Monday 9 November 2015
MATHEMATICIANS STORIES
Mary Somerville
Born 1780 in Burntisland, Scotland
Examples of Contribution to Mathematics: algebra, differential and
integral calculus
Mary was one of the world's first famous female mathematicians. She became interested in mathematics, and desperately wanted to study it, at a time when it was not considered acceptable for a woman to do so. She bought books on algebra and geometry and read them at night. Despite disapproval from the people around her, she persisted with her struggle to learn. Later in her life she began to solve problems in a magazine, and won a prize for her solution to an algebra problem. She went on to write several books about mathematics and science. Later in her life, she reflected on "the long course of years in which I had persevered almost without hope. It taught me never to despair" ( p.6).
"Mary Somerville used an approach to her work that is useful today. If she couldn't find the key to unlock a difficult problem she stopped work and turned to the piano, her needlework, or a walk outdoors. Afterward, she returned to the problem with her mind refreshed and could find the solution. If she could not understand a passage in her reading, she would read on for several pages. Then, going back, she could often understand what was meant in the part which had been confusing" (p.12).
Perl (1993)
Maria Agnesi
(1718-1799) Italy
Examples of Contribution to Mathematics: calculus
"Maria was a child prodigy, but was also shy. She stayed at home, teaching the younger children and following her own studies. When her mother died after giving birth to twenty-one children, Maria took over the running of the household. At the age of twenty she started a ten year project, a book bringing together the work on calculus of Leibnitz and Newton titled Analytic Institutions. Sometimes she would have trouble with a problem. But her mind went on working even in her sleep; she would sleep-walk to her study and back to bed. In the morning, she would find the answer to the problem waiting on her desk. Her book made her famous; she was living proof of what she had argued at nine years old [that women had a right to study science]. But Maria had other interests in her life apart from mathematics. She had always worked with the poor people in her area, and she had asked her father for separate rooms and turned them into a private hospital. She worked at the hospital (and another) until she died at the age of eighty-one. Maria Agnesi wrote an important book on mathematics, as well as another unpublished book. She ran a household of over twenty people, and she worked for people who had not had her luck and opportunities. Each one of these things was remarkable, but she did them all."
(Lovitt and Clarke, 1992, p.560)
Mary Everett Boole
Born 1832 in England and lived in Poissy, France as a child
Examples of Contribution to Mathematics:
geometry of angles and space; string geometry (curve stitching), mathematical psychology (understanding how people learn mathematics)
As a young girl, Mary was very compassionate towards animals. Perl reported that she frequently rescued insects that had been hurt by frost or rain, and nursed them back to health. As an adult, she worked as a librarian in a women's college, and showed the same compassion in becoming a friend and mentor to the students. She invited students to discussion sessions about mathematics and science, and one of these students later wrote; "I found you have given us a power. We can think for ourselves, and find out what we want to know" (p.50). Even as an old lady, during World War I, Mary opened her house to people who needed to "find a quiet place for an hour, away from the turmoil of a country at war and the terrible news in the newspapers" (p.55).
Perl (1993)
SIR ISAAC NEWTON
"We all have something within us which helps us, guides us, gives us the conscience to know what is right and wrong. This "something" also gives us knowledge and wisdom. Whenever we cannot think of a solution to a problem we sit still and calm our mind. Very often the answer will come in a moment of intuition. Sir Isaac Newton, after thinking for some time on the effect of gravity, could not solve the problem. So Newton went for a walk to relax and when sitting quietly under an apple tree, saw an apple fall down; in a flash of understanding Newton understood the law of gravity which governs the movement of minute particles as well as the stars and planets. Many great scientific discoveries have been made not during serious thinking or when doing a lot of calculations but while the mind is relaxed. This is when intuition starts."
Thursday 5 November 2015
online assignment
ONLINE
ASSIGNMENT
Honey.B.H
Mathematics
REG No.18014368002
MATHEMATICS LABORATORY
Mathematics
laboratory is very important one. It is true that the mathematics laboratory
has not yet received the same general acceptance as a science laboratory. This
is probably because the mathematics teacher themselves has not recognized the
significance of mathematic laboratory as the science teacher have. Actually
most mathematical teachers have been very passive as to this respect.
The
mathematics laboratory provides an opportunity for individualized instructions,
introduction to the use of calculators and computers etc. It is a setting with
in which students can develop their independent study programmes. The literal
meaning of the word laboratory is a room where a group of pupils learns the
subject matter actually performing experiments. The laboratory approach
embodies the concepts of active learning, pupil’s involvement and participation
and relevance. Nowadays laboratory approach to mathematics instruction is being
used effectively in many schools.
