MATH Connections

1
MATH Connections

• By The Hollys

2
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

3
Math Connections Description

• Philosophy
• History
• Design

4
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.

5
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.

6
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.

7
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).

8
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 termthat 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 1bgeneralizes 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?
9
Year 2
MATH Connections 2astarts 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
10
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 Euclids 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. InfinityThe Final
Frontier? Chapter 8. Axioms, Geometry, and Choice
11
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

12
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/iatorderse
  t.html

13
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 Theyve 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.

14
Publisher Information and
Web Sites

• http//www.its-about-time.com
• http//www.ithaca.edu/compass
• http//www.project2061.org/publications/textbook/d
  efault.htm
• http//www.ithaca.edu/compass/pdf/mathconx.pdf
  
• http//www.education-world.com/a_curr/curr021.shtm
  l

• Publisher
• IT's ABOUT TIME
• 84 Business Park Drive
• Armonk, NY 10504
• 888-698-TIME
• Email compass_at_ithaca.edu
•  

15
(No Transcript)
16
(No Transcript)
17
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.

18
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 wouldnt 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

19
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 Connections10
  
  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."

20
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 Globes 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.