MATHEMATICS INSTRUCTIONAL ADDED AUTHORIZATION (MIAA)

MIAA candidates' Demonstration of Advanced Practices and knowledge regarding the challenges of developing mathematics literacy among California's diverse student population will be evidenced in their Teacher Action Research through their specialized mathematical knowledge for teaching and thinking as well as their pedagogical knowledge and practices for teaching mathematics. The candidates will gather evidence from each grade span and focus of each course (see Demonstration of Advanced Practices in each course description) included in the TCSJ MIAA program that will serve as proof of their expertise. Lessons, student work, and reflections will also be included from the candidates' fieldwork lesson studies. The final research will be submitted in a format ready for publication, supported by a portfolio of evidence from the MIAA fieldwork that is embedded within course expectations, as well as the lesson studies. The candidates' study is presented to program instructors and peers upon completion of the program.

Mathematical Discourse focuses on the challenges of developing mathematics literacy among California's diverse student population and developing strategies for teachers that cultivate and advance positive attitudes among their students toward mathematics. The course is designed to attend to the specialized vocabulary embedded within mathematics and build understanding of effective pedagogical practices that enable teachers to facilitate meaningful discourse about mathematics, as well as, encourage and maintain the engagement of all learners. Content also includes how to analyze K-A1 students' questions, how to develop questions that promote critical thinking, and strategies that maintain high levels of cognitive demand throughout lessons.

In MIAA 330, a variety of assessment types are explored and developed with particular attention to error analysis, learning trajectories, language assessments, formative and summative (site-based and California Common Core State Standards based) assessments. All discussions and assignments surrounding the varied assessments include the implications to instruction and how to help students use their results to improve their own understanding of mathematics.

Building directly from the information in the course, Mathematics Assessment, the expectations of the coursework in Equity in Mathematics: Intervention, Accommodation, and Differentiation require that the results of K-A1 students' assessments inform MIAA candidates' evaluation, modification, design, and implementation of interventions, accommodations, and differentiation based on California's Common Core State Standards for Mathematics. MIAA teacher teams will design and implement targeted instruction appropriate for each grade span that promotes all students' equitable access to learn high-level mathematics.

MIAA 350 addresses implications to instruction based on the rigorous skills, concepts, and ways of thinking that are essential to students' success and engagement in doing mathematics. This course will provide the framework for mathematics instruction: content, representations, and theories, to increase the mathematical understanding of both the MIAA candidate and K-Algebra One/Integrated One students. Maintaining the collaborative philosophy of the program, participating teachers will be challenged to ensure that everyone in their class has a shared understanding of what the mathematics means as well as the proper sequencing and scaffolding of the content. This course prepares MIAA candidates for the capstone course, Designing Mathematics Instruction.

With attention to the California Common Core State Standards for Mathematics and building on the knowledge gained within the previous courses, the MIAA candidates collaborate with peers (pre-service, novice, and experienced) through co-planning of instructional units and co-teaching to improve student learning. Participants learn to design effective mathematics lessons for each grade span (K - Algebra One/Integrated One) and to plan and implement lessons specified within their units of mathematics content/instruction. All planning attends to the mathematics content as well as the developmental and cultural needs of the diverse student population of California. The MIAA candidate's demonstration of their ability to address the complex interplay of mathematics content and pedagogy for effective teaching for each grade span is the purpose of their capstone project.