Graduate Certificate in Mathematics K-6

To foster high levels of learning and achievement in math, teachers must first have a deep understanding of mathematical concepts and know how best to teach them. In this course,  teachers of K—8 mathematics are introduced to exciting ideas and practices to address their own learning and teaching of mathematics. Authentic and engaging mathematics experiences, including modeling, representing mathematical ideas in multiple ways, and identifying and addressing student misconceptions, are emphasized. Educators engage in effective practices for fostering students' ability to reason, analyze conceptual relationships, and persist in solving challenging problems. Connections across mathematics topics, skills, and levels as well as educational policies that impact the learning and teaching of mathematics are emphasized in this course. The Common Core State Standards for Mathematics, including the Standards for Mathematical Practice, and the National Council for Teachers of Mathematics (NCTM) practices are frameworks for addressing fundamental principles and skills.

Effective elementary mathematics instruction requires a deep understanding of numbers and operations, the real-world situations in which these arise, and how children learn these ideas. In this course, teachers refine their knowledge of the structure of the base-ten number system and how it is used in addition and subtraction. They examine various methods of multi-digit calculations, including methods commonly created by students and variations of standard algorithms. Teachers extend their own conceptual understanding by modeling mathematics visually and explaining relationships between visual representations and mathematical notation. Teachers also learn how to develop appropriate interventions by diagnosing common student misconceptions.

Developing students' mathematical habits of mind and leading them to become mathematical thinkers is an important goal of elementary mathematics education. In this course, educators extend their own understanding of the base ten number system and the relationships among addition, subtraction, multiplication, and division. Educators explore various interpretations and meanings of these operations while working with properties of multiplication, division, and proportionality. They investigate students' misconceptions and struggles and develop effective intervention strategies. Educators further develop their own mathematical habits of mind as they engage in challenging tasks and solve real-world mathematical problems.

Measurement and geometry are often challenging topics for elementary students, but they represent some of the most visible uses of mathematics in students' day-to-day lives. In this course, educators learn strategies for connecting these topics to other mathematical concepts, including fractions, decimals, and the number system. In geometry, educators move beyond strategies for developing a familiarity with basic shapes and their properties to explore higher-order tasks that involve geometric thinking, measurement concepts, and proportional relationships. Using data as a context to support students' learning of these mathematical ideas, educators have the opportunity to explore real-world problems and collect, represent, and interpret data.

Understanding fraction concepts is a critical foundation for learning about proportional relationships and developing algebraic concepts. In this course, educators learn how to extend students' knowledge of whole numbers and basic operations—addition, subtraction, multiplication, division—to fractions and decimals. Educators learn instructional practices to help students understand, represent, develop, and engage in rational number operations with meaning, proficiency, and precision. They also investigate ways to foster deep conceptual understandings of ratios, rates, and proportional relationships, thus building in students the critical skill of proportional reasoning. Educators consider how proportional reasoning builds a bridge to the study of other important mathematical topics, including geometry, measurement, and data as well as the use of proportionality as a connecting thread throughout the elementary and middle math curriculum.