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MATH Connections

- By The Hollys

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 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?

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

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

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/iatorderse

t.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 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.

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

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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.

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

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."

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.