Nature of Mathematics MCQ Quiz in मल्याळम - Objective Question with Answer for Nature of Mathematics - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Mathematics is the study of numbers, shape, quantity, 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.

For a constructionist view of mathematics, it is necessary to visualize the concept.

Important Points

• Constructive learning means encouraging students to make use of active techniques like experiments, real-world problem-solving, etc.
• Constructivist teachers encourage the student to involve in the activity continuously which helps them to gain understanding. In addition, the students become “expert learners” as they start knowing “How to Learn.”
• Visualization is used for 3D mathematics and geometry.
• The role of language and dialogue in learning Mathematics is given due to attention and visualize each and every aspect of a number of possibilities.

Therefore, the statement 'Visualisation is an important aspect of Mathematics.' is in agreement with the constructionist view of Mathematics.

Mathematics is a broad and fascinating field with many different branches and concepts.

Key Points Nature of mathematics include:

• Mathematics helps the child to be creative.  This statement is correct. Mathematics involves problem-solving and thinking outside the box, which can foster creativity. Finding innovative solutions to mathematical problems requires creative thinking.
• Mathematics is based on deductive reasoning. This statement is correct. Deductive reasoning involves drawing conclusions from given premises using logical steps. Mathematics is built upon a system of axioms, definitions, and theorems, and mathematical proofs are constructed through deductive reasoning.
• Mathematics helps in nurturing the child's imagination. This statement is correct. Mathematics often requires abstract thinking and visualization. Concepts like geometry, for example, involve imagining shapes and spatial relationships. Nurturing a child's imagination in mathematics allows them to see beyond the immediate problem and understand the broader patterns and structures within the subject.

Hint 

• Mathematics is always convergent. This statement is not accurate. Convergence in mathematics refers to a sequence or series approaching a particular value. While many mathematical processes involve convergence, not all mathematical concepts are about convergence. For example, divergent series exist in mathematics, where the terms of a sequence do not approach a single value.

So, the most accurate options are A, B and C. 

Mathematics: Mathematics is a systematized, organized, and exact branch of  Science. It plays an important role in accelerating the social, economical, and technological growth of a nation. It helps in solving problems of life that need enumeration and calculation.

Key Points 

The nature of Mathematics can be made explicit by understanding the chief characteristics of Mathematics:

• One concept of math's can be used in the other concept, this is the cumulative nature of mathematics.
• Mathematics is a science of discovery.
• Mathematics is an intellectual game.
• It deals with the art of drawing conclusions.
• It is a tool subject.
• It involves an intuitive method.
• It is the science of exactness, precision, and accuracy.
• It is the subject of a logical and specific sequence.
• It requires the application of rules and concepts to new situations.
• It is a logical study structure and patterns.

Hence, we conclude the above statement is about the cumulative nature of mathematics.

Mathematics is a science that deals with logical reasoning quantitative ,calculation ,practices of counting describing shapes, abstraction of subject matter,etc.Mathematics play a vital role in daily life.

Key Points

National Curriculum Framework, 2005-

• The main goal  is to mathematize the child's mind.
• It focuses on conceptual understanding of any topic. It discourages the rote memorization.
• Mathematics increases the logical thinking.
• The students should be taught in a way so that they will think mathematically and use their logical thinking in their daily life.
• The teaching learning process should not focus on robotic learning of steps of solving any question.
• The questions which only checks  the procedural learning, rote memorization ,drill does not initiates the mathematical thinking of students.
• Mathematics needs to be integrated with a child's experiences inside and outside the classroom.
• Mathematics needs to be integrated with other subjects like Environmental Science and Language.
• Mathematics is the real life subject. It plays a crucial role in daily life experiences.

Thus, National Curriculum Framework, 2005 recommends that teaching-learning of mathematics in primary classes needs to follow an integrated approach which implies that mathematics needs to be integrated with a child's experiences inside and outside the classroom and mathematics needs to be integrated with other subjects like Environmental Science and Language.

Visualization is associated with drawing pictures or diagrams as an aid to getting started on problems.

Representation is a sign or combination of signs, characters, diagrams, objects cover pictures or graphs which can be utilized in teaching and learning mathematics.

Key Points

•  Importance of visualization and representation at primary level-
  • Helps in representing word problems- students are taught how to utilize images, diagrams, tables, graphs, other graphic displays to represent mathematical problems. It can be a powerful tool to explore mathematical problems. For example in algebra, geometry, etc.
  • Representation in geometry- Mathematics teachers cannot think of teaching geometry without using some kind of representation as a pedagogical strategy. It acts as a tool for manipulation and communication and also for the understanding of mathematical ideas.
  • It plays a crucial role in the teaching and learning of mathematics because it helps teachers and students to grasp mathematical concepts and relationships.
  • Representation adds to the power of mathematics. For example, the function may be represented in the algebraic form or in the form of a graph. The representation p/q can be used to denote a fraction as a part of the whole, but can also denote the quotient of two numbers p and q.

