ORGANIZATION
OF THE LEARNING STANDARDS
Learning
Standards define what a child should know and be able to do in every class for
every subject. The Learning Standards for Mathematics are a connected body of
such mathematical understandings and competencies broken up class wise. They
describe a comprehensive base for all students stating the knowledge,
understanding and skills that they should acquire for much used life skills.
The Learning Standards give a common foundation for all students. However, all
students are not alike. The talent and interest of those who are gifted should
be kept engaged and those with special educational needs must be given the
support to acquire a good understanding of important mathematics.
The
Learning Standards for K.G. to class 8 have been organized into the following
five sections. The sections broaden the scope of school mathematics.
It is not acceptable for elementary school mathematics to be concentrated
solely on arithmetic or for high school mathematics to be concentrated solely
on algebra and geometry. Appropriate material from each section should appear
at each class level. Together, the sections describe the range of mathematics
important for today's students. Wherever possible, the sections are meant to be
taught and learnt in a integrated manner. Real mathematical problems rarely
involve just one section. Rather, they demand that the problem solver integrate
ideas from several sections to arrive at a meaningful result. A brief description of each section is as
follows -
I.
Numbers and Operations – This
section develops a sense of quantity, facility with computing and communication
in the language of numbers. It describes numbers, their properties,
relationships and calculations with them. It includes counting objects in a
collection, relating the numbers e.g. ordering, carrying out basic operations
on them and extending to complex situations gradually like factors, multiples,
ratios and so on. It includes properties, special numbers (1, 0, reciprocals,
inverses) and different kinds of numbers (integer, rational, real). Students
learn to think and communicate in the language of numbers (i.e. use various
notations, number sentences and verbal expressions for number sentences). They
become familiar with different techniques for computing algorithmic using paper
and pencil, mental, estimation. In the end, students have an understanding of
how simple elements give rise to a structure capable of representing relations
among quantities in the real world and in the imagination. This section
permeates all of mathematics.
II. Patterns
and Algebra – This
section describes patterns and relationships
using general arithmetic by using variables to range over the numbers. Patterns are a backbone of mathematics. The
patterns section explores informal patterns in early classes and formal numeric
patterns gradually. It helps in recognizing, explaining and extending the many
kinds of relationships among quantities. Thoughtful experiences with a variety
of patterns, formal and informal, helps students make patterns part of their
intellectual repertoire.
Algebra is
generalized arithmetic. It helps make the specific into universal, helps
describe situations, derive relationships with elegance and power, manipulate
expressions and find solutions. By itself it is the language of variables,
operations, and symbol manipulation. Starting with missing addend problems,
students slowly develop the ability to use algebra as a language. Every other
section uses algebra to symbolize, clarify and communicate thus integrating
this section with others. It is important, therefore, to use algebra in the
context of problems and situations arising in other sections. Specifically,
students need the tools of algebra (such as formulas, functions, and equations)
to describe
and clarify geometric relationships; and they need the vehicle of geometry to
provide graphic illustrations for algebraic relationships.
III.
Measurement – This section describes and compares everyday phenomena using direct or
indirect measurement. It is used in all occupations and in
everyday life to compare quantities. Work in measurement begins with comparison:
bigger-smaller, heavier-lighter, warmer-colder.
Numbers are assigned to quantitative aspects of the world by being
compared to a scale of non-standard units (e.g. paper clips, paces, heartbeats,
etc.) and then standard units such as international metric system. By focusing
on obtaining numbers through direct interaction with the universe, the
measurement section makes a physical connection between numbers and the world
through the action of the student. Students learn to create nonstandard units
to help with the comparison. Later, they learn about standard system of units
especially for time, distance, weight, volume, area and temperature. This
section is closely allied with geometry through measurement of length, area,
and volume. Measuring diverse quantities makes connections within mathematics,
especially to statistics, and outside, to the natural and social sciences.
IV. Geometry –This section links
mathematics to space and form in the world around us and in the abstract. In
this section students are exposed to and investigate two-dimensional and
three-dimensional space by exploring shape, area, and volume; studying lines,
angles, points, and surfaces; and engaging in other visual and concrete
experiences. In the early classes this process is informal and highly
experiential; students explore many objects and discover and discuss the
attributes of different shapes and figures. Older students gradually build on
this foundation of hands-on experiences. They become more familiar with the
properties of geometrical figures and get better at using them to solve
problems. They explore symmetry and proportion and begin to relate geometry to
other areas of mathematics - to the benefit of both. For example, graphical
representations of functions can help explain and generalize geometric
relationships while geometrical insights inform the study of functions. As
students become more familiar with geometrical figures, they are better
equipped for mathematical argumentation in that field. They focus on making
convincing arguments with a rigor appropriate to the situation rather than on
being forced into
two-column proofs. The goal is to develop fluency with basic geometrical
objects and relationships and to connect that fluency with spatial reasoning
and visualization skills.
V. Statistics – This section describes the pictorial representation of
data. It describes collecting, organizing,
representing, analyzing the data, making inferences which give an insight into
the data and solving problems involving uncertainty. In an age of
rapid communication and immediate access to information, data is abound.
Descriptive statistics help students learn to collect and organize information
in a variety of graphs, charts, and tables to make those data easier for the
students and others to comprehend. Students also learn to interpret data and to
make decisions based on their interpretations. Probability is a part of this
section because statistical data are often used to predict the likelihood of
future events and outcomes. Students learn probability, the study of chance, so
that numerical data can be used to predict future events as well as record the
past. A command of statistics and probability is essential in all aspects of
adult life.
No comments:
Post a Comment