NEED AND SIGNIFICANCE OF MATHEMATICS LABORATORY
Recently
laboratory work in mathematics is receiving increasing attention. The
underlying idea of a mathematical laboratory is that pupils will develop new
concepts and understandings meaningfully through experimental activities
dealing with concrete situations. It is particularly difficult to understand
mathematical concepts as they are abstract in nature. They can be learned
better through observation of the concrete situations and experiments and
manipulations of concrete objects. Activities such as measuring and drawing,
counting weighing, averaging and estimating, taking the readings from
instruments, recording, comparing, analyzing, classifying and checking data,
working with data and so on will involve the use of physical instruments and
can be labeled as laboratory work.
The activities involved in
laboratory work in mathematics fall broadly into two classes namely
‘demonstrations’ and ‘experimental activities’. However, these two categories
lie not mutually exclusive. In ‘demonstration’ some physical instrument or
device is used to illustrate and clarify the explanation of a mathematical
concept or a method.
Experimental activities include the
kind of activities which are carried on individually or by small groups working
together and are primarily aimed at helping experimenters themselves to
understand concepts/ideas clearly. In the high school mathematics, properties
of geometric figures and concepts of distant, angles weights, areas volumes and
loci etc. can be given a more vivid impact through experimental activities than
through any other means. All these will be more effective if the model, etc are
constructed by the learners themselves. They may be motivated to prepare
learning materials under the guidance of the teacher.
IMPORTANCE OF MATHEMATICS LABORATORY
Mathematics
laboratory in a school is very important and useful. The importance of
mathematics laboratory can be enumerated as follows.
I.
Habits of critical
thinking and logical reasoning can be developed.
II.
Complex theoretical
concepts can be made clear by performing suitable experiments.
III.
Learning of subject
matter can be given a practical shape.
IV.
Practical mindedness
can be developed among the students.
V.
Interest in learning
mathematics can be developed.
VI.
Scientific attitude or
temperament can be developed among the students.
VII.
Bookish knowledge of
the students can be correlated practically with their daily life.
VIII.
Learners can be enabled
to construct mathematical knowledge on their own.
Functions of Mathematical Laboratory
The primary functions of a mathematics
laboratory are to,
I.
Make mathematics
teaching and learning and purposeful for the students.
II.
Provides activities
that arouse the curiosity of the students and maintain their interest in
learning.
III.
Enable students to
develop proper skills in handling equipment and gadgets.
IV.
Help the students
develop powers of observation, analysis and drawing inferences.
V.
Make students
appreciate the practical applicability of mathematical principles and laws.
VI.
Concretise the abstract
mathematical concepts.
VII.
Help the child develop
the ability for keen observation.
VIII.
Develop in pupils a
positive attitude towards problem solving.
Materials and Equipments for the
Mathematical Laboratary
For
the effective functioning of a mathematics laboratory, it should be well
equipped. A mathematics laboratory may contain the following type of materials
and equipments.
Materials
I.
Concrete Materials
II.
Tracing Materials
III.
Pictures and Charts
IV.
Models
Instruments
and Equipments
I.
Drawing instruments
II.
Weighing and Measuring Instruments
III.
Surveying Instruments
IV.
Projected aids
V.
Proportional Dividers
VI.
Computing Devices
Calculators
Calculators
are very helpful in doing complex computations with greater speed and accuracy.
An advantage of calculators over computers is that they are smaller in size and
lend themselves to systematic use of calculators should be explicitly planned
for by the teacher. The use of calculators should be restricted until the
children understand the basic ideas behind the operations particularly the
concept of place value in simple calculations. As the students move to higher
classes they may be trained to make use of the various function keys to find
the required answer. The teacher should plan the use of calculators in such a
way that its use should result in better clarify of concepts and should provide
enough opportunities for mathematical exploration.
Computer
In
this technological age one cannot under estimate the role of computers in
mathematical work. A computer is an effective device for storing information.
Analyzing and interpreting data. So, it is desirable to have a computer in the
mathematical laboratory.
Conclusion
Mathematics
laboratory is very important for teachers and students. Which provide an
opportunity for individualized instructions, instructions to the use of
calculators and computers. A teacher of mathematics can use his discretion in
selecting, the instruments to equip the mathematics laboratory. The type of
instruments and materials for a mathematics laboratory, to a great extent,
depends upon the needs of the students and the nature of the mathematical
activities carried out there.
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