Transcript dream 2014

An Arithmetic Course Redesign
with Proven Positive Results
AMATYC
November 19, 2015
Barbara Lontz, Assistant Professor of Mathematics
Overview
Discuss framework
for change at MCCC
and replicating
institutions
Share the curricular
materials in the
course redesign
Review the
internal and
external evaluative
outcome data
Participate in a
sample lesson
Concepts of Numbers
All learning
outcomes of a
traditional
arithmetic course
are covered but in
a different order
Students are
assessed on the
same skills as
the traditional
arithmetic
course
Lessons
proceed
through
concepts, using
a discovery
approach
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 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
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
Real
Numbers ℝ
Rational Q
Integer Z
Whole W
• Video clip
Natural N
Irrational Q’
Unit 3: Comparisons
<, >, =
Compare
5/8 and 7/8
Compare
0.7 and 3/5
Compare
-3 and -5
4/9 and 5/7
The
concepts of
<, > and =
Like
numbers are
compared
Unlike
numbers are
compared
Numbers
that are like
are easier to
compare
Unit 4: Addition
• Addition (combining) of the following quantities:
whole numbers
decimals
fractions
integers
algebraic expressions
• 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:
whole numbers
decimals
fractions
integers
algebraic expressions
• Application of subtraction (temperature, money
problems)
• Solving equations that use the Addition Property
Unit 6: Multiplication
• Multiplications (repeated combinations) of the following
quantities
whole numbers
decimals
fractions
integers
algebraic expressions
(distributive prop)
• Exponents
• Application of multiplication (area, circumference, percents)
• Properties (commutative, associative, identity & inverse)
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:
whole numbers
fractions
decimals
integers
• 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
MAT010 Concepts of Numbers versus MAT010 Traditional Course
Concepts of
Numbers
Traditional
Arithmetic
Fall
2008
Spring Fall
2009 2009
Spring Fall
2010 2010
74%
63%
68%
N=19
N=19
45%
34%
FA11/
SP12
FA12/ FA13/
SP13 SP14
60%* 58%** 57%
60%
61% 60%
N=19
N=255 N=380
N=289
N=1020 N=872 N=840
41%
40%
38%
40%
N=664 N=429 N=567 N=236 N=284
Spring
2011
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
80.0%
70.0%
60.0%
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
African American/Black
Fall 2009
Latino/Hispanic
Fall 2010
Fall 2011
Fall 2012
White
Fall 2013
External Evaluation
What are some of the predictors of success?
Pedagogy
Sharing
Principles
Skills
Students
Success
Outcomes Discovery
Evaluation
Knowledge
Achievement
Faculty
Concepts
Professional Development
Usefulness
Grade Distribution: Concepts vs. Traditional
20
10
0
Percent
30
40
Grade Distribution
A
A-
B
B+
BC
coursegrade
Concept Section
C+
D
FailureWithdraw
Traditional Section
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
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
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 [email protected]
http://faculty.mc3.edu/Blontz/BLontz_Web_Page/index.html