Problems with Developmental MathNationally Lengthy sequence, low pass rates High school 2.0 Skill-heavy initiativesLocally Successful traditional program but one size fit all Intermediate algebra issues
A New Course, A Simple GoalIn one semester, Mathematical Literacy forCollege Students gives a student at the beginningalgebra level the mathematical maturity to besuccessful in statistics, liberal arts math, orintermediate algebra.
Initiatives2009 AMATYC New Life initiative begins.2010 New Life leads to Statway and Quantway (formerly Mathway), funded by Carnegie. Carnegie AMATYC2011 19 Carnegie grant schools pilot Quantway New Life Statway.2011 Rock Valley College pilots MLCS. MLCS2012 8 Carnegie grant schools pilot MLCS.
Content Philosophy Areas of focus Role of intermediate algebra
A New Perspective:Recognizing a History of Algebra Emphasis on understanding over manipulation alone Focus on application, connections, retention Focus on needs of outcome courses, work, life Incorporate needs of other disciplines
Area 1: NumeracyUnderstand numbers and Example:their uses concretely, then Program cells in Excel to evaluate a formula.generalize.Goal: Understand thatnumbers are quantitieswith units.
Area 2: Algebraic ReasoningAvoid problems devoid of Example:context. When is an e-reader worth it? N=179 + 12.99BStrive for meaningful K=79 + 12.99Bvariables and situations. H=35BGoal: Judge when algebramakes sense and how touse it.
Area 3: Proportional ReasoningMake sense of fractions, Example: Interpret a nutrition label.rates, and proportions inmultiple ways.Goal: Use units to writerates. Scale whenpossible.
Area 4: FunctionsDevelop an understanding of Example:relationships between Build and analyze a model.quantities and variables. Constant vs. variable Hours to pay for gallon of gas 7 Independent vs. dependent 6 variable 5 Input values that make 4 sense 3 2 1Goal: Move between tables, 0 0 10 20 30 40graphs, and equations fluidly.
Additional Embedded AreasGeometry StatisticsMeasurement, units, shapes, simil Centers, variation, correlation, proarity babilityExample: Example:If we overfill a medical measuring How can we measure variabilitycup/spoon by 1 mm, which would within a data set?produce a greater overdose error? ( x mean)2 s n 1
Additional Embedded AreasStudent Success Approach Motivation and metacognition First week and first unit Integrate math with student successMathematical Success Role of accuracy, precision, and error Polya’s method Multiple approaches build understanding Verbal, numeric, algebraic, graphic
Addressing Intermediate AlgebraModeling with non-linear functions quadratic, exponential, rational, radical numerical, graphical, and conceptual approachEmphasis on scatterplots, correlation, and regressionSymbolic manipulation addressed if needed in later course
FAQsWhat about factoring?Does this course “dumb down” developmentalmath standards for entry into college levelcourses?Are you pushing students away from STEM majors?
Development & Instruction Research Content approach Quantway goals Technology
Using Research Researched schools, programs, and countries who are effectively teaching mathematics (not just algebra) Read and incorporated information on how the brain learns
Traditional Approach: Linear Theory, then applications if time Proportions Each strand done Functions separately to Numbers Algebra completion Algebra is primary focus Skill based Examples of every possible variation of skill (problem recognition)
New Approach: Integrated & Layered Applications to motivate, then theory as needed Proportional Reasoning Reasoning Numeracy Functions Algebraic Strands addressed each unit in an integrated fashion going deeper each time Equal time on each strand Concepts-based Fewer skills, more connections Undercurrent of geometry, statistics, student success, mathematical success
Lesson and Unit Protocol MOTIVATE DEVELOP CONNECT REFLECT Self-similarity approach PRACTICE
Technology for the 21st Century Mental arithmetic is encouraged whenever possible. Calculators are used when they are needed. Excel is used for analyzing patterns and making graphs.
Quantway Goals for InstructionEngagement Active work on rich problems Application of concepts in newConnections contextsProductive persistence Struggling is permitted but assistance is given when needed Specific practice forges connectionsDeliberate practice and deepens conceptual understanding
Strike a BalanceBetween Structure and Monotony Accessibility Challenges
FAQsWhat reaction do you get from students? Do theybuy-in?Will students be able to transition back to atraditional course?What do assessments look like?
Making MLCS a Reality Lessons from RVC redesign & pilot Implementation ideas Tips for getting started
Using experience to redesign with MLCS Incorporated lessons learned in our redesign Advising Pace A comprehensive approach Materials Continual assessment Training sessions and materials
Lessons from the pilotStudents want to mimic.Teach students how to study since the coursehas college level expectations.Mastery learning in online systems ≠ learning.Context improves connections and understanding.We cannot help them all, but we can accelerate the process formany.
Implementation IdeasReplace Beginning Algebra STEM Intermediate College Algebra Level MathPrealgebra MLCS Non-STEM College Level Math (Statistics, Libe ral Arts Math)
Implementation IdeasUse MLCS lessons in an emporium for once-weekly problem solving sessions Beginning Intermediate College Prealgebra Algebra Algebra Level Math 0 Previews content for some, connects for others 0 Everyone is engaged 0 More than just skills
Implementation IdeasAugment traditional sequence with MLCSas a non-STEM alternative preparationfor statistics/liberal arts math. STEM Beginning Intermediate College Algebra Algebra Level Math Prealgebra Non-STEM MLCS College Level Math (Statistics, Libe ral Arts Math) Students who change their major can take intermediate algebra as a bridge to STEM courses.
Getting Started with MLCS Choose materials Create a collaboratory for pilot Sit in on other MLCS classes is possible Meet with other MLCS instructors regularly Test with common instruments Train new faculty Developing training workshops Materials provide great faculty support
FAQsWhat is your placement tool?How many credit hours is the course?Can we omit topics that you may need?