Advanced Specialization Competencies

Evidence of development/mastery provided for the following areas:



Contemporary Issues/Challenges

Provides advanced study in mathematics education with emphasis on contemporary issues and challenges confronting K-12 mathematics education at the K-12 levels. Focus on applying the mathematics principles and standards to improve curriculum, teaching and learning, assessment, technology usage and equity.

  • Analyze the six mathematical principles as applied to curriculum development for K-12 mathematics education.
  • Apply state and national mathematics standards using a variety of instructional strategies.
  • Analyze student learning outcomes on the California State Test (CST) for quality, validity and reliability.
  • Evaluate the challenge of using technology, video and other electronic applications for teaching mathematics.
  • Analyze the six mathematical principles as applied to curriculum development for K-12 mathematics education.
  • Analyze current principles, state and national standards, trends and issues in teaching Mathematics in grades K-9.
  • Apply evidence-based best practices research in the delivery and evaluation of a balanced mathematics education program.
  • Demonstrate the ability to develop a balanced program of mathematics instruction that includes conceptual understanding, procedural fluency and problem solving in Algebra, Geometry, Statistics, Probability and Number Theory.
Algebra & Number Theory

Provides K-9 advanced study in teaching and learning algebra and number theory content. Presents effective strategies and models of instruction to improve pedagogy and assessment in mathematics classrooms.

  • Analyze issues, challenges and problems involved in teaching algebra and number theory.
  • Apply research based solutions and approaches to teaching algebra and number theory.
  • Create instrument for measuring effectiveness of teaching and assessment of student learning related to algebra and number theory.
  • Develop learning activity for teaching algebra and number theory, illustrating and justifying the use of varied instructional strategies.
Teaching Geometry & Measurement

Provides K-9 advanced study in teaching and learning geometry and measurement content. Presents effective strategies and models of instruction to improve pedagogy and assessment in mathematics classrooms.

  • Analyze issues, challenges and problems involved in teaching geometry and measurement.
  • Apply research based solutions and approaches to teaching geometry and measurement.
  • Create instrument for measuring effectiveness of teaching and assessment of student learning related to geometry and measurement.
  • Develop learning activity for teaching geometry and measurement, illustrating and justifying the use of varied instructional strategies.
Probability and Statistics

Provides K-9 advanced study in teaching and learning probability and statistics content. Presents effective strategies and models of instruction to improve pedagogy and assessment in mathematics classrooms.

  • Analyze issues, challenges and problems involved in teaching probability and statistics.
  • Apply research based solutions and approaches to teaching probability and statistics.
  • Create instrument for measuring effectiveness of teaching and assessment of student learning related to probability and statistics.
  • Develop learning activity for teaching probability and statistics, illustrating and justifying the use of varied instructional strategies.


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