Masters Degree in Education: Option in Mathematics Education, California State University, Long Beach
Mathematics Instructional Added Authorization (MIAA) Standards
Writing Outline
Guiding Writing Principles:
1. Tell how each standard element is addressed in the program.
2. Tell where each standard element is addressed in the program.
3. Give evidence, e.g., standard course outlines (reference to relevant SLOs), text used (name of
chapter), signature assignments (by name and description), program advisory materials, program
website.
4. Do not simply repeat the element.
Category A: Program Design
Standard 1: Program Design
The preparation programs and any prerequisites include a purposeful, interrelated, and developmentally
designed sequence of coursework and field experiences. The design of the program follows an explicit
statement of program philosophy and purpose based on a sound rationale informed by theory, research,
and practice. It effectively coordinates and articulates expertise in integrating and applying K-PreAlgebra and/or K-Algebra I content knowledge, specialized mathematical knowledge for teaching and
thinking, and pedagogical knowledge and practices for teaching mathematics.
The sponsoring institution demonstrates a commitment to candidate preparation by providing
appropriate support for the program. The program has a qualified leadership team with expertise in
mathematics content, mathematics education, teacher education, and teacher leadership.
The program provides extensive opportunities for candidates to demonstrate mathematical and
pedagogical content knowledge and skills to support effective mathematics instruction and student
learning. Coursework and fieldwork address the complex interplay of math content and pedagogy in
effective teaching. Candidates are prepared to enhance mathematical development for all students1
including English learners, students with disabilities, students who are gifted and talented, and students
at risk. Candidates are prepared to collaborate and co-teach with other math teachers as well as
teachers of other subject matter disciplines. The program includes a planned process of comprehensive
assessments ensuring that candidates are prepared to teach K through Pre-Algebra or K through Algebra
I. In addition, its design ensures that candidates are equipped to understand the challenges of
developing mathematics literacy among California’s diverse student and teaching population.
Element 1:
The preparation programs and any prerequisites include a purposeful, interrelated, and developmentally
designed sequence of coursework and field experiences.
Response:
1
All “students” refers to, but is not limited to, struggling students, English learners, gifted and talented students,
and students with special needs. Program Sponsors will need to address all levels whenever the word “students” is
used in this document.
2-14-11
1
Masters Degree in Education: Option in Mathematics Education, California State University, Long Beach
Mathematics Instructional Added Authorization (MIAA) Standards
Writing Outline
Element 2:
The design of the program follows an explicit statement of program philosophy and purpose based on a
sound rationale informed by theory, research, and practice.
Response:
Element 3:
The program effectively coordinates and articulates expertise in integrating and applying K-Pre-Algebra
and/or K-Algebra I content knowledge, specialized mathematical knowledge for teaching and thinking,
and pedagogical knowledge and practices for teaching mathematics.
Response:
Element 4:
The sponsoring institution demonstrates a commitment to candidate preparation by providing
appropriate support for the program.
Response:
Element 5
The program has a qualified leadership team with expertise in mathematics content, mathematics
education, teacher education, and teacher leadership.
Response:
Element 6:
The program provides extensive opportunities for candidates to demonstrate mathematical and
pedagogical content knowledge and skills to support effective mathematics instruction and student
learning.
Response:
Element 7:
Coursework and fieldwork address the complex interplay of math content and pedagogy in effective
teaching. Candidates are prepared to enhance mathematical development for all students2 including
English learners, students with disabilities, students who are gifted and talented, and students at risk.
2
All “students” refers to, but is not limited to, struggling students, English learners, gifted and talented students,
and students with special needs. Program Sponsors will need to address all levels whenever the word “students” is
used in this document.
2-14-11
2
Masters Degree in Education: Option in Mathematics Education, California State University, Long Beach
Mathematics Instructional Added Authorization (MIAA) Standards
Writing Outline
Response:
Element 8:
Candidates are prepared to collaborate and co-teach with other math teachers as well as teachers of
other subject matter disciplines.
Response:
Element 9:
The program includes a planned process of comprehensive assessments ensuring that candidates are
prepared to teach K through Pre-Algebra or K through Algebra I. In addition, its design ensures that
candidates are equipped to understand the challenges of developing mathematics literacy among
California’s diverse student and teaching population.
Response:
Element 10:
The program design ensures that candidates are equipped to understand the challenges of developing
mathematics literacy among California’s diverse student and teaching population.
