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Spring and Summer Content Institutes 2002

Mathematics

Elementary, Middle

24

Accelerating Mathematics for Grades 3-8 Teachers

This institute's objective is to provide teachers with a solid foundation of number sense, functions and algebra. The institute goals, objectives, and assessments are designed to increase algebraic thinking through the understanding of rational numbers and operations, representation of quantitative relationships and symbolic expressions in problem-solving contexts. Emphasis will be on mathematical models to represent and understand quantitative relationships utilizing the Singapore Mathematics Curriculum. Participants will analyze change in various contexts, represent problems and solutions using algebraic symbols, and apply algebraic concepts to other strands.

Elementary, Middle

25

Leadership Program in Discrete Mathematics

This institute will focus on discrete mathematical topics appropriate for the K-8 classroom. The institute will address four of the major themes of discrete mathematics: finding the best solution using algorithms; using discrete mathematical models such as graphs or networks; systemic listing and counting (combinatorics); and applying iterative patterns and processes. Participants will solve a number of real-world problems, such as finding the most efficient route to deliver mail or the smallest amount of pipes to provide water for a system. Participants will explore a variety of contexts including patterns with networks, colors, numbers, letters and shapes.

Middle

26

Accessing the Mathematics Framework through Content and Integration of Technology

This institute focuses on the content and learning standards embedded in the middle school Mathematics Curriculum Framework strand: Patterns, Relations, and Algebra. Participants will conduct an investigation to determine the relationship between two variables; observe patterns in graphs and tables; develop a deeper understanding of linear situations; and use various functions of the TI 83 Plus graphing calculator. Web-based technologies will be utilized to assist teachers in the development of content knowledge and the use of diversified instructional and inclusionary teaching strategies.

Middle

27

Algebraic and Geometric Topics from the Massachusetts Framework for Middle School Mathematics Teachers

Participants will learn how algebraic algorithms relate to systems of equations, ratio and proportions, and equalities and inequalities as taught in middle school. The institute will focus on properties of graphs of linear functions, data collection techniques, and the central tendency theory. The institute will also focus on properties of the rates of change, volume, order of operations, counting principles and graph theory and how they relate to problem solving techniques. These concepts will be taught through discussion, hands-on activities, and reading assignments. For example, properties of angles, triangles and applications of reflection will be explained through the construction of a kaleidoscope from two mirrors.

Middle

28

Algebraic Thinking in the Middle School: Patterns and Functions

The goal of this institute is to help teachers of middle school mathematics develop an understanding of the core foundational ideas of algebraic thinking and become more effective in helping their students learn algebra. Participants will conduct open-ended standards-based mathematical investigations to develop profound understandings of patterns, functions, and relations. They will apply their understanding of algebraic thinking with their understanding of how students learn as they develop algebra units to use with their students.

Middle

29

Developing Algebraic Thinking in the Middle School

The primary goal of the institute will be to strengthen middle school teachers' content knowledge in the area of algebraic thinking. Informal exploration emphasizing physical models, data, graphs, and tables will enable participants to develop an understanding of patterns, relations, functions, and the language of algebra. Instruction will focus on real-world situations to demonstrate how algebra provides tools for solving real-life problems. The institute will model ways in which manipulatives and technology can effectively be used to deepen understanding of mathematics content. Algebra models, graphing calculators, spreadsheet applications, online interactive tools, and simulations will be utilized to explore key mathematics concepts. Participants will be provided with exemplary models of instruction and assessment, which will be incorporated into the design of a curriculum unit.

Middle

30

Maritime Mathematics

The operation of a ship at sea, as well as the general skills necessary for vessel design, construction, and maintenance apply many principles of mathematics. The Institute will include hands-on workshops, both on the water on the Schooner Ernestina and ashore in New Bedford and at Bridgewater State College. The workshops will include topics such as applied mathematics focused on navigation, scientific sampling, spar construction, buoyancy and the technology of a 19th century schooner. Participants will develop a comprehensive knowledge of mathematics as it relates to the learning standards in the classroom.

Middle

31

Mathematics for Middle School Teachers

This institute will focus on providing a theoretical background to mathematics and its practical applications for middle school teachers who are not certified in mathematics. The content of the Institute will focus on: number sense and theory; patterns and relationships including sequences, constant growth, and variables; geometry and measurement including categorization of shape and geometric problem solving; statistics and probability; problem solving and algebraic application; analyzing and explaining including reductionism and probability; computing and estimating; and the description of graphs, tables, and relationships. Participants will develop their own mathematics project with the assistance of the instructors including a graphics artist/animator.

