Module-1: Advanced Mathematics Content

1.1: MATH 501 – Advanced Concepts in Algebra and Number Theory

Unit 1: Number Theory Foundations

• Properties of integers and rational numbers

• Divisibility and modular arithmetic

• Prime numbers and fundamental theorem of arithmetic

• Diophantine equations

• Applications in cryptography and coding theory

Unit 2: Abstract Algebra Structures

• Groups, rings, and fields

• Symmetry groups and applications

• Polynomial rings and field extensions

• Applications to geometry and number theory

• Connecting abstract structures to high school algebra

Unit 3: Linear Algebra and Applications

• Vector spaces and subspaces

• Linear transformations and matrices

• Eigenvalues and eigenvectors

• Applications to computer graphics, data analysis, and dynamical systems

• Connections to high school mathematics

---

1.2: MATH 502 – Analysis and Calculus (3 credits)

Unit 1: Real Analysis Foundations

• Properties of real numbers and completeness

• Sequences, series, and convergence

• Limits, continuity, and differentiability

• The Fundamental Theorem of Calculus revisited

• Rigor and proof in calculus concepts

Unit 2: Advanced Calculus Topics

• Multi-variable calculus and applications

• Vector calculus and field theory

• Differential equations and modeling

• Numerical analysis techniques

• Technology integration for calculus teaching

Unit 3: Applications and Connections

• Calculus in physics and engineering

• Optimization problems

• Discrete vs. continuous models

• Approximation methods

• Connections to high school curriculum

---

1.3: MATH 503 – Geometry and Measurement (3 credits)

Unit 1: Advanced Euclidean Geometry

• Axiomatic systems and proof

• Transformational geometry

• Geometric constructions

• Coordinate geometry connections

• Applications of geometric concepts

Unit 2: Non-Euclidean Geometries

• Spherical geometry

• Hyperbolic geometry

• Projective geometry

• Fractal geometry

• Historical and cultural perspectives

Unit 3: Measurement Theory and Applications

• Dimensional analysis

• Measurement systems and conversions

• Accuracy, precision, and error analysis

• Geometric measurement in 2D and 3D

• Applications in science and engineering

---

1.4: MATH 504 – Probability, Statistics, and Data Analysis (3 credits)

Unit 1: Probability Theory

• Probability axioms and properties

• Discrete and continuous probability distributions

• Conditional probability and independence

• Random variables and expected value

• Simulation and computational methods

Unit 2: Statistical Inference

• Sampling distributions

• Estimation and confidence intervals

• Hypothesis testing

• Regression and correlation

• Analysis of variance

Unit 3: Modern Data Analysis

• Exploratory data analysis

• Data visualization techniques

• Statistical computing using R or Python

• Big data concepts and challenges

• Statistical modeling and machine learning basics

---

Module-2: Mathematics Education and Pedagogy (9 credits)

2.1: EDMT 511 – Theories of Mathematics Learning and Teaching (3 credits)

Unit 1: Learning Theories in Mathematics Education

• Constructivist approaches to mathematics learning

• Cognitive development theories

• Social aspects of mathematics learning

• Mathematical habits of mind

• Research on how students learn mathematics

Unit 2: Effective Mathematics Teaching Practices

• Establishing mathematics learning goals

• Designing and implementing rich mathematical tasks

• Facilitating meaningful mathematical discourse

• Using and connecting mathematical representations

• Supporting productive struggle in learning mathematics

Unit 3: Equity and Access in Mathematics Education

• Cultural relevance and responsiveness in mathematics teaching

• Gender and diversity issues in mathematics education

• Supporting students with special needs

• Teaching mathematics to multilingual learners

• Creating inclusive mathematics classrooms

---

2.2: EDMT 512 – Curriculum Development and Assessment in Mathematics (3 credits)

Unit 1: Mathematics Curriculum Design

• Standards-based curriculum development

• Vertical alignment of mathematical content

• Curriculum mapping and pacing

• Textbook and resource evaluation

• Adapting curriculum for diverse learning needs

Unit 2: Assessment of Mathematical Learning

• Formative and summative assessment strategies

• Performance tasks and authentic assessment

• Rubric development and scoring

• Error analysis and misconception diagnosis

• Standardized testing and preparation strategies

Unit 3: Technology Integration in Mathematics Curriculum

• Digital tools for mathematics instruction

• Dynamic geometry and algebra software

• Graphing calculators and computation tools

• Online mathematics resources and platforms

• Digital assessment tools and techniques

---

2.3: EDMT 513 – Mathematical Problem Solving and Reasoning (3 credits)

Unit 1: Problem-Solving Approaches

• Problem-solving frameworks and heuristics

• Metacognition in mathematical problem solving

• Non-routine and open-ended problems

• Problem posing and problem modification

• Teaching through problem solving

Unit 2: Mathematical Reasoning and Proof

• Types of mathematical reasoning

• Developing logical thinking skills

• Proof techniques and structures

• Teaching proof concepts across grade levels

• Connecting reasoning to other mathematical practices

Unit 3: Mathematical Modeling

• The modeling cycle and process

• Real-world applications and contextualized problems

• Interdisciplinary connections

• Technology tools for modeling

• Project-based learning approaches

---

Module-3: Teaching Applications and Field Experience (6 credits)

3.1: EDMT 521 – Mathematics Teaching Practicum (3 credits)

Unit 1: Lesson Planning and Implementation

• Standards-based lesson design

• Differentiation strategies for mathematics instruction

• Planning for productive discourse

• Technology integration in lesson planning

• Teaching mathematics lessons in diverse settings

Unit 2: Classroom Management for Mathematics Classrooms

• Creating a positive mathematics learning environment

• Promoting student engagement and motivation

• Managing group work and collaborative learning

• Addressing behavioral challenges

• Supporting diverse learning needs

Unit 3: Professional Growth and Reflection

• Reflective teaching practices

• Video analysis of teaching

• Peer observation and feedback

• Professional learning communities

• Action research in the mathematics classroom

---

3.2: EDMT 522 – Advanced Field Experience in Mathematics Teaching (3 credits)

Unit 1: Teaching in Diverse Mathematics Classrooms

• Supervised teaching in diverse school settings

• Working with students from varied backgrounds

• Co-teaching and collaboration with school personnel

• Documentation of student learning

• Implementation of research-based practices

Unit 2: Mathematics Coaching and Leadership

• Peer coaching techniques

• Leading professional development activities

• Curriculum development and improvement

• Parent and community engagement

• Mathematics program evaluation

Unit 3: Professional Portfolio Development

• Creating a teaching philosophy statement

• Documenting teaching accomplishments

• Collecting evidence of student learning

• Building a digital teaching portfolio

• Presenting professional work to stakeholders

---

Module-4: Capstone Experience (3 credits)

4.1: EDMT 590 – Mathematics Education Capstone Project/Thesis (3 credits)

Option A: Action Research Project

• Identification of a classroom-based research question

• Literature review on selected topic

• Research design and methodology

• Data collection and analysis

• Reporting findings and implications for practice

Option B: Curriculum Development Project

• Designing an innovative curriculum unit

• Creating supporting instructional materials

• Pilot implementation and evaluation

• Revision based on feedback

• Documentation and dissemination plan

Option C: Professional Development Module

• Needs assessment for mathematics teachers

• Development of professional learning materials

• Implementation with mathematics teachers

• Evaluation of effectiveness

• Refinement and recommendations