Transcript CONNECT: Online Orientation

Concepts of Numbers:
A Scaling Innovation in
Developmental Math
N.A.D.E
2014
Barbara Lontz, Assistant Professor of Mathematics
Jim Muscatell, Assistant Professor of Mathematics
Overview
Share the triumphs
and struggles of
bringing ideas to
scale
Review the
evaluative outcome
data
Learn about the
course redesign:
Participate in
sample lessons
MCCC Causes for Concern
The success rates*
for the past six years
in our arithmetic
classes have been
declining
The success rates fell
between
35% - 45%
*success rates are grades of C or better
Our numbers reflect
a national trend of
declining math
scores
A course redesign began after …
• Investigating causes and
solutions
• Researching best practices, e.g.
learning communities &
supplemental instruction
models
• Reviewing textbooks
Conclusion: No interventions were making a
significant difference; why do the same?
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’
Discovery Approach Lesson #1
Locate the following points on the number line:
0.3, -21/7, 2, √7, 9/11, 0.3, -1.5, -5/3
Unit 3: Comparisons
<, >, =
Compare
5/8 and 7/8
The
concepts of
<, > and =
Like
numbers are
compared
Compare
0.7 and 3/5
Unlike
numbers are
compared
Compare
-3 and -5
4/9 and 5/7
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)
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
Fall
2008
Concepts of
Numbers
Traditional
Arithmetic
Spring Fall
2009 2009
Spring Fall
2010 2010
Spring Fall
2011 2011
74% 63% 68% 60%* 58%** 57% 58%
Spring Fall
2012 2012
Spring Fall
2013
2013
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
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)
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
Fall 2011 Concepts received a William And Flora Hewlett
Scaling Innovation Project two-year grant through the
Community College Research Center (CCRC) to replicate
at other colleges (Reading Area Community College &
Berkshire Community College) and improve learning
within.
Course Enhancements
• 4th edition of text
• Universal portal through Pearson Learning Solutions with
faculty and student access
• Faculty teaching notes (portal)
• Supplemental problems (text)
• Online MathXL student support component (portal)
• Online course orientation for faculty /tutors with voiceover
(portal)
• Glossary of terms (text)
• Flashback problems (text)
• Final exam preparation (text)
Other Replicating Colleges …
“Planning and plodding
wins the race”
The Tortoise and the Hare, Aesop
Information
Barbara Lontz [email protected]
Jim Muscatell [email protected]