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By: The Holly’s

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Goals of Math Connections Learn More Mathematics Be Able To Apply Math In Real-World Settings Perform Better On Standardized Tests Succeed In Mathematics Develop Higher Order Thinking Skills

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Math Connections Description Philosophy History Design

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Philosophy Using the NCTM standards as a guideline, MATH Connections blends algebra, geometry, probability, statistics, trigonometry and discrete mathematics into a meaningful package that is interesting and accessible to all students. The text materials are designed to provide students with mathematical experiences that excite their curiosity, stimulate their imagination and challenge their skills. All the while, the primary concern is the conceptual development of the learner while focusing on these goals: 1) mathematics as problem solving; 2) mathematics as communication; 3) mathematics as reasoning; and 4) mathematics as making connections. MATH Connections is based on topical (rather than problem) themes. That is, it is concept driven. It uses a common thematic thread that connects and blends many mathematical topics that traditionally have been taught separately and independently. This approach emphasizes the unity and interconnectedness among mathematical ideas.

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History MATH Connections, a Secondary Mathematics Core Curriculum, is a project undertaken with a five-year National Science Foundation (NSF) grant awarded in 1992 to the Connecticut Business and Industry Association (CBIA) Education Foundation. The overall mission of the project was to develop a core curriculum for grades 9-12 that opens the concepts of higher mathematics to all students and inspires new interest and excitement in mathematics for both students and faculty. Following four years of intensive field-testing, MATH Connections is now available.

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Design of Textbooks for MATH Connections This integrated series is designed for grades 9-11. Each grade level is divided into two books, a and b. The books are labeled 1a, 1b, 2a, 2b, 3a, and 3b. Each book is divided into chapters which are divided into several sub sections. This is a three year curriculum. Year 1 material is heavily concentrated in algebra, Year 2 material is heavily concentrated in geometry, and Year 3 contains considerable material in pre-calculus and discrete mathematics. MATH Connections usually does not contain traditional drill and practice problems.

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Design of Textbooks for MATH Connections In each chapter, students read a profile about an individual who uses mathematics in his or her everyday work. In each section of the chapter, students (1) read expected learning outcomes; (2) are introduced to a concept by thinking about what they already know, which prompts discussion; (3) read commentary and explanations to support the discussion; and (4) answer questions in the sections problem set. Each section is divided into chapters and each chapter is divided into several sub-sections. Each sub-section begins with stated learning objectives for that subsection and several student activities within explorations followed by a problem set. The activities are coded with icons indicating either a discussion topic, a writing topic, or an activity that should be done before proceeding. Some sub-sections contain ideas for longer student projects. The margins of the student materials contain Thinking Tips, About Symbols, and About Words (notes that detail how some everyday words have more specific meanings in mathematics). Appendices for each level detail technology information helping students learn to use a TI-82 (83) Graphing Calculator, use a spreadsheet, and program a TI-82 (83).

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Year 1 MATH Connections 1a begins and ends with data analysis. It starts with hands-on data gathering, presentation, and analysis, then poses questions about correlating two sets of data. This establishes the goal of the term—that students be able to use the linear regression capabilities of a graphing calculator to do defensible forecasting in real-world settings. Students reach this goal by mastering the algebra of first-degree equations and the coordinate geometry of straight lines, gaining familiarity with graphing calculators. Chapter 1. Turning Facts into Ideas Chapter 2. Welcome to Algebra Chapter 3. The Algebra of Straight Lines Chapter 4. Graphical Estimation MATH Connections 1b generalizes and expands the ideas of Book 1a. It begins with techniques for solving two linear equations in two unknowns and interpreting such solutions in real-world contexts. Functional relationships in everyday life are identified, generalized, brought into mathematical focus, and linked with the algebra and coordinate geometry already developed. These ideas are then linked to an examination of the fundamental counting principle of discrete mathematics and to the basic ideas of probability. Along the way, Book 1b poses questions about correlating two sets of data. Chapter 5. Using Lines and Equations Chapter 6. How Functions Function Chapter 7. Counting Beyond 1, 2, 3 Chapter 8. Introduction to Probability: What Are the Chances?

