Pre-Algebra Using the Discovery Method

A project of the Community College Research Center funded by the William and Flora Hewlett Foundation CCRC and partner colleges work to adapt and scale promising reforms at new institutions Faculty-driven effort, with intentional focus on professional learning and classroom practice For more information visit

CONCEPTS OF NUMBERS All learning outcomes of a traditional arithmetic course are covered but in a different order Lessons proceed through concepts using a discovery approach Students are assessed on the same skills as the traditional arithmetic course

CONCEPTS' GUIDING PRINCIPLES Faculty become facilitators of knowledge; students learn through discovery New embedded skills are introduced on an as-needed basis If a student understands a skill and its usefulness, practice problems can be kept to a minimum Calculators are not used in this course All students can learn math “Teach me, and I will forget. Show me, and I will remember. Involve me, and I will understand.” Chinese Proverb

CONCEPTS OF NUMBERS OUTLINE Unit 1: History of NumbersUnit 2: The Real Number SystemUnit 3: ComparisonsUnit 4: AdditionUnit 5: SubtractionUnit 6: MultiplicationUnit 7: DivisionUnit 8: Combinations For more information, watch “Concepts of Numbers – Faculty Online Orientation” at:

UNIT 1: HISTORY OF NUMBERS In understanding the evolution of numbers, students will better understand/appreciate our present system The following civilizations are covered: Babylonian Greek Egyptian Roman African Mayan The concepts of place value and place holders are explored

DISCOVERY APPROACH LESSON #1 Locate the following points on the number line:

UNIT 4: ADDITION Addition (combining) of the following quantities: Application of the addition concept (perimeter, money problems) Identity element, commutative & associative properties, and binary operation concepts are introduced whole numbers decimals fractions integers algebraic expressions

UNIT 8: COMBINATIONS Simplifying expressions involving multiple operations (order of operations) Solving multiple step applications, (ratio & proportion) Solving algebraic equations: 6(x+5) = -2(x -5)

MONTGOMERY: OUTCOME DATA Success Rates : Success is a grade of C or better: Withdrawals count as non-success * the top 13% of Arithmetic Accuplacer scorers were accelerated into the next course (a 4 credit beginning algebra class) ** an additional top 12% of Arithmetic Accuplacer scorers were accelerated into the next course (a 4 credit beginning algebra class)

BERKSHIRE COMMUNITY COLLEGE Rural 80% of students test into developmental mathematics Students placing into prealgebra may need up to 9 credits of developmental mathematics before college level

Selected to participate in Concepts in Fall 2012 Three sections of concepts: traditional (2 days/week; late start 2 days /week; evening 3 hours) One faculty member: Annette Guertin Success rate = 72 % for n = 43 students (W’s not included) BCC

STUDENT FEEDBACK : THE BEST PART OF THE COURSE WAS… Learning Refreshing my math skills I learned … and had fun. Focused on the work instead of correct answers. The clickers The help we received Learning new things in math and new people

FEEDBACK : THE PART OF THE COURSE THAT CAN BE IMPROVED… More time Fractions The textbook MathXL

FACULTY REFLECTIONS Excitement in adopting a new pedagogy The approach empowered my students to share and learn mathematics. Bridging the divide between arithmetic and algebra Part of a committed group of faculty within the grant Success rates for students exceeded expectations! Accuplacer retest data

MOVING FORWARD 2 additional faculty 4 sections, one with supplemental instruction model Professional development group : Mat 018 faculty, support staff : Tutorial, Disability Resource Center, Personal Counseling

Annette Guertin Barbara Lontz FOR MORE INFORMATION