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Educator Services Teaching & Learning Curriculum Resources
2010 Professional Development Institutes

Mathematics

Fractions for Elementary School Teachers

Course Description:

Teaching Fractions is an eight week online institute designed to promote the understanding of fractions for elementary school teachers both from a conceptual and a mechanical perspective. Participants will create a standards-based lesson, specific to their own grade level, to teach fractions to their own students. Institute topics include Moodle Orientation, Differentiated Instruction, Teaching Fractions, Preparing to Do Operations, Summing Up the Difference, Products, and Creating Lessons.

High School Mathematics: The Bird's View and the Frog's View

Course Description:

"Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time" (Freeman Dyson, 2009). This institute provides an intensive mathematics immersion experience by zooming into, and out of, various functions (linear, quadratic, exponential, logarithmic, trigonometric, polynomial, rational, etc.) to develop an in-depth and coherent understanding of high school algebra and geometry. Applications and topics in other strands will be explored on request. Participants will have a chance to experience high-level synthesis (Bird's view) as well as empirical problem solving (Frog's view). This course will be taught by active research scientists and is ideal for teachers teaching, or preparing students for, Algebra II, Pre-calc, AP Calc and beyond. The course models instruction based on the mathematics standards, and explores the topics of ongoing formative assessments, instructional differentiation, multiple representations, a variety of grouping strategies, student misconceptions, and remediation. Participants will practice multi-topic concept mapping, visual explanations, and challenging problems.

Middle School Mathematics: The Bird's View and the Frog's View

Course Description:

"Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. They delight in concepts that unify our thinking and bring together diverse problems from different parts of the landscape. Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time" (Freeman Dyson, 2009). This institute provides an intensive mathematics immersion experience that starts by exploring a connected sequence of foundational topics: real numbers, rate and speed, ratio, direct and inverse proportion. Then participants explicitly zoom into, and out of, topics in middle school algebra and geometry to develop an in-depth and coherent understanding of linear equations in two variables and systems of linear equations. Applications and topics in non-linear functions, geometry and other strands will be explored on request. Participants will have a chance to experience high-level synthesis (Bird's view) as well as empirical problem solving (Frog's view). The course models instruction based on the mathematics standards, and explores the topics of ongoing formative assessments, instructional differentiation, multiple representations, a variety of grouping strategies, student misconceptions, and remediation. Participants will practice multi-topic concept mapping, visual explanations, and challenging problems.

Reasoning and Problem Solving: Number Sense, Algebra, and Measurement

Course Description:

This institute focuses on developing and enriching teachers' toolkit of problem solving strategies through engaging participants in the process of inquiry while solving rich problems and tasks. The course emphasizes the importance of multiple solution methods and of various representations in organizing and displaying information in selected areas of number sense, algebraic reasoning, geometry, and measurement. It enhances and deepens participants' mathematics and pedagogical content knowledge in fundamental key mathematical ideas such as inverse operations, arithmetic vs. algebraic reasoning, algorithms for whole number computation, operations with integers, solving linear equations, meaning of rational numbers, operations with rational numbers, exponents and laws of exponents. Concepts such as area, the Pythagorean Theorem and performing constructions will be uncovered using various methods including hands-on explorations.

Teaching Advanced Mathematical Decision Making

Course Description:

This institute will prepare teachers to implement Advanced Mathematical Decision Making (AMDM) during the 2010-11 school year. AMDM is a mathematics course designed to follow Algebra I, Geometry, and Algebra II and emphasizes statistics and financial applications, as it prepares students to use algebra, geometry, trigonometry, and discrete mathematics to model a range of situations and solve problems. The institute facilitators, including experienced AMDM teachers, will help participants to develop the unique combination of mathematical content as well as pedagogical skills called for in implementing AMDM. Because of the challenging mathematical content and the course's unique instructional design participant teachers should have a strong mathematical background. Participants will be expected to attend two follow-up days, participate in a facilitated online community, and have access to a wide range of web resources.

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