Maths Pedagogy Paper 2 (Language, Place and Community Mathematics) - CTET & State TET MCQ

Mathematics is the study of numbers, shapes, quantities, and patterns. Mathematics is the ‘queen of all sciences’ and its presence is there in all the subjects. It acts as the basis and structure of other subjects.

Important Points

There is a common notion among the student community that ‘Mathematics is always a difficult subject’ and they approach Mathematics with a lot of fear. The fear of Mathematics learning may be due to various reasons. 

The main reason for Maths phobia are:

• Presence of various symbols and notations
• Use of different equations and formulae
• Poor understanding of concepts due to the gap created between teachers' explanations transmitted and those received by the students.
• Lack of basic mathematical knowledge
• Rumors about its difficulty, and so on

NOTE: Differences based on age and gender is not responsible for maths phobia. It affects anyone irrespective of differences based on age and gender.

The most appropriate reason for gender-based differences in mathematical achievement in school mathematics education is the persistent social stereotype carried out in the classroom that mathematics is a male domain.

Key Points

• Research has consistently shown that societal and cultural factors significantly influence gender disparities in mathematics.
• The stereotype that mathematics is a male domain creates an environment where girls may feel less confident, have reduced self-belief in their mathematical abilities, and experience lower motivation to engage in the subject.
• This stereotype can lead to fewer opportunities for girls to participate actively in mathematics discussions, resulting in reduced achievement and limited access to advanced mathematical courses.
• Addressing this stereotype is crucial for creating an inclusive and equitable learning environment where all students, regardless of gender, feel empowered and encouraged to explore and excel in mathematics. 

Hence, it can be concluded that option 2 is the correct answer. 

It is known that language can either help or hinder learning. If language is used correctly and with clarity, it helps in thinking but if it reveals imperfect meanings it creates a misunderstanding.

• Since mathematics deals in abstractions and itself is a way of thinking, it creates a dependent relationship between the notions and the language used to describe them. Mathematical language facilitates thinking by complementing ordinary language.
• To use or communicate that abstract idea, one requires language. So mathematical language walks hand in hand with tlie growth of mathematical understanding, permeating the general linguistic development of children.
• Also, mathematics is itself a language. It has its own symbols and rules for correct usage. Mathematical language is clear, concise, consistent, and cogent. Pupils who get the idea and describe it in correct language are less confused than pupils who memorize terms representing ideas that remain as strange as the terms themselves.

Key Points

Translating verbal language to the language of mathematics, that is solving a word problem, involves three stages: (i) encoding, (ii) operations, (iii) decoding.

• Encoding - It is the process of building a mathematical model from a given verbal statement. Suppose we say that "a father's age is 5 years more than twice his son's age". If we
• assume the two ages to be x and y years respectively, then the corresponding mathematical model is  X = 2Y + 5.
• Operations - It refer to the stage when a model has been set up, we operate on it according to given conditions, obtain a solution and then translate it back into verbal language.
• Decoding - The skill of model-building requires a clear understanding of the mathematical equivalent of words that have mathematical meanings. Words such as more, less, times, difference, is equal to, square, etc., have to be identified and used in the model for the verbal statement. 

Therefore, Suppose we say that "a father's age is 5 years more than twice his son's age". If we assume the two ages to be x and y years respectively, then the corresponding mathematical model is X = 2Y + 5 is correct in the context of the question.

Mathematics develops the ability to perform necessary computations with accuracy and reasonable speed.  It also develops an understanding of the processes of measurement and the skill needed in the use of instruments of precision. 

• One of the major objectives of teaching primary mathematics is to enable children to solve speedily and accurately the numerical and spatial problems which they encounter at home, in the school, and the community.
• It should help children develop an understanding of key mathematical concepts through appropriate experiences with the physical world and the immediate environment. 
• These include subject matter which must be thoroughly mastered so that speed and accuracy are ensured on which future learning can be based. 

Important Points

• Speed in mathematics can be defined as the time taken to solve the problem.
• Accuracy in mathematics can be defined as how close the obtained value (answer) to the acute (true) value.

