Maths Pedagogy Paper 1 (Language, Place and Community Mathematics) - Free

The development of children's abilities to perform mathematical operations and to make them skilled to use mathematical knowledge in real life is the main goal of mathematics education.

• The teacher should start with concrete or simple concepts first and then he should move towards the complex abstractions of mathematics.
• The students should be provided with more opportunities to apply their acquired knowledge to real life so that they can understand the usability of mathematics.​ 

Key Points

• The children in their initial years start their process of learning numbers before entering school.
• They are able to verbally speak the counting but it depends on the individual differences. One child can speak up to 20 numbers and the other can only up to 10.
• They are made familiar with rhymes that include learning numbers while playing. The children imitate them and try to speak the numbers verbally.
• The parents also indulge them in various activities such as counting, adding, multiplying, dividing, or subtracting the numbers based on the situations in their daily lives. 
• It makes the children express the situations of daily life through mathematical language.
• Let's take an example of the real situation, the calculation of the monthly expenditure for purchasing milk in April.
• If daily 2 liters of milk are brought into the house at 60 rupees per liter then for the month of April, the total expenditure would be, One liter of milk costs 30 rupees, 30 days = 2 × 30 = 60 Liters of milk, 60 × 60 = 3600 rupees.

Hence, it could be concluded that to learn the mathematization of situation language the child's everyday language is a prerequisite.

The knowledge base behind mathematics teaching includes the knowledge of mathematics of connections among mathematical ideas, of student learning, and school culture. The process of teaching involves creating a learning community, challenging students to make sense of mathematical ideas, and supporting students’ developing understanding. In the process of mathematics teaching and learning, we develop abstraction, investigation, optimization, problem-solving, logical thinking, understanding, etc.

Key Points

• Abstraction in math: Abstraction in mathematics, or mental abstraction, is a significant component of the mental activity aimed at the formulation of basic mathematical concepts. The most typical abstractions in mathematics are "pure" abstractions, idealizations, and their various multi-layered superpositions. Abstraction is an ongoing process in mathematics and the historical development of many mathematical topics exhibits a progression from the concrete to the abstract. Abstraction in mathematics is the process of extracting the underlying structures, patterns, or properties of a mathematical concept, removing any dependence on real-world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena.
• Investigation in math: It is applied in numerous areas of mathematics for specifying the theory of optimization. Optimization means examining “best available” values of the specific objective function in a defined domain including multiple types of objective functions.
• Optimization in math: Teaching through mathematical investigation allows for students to learn about mathematics, especially the nature of mathematical activity and thinking. It also makes them realize that learning mathematics involves intuition, systematic exploration, conjecturing and reasoning, etc, and not about memorizing and following existing procedures.

Important Points

• Rote Memorization: Rote memorization, or rote learning, is the process of learning through repetition and memorization. The goal of rote memorization is to be able to instantly recall information once it is presented to you. In process of mathematics, the teaching-learning teacher does not focus on rote memorization, he focuses on developing meaningful learning, understanding, logic, and inquiry-based approach in children.

Hence, we can conclude that the right answer to this question is Rote Memorization. 

Mathematics is systematic, organized, and definite. It is a quantitative aspect of human life and knowledge. knowledge of mathematics is exact, systematic, logical, and clear so it can be forgotten. It develops confidence and self-reliance in the student.

Key Points The main motivation for the learning of mathematics came from its functional utility. While geometry was necessitated by problems of land surveying; arithmetic and algebra found their uses in commerce, problems of measurement, and mensuration. Some of the aspects of geometry like symmetry are manifest in architecture, sculpturing, and fine arts. The best characteristics of functional mathematics are:

• Computation with numbers, fractions, and decimals involving addition, subtraction, multiplication, and division.
• Ability to apply skills.
• Measurement and use of devices.
• Use mathematics in different contexts.
• Interpret results and discuss their validity.
• It describes any situation in which one quantity depends on another.
• It develops the ability to make dependable estimates and approximations.
• Functional mathematics needs to teach children in order for them to live independently in the community.
• It builds confidence and experience success when using mathematics in everyday contexts.
• It improves their preparedness for entry to work or further study by developing their numeracy.
• It develops skills such as identifying, measuring, locating, interpreting, approximating, applying, communicating, explaining, problem-solving and working cooperatively with others and in teams.
• To make decisions informed by mathematical knowledge.

Thus, it is concluded that drawing conclusions but no need to justify them is not the best characteristic of functional mathematics.

Effective mathematics takes place in an effective classroom.

Mathematics teaching often criticised for its emphasis on memorizing basic facts, rules and formulae. It is always suggested that emphasis should be laid on mathematical reasoning and higher-order thinking skills such as application, analysis, synthesis, evaluation and creation (Bloom’s revised taxonomy). Mathematical concepts are abstract in nature and helping learners construct these meaningfully has always been a challenge for teachers. Teaching mathematics requires thinking about concepts, learner-centred pedagogy and diversified creative assessment.

Key Points

Characteristic of an effective mathematics classroom are as follows:

• Using different techniques, methods and approaches for students based on their differences.
• Multiple ways of approaching a problem are encouraged while teaching mathematics effectively in a classroom as it helps in divergent thinking.
• Providing students with the opportunity to solve problems by themselves
• Providing students with project works and assignment that enhances their thinking and mathematical skills
• Group work and problem-solving should be encouraged.
• Engaging students in different activity-based learning.​

Hence, we conclude that effective mathematics teaching occurs when the teacher ​challenges students' curiosity by setting them problems proportional to their knowledge.

