An Arithmetic Course Redesign with Proven Positive Results

AMATYCNovember 13, 2014

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 NumbersAll 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

Faculty Facilitate

Limited Assignments

Embedded Skills

Students Discover Success

Concepts of Numbers OutlineUnit 1: History of Numbers

Unit 2: The Real Number System

Unit 3: Comparisons

Unit 4: Addition

Unit 5: Subtraction

Unit 6: Multiplication

Unit 7: Division

Unit 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 GreekEgyptianRomanAfricanMayan

• 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 Q

Integer Z

Whole 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 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

whole numbers

decimals

fractions

integers

algebraic expressions

Unit 5: Subtraction• Subtraction (find differences) of the following

quantities:

• Application of subtraction (temperature, money problems)

• Solving equations that use the Addition Property

whole numbers

decimals

fractions

integers

algebraic expressions

Unit 6: Multiplication• Multiplications (repeated combinations) of the following

quantities

• Exponents

• Application of multiplication (area, circumference, percents)

• Properties (commutative, associative, identity & inverse)

whole numbers

decimals

fractions

integers

algebraic expressions(distributive prop)

Discovery Approach Lesson

Multiply: 0.042 x 0.76

−Multiply 42 x 76

−Where does the decimal go? Why?

0.042 = 0.76 =

Unit 7: Division• Division (repeated subtractions) of the

following quantities:

• Application of division (percents, unit pricing)

• Solving equations using the Multiplication Property

whole numbers

fractions

decimals

integers

Unit 8: Combinations

Simplifying expressions involving multiple operations

Solving multiple step applications, (ratio & proportion)

Solving algebraic equations:6(x+5) = -2(x -5)

Evaluation

• Does this new approach work? That is, are the success rates higher with the new approach, Concepts of Numbers, than the traditional arithmetic course?

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 DataSuccess Rates: Success is a grade of C or better; Withdrawals count as non-success

MAT010 Concepts of Numbers versus MAT010 Traditional Course Fall

2008Spring 2009

Fall2009

Spring 2010

Fall2010

Spring2011

Fall2011

Spring 2012

Fall2012

Spring 2013

Fall 2013

Concepts of Numbers

74% 63% 68% 60%* 58%** 57% 58% 61% 60% 62% 62%

N=19 N=19 N=19 N=255 N=380 N=289 N=704 N=316 N=545 N=327 N=523

Traditional Arithmetic

45% 34% 41% 40% 40% 38%

N=664 N=429 N=567 N=236 N=284 N=150

* 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

African American/Black Latino/Hispanic White0.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

Fall 2009 Fall 2010 Fall 2011 Fall 2012 Fall 2013

Success Chart: By Ethnicity/Race

Fall 2009 Fall 2010 Fall 2011 Fall 2012 Fall 20130%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

African American/Black Latino/Hispanic White

External Evaluation

What are some of the predictors of success?

Grade Distribution: Concepts vs. Traditional0

10

20

30

40

Pe

rcen

t

A A- B B+ B- C C+ D FailureWithdrawcoursegrade

Concept Section Traditional Section

Grade Distribution

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.

Next Steps at the Institutional Level

• Need to address the issue of students being successful in MAT 010 but the higher success rate not carrying over to the next developmental sequence: MAT 011.

• Need to deconstruct MAT 011 in a similar way that we worked on MAT 010 so that students experience success through the developmental sequence and in their college-level math courses.

• Still a gap between African-American students and their Caucasian counterparts. This is especially true with African-American males, but the outcomes are improving.

Scaling a Promising Practice

Administrative support

• financial• time for development

Department approval• bringing to a larger scale• faculty willingness to try something new• training that includes teachers and tutors

Monitoring/Assessment

• on-going quantitative data

Beyond the Scaling ProjectFor Spring 2014, the following colleges offered Concepts:

Palomar College & Imperial College

Triton College & Kankakee Community College

Luzerne County Community College, Penn State University (Abington) & Reading Area Community College

University of Alaska Anchorage

Berkshire Community College & Springfield Technical Community College

Shawnee State University

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 blontz@mc3.edu

http://faculty.mc3.edu/Blontz/BLontz_Web_Page/index.html