate notebook for work in ALEKS. Both notebooks are submitted and graded. 0-10% Homework 10% ALEKS work The grade will be based on the number of objectives mastered over the semester. 10-15% Quizzes 15-25% Group or Individual Projects 50% Unit Exams Retakes on exams are not allowed. Some tests will have portions that allow calculators in order to pose real-world questions. Extra Credit should not be offered in this course. For the purposes of placement into a pathway, grades should be based on a 10-point scale: 90-100 is an A, 80-89 is a B, etc.
Each of the three pathways has a target score the student is working to earn, as well as a minimum cutoff score. A student s highest proctored score for the course will count as their assessment score. A student s placement is determined according to the tables below. Quantitative Literacy Pathway 2 nd Semester Course Average without ALEKS AND Highest ALEKS Assessment Score Assessment A B C 37 or above 39 or above 41 or above Technical Mathematics Pathway 2 nd Semester Course Average without ALEKS AND Highest ALEKS Assessment Score Assessment A B C 25 or above 26 or above 27 or above Basic Mathematics Pathway 2 nd Semester Course Average without ALEKS AND Highest ALEKS Assessment Score Assessment A B C 10 or above 11 or above 12 or above A student s 2 nd semester grade in the course together with their highest ALEKS assessment will be submitted to COD. Students will earn placement into one of three different levels. Each pathway will be transcripted with its own course code. COURSE DESCRIPTIONS CAN BE FOUND AT THE END OF THIS DOCUMENT.
Quantitative Literacy Pathway: Students placing into this level are eligible to register in COD s Math 1218 or Math 1220. Technical Mathematics Pathway: Students placing into this level are eligible to register in COD s Math 1102 or Math 1115. Basic Mathematics Pathway: Students placing into this level are eligible to register in COD s Math 1100. Expiration of placement: For the purposes of this pilot in the 2018-2019 school year, students gaining placement into a COD course must register for that course in the Summer 2019 or Fall 2019 semester immediately following their graduation from high school. Note: A student who does not earn the desired placement via this course can, after completing an application for admission at COD, retake the ALEKS assessment at any COD Testing Center as a new COD student. This would give the student 3 additional attempts at earning the needed placement score. Standard COD placement scores would apply. (A student s placement will not be lowered by retaking the ALEKS assessment after the course has ended; the highest score during or after the course will be recorded.) Additional Policies: Syllabus: Students should be given a syllabus at the beginning of the semester detailing their responsibilities in the course and the rubric by which they will be graded. Calculator Use: Calculators should be used rarely and only when essential to the topic under discussion. It is anticipated that calculators will be useful for the objectives marked with an asterisk in the list of course objectives. Calculators should not be used regularly and should not be used to add, subtract, multiply, or divide, including numbers containing fractions and decimals. Studying for Exams: Students often struggle with properly preparing for a math exam. Writing summaries of topics; creating their own review sheets; re-working past quizzes and assignments; and working additional problems are good techniques for students to use to prepare for an exam. Practice exams that closely mirror the exam should not be given; however, large problem sets that cover the unit s topics may be helpful. Homework: Homework should be assigned routinely and should be completed outside of class. Students often arrive at the College unaccustomed to working regularly outside of class. They attempt to complete large quantities of work in one sitting and are rarely successful in completing what they expect they will be able to complete. Organization: Significant emphasis should be placed on organization of math writing. We find an extremely high correlation between organized math writing and the ability to solve problems.
