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Mathematical Literacy for College Students (MLCS) 3 – 6 semester hours (depending on depth and breadth desired) Prerequisite: Appropriate placement or prealgebra with a grade of “C” or better

One goal of developmental mathematics education is to provide students with the necessary skills and understanding required to be successful in college level mathematics. Mathematical Literacy for College Students (MLCS) is a new course being developed at the national level by AMATYC’s New Life for Developmental Mathematics. Its origins are related to Quantway, funded by the Carnegie Foundation. MLCS is an alternative path to certain college level math courses or further algebra. It integrates numeracy, proportional reasoning, algebraic reasoning, and functions with statistics and geometry as recurring course themes. Throughout the course, college success components are integrated with the mathematical topics. The course focuses on developing mathematical maturity through problem solving, critical thinking, writing, and communication of mathematics. Content is developed in an integrated fashion, increasing in depth as the course progresses. Upon completion of the course, students will be prepared for a statistics course or a general education mathematics course. Students may also take traditional intermediate algebra upon completion if they choose to pursue STEM courses.

MLCS provides an alternative to beginning algebra, creating multiple pathways for the developmental students. However, it is more difficult than beginning algebra to ensure students are prepared for a college level math course upon successful completion. It allows students to potentially complete their developmental math and college level math requirement for an Associate in Arts degree in one year total (one semester each), working toward the goal of improving college completion rates. It promotes 21st century skills to prepare students for both the workplace and future coursework. Further, it does not diminish requirements for non-STEM college level math courses but instead creates appropriate paths to these courses with the same level of intensity and complexity as the current path through intermediate algebra. The course has college level expectations and coursework but with a pace and instructional design intended for the adult, developmental learner. This strategy emulates the approach taken by the Common Core Standards and aligns with them as well.

For more information on MLCS

Contact: Kathleen Almy, Heather Foes (Rock Valley College) Emails: kathleenalmy@gmail.com heather.foes@gmail.com

Blog: http://almydoesmath.blogspot.com

Blog contains video, pilot updates, presentations, and more.

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MLCS Course Description and Objectives

Mathematical Literacy for College Students is a one semester course for non-math and non-science majors integrating numeracy, proportional reasoning, algebraic reasoning, and functions. Students will develop conceptual and procedural tools that support the use of key mathematical concepts in a variety of contexts. Throughout the course, college success content will be integrated with mathematical topics.

Prerequisite: Appropriate placement or prealgebra with a grade of “C” or better COURSE OUTCOMES

1. Apply the concepts of numeracy in multiple contexts. 2. Recognize proportional relationships and use proportional reasoning to solve problems. 3. Use the language of algebra to write relationships involving variables, interpret those relationships, and solve

problems. 4. Interpret and move flexibly between multiple formats including graphs, tables, equations, and words. 5. Demonstrate student success skills including perseverance, time management, and appropriate use of

resources. 6. Develop the ability to think critically and solve problems in a variety of contexts using the tools of mathematics

including technology.

COURSE OBJECTIVES

Upon successful completion of this course, the student will be able to:

Numeracy

1. Demonstrate operation sense and the effects of common operations on numbers in words and symbols. 2. Demonstrate competency in the use of magnitude in the contexts of place values, fractions, and numbers written in

scientific notation. 3. Use estimation skills. 4. Apply quantitative reasoning to solve problems involving quantities or rates. 5. Demonstrate measurement sense. 6. Demonstrate an understanding of the mathematical properties and uses of different types of mathematical

summaries of data. 7. Read, interpret, and make decisions based upon data from line graphs, bar graphs, and charts. Proportional reasoning

8. Recognize proportional relationships from verbal and numeric representations. 9. Compare proportional relationships represented in different ways. 10. Apply quantitative reasoning strategies to solve real-world problems with proportional relationships. Algebraic reasoning

11. Understand various uses of variables to represent quantities or attributes. 12. Describe the effect that changes in variable values have in an algebraic relationship. 13. Construct and solve equations or inequalities to represent relationships involving one or more unknown or variable

quantities to solve problems.

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Functions

14. Translate problems from a variety of contexts into a mathematical representation and vice versa. 15. Describe the behavior of common types of functions using words, algebraic symbols, graphs, and tables. 16. Identify the reasonableness of a linear model for given data and consider alternative models. 17. Identify important characteristics of functions in various representations. 18. Use appropriate terms and units to describe rate of change. 19. Understand that abstract mathematical models used to characterize real-world scenarios or physical relationships

are not always exact and may be subject to error from many sources. Student success

20. Develop written and verbal skills in relation to course content. 21. Evaluate personal learning style, strengths, weaknesses, and success strategies that address each. 22. Research using print and online resources. 23. Apply time management and goal setting techniques.

Mathematical success

24. Develop the ability to use mathematical skills in diverse scenarios and contexts. 25. Use technology appropriately including calculators and computers. 26. Demonstrate critical thinking by analyzing ideas, patterns, and principles. 27. Demonstrate flexibility with mathematics through various contexts, modes of technology, and presentations of

information (tables, graphs, words, equations). 28. Demonstrate and explain skills needed in studying for and taking tests.

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Implementation Options

MLCS is a 3 – 6 credit hour course depending on the depth and breadth desired.

1. Replacement Model: Use MLCS to replace beginning algebra.

2. Augmented Model: Use MLCS to create a non-STEM alternative to beginning algebra that provides sufficient

preparation for statistics or liberal arts math.

3. Supplemental Model: Use MLCS lessons for problem solving sessions in an Emporium model (lab-based traditional redesign.), engaging all students and moving beyond skills alone.