Middle

32

The Missing Link

Pairs or teams of middle school classroom and special education teachers are invited to an intensive institute addressing proportionality and similarity; pattern and function; polygons and angles; and sampling and probability. Institute participants will solve problems involving proportional relationships and units of measurement. Participants will identify polygons based on their properties, including types of interior angles, perpendicular or parallel sides, and congruence of sides. Participants will also use appropriate ratios to represent the probability of the outcome and associate the probability with the likelihood of the event.

Middle

33

Promoting Algebraic Thinking

This program will focus on improving the knowledge of mathematical content through problem-solving and real life applications. The institute will focus on those areas that prepare for the learning of algebraic concepts, as well as areas that make use of algebraic ideas. The central focus of the course will be patterns, functions and algebra. To ensure the background necessary for the understanding of algebra, topics will be included from the number sense and operations strands of the Framework. Particular emphasis will be placed on those mathematical topics that have shown up as weaknesses based on the item-analysis of MCAS results.

Middle

34

Teacherline and Technology Tools - T3

The institute will allow teams of middle school math, science, and special education teachers to deepen their understanding of geometry and physical science content. Participants will be able to use technology as a tool for collecting and analyzing data, modeling real world functions, and problem-solving. Concepts and skills in geometry to be learned include: formulating and testing conjectures about shapes that tessellate; investigating trigonometric ratios in right triangles; investigating right triangle relationships; and exploring proofs of the Pythagorean Theorem. Concepts and skills to be learned in physical science include: measuring volume and mass; explaining the motion of an object; interpreting distance and time graphs; and differentiating between potential and kinetic energy.

Middle

35

Unlocking Linear Equations

This institute will have two primary foci: solving linear equations in two variables and solving systems of linear equations. Participants will explore linear equations in two variables through the use of the Cartesian coordinate system, tables and graphs, slopes and linear equations. They will then analyze and evaluate systems of linear equations by utilizing the following methods: graphical, elimination, substitution, and use of a graphing calculator. This institute will provide teachers with the content tools to explain algebraic concepts at the student's point of readiness and through the student's learning preference, thus meeting the needs of the diverse learning population. Participants will also receive training in adaptive strategies to make content accessible to all students.

Middle, High

36

Increasing Secondary MCAS Performance Using Innovative Ways of Teaching Pre-Algebra through Geometry (Site A)

This institute is intended to provide teachers with insights into content topics that students may have difficulty understanding. The concepts are from pre-algebra, algebra, and geometry. Teachers will be provided with innovative ways to teach these critical topics to help students better understand the concepts. In particular, teachers will learn how graphing calculators can assist students in visualizing functions and relations. Geometric figures will be investigated using the Geometer's Sketch Pad, revealing the underlying relationships that lead to the specific properties of various figures.

Middle, High

37

Increasing Secondary MCAS Performance Using Innovative Ways of Teaching Pre-Algebra through Geometry (Site B)

The priority of this institute is to increase teacher content knowledge and expertise with innovative teaching strategies in pre-algebra, algebra, geometry, and probability and statistics. Teachers will be shown how graphing calculators can assist students in visualizing functions and relations. They will learn how geometric figures can be investigated using the Geometer's Sketch Pad revealing the underlying relationships that lead to the specific properties of various figures.

Middle, High

38

Preparing Middle School and High School Students for Success in Mathematics

The mathematical content focus of this institute will be learning standards that cut across the Patterns, Relations & Algebra and the Geometry strands. Instructional strategies such as learning stations, projects and math labs will focus on meeting the needs of all students. The use of multiple representations for data and problem solving will be emphasized throughout the institute. Graphing calculators will be used where appropriate. TI-83's will be available for participants to borrow. All levels of calculator expertise (including beginners) will be accommodated.

High

39

Investigating Functions in the Real World

This institute is designed to (1) strengthen content knowledge in the patterns, relations, and algebra strand of the mathematics framework and, (2) model effective classroom instructional techniques for improving student learning experiences. While developing a deeper understanding of mathematical functions, participants will be engaged in inquiry based, high quality math tasks and learn how to adapt these to meet the needs of a diverse student population.

High

40

Unlocking Linear and Quadratic Equations

This institute has two primary foci: linear equations in two variables and quadratic equations. Participants will: analyze linear equations through numerical, graphical, and algebraic methods; explore solution space of systems of linear equations and inequalities. Then the participants will engage in understanding quadratic equations through factoring, completing the square and deriving/using the quadratic formula. They will make connections between geometrical/algebraic interpretations and engage in the formulation, exploration and solution of application problems and open-ended projects that exemplify the concepts and methods of the institute topics. This institute will prepare teachers to explain algebraic concepts at the student's point of readiness and through the student's learning preference, thus making content accessible to the diverse learning population.






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