An Arithmetic Course Redesign with Proven Positive Results AMATYC November 19, 2015 Barbara Lontz, Assistant Professor of Mathematics

Overview Share the curricular materials in the course redesign Participate in a sample lesson Review the internal and external evaluative outcome data Discuss framework for change at MCCC and replicating institutions

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

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

Unit 2: Real Number System All sets of numbers are introduced: natural, whole, integers, rational, irrational & real Numbers are classified according to their sets Numbers are located on a number line Video clip Real Numbers ℝ Rational QInteger ZWhole W Natural N Irrational Q’

Unit 3: Comparisons The concepts of and = Like numbers are compared Unlike numbers are compared Numbers that are like are easier to compare, = Compare -3 and -5 4/9 and 5/7 Compare -3 and -5 4/9 and 5/7 Compare 0.7 and 3/5 Compare 5/8 and 7/8

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

Unit 5: Subtraction Subtraction (find differences) of the following quantities: Application of subtraction (temperature, money problems) Solving equations that use the Addition Property

Unit 6: Multiplication Multiplications (repeated combinations) of the following quantities Exponents Application of multiplication (area, circumference, percents) Properties (commutative, associative, identity & inverse)

Discovery Approach Lesson Multiply: x 0.76 − Multiply 42 x 76 − Where does the decimal go? Why? = 0.76 = Multiply: x 0.76 − Multiply 42 x 76 − Where does the decimal go? Why? = 0.76 =

Unit 7: Division Division (repeated subtractions) of the following quantities: Application of division (percents, unit pricing) Solving equations using the Multiplication Property

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

What Students Think ….

Internal Evaluation Are there differences among the success rates of the two formats? Did the success rates continue to increase once the approach had gone to scale?

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)

Success Chart: By Ethnicity/Race

External Evaluation What are some of the predictors of success? Evaluation Knowledge Discovery Success Sharing Skills Concepts Professional Development Outcomes Students Faculty Usefulness Principles Pedagogy Achievement

Grade Distribution: Concepts vs. Traditional

Results Concepts course pass rates indicate that this new curricular and pedagogical approach is effective for many students referred to the lowest level of developmental mathematics. Comparative analysis completed for this study showed that students enrolled in Concepts (N=866) were more likely to be successful than their peers enrolled in the traditional arithmetic/prealgebra course (N=1,303). Specifically, Concepts students were more likely to earn a C or higher, less likely to withdraw from the course, and more likely to enroll in algebra, the subsequent developmental math course Student achievement indicates many students benefit from a conceptually oriented curriculum and an instructional approach that allows their understandings of mathematics to emerge.

Results In terms of subsequent outcomes, however, the results are less promising. The only positive outcome is that students who took the Concepts section of MAT 010 were slightly more likely to enroll in MAT 011, which is the subsequent math remedial course in sequence. Concepts students success rates in the MAT 011 course were not higher, nor lower than our previous MAT 011 course data.

Scaling a Promising Practice financial time for development Administrative support bringing to a larger scale faculty willingness to try something new training that includes teachers and tutors Department approval on-going quantitative data Monitoring/Assessment

Replicating Challenges Strong faculty leadership Orientation Moving at a comfortable pace Continuing communication Accepting/valuing input

“Planning and plodding wins the race” The Tortoise and the Hare, Aesop

Information: Barbara Lontz