Hence we can conclude that Visualization and Representation are important processes in mathematics teaching at the primary level because they have implications for teaching algebra and geometry in higher mathematics.

Three Divisions of Knowledge: Based on the way and manner in which it is obtained, knowledge can be classified under three heads.

Key Points Three heads are:

• A Priori Knowledge: A priori knowledge is a knowledge whose truth or falsity can be decided before or without recourse to experience (a priori means ‘before’). The knowledge that is prior has universal validity and once recognized as true (through the use of pure reason) does not require any further evidence. Logical and Mathematical truths are a priori in nature. They do not stand in need of empirical validations. It asserts that any justified assertion must be based on experience directly or indirectly. Even the axioms of mathematics and also first principles of logic are based on experience.
• A Posteriori Knowledge: A posteriori knowledge is knowledge-based upon observation and experience. This is the knowledge of the scientific method stressing accurate observation and exact descriptions. The propositions that fall under this category can be locked from the point of view of whether they contain any factual content and from the standpoint of the criteria employed for deciding their truth or falsity. For example, we have propositions like Ice melts, Snow is white, and Metals conduct heat and electricity These propositions give us factual information whose truth or falsity can be decided only through observation and verification. These are called synthetic propositions.
• Experienced Knowledge: Experienced knowledge is always tentative and cannot exist prior to experience or be conducted from observation. It must be experienced to have value. Basic to the three types is propositional knowledge (a priori and a posteriori) and it is to this type that the structure of the knowledge question is addressed. This has important implications for curriculum planning.

Mental computation is the method of "solving a problem in one's head" and obtaining accurate or approximate results without the aid of a calculator, paper or any other means.

Key Points

•  Mental computation in primary classrooms
  • ​Mental computation skill has many applications in almost every calculation children will attempt throughout their school life and beyond. It should be encouraged in the classroom to develop higher-order thinking, reasoning, and making sense of number and number operations in children.
  • Mental computational skills can be developed by using many methods and activities like card games.
  • It encourages the use of formal and informal strategies to solve a problem. Informal strategies of calculation should be introduced in the Class to let children know about the calculation skills used by shopkeepers and street vendors. 

Hence, it is concluded that the correct statements are (a) and (c).

The basic structure of mathematics includes arithmetic, algebra, geometry, and trigonometry that helps in learning the techniques to handle abstractions and structures.

• The teaching of mathematics must develop attitudes to think, reason, analyze, and articulate logically.
• The nature of mathematics highly influences the nature of the teaching-learning process in mathematics.

Key PointsNature of mathematics:

• Mathematics plays a very important role in education because it has universal applicability i.e., it is present everywhere in our life from buying vegetables to predicting the weather of different cities at a time. Therefore, it has a wide scope of generalization.
• The teaching of mathematics proceeds from the concrete to abstract concepts of mathematics. In primary classes, the mathematical concepts are concrete in nature which moves to abstract from one class to the next class.
• At the primary level, the teaching of concrete concepts helps in developing the basic mathematical skills that are required to handle abstractions in the later level of learning.
• And then in the upper primary and higher classes the abstract concepts of mathematics are taught like algebra, trigonometry, etc.
• The mathematical concepts are hierarchical in nature which add on the practical and conceptual knowledge from one class to the next class i.e., the mathematical concepts are taught in a pre-defined order like first the teaching of arithmetic and then the algebra, trigonometry, and calculus are taught.
• 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.
• So, there exists a considerable and specific vocabulary of mathematics. For example, terms like percent, discount, commission, dividend, invoice, profit, and loss, etc.

Thus it is clear that primary level mathematics is concrete and does not require abstraction is not correct with regard to the nature of mathematics.

Learning mathematics serves both as a means and an end. It is a means to develop logical and quantitative thinking abilities.

• In the early grades, children’s learning of mathematics should be a natural outgrowth of children themselves.
• Such experiences must be interesting and should challenge their imagination so that while observing any natural phenomena they can think mathematically.

Key Points Let us now discuss in detail the nature of mathematics:

• Mathematics aims at abstraction.
• Mathematics is logical.
• Mathematics is symbolic.
• Mathematics is precise.
• Mathematics is the study of structures.

Hence, we conclude that the Nature of Mathematics is Abstract,Logical, Symbolic, Specific

Fear of mathematics, also known as math anxiety, is a type of anxiety that is specifically related to mathematics. 

Key Points

• Mathematics is a very abstract subject. The primary concepts in mathematics, such as numbers, shapes, and functions, are not concrete objects that we can see or touch.
• This can make mathematics difficult for some students, especially those who are more concrete learners.
• Some students simply lack confidence in their ability to do mathematics.
• This can be due to a number of factors, such as a poor understanding of the concepts, a lack of practice, or a fear of failure.

Hence, we can conclude that the abstract nature of primary concepts in mathematics is an aspect of the nature of mathematics that adds to this fear.