Mathematics Education Courses
MAED 501 Rational Number Operations and Problem Solving
This course will be an interactive exploration and development of problem solving skills and strategies. A problem may be solved by several approaches; also, two problems that seem solvable by a similar approach may use very different forms of that approach. To that end, problems and their solutions are unique. Confidence and skill in problem solving, then, are built through practice. The class time and the related assignments will be structured around this practice. A variety of strategies will be suggested and modeled, however the focus will be on student-generated solutions. Participants will be expected to work both individually and cooperatively in small groups in this process.
MAED 502 Geometry and Spatial Reasoning
This course will examine the major topics of geometry, including inductive and deductive reasoning; area, perimeter, and volume; similarity, congruence, and proportional reasoning; application and proofs of the Pythagorean Theorem; symmetry and transformational geometry, constructions, and proof. A major project is required.
MAED 503 Algebraic Reasoning
The course is designed to help the participants improve their technical skills in algebra while deepening their understanding of the major concepts and principles underlying algebraic reasoning. Graphing calculators will be used to develop conceptual understanding of algebraic concepts, procedures, and problem solving strategies.
MAED 504 Statistics, Data Analysis, and Probability
This course is an introduction to the basic concepts of statistics and probability, including measures of central tendency and variability, sampling distributions, correlation and regression, and the empirical determination of probabilities. Much of the course is spent on analysis of data, examining measures of center, spread and correlation, and the mathematics involved with drawing inferences and making predictions. Calculator-based methods for data collection and display, statistical calculation, and simulation of probability experiments are also explored.
MAED 505 Advanced Algebra and Trigonometry
This course is designed to help the participants improve their technical skills in advanced algebra and trigonometry while deepening their understanding of the major concepts and principles underlying algebraic and trigonometric reasoning. This course is a prerequisite for MAED 506, Concepts and Applications of Calculus.
MAED 506 Concepts and Applications of Calculus
Calculus is the study of how things change mathematically. It also studies how continuous data can be accumulated and manipulated. In this course, participants will learn to use derivatives and integrals to calculate rates of change, areas and volumes, velocity and acceleration, growth and decay, and to produce sketches of unknown objects. Participants will learn to use these tools of calculus, through class discussions and problem sessions, with the goal of understanding and quantifying the physical world.
MAED 507 Advanced Teaching, Learning, and Curricula in Mathematics
This course is designed to improve student learning in the mathematics classroom by deepening the participants’ understanding of how children learn mathematics, how to select instructional tasks and strategies that will enhance the learning of mathematics, and how to integrate assessment with instruction to implement change in the mathematics program.
MAED 5** Number, Number Systems, and Operations
This course examines the foundations of number, number systems, and operations. Emphasis is on whole number, integers, and rational numbers. Teachers use manipulatives, calculators, and a variety of visual technologies to represent number concepts and processes. Emphasis is on inquiry to develop students’ number sense. Focus on student thinking samples and diagnosis and development of student thinking.
MAED 5** Culturally Responsive Instruction in Mathematics
Culturally Responsive Instruction is a dynamic form of teaching which considers students’ culture to choose and implement instruction in a way that builds and supports the culture and individual characteristics of all students in the mathematics classroom. Culturally Responsive Instruction includes but is not limited to the following instructional strategies: relating mathematics to real-life experiences, creating a safe and supportive learning community within the classroom which is student-centered and teacher facilitated, and helping students develop the language and concepts of mathematics.
MAED 5** Mathematical Reasoning
This course examines different types of mathematical reasoning. Topics include but are not limited to arithmetic, proportional, algebraic, probabilistic, spatial, analogic, deductive, inductive, and axiomatic thinking. Inquiry experiences provide course participants with opportunities to experience, compare these different forms of reasoning and a variety of problem-solving strategies. Research on learning and teaching mathematical reasoning in school mathematics will be explored and applied through a case study of children’s mathematical reasoning.
MAED 5** Inquiry I: Patterns, Functions, and Algebra
This course uses an inquiry approach to investigate essential and advanced algebraic concepts. Topics include but are not limited to patterns, functions, relations, variables, equality, algebraic representation, justification, and proof. Course participants learn how to use manipulatives, graphing calculators, and other visual technologies to create active learning classroom communities. Research on learning and teaching algebra, with emphasis on linear, quadratic, and exponential functions is the foundation for developing research-based teaching practices in algebra. Course participants assess student work samples in algebra, and design intervention strategies to deepen students’ algebraic understanding.
MAED 5** Inquiry II: Probability, Data Analysis, and Statistics
This course uses an inquiry approach to investigate essential concepts from data analysis, probability, and statistics including descriptive and inferential statistics topics. Course participants learn how to use manipulatives, graphing calculators, software, and other analogical reasoning tools to create active learning classroom communities. Research on learning and developing students’ probabilistic and statistical reasoning is the foundation for developing research-based teaching practices in probability and statistics. Course participants assess student work samples in data analysis, probability,
and statistics, and design intervention strategies to move students’ mathematical thinking forward.
MAED 5** Inquiry III: Geometry, Spatial Reasoning, and Proof
This course uses an inquiry approach to investigate essential and advanced geometric concepts and spatial reasoning. Course participants will explore Euclidean, Non-Euclidean, and finite geometries to develop an appreciation of axiomatic systems and proof. Additionally, students will use manipulatives, graphing calculators, dynamic geometry drawing tools to create inquiry experiences and active learning classrooms. Exposure to research on learning and teaching geometry, measurement, and proof as the foundation for developing research-based teaching and assessment practices in geometry. Course participants assess student work samples in geometry, and design intervention strategies to move the thinking of geometry students forward using the Van Hiele Levels of Geometric Understanding. Applications to geometry in art, architecture, nature, computer graphics, and other fields are incorporated.
MAED 5** Inquiry IV: Trigonometry and Calculus
This course uses an inquiry approach to investigate essential and advanced concepts from trigonometry and the calculus with an emphasis on calculus as the mathematics of motion. Topics include limit, continuity, derivative, and integral. Course participants learn how to use manipulatives, graphing calculators, software, and other visual technologies to create active learning classroom communities. Research on calculus reform and learning and teaching calculus is the foundation for developing research-based active-learning experiences in calculus. Course participants assess student work samples in trigonometry and calculus.
MAED 5** Mathematical Modeling
This course explores the mathematics of real life. Course participants investigate the connections of mathematics to many other fields including architecture, art, engineering, history, nature, and the sciences. Students will learn how to use mathematics to model real-life situations, and how to incorporate mathematical modeling into their own classrooms and across the school mathematics curriculum. A Mathematics Modeling Project is required.
MAED 5** Discrete Mathematics
This course explores discrete mathematics and its applications in science and technology. Topics include logic and proof, induction and recursion, number theory, set theory, combinatorics and discrete probability, algorithms, algorithm analysis, and discrete structures. Mathematical modeling will be incorporated into the course. Students will also investigate how discrete mathematics concepts are embedded in the national standards of K-12 mathematics courses and ways to teach discrete mathematics in the K-12 classroom.
EDUC 771 Analyzing Educational Research
This course provides an overview of designs used in educational research. Topics include experimental, quasi-experimental, historical, ethnographic, and phenomenological modes of inquiry. Emphases are on the assumptions, applications, tools and procedures associated with each of the designs. Study of experimental and quasi-experimental designs will consider issues such as validity, randomization, and multi-variate statistics. A detailed literature review and an abstract of a research study are required.
EDUC 772 Assessment and Evaluation
This course focuses on the fundamental skills, concepts, and understandings needed to accelerate and document student achievement, using multiple sources of data. Participants will examine and develop essential characteristics of exemplary practices and quality assessments. They will also model and design assessment items, including selected response and brief constructed response items, analyze and compare classroom and state level assessments, and provide criteria for more effective differentiation of instruction.
EDUC 795 Seminar in the Study of Teaching
This seminar examines the knowledge base on teaching and learning as it applies to the solution of selected teaching and instructional problems. Participants will analyze theoretical perspectives, research and informed practice related to their selected problems. They then will design and develop a strategy for addressing the problem.
This course will also serve as an opportunity to define and begin to develop a program plan for the capstone project.
EDUC 781 Teacher Leadership
This course offers experienced participants an opportunity to develop leadership qualities, including designing and implementing a mentoring/coaching experience for a novice teacher or student teaching intern. Drawing on the participants’ current knowledge, skills, and resourcefulness in the critical teaching areas of planning, instruction, and classroom organization and assessment, the experienced teacher will develop expertise in adult learning, observation, feedback, and instructional improvement. The goal is for the teacher to become a leader in his/her school, in the areas of content and methodology.
EDUC 792 Project Seminar (Capstone Project)
The Capstone Project is designed to provide the opportunity for participants to demonstrate the synthesis of understandings developed throughout the entire master’s program. Beginning in EDUC 771 and 795, participants will work with faculty to develop the question to be investigated. In this final course, under the direction of the Seminar Instructor, the project is fully developed, presented in a “public” forum and made available in the UMBC curriculum resource center.