Response:
Evidence for Standard 1: (provide exact titles of materials referenced; all materials will need to be
electronic; books can be identified by title page and table of contents)
Appendix XX:
Appendix XX:
Appendix XX:
2-14-11
3
Masters Degree in Education: Option in Mathematics Education, California State University, Long Beach
Mathematics Instructional Added Authorization (MIAA) Standards
Writing Outline
Category B: Curriculum and Fieldwork
Standard 2: Specialized Mathematics for Teaching and Learning
The program provides opportunities for candidates to develop Mathematical Knowledge for Teaching
and understand mathematics content, consistent with the candidate’s level of certification. The program
provides opportunities for candidates to develop advanced competency to:
Element 1:
Plan and implement instruction that includes differentiation, accommodations, and interventions and is
based on students’ mathematical thinking by:
1. Using error analysis processes to review and understand students’ misconceptions and to
distinguish whether a specific error reflects a misunderstanding of the mathematical process or a
need for language development in the area of mathematical concepts
2. Understanding the order of presentation of mathematical concepts that lead to student proficiency
in mathematics
3. Analyzing the learning trajectories of individual students
4. Explaining standard and alternative algorithms and solution strategies
Response:
Element 2:
Use a variety of appropriate methods of mathematical representation, including technology, oral
language, written symbols, pictures, concrete materials/models, real-world situations, while also:
1. Identifying and understanding strengths and limitations of various representations of
mathematical concepts
2. Linking representations to underlying mathematical theories and to other representations.
Response:
Element 3:
Use and understand the correct usage of mathematical language by:
1. Analyzing mathematical vocabulary in the context of mathematical concepts when listening and
responding to students’ questions and comments
2. Evaluating their own and colleagues’ presentation of mathematical definitions and terms, as well
as considering students’ culture, language, and cognitive needs when using academic language to
scaffold instruction
Response:
Evidence for Standard 2: (provide exact titles of materials referenced; all materials will need to be
electronic; books can be identified by title page and table of contents)
Appendix XX:
2-14-11
4
Masters Degree in Education: Option in Mathematics Education, California State University, Long Beach
Mathematics Instructional Added Authorization (MIAA) Standards
Writing Outline
Appendix XX:
Appendix XX:
2-14-11
5
Masters Degree in Education: Option in Mathematics Education, California State University, Long Beach
Mathematics Instructional Added Authorization (MIAA) Standards
Writing Outline
Standard 3: Pedagogical Knowledge and Practices for Teaching Mathematics
The program provides candidates with opportunities to develop advanced practices in the use of
students’ mathematical thinking, mathematical representation, mathematical language, mathematics
curriculum, instructional planning, classroom discourse, and assessment. The program will provide
opportunities for candidates to develop advanced skills in evaluating, planning, and implementing
appropriate interventions to increase student achievement.
The program will provide opportunities for candidates to develop the type of pedagogical expertise
needed to modify curriculum to address the specific needs of diverse groups of students, including but
not limited to struggling students, English language learners, gifted and talented students, and students
with special needs.
Element 1:
Plan and implement mathematics instruction in developmentally and culturally responsive ways to meet
specific student needs, including the ability to
1. Analyze and adapt resources, technologies, and standards-aligned instructional materials,
including adopted materials, for targeted audiences based on students’ cultural, linguistic, and
cognitive development
2. Identify and connect concepts that are fundamental to learning mathematics, such as place value,
fractions, real numbers and algebra
Response:
Element 2:
Plan instruction that supports students’ learning of mathematics by:
1. Selecting and developing student learning tasks that enable teachers to understand the
conjectures and generalizations that students make
2. Aligning instructional goals, assessments, instructional strategies, and practice (e.g., assignments,
homework) using SDAIE strategies as appropriate
3. Designing and implementing flexible grouping strategies (homogeneous, semi-homogeneous,
heterogeneous, large group, small group, and individual learning) according to students’ needs
and level of achievement
4. Focusing on the mathematics content standards and the key concepts within the standards
5. Collaborating with individual teachers (pre-service, novice, and experienced) through co-planning
and co-teaching to improve student learning
Response:
Element 3:
Develop strategies for classroom discourse by being able to:
1. Facilitate student to student interaction
2. Analyze questioning strategies to lead discussions that actively involve all students
2-14-11
6
Masters Degree in Education: Option in Mathematics Education, California State University, Long Beach
Mathematics Instructional Added Authorization (MIAA) Standards
Writing Outline
3. Select culturally appropriate examples and reframe problems to encourage students’ deep
understanding within a mathematical context
4. Advance and cultivate positive attitudes toward mathematics; encouraging curiosity, flexibility,
and persistence in solving mathematical problems
Response:
Element 4:
Use assessments for:
1. Identifying gaps in students’ knowledge and for designing instruction to bridge the gaps, language
assessments for identifying gaps in understanding mathematics terms, summative assessments
and standardized assessments for measuring student growth
2. Guiding instruction and developing curriculum that is targeted, accommodated, and differentiated
for intensive intervention as necessary
3. Communicating progress to students, parents, colleagues, and other appropriate service providers
4. Deriving demographic, process, and outcome data at the student, school, and district levels to
support informed decisions in designing targeted instruction that promotes students equitable
access to learn high-level mathematics
Response:
Evidence for Standard 3: (provide exact titles of materials referenced; all materials will need to be
electronic; books can be identified by title page and table of contents)
Appendix XX:
Appendix XX:
Appendix XX:
2-14-11
7
Masters Degree in Education: Option in Mathematics Education, California State University, Long Beach
Mathematics Instructional Added Authorization (MIAA) Standards
Writing Outline
Standard 4: Field Experiences
Programs facilitate individualized and balanced field experiences that provide candidates with timely and
ongoing feedback to guide improvements in practice as described in Category B. These field experiences
are integrated into coursework and are aligned with the candidate competence standard.
