1 What is the Foundational- Level Mathematics Credential? Teacher Educators: Partners and Collaborators October 23, 2007 Mark W. Ellis, Ph.D. California State University, Fullerton

2 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 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 and

3 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!! (

4 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.

5 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

6 Why the FLM Credential? Created by CA in 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.

7 Why the FLM Credential? CoursePercent of all classes Basic or Remedial Mathematics30% Pre-Algebra11% Beginning and Intermediate Algebra33% Plane and Solid Geometry9% Trigonometry1% Pre-calculus and Calculus3% Integrated Mathematics7% Other Mathematics Subjects6% 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.

8 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)

9 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

10 Single Subject Credential Program Overviews October/November WednesdayOctober 2410:00amEC 379 MondayOctober 297:00pmEC 379 MondayNovember 511:00amEC 379 WednesdayNovember 147:00pmEC 379 ThursdayNovember 2912:00pm**IRVC 2-131

11 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

12 Sample CSET Math Items

13 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

14 What Does It Mean to Teach Mathematics to ALL Students? What percentage of California 8 th 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?

15 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)

16 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.

17 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

18 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?

19 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?

20 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

21 Contact Information Mark W. Ellis, Ph.D. California State University Fullerton, EC We can come to your campus to do presentations about careers in math and science teaching! Visit my website for more information about FLM: