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COURSE A4
Pedagogy of Teaching Mathematics
(B Ed Special Education – Hearing Impairment/
B Ed Special Education-- Learning Disability
University of Mumbai
TOPIC : 2.1. Aims and Objectives of Teaching Mathematics
Dr.Amit Hemant Mishal,
Associate Professor
CCYM’S Hashu Advani College of Special Education
https://www.hashuadvanismarak.org/hacse/introduction.html
Dr.Amit Hemant Mishal, Associate Professor 1
NCF 2005 -MATHEMATICS
• The teaching of mathematics should
-enhance the child’s resources to think and reason, to visualise and handle
abstractions, to formulate and solve problems.
-This broad spectrum of aims can be covered by teaching relevant and
important mathematics embedded in the child’s experience.
• Succeeding in mathematics should be seen as the right of every child.
For this, widening its scope and relating it to other subjects is essential.
• The infrastructural challenge involved in making available computer
hardware, and software and connectivity to every school should be
pursued
• Some problems in school Mathematics education
• 1. A majority - sense of fear /failure . Give up early / drop out
• 2. Curriculum is disappointing
• 3. Problems, exercises, methods of evaluation – mechanical, repetitive, much
emphasis on computation. Areas of Mathematics such as spatial thinking are not
developed enough in the curriculum.
• 4. Teachers lack confidence, preparation and support.
• Students feel need to solve such problems, that teachers & students find it worth
their time and energy to address these problems.
• Twin concerns of Mathematics curriculum
• What can mathematics education do to engage the mind of every student?
• How can it strengthen the student's resources?
• Developing children's abilities for mathematisation -main goal
• Narrow aim - to develop 'useful' capabilities, those relating to numeracy–
numbers, number operations, measurements, decimals and percentages.
• Higher aim - to develop child's resources to think and reason mathematically,
to pursue assumptions to their logical conclusion and to handle abstraction.
Includes a way of doing things, ability and attitude to formulate and solve
problems.
• Should be ambitious, in sense ,it seeks to achieve higher aim mentioned
above, rather than only narrower aim.
• Be coherent in sense- variety of methods / skills available piecemeal (in
arithmetic, algebra, geometry) cohere into an ability to address problems that
come from other
Pre-primary stage
• At the pre-primary stage, all learning occurs through play rather than through
didactic communication.
• Rather than the rote learning of the number sequence, children need to learn and
understand, in the context of small sets, the connection between word games and
counting, and between counting and quantity.
• Making simple comparisons and classifications along one dimension at a time, and
identifying shapes and symmetries, are appropriate skills to acquire at this stage.
• Encouraging children to use language to freely express one's thoughts and
emotions, rather than in predetermined ways, is extremely important at this and
at later stages.
• Having children develop a positive attitude towards, and a liking for, Mathematics
at the primary stage is as important, if not more than the cognitive skills and
concepts that they acquire.
• Mathematical games, puzzles and stories help in developing a positive attitude and
in making connections between mathematics and everyday thinking.
• It is important to Problem posing √ If you know that 235 + 367 = 602, how much is
234 + 369? How did you find the answer? √ Change any one digit in 5384.
• Did the number increase or decrease? By how much? 45 note that mathematics is
not just arithmetic.
• Besides numbers and number operations, due importance must be given to shapes,
spatial understanding, patterns, measurement and data handling.
• The curriculum must explicitly incorporate the progression that learners make
from the concrete to the abstract while acquiring concepts.
• Apart from computational skills, stress must be laid on identifying, expressing and
explaining patterns, on estimation and approximation in solving problems, on
making connections, and on the development of skills of language in
communication and reasoning.
Upper Primary
• Students get first taste of power of Mathematics through application of
powerful abstract concepts that compress previous learning and experience.
• Enables them to revisit/consolidate basic concepts and skills learnt at primary
stage, which is essential from view of achieving universal mathematical
literacy.
• Students are introduced to algebraic notation and its use in solving problems
and in generalization , to systematic study of space/shapes, and for
consolidating their knowledge of measurement.
• Data handling, representation and interpretation form a significant part of the
ability of dealing with information in general, which is an essential 'life skill'.
• Learning at this stage also offers an opportunity to enrich students' spatial
reasoning and visualization skills.
SECONDARY STAGE
• Students begin to perceive the structure of Mathematics as a discipline.
• They become familiar with characteristics of mathematical communication: carefully
defined terms and concepts, the use of symbols to represent them, precisely stated
propositions, and proofs justifying propositions.
• These aspects are developed particularly in area of geometry.
• Students develop their facility with algebra, important not only in application of
mathematics, but also within mathematics in providing justifications and proofs.
• At this stage, students integrate many concepts and skills that they have learnt into a
problem-solving ability.
• Mathematical modelling, data analysis and interpretation taught at this stage can
consolidate a high level of mathematical literacy.
• Individual and group exploration of connections and patterns, visualisation and
generalisation, and making and proving conjectures are important at this stage, and
can be encouraged through the use of appropriate tools that include concrete
models as in Mathematics laboratories and computers
Higher Secondary Stage
• Aim is to provide students with an appreciation of wide variety of the application
of Mathematics, and equip them with the basic tools that enable such application.
• A careful choice between often conflicting demands of depth versus breadth needs
to be made at this stage.
• Rapid explosion of Mathematics as a discipline, and of its range of application,
favors an increase in the breadth of coverage.
• Such increase must be dictated by mathematical considerations of importance of
topics to be included.
• Topics that are more naturally province of other disciplines may be left out of the
Mathematics curriculum.
• Treatment of topics must have an objective, that is, communication of
mathematical insights and concepts, which naturally arouse the interest and
curiosity of students.