The guided field experiences extend candidates’ understandings of the three domains and their elements.
Element 1:
The candidate is provided substantive opportunities to observe and practice each of the proficiencies
described in Category B:
1. Facilitate student to student interaction
2. Analyze questioning strategies to lead discussions that actively involve all students
3. Select culturally appropriate examples and reframe problems to encourage students’ deep
understanding within a mathematical context
4. Identifying gaps in students’ knowledge and for designing instruction to bridge the gaps, language
assessments for identifying gaps in understanding mathematics terms, summative assessments
and standardized assessments for measuring student growth
5. Guiding instruction and developing curriculum that is targeted, accommodated, and differentiated
for intensive intervention as necessary
6. Communicating progress to students, parents, colleagues, and other appropriate service providers
7. Deriving demographic, process, and outcome data at the student, school, and district levels to
support informed decisions in designing targeted instruction that promotes students equitable
access to learn high-level mathematics
Response:
Element 2:
The fieldwork component will include the following grade spans: Kindergarten through Grade 3 and
Grade 4 through Grade 7 for the candidates that are prepared to teach K through Pre-Algebra. In
addition, candidates prepared to teach K through Algebra I also have field experience in Algebra 1.
Response:
Element 3:
The program collaborates with local educational agencies in providing guidance, site-based support, and
coordination of field experiences to ensure the candidate has successful experiences working with English
learners, students with disabilities, students who are gifted and talented, and students at risk.
Evidence for Standard 4: (provide exact titles of materials referenced; all materials will need to be
electronic; books can be identified by title page and table of contents)
Appendix XX:
2-14-11
8
Masters Degree in Education: Option in Mathematics Education, California State University, Long Beach
Mathematics Instructional Added Authorization (MIAA) Standards
Writing Outline
Appendix XX:
Appendix XX:
2-14-11
9
Masters Degree in Education: Option in Mathematics Education, California State University, Long Beach
Mathematics Instructional Added Authorization (MIAA) Standards
Writing Outline
Category C: Candidate Competence
Standard 5: Determination of Candidate Competence
Program sponsors use multiple measures to determine that each candidate has demonstrated
competence across the proficiencies described in Category B, including advanced level culminating
projects to demonstrate professional competency. Program options for advanced level culminating
projects to demonstrate professional competency may include, but are not limited to, professional
presentations, action research, designing curriculum, and school, district, or county collaborative
projects.
Element 1:
Program sponsors use multiple measures to determine that each candidate has demonstrated
competence across the proficiencies described in Category B.
1. Plan and implement instruction that includes differentiation, accommodations, and interventions
and is based on students’ mathematical thinking
2. Use a variety of appropriate methods of mathematical representation, including technology, oral
language, written symbols, pictures, concrete materials/models, real-world situations
3. Use and understand the correct usage of mathematical language
4. Plan and implement mathematics instruction in developmentally and culturally responsive ways to
meet specific student needs
5. Plan instruction that supports students’ learning of mathematics
6. Develop strategies for classroom discourse
7. Use assessments
Response:
Element 2:
Program options for advanced level culminating projects to demonstrate professional competency may
include, but are not limited to, professional presentations, action research, designing curriculum, and
school, district, or county collaborative projects.
Evidence for Standard 5: (provide exact titles of materials referenced; all materials will need to be
electronic; books can be identified by title page and table of contents)
Appendix XX:
Appendix XX:
Appendix XX:
2-14-11
10