COD Math Placement After 12th Grade Transition Mathematics Offered at Partner High Schools QUANTITATIVE LITERACY PATHWAY: Placement into Gen Ed Math (1218) or Quantitative Literacy (1220) These are courses Illinois Articulation Initiative (IAI) approved. MATH 1218 (IAI M1 904): General Education Mathematics (3 credit hours) Designed to fulfill general education requirements and not designed as a prerequisite for any other college mathematics course. Focuses on mathematical reasoning and the solving of reallife problems, rather than routine skills. Logic and set theory are studied. Two other topics from the following list are to be studied in depth: counting techniques and probability, game theory, geometry, graph theory, statistics, and mathematics of finance. The regular use of calculators and/or computers are emphasized. Prerequisite: Demonstrated geometry competency (level 2), and Mathematics 0465 or Mathematics 0482 or college equivalent with a grade or C or better or a qualifying score on the mathematics placement test. (3 lecture hours) MATH 1220 (IAI M1 901): Quantitative Literacy (3 credit hours) Designed to fulfill general education requirements, and not designed as a prerequisite for any other college mathematics course. Provides the basic numeracy needed by a college graduate to reason about quantities, their magnitudes, and their relationships between and among other quantities. Topics include linear systems, linear programming, analysis and interpretation of graphs, logic and reasoning, descriptive statistics, the normal distribution, statistical inference, estimation and approximation. Prerequisite: Demonstrated geometry competency (level 2), and Mathematics 0465 or Mathematics 0482 or college equivalent with a grade of C or better or a qualifying score on the mathematics placement test. (3 lecture hours) Grade Pre-Final Minimum Required Final score (ALEKS PPL) A 37 B 39 C 41 A score of 37-43 on the ALEKS placement test typically means that a student is: Proficient: Operations with Whole Numbers, Fractions and Decimals Percents, Proportions and Geometry Signed Numbers, Linear Equations and Inequalities
Nearly Proficient: Systems of Linear Equations and Lines Integer Exponents and Factoring Not Proficient: Relations and Functions Quadratic and Polynomial Functions Rational Expressions and Functions Rational Exponents and Radicals Exponential and Logarithmic Functions Trigonometry TECHNICAL MATHEMATICS PATHWAY: Placement into Technical Math (1102 or 1115) MATH 1102: Mathematics for Health Sciences (3 credit hours) Designed for health science majors. Topics include systems of measurements, use of formulas, dimensional analysis, percents, decimals, fractions, ratio and proportion, direct and inverse variation, solutions, and dosage calculations. Prerequisite: Mathematics 0465 or Mathematics 0481 or college equivalent with a grade of C or better or a qualifying score on the mathematics placement test. (3 lecture hours) MATH 1115: Technical Mathematics I (3 credit hours) For technical/occupational programs. Emphasizes problem-solving skills using elementary algebra, right angle trigonometry, and ratio and proportion. Prerequisite: Mathematics 0481 or college equivalent with a grade of C or better or a qualifying score on the mathematics placement test. (3 lecture hours) Grade Pre-Final Minimum Required Final score (ALEKS PPL) A 25 B 26 C 27 A score of 25-36 on the ALEKS placement test typically means that a student is: Proficient: Nearly Proficient: Operations with Whole Numbers, Fractions and Decimals Signed Numbers, Linear Equations and Inequalities Percents, Proportions and Geometry Systems of Linear Equations and Lines Integer Exponents and Factoring
Not Proficient: Relations and Functions Quadratic and Polynomial Functions Rational Expressions and Functions Rational Exponents and Radicals Exponential and Logarithmic Functions Trigonometry BASIC MATHEMATICS PATHWAY: Placement into Business Math (1100) MATH 1100: Business Mathematics (3 credit hours) Applications of mathematics to business transactions. Analysis and solution of the business problems in profit and loss, interest, installment transactions, percent discounts, taxes and payroll. Prerequisite: Mathematics 0460 or college equivalent with a grade of C or better or a qualifying score on the mathematics placement test. (3 lecture hours) Grade Pre-Final Minimum Required Final score (ALEKS PPL) A 10 B 11 C 12 A score of 10-24 on the ALEKS placement test typically means that a student is: Proficient: Nearly Proficient: Not Proficient: Operations with Whole Numbers, Fractions and Decimals Signed Numbers, Linear Equations and Inequalities Percents, Proportions and Geometry Systems of Linear Equations and Lines Integer Exponents and Factoring Relations and Functions Quadratic and Polynomial Functions Rational Expressions and Functions Rational Exponents and Radicals Exponential and Logarithmic Functions Trigonometry