References:
• https://ncert.nic.in/pdf/nc-framework/nf2005-english.pdf Retrieved on
16.4.2024)
THANK YOU!!!!!!!!!!!!!!!!!

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2.1 Aims and Objectives of Teaching Mathematics.pptx

  • 1. COURSE A4 Pedagogy of Teaching Mathematics (B Ed Special Education – Hearing Impairment/ B Ed Special Education-- Learning Disability University of Mumbai TOPIC : 2.1. Aims and Objectives of Teaching Mathematics Dr.Amit Hemant Mishal, Associate Professor CCYM’S Hashu Advani College of Special Education https://www.hashuadvanismarak.org/hacse/introduction.html Dr.Amit Hemant Mishal, Associate Professor 1
  • 2. NCF 2005 -MATHEMATICS • The teaching of mathematics should -enhance the child’s resources to think and reason, to visualise and handle abstractions, to formulate and solve problems. -This broad spectrum of aims can be covered by teaching relevant and important mathematics embedded in the child’s experience. • Succeeding in mathematics should be seen as the right of every child. For this, widening its scope and relating it to other subjects is essential. • The infrastructural challenge involved in making available computer hardware, and software and connectivity to every school should be pursued
  • 3. • Some problems in school Mathematics education • 1. A majority - sense of fear /failure . Give up early / drop out • 2. Curriculum is disappointing • 3. Problems, exercises, methods of evaluation – mechanical, repetitive, much emphasis on computation. Areas of Mathematics such as spatial thinking are not developed enough in the curriculum. • 4. Teachers lack confidence, preparation and support. • Students feel need to solve such problems, that teachers & students find it worth their time and energy to address these problems. • Twin concerns of Mathematics curriculum • What can mathematics education do to engage the mind of every student? • How can it strengthen the student's resources?
  • 4. • Developing children's abilities for mathematisation -main goal • Narrow aim - to develop 'useful' capabilities, those relating to numeracy– numbers, number operations, measurements, decimals and percentages. • Higher aim - to develop child's resources to think and reason mathematically, to pursue assumptions to their logical conclusion and to handle abstraction. Includes a way of doing things, ability and attitude to formulate and solve problems. • Should be ambitious, in sense ,it seeks to achieve higher aim mentioned above, rather than only narrower aim. • Be coherent in sense- variety of methods / skills available piecemeal (in arithmetic, algebra, geometry) cohere into an ability to address problems that come from other
  • 5. Pre-primary stage • At the pre-primary stage, all learning occurs through play rather than through didactic communication. • Rather than the rote learning of the number sequence, children need to learn and understand, in the context of small sets, the connection between word games and counting, and between counting and quantity. • Making simple comparisons and classifications along one dimension at a time, and identifying shapes and symmetries, are appropriate skills to acquire at this stage. • Encouraging children to use language to freely express one's thoughts and emotions, rather than in predetermined ways, is extremely important at this and at later stages. • Having children develop a positive attitude towards, and a liking for, Mathematics at the primary stage is as important, if not more than the cognitive skills and concepts that they acquire.
  • 6. • Mathematical games, puzzles and stories help in developing a positive attitude and in making connections between mathematics and everyday thinking. • It is important to Problem posing √ If you know that 235 + 367 = 602, how much is 234 + 369? How did you find the answer? √ Change any one digit in 5384. • Did the number increase or decrease? By how much? 45 note that mathematics is not just arithmetic. • Besides numbers and number operations, due importance must be given to shapes, spatial understanding, patterns, measurement and data handling. • The curriculum must explicitly incorporate the progression that learners make from the concrete to the abstract while acquiring concepts. • Apart from computational skills, stress must be laid on identifying, expressing and explaining patterns, on estimation and approximation in solving problems, on making connections, and on the development of skills of language in communication and reasoning.
  • 7. Upper Primary • Students get first taste of power of Mathematics through application of powerful abstract concepts that compress previous learning and experience. • Enables them to revisit/consolidate basic concepts and skills learnt at primary stage, which is essential from view of achieving universal mathematical literacy. • Students are introduced to algebraic notation and its use in solving problems and in generalization , to systematic study of space/shapes, and for consolidating their knowledge of measurement. • Data handling, representation and interpretation form a significant part of the ability of dealing with information in general, which is an essential 'life skill'. • Learning at this stage also offers an opportunity to enrich students' spatial reasoning and visualization skills.
  • 8. SECONDARY STAGE • Students begin to perceive the structure of Mathematics as a discipline. • They become familiar with characteristics of mathematical communication: carefully defined terms and concepts, the use of symbols to represent them, precisely stated propositions, and proofs justifying propositions. • These aspects are developed particularly in area of geometry. • Students develop their facility with algebra, important not only in application of mathematics, but also within mathematics in providing justifications and proofs. • At this stage, students integrate many concepts and skills that they have learnt into a problem-solving ability. • Mathematical modelling, data analysis and interpretation taught at this stage can consolidate a high level of mathematical literacy. • Individual and group exploration of connections and patterns, visualisation and generalisation, and making and proving conjectures are important at this stage, and can be encouraged through the use of appropriate tools that include concrete models as in Mathematics laboratories and computers
  • 9. Higher Secondary Stage • Aim is to provide students with an appreciation of wide variety of the application of Mathematics, and equip them with the basic tools that enable such application. • A careful choice between often conflicting demands of depth versus breadth needs to be made at this stage. • Rapid explosion of Mathematics as a discipline, and of its range of application, favors an increase in the breadth of coverage. • Such increase must be dictated by mathematical considerations of importance of topics to be included. • Topics that are more naturally province of other disciplines may be left out of the Mathematics curriculum. • Treatment of topics must have an objective, that is, communication of mathematical insights and concepts, which naturally arouse the interest and curiosity of students.