What is Foundational Level Mathematics by coold

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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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