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Year 2 MATH Connections 2a starts with the most basic ways of measuring length and area. It uses symmetries of planar shapes to ask and answer questions about polygonal figures. Algebraic ideas from Year 1 are elaborated by providing them with geometric interpretations. Scaling opens the door to similarity and then to angular measure, which builds on the concept of slope from Year 1. Extensive work with angles and triangles, of interest in its own right, also lays the groundwork for right angle trigonometry, the last main topic of this book. Standard principles of congruence and triangulation of polygons are developed and employed in innovative ways to make clear their applicability to real-world problems. Chapter 1. The Building Blocks of Geometry: Making and Measuring Polygons Chapter 2. Similarity and Scaling: Growing and Shrinking Carefully Chapter 3. Introduction to Trigonometry: Tangles with Angles MATH Connections 2b begins by exploring the role of circles in the world of spatial relationships. It then generalizes the two-dimensional ideas and thought patterns of Book 2a to three dimensions, starting with fold up patterns and contour lines on topographical maps. This leads to some fundamental properties of three-dimensional shapes. Coordinate geometry connects this spatial world of three dimensions to the powerful tools of algebra. That two-way connection is then used to explore systems of equations in three variables, extending the treatment of two variable equations in Year 1. In addition, matrices are shown to be a convenient way to organize, store, and manipulate information. Chapter 4. Circles and Disks Chapter 5. Shapes in Space Chapter 6. Linear Algebra and Matrices

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Year 3 MATH Connections 3a examines mathematical models of real-world situations from several viewpoints, providing innovative settings and a unifying theme for the discussion of algebraic, periodic, exponential, and logarithmic functions. These chapters develop many ideas whose seeds were planted in Years 1 and 2. The emphasis throughout this material is the utility of mathematical tools for describing and clarifying what we observe. The modeling theme is then used to revisit and extend the ideas of discrete mathematics and probability that were introduced in Year 1. Chapter 1. Algebraic Functions Chapter 2. Exponential Functions and Logarithms Chapter 3. The Trigonometric Functions Chapter 4. Counting, Probability, and Statistics MATH Connections 3b begins by extending the modeling theme to Linear Programming, optimization, and topics from graph theory. Then the idea of modeling itself is examined in some depth by considering the purpose of axioms and axiomatic systems, logic, and mathematical proof. Various forms of logical arguments, already used informally throughout Years 1 and 2, are explained and used to explore small axiomatic systems, including the group axioms. These logical tools then provide guidance for a mathematical exploration of infinity, an area in which commonsense intuition is often unreliable. The final chapter explores Euclid’s plane geometry, connecting his system with many geometric concepts from Year 2. It culminates in a brief historical explanation of Euclidean and non- Euclidean geometries as alternative models for the spatial structure of our universe. Chapter 5. Optimization: Math Does It Better Chapter 6. Playing By the Rules: Logic and Axiomatic Systems Chapter 7. Infinity—The Final Frontier? Chapter 8. Axioms, Geometry, and Choice

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Teacher Support And Resources Teacher Resources: The teacher resource book is a collection of assessment tools with a variety of quizzes, tests, and exams. Also included are Answer Keys for all assessments, as well as the answer keys for the Practice Problems (Practice Problems are a separate volume). Graphs and Tables are found at the end of the book, providing blackline masters for any charts or diagrams the teacher might want to make into transparencies or use in other ways. The MATH Connections Teacher Edition covers the program soup-to-nuts. It contains background on the program and philosophy. It also contains solid information to help you teach the program. This includes pacing guides, observations and comments from MATH Connections' classroom teachers, and a page-by-page commentary on the entire program. The commentary contains not only the answers, but the rationale as well. The Teacher Edition is three-hole punched with the teacher commentary next to the student text, allowing you to slip out only the pages you need for class

