Transcript Math Connections

By: The Holly’s
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
Math Connections Description
Philosophy
History
Design
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.
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.
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.
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).
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?
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
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 nonEuclidean 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
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
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
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.
Publisher Information and
Web Sites
http://www.its-about-time.com
Publisher:
IT's ABOUT TIME
84 Business Park Drive
Armonk, NY 10504
888-698-TIME
Email:
[email protected]
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.educationworld.com/a_curr/curr021.shtml
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.
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 14th 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
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."
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.