4. High School Model: Use MLCS lessons for 4th year high school course to develop college readiness and help

students place into college level math.

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Sample lesson from the text Math Lit, by Kathleen Almy and Heather Foes.

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Solutions for Acceleration, Redesign, and Readiness

Math Lit, by Kathleen Almy and Heather Foes, provides a one-semester alternative to the traditional two-semester developmental algebra sequence. This new approach offers an accelerated pathway to college readiness through developmental math, allowing non-STEM (Science, Technology, Engineering, and Math) students to move directly into liberal arts math or introductory statistics. Through its emphasis on contextual problem-solving, the Almy/Foes text and its accompanying MyMathLab® course help students understand and practice the major themes of numeracy, proportional reasoning, algebraic reasoning, and functions.

The textbook and MyMathLab content are organized into cycles (rather than linear chapters) that take a spiral approach to covering topics that relate to four thematic strands—numeracy, proportional reasoning, algebraic reasoning, and functions. Once introduced, these thematic topics are revisited several times as appropriate, going into a little more detail each time.

• Each cycle is divided into three parts:

˚ Gear Up—introduces key ideas for the cycle. ˚ Shift Gears—contains the bulk of the content and skills for the cycle. ˚ Wind Down—connects the main ideas and wraps things up.

• Cycles are composed of activity-based lessons that include carefully designed tasks, explorations, and instruction—all paced for the developmental learner. Most lessons are divided into 4 segments:

˚ Explore—offers an interesting problem or group activity opens the lesson and sets the stage for the new material ˚ Discover—presents a new theory with examples and practice problems. ˚ Connect—connects content to past or future lessons through a group or class problem. ˚ Reflect—provides an opportunity to look back at what has been learned.

• End-of-lesson homework begins with skills-based assignments in MyMathLab® and the worktext. Students are also asked to complete conceptual and application-based problems in the text to expand their understanding beyond a procedural level.

• End-of-Cycle Wrap Ups provide a five-step action plan to help students study and prepare for the Cycle test. A Cycle Profile gives a brief overview of important topics, and a Self Assessment asks students to indicate their level of expertise with each topic.

continued on reverse

© 2013 Pearson Education, Inc. All rights reserved. Printed in the U.S.A. DEVMATH2696/0113

Kathleen Almy has been a professor of

mathematics at Rock Valley College for

over 10 years and has taught high school

and college level math for 15 years. She

has a bachelor’s degree in mathematics

education from Southern Illinois University

and master’s degree in pure mathematics

from Northern Illinois University. As her department’s

developmental math coordinator, she has organized and led

a successful comprehensive redesign of the program over the

past 5 years. As a result of giving talks about the redesign,

she has been consulting with colleges throughout Illinois

and across the country to improve their developmental math

programs. Since 2009, she has been a member of AMATYC’s

Quantway project which is affiliated with the Carnegie

Foundation. She was AMATYC’s Developmental Math

Committee chair and serves on several state committees

on developmental education.

Cycle Question Goal Focus Problem Topics Developed in Depth

1 What can be learned?

Establish foundation skills used in all cycles as well as skills necessary to make the course operate well

Explore a situation involving medical error to understand the role of error, technology, rates, units, and open-ended problem solving

Graphs (Venn diagrams, pie graphs, bar graphs, scatterplots), percent skills (increase/decrease, percent of change), fraction review, rates/ratios, function basics, proportionality, reasoning and conjectures, types of change (linear/exponen-tial), types of graphs (non-linear), concepts of area/ perimeter/volume, similarity

2 Why does it matter? Develop understanding of numbers and operations that will be used in cycle 3 with equations

Explore the magic number in baseball to understand integers, expressions, and order of operations

Signed number concepts and operations, means, exponent properties with whole number exponents, polynomial basics, order of operations, FOIL, polynomial multiplication, properties of real numbers (distributive, commutative, associative), geometric and other formulas, Pythagorean Theorem, slope, distance formula

3 When is it worth it? Build on cycle 2’s skills to develop understanding of building, solving, and graphing equations, both linear and non-linear

Determine when it is worth it to buy print copies of a book or an e-reader to develop graphical, numerical, and algebraic comparison skills

Theory, creation, and solving of equations (both linear and some basic non-linear situations), median, weighted averages, correlation, standard deviation, volume and surface area calculations, Pareto charts, slope-intercept form, graphing linear equations, variation, rational function modeling with a basic situation

4 How big is big? Understand large and small numbers and quantities in absolute and relative contexts through numerical and functional means

Make sense of the national debt in terms of height, weight, area, time, and relationship to other countries’ debts to develop understanding of size, scale, scientific notation, and measurement

Proportionality, dimensional analysis, exponential vs. linear revisited with modeling, scientific notation, exponent properties with negative exponents, solving a formula for a variable, factoring the GCF, probability concepts, solving proportions algebraically, writing equations of lines, 2x2 systems of equations, compound inequalities, quadratic modeling with a basic situation, z-scores, Golden ratio, order of magnitude

Math Lit CyCLE OvERviEW

Heather Foes is a professor of

Mathematics at Rock Valley College in

Rockford, Illinois and has also taught at

Illinois State University, Northern Illinois

University and the University of Illinois.

Heather has a bachelor’s degree in chemistry

and mathematics and a master’s degree in

mathematics from Illinois State University. She has written

solution manuals and other supplemental materials over the

last ten years, as well as algorithmic questions for test-generator

software and conceptual questions for MyStatLab for Pearson.

AbOUT THE AUTHORS