Transcript What is Foundational Level Mathematics?

What is the FoundationalLevel Mathematics
Credential?
Teacher Educators: Partners and Collaborators
October 23, 2007
Mark W. Ellis, Ph.D.
California State University, Fullerton
[email protected]
http://faculty.fullerton.edu/mellis
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Why Teach Mathematics?
BECOME A MATH TEACHER SO THAT YOU CAN . . .
 Educate Citizens Who Understand and Appreciate Math
Mathematics learned today is the foundation for future decisionmaking. 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.
From http://www.nctm.org/teachmath/consider.htm and http://www.people.ex.ac.uk/PErnest/why.htm
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Attitudes about Mathematics
 “One-half of Americans hate math and the
other two-thirds don’t care.” (Anonymous)
PERSONALLY i THiNK THERE iS NO POiNT FOR MATH i MEAN ALL U
GOTTA KNOW iS HOW TO COUNT FORWARDS AND BACKWARDS i
MEAN THERES NO POiNT FOR VARiABLES AND ALL THAT BULL
COME ON NOW i HATE MATH AND i WiLL NEVER GET iT i KNOW
THAT FOR A FACT!! (www.gurl.com)
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Word Association
 List three words that come to mind when you think back
to your experiences doing/learning mathematics as a
middle or high school student.
 List three words that describe how you best learn
(mathematics or otherwise).
 Share your lists with 3-4 others. What themes do you
find? Similarities? Differences? Recurrences?
 Discuss as a whole group.
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Credentials for Teachers of Math
 Multiple Subjects Credential
 Typically teach all subjects, including math, to students in
grades K-6
 Can earn Single Subject FLM credential by passing
CSET Math I and II PLUS one methods course (EDSC
542M – summer only)
Two Single Subject credentials in Mathematics
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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 K12, including AP Calculus, typically in high schools
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Why the FLM Credential?
 Created by CA in 2003.
 NCLB compliant, 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 of courses through Algebra II. No AP courses
can be taught.
 NOTE: While in the CSU Fullerton FLM credential program,
students may teach only up to Algebra I per program policy.
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Why the FLM Credential?
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 Algebra
33%
Plane and Solid Geometry
9%
Trigonometry
1%
Pre-calculus and Calculus
3%
Integrated Mathematics
7%
Other Mathematics Subjects
6%
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Pre-Requisites for Entering the
FLM Credential Program
 At least a Bachelor’s degree (prefer math-based major)
 Coursework
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EDSC 310 The Teaching Experience
EDSC 320 Adolescent Development
EDSC 330 Developing Literacy
EDSC 340 Diversity and Schooling
EDSC 304 Proficiency in Educational Technologies (recommended)
If entering as a paid Intern Credential Teacher, two more courses:
EDSC 400 Instructional Methods for Secondary Internship
Candidates
 EDSC 410 Teaching English Learners
 Passing scores on CSET Mathematics I and II Exams
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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
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303A/B & Math 403A/B)
Once in the Credential Program
 Coursework
EDSC 440 Methods of Teaching
 EDSC 442M Methods of Teaching FLM
 EDSC 410 Teaching English Learners
 Pre-requisite for those starting as paid interns
 EDSC 304 Proficiency in Educational Technologies
 EDSC 449S Seminar in FLM Teaching
 EDSC 460 Seminar in Teaching Performance Assessment
 Two (2) semesters of student teaching or paid internship teaching
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Placement negotiated by school district and program advisor
 Passing scores on Teacher Performance Assessments I, II, and III
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Single Subject Credential Program
Overviews
October/November 2007
http://ed.fullerton.edu/adtep/EDSCOVERVIEWS.htm
Wednesday
October 24
10:00am
EC 379
Monday
October 29
7:00pm
EC 379
Monday
November 5
11:00am
EC 379
Wednesday
November 14
7:00pm
EC 379
Thursday
November 29
12:00pm
**IRVC 2-131
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CSET Exams in Mathematics
 Mathematics Exam I and II required for FLM
eligibility
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Exam I: Algebra and Number Theory
Exam II: Geometry and Probability & Statistics
 Information on preparing for CSET exams is
on my website

http://faculty.fullerton.edu/mellis
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Sample CSET Math Items
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FLM Credential Program at CSUF
 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?
 What percentage of California 8th graders
take algebra?
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1996: 25%
2003: 45%
 The pass rate for Algebra I, historically, has
been about 50-60%.
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How can we meet the needs of all students,
particularly those whose needs have not been
well-served by “traditional” education
practices?
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Bridging from Number Operations to
Algebraic Thinking
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Pre-K to 5 mathematics develops:
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Number sense within the Base 10 system
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Procedural fluency with whole number operations (+, –, x, ÷)
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Concept of rational number
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Concrete methods of mathematical reasoning
Grade 6 – 8 mathematics develops:
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Number sense with rational numbers
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Procedural fluency with rational number operations
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Movement from additive to multiplicative comparisons
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Communication skills in math, written and oral
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Reasoning and problem solving skills
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Abstract models of mathematical reasoning (algebra)
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Mathematical Proficiency
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Adding It Up: Helping 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.
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Teaching Foundational-Level Mathematics
 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
 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.
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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
 What prerequisite knowledge do students need to
solve this problem?
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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
 We might use a visual representation of
these fractions:
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2/3
4/5
What is a reasonable estimate?
 Then we could make the “pieces” the
same size for easy addition:
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2/3 * (5/5) = 10/15
4/5 * (3/3) = 12/15
(10+12)/15 = 22/15 or 1 7/15
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Contact Information
Mark W. Ellis, Ph.D.
California State University Fullerton, EC-512
[email protected]
714-278-2745
We can come to your campus to do presentations about
careers in math and science teaching!
Visit my website for more information about FLM:
http://faculty.fullerton.edu/mellis
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