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Teacher Support And Resources Books 1a, 1b, 2a, 2b include: 1) Assessments A & B, 1 in-depth Exam per chapter, and 2 Quizzes for each section 2) Outcome – based Assessments on Learing Objectives: 3 Tests for each chapter and 1 Quiz for each section 3) Answer Keys: for all Assessments and Practice Problems 4) Graphs & Tables: for printing or making transparencies Books 3a, 3b include: 1) Assessments A & B, 1 in-depth Exam per Chapter, and 2 Quizzzes for each Section Ordering Textbooks: go to http://www.its-about time.com/iathome/iatorderset.html

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How Project 2061 Addresses MATH Connections The idea sets of functions, variables and operations each had an overall rating of fair and a rating of some potential for learning to take place across all the instructional categories. 11 subcategories out of 21 of the first 6 instructional categories did satisfactory in the average ratings The subcategories of Alerting Teacher to Student Ideas, Connecting Standards Ideas and Encouraging Students to Think about What They’ve Learned did the poorest across all the idea sets Some of the best rated subcategories were Justifying Sequence of Activities, Introducing Terms and Procedures, Demonstrating/Modeling Procedures and Providing Practice.

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Publisher Information and Web Sites Publisher: IT's ABOUT TIME 84 Business Park Drive Armonk, NY 10504 888-698-TIME Email: compass@ithaca.edu http://www.its-about-time.com http://www.ithaca.edu/compass http://www.project2061.org/public ations/textbook/default.htm http://www.ithaca.edu/compass/p df/mathconx.pdf http://www.education- world.com/a_curr/curr021.shtml

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Math Correlation to New York State Mathematics Curriculum Framework Math Connections are associated with the Content Standards and Performance Indicators for Math Level A and Math Level B (Refer to handout)There are two levels of association. The core concepts and skills of each section are associated with NY State curriculum and are listed in the “focus” column. The “included” column indicates the Performance Indicators that are included in the section as prior knowledge or are being introduced at the exploration level of learning.

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Case Study: Eleanor Ferri Portsmouth, RI Implementation Site: Portsmouth High School - 900 Students Number of students presently using MATH Connections: over 100 Number of teachers presently using MATH Connections: 3 Implemented 1998 Reasons for selection The results from the previous years of State testing indicated they needed a change to their approach It was a data-driven, problem-based approach After visiting schools- and talking to the teachers and students who were using this program – the search committee felt Math Connections had the elements they wanted “Our school went from around 14 th place overall in the State to #2 Overall, and the #1 position in Problem Solving. The teachers have told me that they wouldn’t give MATH Connections up for anything. We began a pilot with our lowest level students, but now we want to place some of our regular Algebra 1 students into the program too. What I have seen with these students in MATH Connections is that many of them are now far above our regular students who are not in MATH Connections. And to think that these were the students who used to be completely turned off to math.” – Eleanor Ferri, Math Chairperson

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Case Study: Nancy Nichols Saugus, Massachusetts Implementation Site: Saugus High School - 910 Students Number of students presently using MATH Connections: 300 Number of teachers presently using MATH Connections:10 Recent HS Adoption: MATH Connections - three levels this year Reasons For Selection: Program aligns with the Massachusetts Curriculum Frameworks Reasonable reading level Technology integrated as a tool "The real-world scenario of a problem-solving context makes math meaningful to students. They understand through application and these threads of a theme are woven through the topics to provide a bigger picture. Students performed in a much stronger fashion on our MCAS test and investigated a wide spectrum of concepts spanning over a two-year course. We have been able to shift our least abstract learners in a positive direction."

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Press Clippings The Boston Globe: In Hartford, Connecticut, students enrolled in Math Connections scored slightly higher on their SATs than students not enrolled. Also stated in this article is how the curriculum gives students a clear idea of math is used in the work place as well as daily lives. Hartford Courant: This article correlates to the Boston Globe’s article. There is a chart provided that compares the average SAT scores for Manchester, state and nation students. They attributed the improvement in math scores in part to the Math Connections program, a school wide integrated math program they started four years ago. Rather than teach algebra to freshman, geometry to sophomores, and algebra 2 to juniors, for example freshman will be taught a combination of algebra and geometry. This way learning is not done in vacuum. The Day: Math Connections answered the “When are we ever going to use this?” question due to the activity based lessons that involve real life situations to teach math.

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