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What is the Foundational-Level Mathematics Credential? TEPAC 0011 0010 1010 1101 0001 0100 1011 October 24, 2006 Mark W. Ellis, Ph.D. California State University, Fullerton mellis@fullerton.edu http://faculty.fullerton.edu/mellis 1 Why Teach Mathematics? 0011 0010 1010 1101 0001 0100 1011 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. 2 From http://www.nctm.org/teachmath/consider.htm and http://www.people.ex.ac.uk/PErnest/why.htm Attitudes about Mathematics 0011 0010 1010 1101 0001 0100 1011 • “One-half of Americans hate math and the other two-thirds don’t care.” (Anonymous) 3 Credentials for Teachers of Math 0011 0010 1010 1101 0001 0100 1011 • 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 4 high schools Why the FLM Credential? 0011 0010 1010 1101 0001 0100 1011 • 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. 5 Why the FLM Credential? 0011 0010 1010 1101 0001 0100 1011 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? 0011 0010 1010 1101 0001 0100 1011 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 0011 0010 1010 1101 0001 0100 1011 • 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/ 8 Sample CSET Math Items 0011 0010 1010 1101 0001 0100 1011 9 FLM Credential Program at CSUF 0011 0010 1010 1101 0001 0100 1011 • 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 10 What Does It Mean to Teach Mathematics to ALL Students? 0011 0010 1010 1101 0001 0100 1011 • 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 0011 0010 1010 1101 0001 0100 1011 • 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 12 – Abstract models of mathematical reasoning (algebra) Mathematical Proficiency Adding It Up: Helping 0011 • 0010 1010 1101 0001 0100 1011 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 0011 0010 1010 1101 0001 0100 1011 • 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 14 Knowing Math vs. Teaching Math 0011 0010 1010 1101 0001 0100 1011 • 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? 15 Learning to Find 2/3 + 4/5 0011 0010 1010 1101 0001 0100 1011 • 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? 16 Learning to find 2/3 + 4/5 0011 0010 1010 1101 0001 0100 1011 • 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 0011 0010 1010 1101 0001 0100 1011 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 18