Language helps an individual to communicate with others in an effective way with words, symbols, and expressions as the mediums. As mathematics is considered a non-linguistic subject but still possess similarities with the language. It uses symbols and expressions to describe the lengthy problems in a precise and accurate manner which makes it an economical language.
Key Points

• With the help of language, one individual can express mathematics in terms of mathematical equations, laws, and principles. 
• Also, to express any mathematical fact, theorem, or statement, we need to use the language.
• Just like we use letters, alphabets, and words to write or speak a language, mathematical language uses symbols, numbers, diagrams, and graphics to express, define, or prove the mathematical statements and concepts.
• The symbols that are generally used in mathematics are '×', '÷', '+', '-', '%' etc.

Hint

• The mathematical expressions remain constant irrespective of the languages that are used to describe them i.e., to explain any of the mathematical theorems in different regional languages.
• /, ? and & are symbols used in all the subjects being learned.

Therefore, the symbol that is unique to the mathematics language is %.

The language of mathematics refers to the language used to express mathematical thoughts and ideas.

It makes learners able to assimilate mathematical terms, reason logically, and recognize and employ patterns of mathematical thought.

Language of mathematics comprises:

• Formulae

• Sign and digit

• Greek alphabet

• Letter convention

• Symbol and syntax

• Theories and principles

• Number-number variable, etc.

Hence it could be concluded that all the given options are true in the context.

The language of mathematics refers to the language used to express mathematical thoughts, expressions, and ideas.

Key Points Language of mathematics makes learners able to:

• reason logically
• assimilate mathematical terms
• recognize and employ patterns of mathematical thought.

Language of Mathematics Includes:

• Sign, symbol, graphs

• Formulae, syntax
• Number variable

• Greek alphabet

• Letter convention

Hence, from the above-mentioned points, it becomes clear that sign, formulae, and number variables are parts of the language of mathematics.

The subject of Social Studies has a critical role in the learning process. This helps in formulating social attitudes, building patriotism, internationalism, brotherhood, and understanding of social dynamics, roles, and responsibilities of social institutions and the process of governance.
Important Points

• Social Studies in the CBSE syllabus from  3rd standard to 5th focuses on teaching Social Science as an integrated subject understanding the cross-links between its various components and seeing social orders in a unified manner.
• However, from 6th standard 6 onwards, there is a greater thrust on studying History, Geography, Political Structures, and Economics as individual components under the umbrella of Social Studies. 
• So, Social Studies is taught to the student at lower primary (I-V) and upper primary level (VI-VII) besides mathematics, language, and science.
• In the CBSE curriculum, Social Studies is divided into 4 subjects i.e. History, Political Science, Geography, and Economics.

Thus, it is clear that allied subjects taught to the student at lower primary (I-V) and upper primary level (VI-VII) besides mathematics, language, and science are social studies. Additional Information

• The main difference between social science and social studies is in their intended purposes.
  • The social sciences are branches of study that analyze society and the social interactions of people within a society.
  • Subjects that fall under the umbrella of social sciences are anthropology, history, economics, geography, and many others that explore societal relations.
• Social studies is the systematic study of an integrated body of content drawn from the social sciences and the humanities.
  • It enables students to develop their knowledge and understandings of the diverse and dynamic nature of society and of how interactions occur among cultures, societies, and environments.
  • At lower primary (I-V) and upper primary level (VI-VII) subject Science is known as General Science.

Developing logical and problem-solving abilities in children is the main objective of teaching Math, according to NCF 2005 the development of children's abilities for mathematization is the main goal of mathematics education which means the child's thought process should be mathematized. Key PointsAccording to the National curriculum Framework 2005, school Mathematics takes place in a situation where

• Students avoid rote memorization and develop concepts with understanding.
• Students are treated as the center of the class and the teaching and learning activities are developed according to their abilities.
• Students see mathematics as a part of their daily life experiences and something to talk and discuss about. 
• Students start using the concepts of mathematics they learned in the classroom in their daily life as well.
• Students enjoy solving different types of problems in different methods according to their understanding.

​Hence According to the National Curriculum Framework 2005, school Mathematics takes place in a situation where students see mathematics as a part of their daily life experiences and something to talk about and discuss.Additional Information ​On the other hand students reciting multiplication tables, teachers becoming active narrators, and students solving higher education-related problems are not given importance by NCF 2005 as these don't allow students to see mathematics as a part of/her daily life experiences.

The National Council for Educational Research and Training (NCERT) published a document called the National Curriculum Framework (NCF). NCF 2005 has been translated into 22 languages and influenced the syllabi in 17 states.

According to National Curriculum Framework-2005:

• The main goal of Mathematics education in school is the mathematization of the child’s thought process.
• Children should learn to think about any situation using the language of Mathematics.
• The aim of teaching mathematics is to develop the child to think and reason mathematically, to pursue assumptions to their logical conclusions, and to handle abstractions.
• The school Mathematics curriculum should help the children learn to enjoy Mathematics.
• Mathematics takes place in a situation where mathematics is a part of children's life experience.
• Mathematics subject to be learned in order to perform daily life activities in a better way.
• Constructing the Mathematics curriculum we need to consider those topics Mathematics or themes, which would help children to succeed in their everyday life.
• The curriculum of mathematics should be introduced by connecting it to real-life situations and through its use in solving various life problems.

NOTE: According to NCF 2005, given all other options are not appropriate in context of mathematics.

Hence, it becomes clear that according to NCF 2005, mathematics takes place in a situation where mathematics is a part of children's life experience.