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What is the Foundational-Level
Mathematics Credential?
TEPAC
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October 24, 2006
Mark W. Ellis, Ph.D.
California State University, Fullerton
mellis@fullerton.edu
http://faculty.fullerton.edu/mellis
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Why Teach Mathematics?
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BECOME A MATH TEACHER SO THAT YOU CAN . . .
• Educate Citizens Who Understand and Appreciate Math
Mathematics learned today is the foundation for future decision-
making. Students should develop an appreciation of mathematics
as making an important contribution to human society and
culture.
• Develop Creative Capabilities in Mathematics
Today’s math students need to know more than basic skills. The
workplace of the future requires people who can use technology
and apply mathematics creatively to solve practical problems.
Mathematics = Opportunities!
• Empower Mathematical Capabilities
The empowered learner will not only be able to pose and solve
mathematical questions, but also be able to apply mathematics to
analyze a broad range of community and social issues.
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From http://www.nctm.org/teachmath/consider.htm and http://www.people.ex.ac.uk/PErnest/why.htm
Attitudes about Mathematics
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• “One-half of Americans hate math and
the other two-thirds don’t care.” (Anonymous)
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Credentials for Teachers of Math
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• Multiple Subjects Credential
– Typically teach all subjects, including math,
to students in grades K-5
• Two Single Subject credentials in
Mathematics:
– Foundational Level Math (FLM) – teach
math courses through geometry in grades K-
12, typically in middle schools and high
schools; and
– Secondary Math – teach all math courses in
grades K-12, including Calculus, typically in
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high schools
Why the FLM Credential?
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• Created by CA in 2003.
• NCLB compliance, especially middle grades.
• Aimed at those with a strong mathematics
background but not necessarily a major in math.
• “Foundational-Level Mathematics” connotes the idea
that content preceding algebra and continuing
through geometry forms the foundation for higher
level coursework in mathematics.
• Allows teaching in general mathematics, algebra,
geometry, probability and statistics, and consumer
mathematics. No AP courses can be taught.
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Why the FLM Credential?
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More than 80% of mathematics classes in grades 6-12 can be
taught by FLM teachers in addition to any math in grades K-5.
Course Percent of all classes
Basic or Remedial Mathematics 30%
Pre-Algebra 11%
Beginning and Intermediate
33%
Algebra
Plane and Solid Geometry 9%
Trigonometry 1%
Pre-calculus and Calculus 3%
Integrated Mathematics 7%
Other Mathematics Subjects 6% 6
What is Required for Earning an
FLM Teaching Credential?
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Before applying to the credential program
• At least a Bachelor’s degree (prefer math-based major)
• Pre-requisite Education Coursework:
– The Teaching Experience (EDSC 310); Adolescent Development (EDSC 320);
Developing Literacy (EDSC 330); Diversity and Schooling (EDSC 340);
Proficiency in Educational Technologies (EDSC 304)
• Passing scores on CSET Mathematics I and II Exams
Suggested Mathematics coursework to prepare for exams: Algebra (Math 115);
Trigonometry/Pre-Calculus (Math 125); Probability and Statistics (Math 120);
Calculus (1 semester; Math 130 or Math 135 or Math 150A); Geometry; Math for
Teachers courses (e.g., Math 303A/B & Math 403A/B)
Once admitted to the credential program
• Coursework
– Methods of Teaching (EDSC 440); Methods of Teaching FLM (EDSC 442M);
Teaching English Learners (EDSC 410); Seminar in FLM Teaching (EDS449S)
• Two (2) semesters of student teaching or paid internship teaching
• Passing scores on Teacher Performance Assessments I, II, and III
NOTE: If you are Multiple Subjects credentialed, you may earn FLM certification by passing the CSET
requirements and taking EDSC 442M , Methods for Teaching Foundational Level Math (summer 7
only)
CSET Exams in Mathematics
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• Mathematics Exam I and II required for FLM eligibility
– Exam I: Algebra and Number Theory
– Exam II: Geometry and Probability & Statistics
• CSET website with list of content and sample items:
http://www.cset.nesinc.com/CS_testguide_Matho
pener.asp
• Orange County Department of Education (OCDE)
offers a CSET Mathematics Preparation course. Call
714-966-4156.
• Website of a mathematics teacher in Riverside who
has passed all of the CSET Mathematics exams:
http://innovationguy.easyjournal.com/
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Sample CSET Math Items
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FLM Credential Program at CSUF
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• After completing pre-requisite courses,
the program takes two semesters
• Fall and Spring cohorts
• Focus on teaching middle school
mathematics through algebra
• Placements mostly in middle schools
• Emphasis on making learning accessible
to all students
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What Does It Mean to Teach
Mathematics to ALL Students?
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• What percentage of California 8th
graders take algebra?
– 1996: 25%
– 2003: 45%
• The pass rate for Algebra I, historically,
has been about 50-60%.
– How can we meet the needs of all
students, particularly those whose needs
have not been well-served by “traditional”
education practices? 11
Bridging from Number Operations
to Algebraic Thinking
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• Pre-K to 5 mathematics develops:
– Number sense within the Base 10 system
– Procedural fluency with whole number operations (+, –, x, ÷)
– Concept of rational number
– Concrete methods of mathematical reasoning
• Grade 6 – 8 mathematics develops:
– Number sense with rational numbers
– Procedural fluency with rational number operations
– Movement from additive to multiplicative comparisons
– Communication skills in math, written and oral
– Reasoning and problem solving skills
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– Abstract models of mathematical reasoning (algebra)
Mathematical Proficiency
Adding It Up: Helping
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Children Learn Mathematics,
NRC (2001)
• Must get beyond skills only
focus and work toward
developing reasoning and
understanding in order to
cultivate a productive
disposition.
• Proficiency is defined in
terms of five interwoven
strands. 13
Teaching Foundational-Level
Mathematics
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• Focus on relationships, connections
• Allow for and support student
communication and interaction
• Use multiple representations of
mathematical concepts and relationships
• Use contextualized and non-routine
problems
• Explicitly bridge students from concrete to
abstract thinking
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Knowing Math vs. Teaching Math
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• Think about the problem 2/3 + 4/5
– You might know how to get the answer.
– Teaching requires that you help students to
make sense of how and why the process
works.
• What prior knowledge is needed?
• What possible confusion might students have?
• What are some visual representations and/or
real-life examples that would help students to
make sense of this?
• How would you structure a lesson (or lessons)
to help students build understanding?
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Learning to Find 2/3 + 4/5
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• What prerequisite knowledge do students
need to solve this problem?
– That a fraction is a part of a whole.
– That the denominator is the number of parts in one
whole
– How to create equivalent fractions
• (e.g., 2/3 * 4/4 = 8/12)
• Where might students be confused?
– Students might just add across the “top” and across
the “bottom” 6/8
– They may not understand fraction as part of a
whole.
• How can we address this misunderstanding?
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Learning to find 2/3 + 4/5
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• We might use a visual representation
of these fractions:
2/3
4/5
What is a reasonable estimate?
• Then we could make the “pieces” the
same size for easy addition:
2/3 * (5/5) = 10/15
4/5 * (3/3) = 12/15
(10+12)/15 = 22/15 or 1 7/15 17
Contact Information
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Mark W. Ellis, Ph.D.
California State University Fullerton, EC-512
mellis@fullerton.edu
Visit my website for more information:
http://faculty.fullerton.edu/mellis
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