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What is the Foundational-Level Mathematics Credential?

Teacher Educators: Partners and CollaboratorsOctober 23, 2007

Mark W. Ellis, Ph.D.California State University, Fullerton

mellis@fullerton.eduhttp://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 decision-making. Students should develop an appreciation of mathematics as making an important contribution to human society and culture.

Develop Creative Capabilities in MathematicsToday’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 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 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?

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%

More than 80% of mathematics classes in grades 6-12 can betaught by FLM teachers in addition to any math in grades K-5.

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Pre-Requisites for Entering the FLM Credential Program

At least a Bachelor’s degree (prefer math-based major) Coursework

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

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)

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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 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 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? 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?

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Bridging from Number Operations to Algebraic Thinking

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 Abstract models of mathematical reasoning (algebra)

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Mathematical Proficiency

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.

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? 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: 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

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Contact Information

Mark W. Ellis, Ph.D.California State University Fullerton, EC-512

mellis@fullerton.edu714-278-2745

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