Mathematics
The Illinois Learning Standards for Mathematics were
developed by Illinois teachers for Illinois schools. These
goals, standards and benchmarks are an outgrowth of the 1985
Illinois State Goals for Learning influenced by the latest
thinking in school mathematics. This includes the National
Council of Teachers of Mathematics; Curriculum and Evaluation
Standards for School Mathematics; ideas underlying recent
local and national curriculum projects; results of state,
national, and international assessment findings; and the work
and experiences of Illinois school districts and teachers.
Mathematics is a language we use to identify, describe and
investigate the patterns and challenges of everyday living.
It helps us to understand the events that have occurred and
to predict and prepare for events to come so that we can more
fully understand our world and more successfully live in it.
Mathematics encompasses arithmetic, measurement, algebra,
geometry, trigonometry, statistics, probability and other
fields. It deals with numbers, quantities, shapes and data,
as well as numerical relationships and operations. Confronting,
understanding and solving problems is at the heart of mathematics.
Mathematics is much more than a collection of concepts and
skills; it is a way of approaching new challenges through
investigating, reasoning, visualizing and problem solving
with the goal of communicating the relationships observed
and problems solved to others.
All students in Illinois schools need to have the opportunity
to engage in learning experiences that foster mastery of these
goals and standards. Knowledge of mathematics and the ability
to apply math skills to solve problems can be an empowering
force for all students—both while in school and later
in their lives. Students reaching these goals and standards
will have an understanding of how numbers are used and represented.
They will be able to use basic operations (addition, subtraction,
mulitiplication, division) to both solve everyday problems
and confront more involved calculations in algebraic and statistical
settings. They will be able to read, write, visualize and
talk about ways in which mathematical problems can be solved
in both theoretical and practical situations. They will be
able to communicate relationships in geometric and statistical
settings through drawings and graphs. These skills will provide
all Illinois students with a solid foundation for success
in the workplace, a basis for continued learning about mathematics,
and a foundation for confronting problem situations arising
throughout their lives.
Applications of Learning
Through Applications of Learning, students demonstrate and
deepen their understanding of basic knowledge and skills.
These applied learning skills cross academic disciplines and
reinforce the important learning of the disciplines. The ability
to use these skills will greatly influence students' success
in school, in the workplace and in the community.
Solving Problems
Recognize and investigate problems; formulate and propose
solutions supported by reason and evidence.
The solving of problems is at the heart of "doing mathematics."
When people are called on to apply their knowledge of numbers,
symbols, operations, measurement, algebraic approaches, geometric
concepts and relationships, and data analysis, mathematics'
power emerges. Sometimes problems appear well structured,
almost like textbook exercises, and simply require the application
of an algorithm or the interpretation of a relationship. Other
times, particularly in occupational settings, the problems
are non-routine and require some imagination and careful reasoning
to solve. Students must have experience with a wide variety
of problem-solving methods and opportunities for solving a
wide range of problems. The ability to link the problem-solving
methods learned in mathematics with a knowledge of objects
and concepts from other academic areas is a fundamental survival
skill for life.
Communicating
Express and interpret information and ideas.
Everyone must be able to read and write technical material
to be competitive in the modern workplace. Mathematics provides
students with opportunities to grow in the ability to read,
write and talk about situations involving numbers, variables,
equations, figures and graphs. The ability to shift between
verbal, graphical, numerical and symbolic modes of representing
a problem helps people formulate, understand, solve and communicate
technical information. Students must have opportunities in
mathematics classes to confront problems requiring them to
translate between representations, both within mathematics
and between mathematics and other areas; to communicate findings
both orally and in writing; and to develop displays illustrating
the relationships they have observed or constructed.
Using Technology
Use appropriate instruments, electronic equipment, computers
and networks to access information, process ideas and communicate
results.
Technology provides a means to carry out operations with
speed and accuracy; to display, store and retrieve information
and results; and to explore and extend knowledge. The technology
of paper and pencil is appropriate in many mathematical situations.
In many other situations, calculators or computers are required
to find answers or create images. Specialized technology may
be required to make measurements, determine results or create
images. Students must be able to use the technology of calculators
and computers including spreadsheets, dynamical geometry systems,
computer algebra systems, and data analysis and graphing software
to represent information, form conjectures, solve problems
and communicate results.
Working on Teams
Learn and contribute productively as individuals and as members
of groups.
The use of mathematics outside the classroom requires sharing
expertise as well as applying individual knowledge and skills.
Working in teams allows students to share ideas, to develop
and coordinate group approaches to problems, and to share
and learn from each other in communicating findings. Students
must have opportunities to develop the skills and processes
provided by team problem-solving experiences to be prepared
to function as members of society and productive participants
in the workforce.
Making Connections
Recognize and apply connections of important information
and ideas within and among learning areas.
Mathematics is used extensively in business; the life, natural
and physical sciences; the social sciences; and in the fine
arts. Medicine, architecture, engineering, the industrial
arts and a multitude of occupations are also dependent on
mathematics. Mathematics offers necessary tools and ways of
thinking to unite the concepts, relationships and procedures
common to these areas. Mathematics provides a language for
expressing ideas across disciplines, while, at the same time,
providing connections linking number and operation, measurement,
geometry, data and algebra within mathematics itself. Students
must have experiences which require them to make such connections
among mathematics and other disciplines. They will then see
the power and utility that mathematics brings to expressing,
understanding and solving problems in diverse settings beyond
the classroom.
Goals
Goal 6 - Number Sense  
Goal 7 - Estimation and Measurement
Goal 8 - Algebra and Analytical Methods
Goal 9 - Geometry
Goal 10 - Data Analysis and Probability
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