 Thus from the above-mentioned points, it is clear that Accuracy and speed can go together.

Language helps an individual to communicate with others in an effective way with wor ds, symbols, and expressions as the mediums.

• As mathematics is considered a non-linguistic subject but still it 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

Mathematical Language:

•  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 depicted in the image below:
  
• 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.

Hence, it is concluded that the term "symbolic" refers to the statements and concepts that can be expressed using symbols.

Gender refers to the socially constructed differences between men and women. It refers to the masculine and feminine qualities, behavior, roles, and responsibilities that society upholds. Gender can be changed / re-oriented.

Gender stereotype is an oversimplified and unfair belief or idea that groups of people have particular characteristics or that all people in a group are the same.

Key Points

• Gender stereotype type of thought or belief reduced the ability of the students, and make them the same stereotypes as they are.
• Gender stereotype is the belief that set the limit on the learning of the students and also demotivates them if they are willing to learn some new skills.
• Gender stereotype is a belief of the society that boys have a good command of tools and utensils as compared to the girls, this shows Gender Stereotyping thought.
•  It is believed that girls are not much intelligent in mathematics as boys, so in the middle classes, boys should have to choose Mathematics and Science as a subject, and girls have to choose languages and arts.

So this belief that mathematics and Science are good for boys and languages are good for girls is a gender stereotype belief that increases the gap between both sexes.

Important Points Gender stereotypes can be reduced in the classroom by the following:

• Making the environment of the classroom flexible for all, all as treated as students instead of girls or a boy.
• In a classroom, teachers should have to treat boys and girls equally.
• Teachers should provide equal opportunities to both girls and boys.
• To avoid the situation of gender stereotype, a family should start involving boys in household chores that were mainly concerned with girls traditionally which gave rise to gender biasing and stereotyping.

It is known that language can either help or hinder learning. If language is used correctly and with clarity, it helps in thinking but if it reveals imperfect meanings it creates a misunderstanding. Since mathematics deals in abstractions and itself is a way of thinking, it creates a dependent relationship between the notions and the language used to describe them.

• Mathematical language facilitates thinking by complementing ordinary language. Consider how a child gets the notion of a circle. A child handles, manipulates, and observes the shapes of objects like a wheel, bangles, the ring, etc. He may experiment with a model or may stand in a circle while playing.

Important Points

• Also, mathematics is itself a language; it has its own symbols and rules for correct usage. In spoken language, a usage indicates what words mean, in mathematics, careful defining sharpens word meanings. Mathematical language is clear, concise, consistent, and cogent. Pupils who get the idea and describe it incorrect language are less confused than pupils who memorize terms representing ideas that remain as strange as the terms themselves. 

Thus from the above-mentioned points, it is clear that if the language of mathematics reveals imperfect meanings then it creates a misunderstanding.

The Study of Mathematics helps to enable students to solve speedily and accurately the numerical and spatial problems which they encounter at home, in school, and the community.

Key PointsPersonality characteristics developed through the study of Mathematics:

• Problem-solving
• Ability to recognize order and pattern
• Abstract thinking
• Ability to apply mathematical concepts and skills to solve simple problems of day-to-day life.
• Logical thinking
• Communication skills
• Ability to perform computations with speed and accuracy
• Creativity
• Critical thinking

Hence, we can conclude that faith in cramming could not be developed through the 'study of Mathematics'.

The Hindi meaning of mathematics is ‘Ganita’, the science of calculation. mathematics is a beautiful domain,  as it helps in better understanding of the other subjects. Various definitions were given by great scholars and Mathematician for the understanding of mathematics as follows:

Hence, it is clear that while referring to the fundamental importance of mathematics to the understanding of the universe, Galileo proclaimed "Mathematics is a science that draws necessary conclusions".

Additional Information Plato viewed mathematics in a metaphysical view where abstract mathematical objects are independent of our language, thought, and practices.

G. H. Hardy was an English mathematician known for number theory and mathematical analysis.