CTET Paper 2 Maths & Science May 2016 (English-Hindi-Sanskrit) (Previous Year Paper)

Assessment plays a significant role in the teaching-learning process. Assessment of learning helps a teacher to design his/her teaching in a better way and to know the attainment level of learners in the subject content.

The student understands exactly what they are to learn, what is expected of them and are given feedback and advice on how to improve their work, this is also creative as feedback is given to students based on the results obtained from this assessment so that both the student and teacher can improve their learning process.

• Differentiated learning and teaching strategies refer to those strategies which fulfil the need of every individual whether it is learner, curriculum or teacher.
• An assessment helps a learner to know his /her learning progress.
• Assessment of performance of learners not only helps a teacher to make academic decisions but also provides him/her feedback on the teaching strategies adopted by him/her, his/her level of teaching.
• Assessment is the determinant of learning. Learning can be enhanced by enhancing suitable teaching-learning strategies.
• Assessment is feedback given by teachers, differentiated instructions and opportunities to respond enabled the students to develop concepts at a higher rate.

Thus from above-mentioned points, it is clear that assessment is carried out during teaching-learning to create differentiated teaching and learning strategies.

Important Points

Assessment can be classified into four types on the basis of their purposes-

First Generation Learners are the first in their family lineage to get formal education. The ancestors of such learners were deprived of education due to various reasons. 

They generally belong to the socio-economically disadvantaged communities like Scheduled Castes (SCs), Scheduled Tribes (STs) and Other Backward Classes (OBCs).

• Such children mostly participate a great deal in domestic work and have poor exposure to the outside world.
• They suffer from many problems arising out of poverty and ignorance such as poor health, poor self-confidence, malnutrition etc.
• First Generation learners should be allowed to set their own pace and be given supplementary remedial instruction.
• First generation learners appear to be the most disadvantaged among all learners. They have the double handicap of having class/caste disadvantage as well as a totally illiterate background.

Two broad influencing factors with respect to students’ challenges have been identified as parental support and teacher intervention.

• The teacher must have talk to the children to understand them and make the classroom environment conducive to their learning.
• Teachers also felt a need to pay more attention and spend more time on these students.

A socially disadvantaged child is one who is from a socially and economically backward section of the community, who cannot avail from school because of deprivation of one sort or another.

Such children show cumulative academic deficits, high dropout rate and progressive decline in intellectual functioning.

Remedial Measures-

• The curriculum should be specific and related to the needs and real-life experiences.
• Emphasis should be on learning manual skills, life skills and technical efficiency.
• Interest in learning has to be, created by the teacher, effort should be towards developing self-confidence, self-respect and a sense of cultural identity.
• The socially disadvantaged child need special requirements of a learner calling for a specific adjustment in regular education programmes.

Here it is clear that students from disadvantaged backgrounds should be placed in regular schools and efforts should be made to adapt the curriculum and facilitate learning for all the students in the context of their social and cultural context. 

Additional Information

Causes of Social Disadvantage- 

• Some of the major causes are unstimulating environment, lack of verbal interaction with adults, poor sensory experience, poverty, low social status, malnutrition and broken homes. Most of these causes are due to socio-cultural disadvantage.
• Such a child has characteristics like backwardness, frustration, aggression, inferiority complex, alienation and lack of motivation.

Learning disability is a syndrome found in children of normal or above intelligence characterized by specific difficulties in learning to read (dyslexia), to write (dysgraphia), and to do grade-appropriate mathematics (dyscalculia). 

Key Points

Education of a child with a learning disability-

• Inclusion strategies are the provisions by state and national authorities that students with learning disabilities should be educated with nondisabled students of their age.
• Additional instructional resources can be used for children with LD while teaching them in a general classroom.
• Teachers should make effort to adopt such methods to enhance the understanding and participation of LD children with other children.
• Feedback and corrections are used and are shown to affect children’s participation and performance positively.
• Peer-mediated instruction and computer-assisted instruction are the other methods used.
• An individualized teaching program is required so that the child may get specific instruction in the areas of specific need, like reading, writing, or math.

Thus it is clear that a child with Learning Disability has a right to study in a regular school where there are special provisions for him.

Important Points

Some learning disabilities-

Children are divided into different categories based on their interests, behavior, nature, I.Q level, understandings, grasping abilities, etc.

Important Points 

• Creative children: 
• These categories of children have divergent thinking, curious in nature, exceptional from normal children, have I.Q ≥ 120, and is able to find solutions for different problems on their own.
• Talented children:
• They are those who show high-performance capability in several areas such as artistic and creative work, leadership quality, keen power of observation, etc.

Key Points

Talented and creative children need to be given special attention to enable them to reach their full potential as:

• these children have divergent thinking and are very curious in nature that's why sometimes the classroom seems monotonous to them because they grab things fastly than of their age-peers.
• so, it's a teacher's responsibility to use customized and stimulating instructions method to make learning interesting for them.

Education of Talented and creative child:

• Reform in evaluation system
• Experimentation and independent research.
• Opportunity for involvement for creative expression.
• Special attention to enable them to reach their full potential.

Hence, it is clear that talented and creative children need to be given special attention to enable them to reach their full potential.

Progressive education advocates that young learners should be given the freedom to learn according to their preferences and likes

Important Points

• Based on the belief that education should primarily serve the needs of children and focus on understanding, action, and experience rather than rote knowledge and memorization.
• Children with special needs are taught along with other children while making special provisions for their needs.
• Special education is individualized education for children with special needs. Special education means, “Specially designed instruction, to meet the unique needs of a child with special needs including instructions conducted in the classrooms.
• A free and democratic atmosphere should be provided in the classroom for the proper development of an individual.

Hence, children with special needs do not have to always study in a separate institution In fact, most of them can learn quite well in general classes of a school. 

Thus from the above-mentioned points, it is clear that in a progressive set-up children with special needs are taught along with other children while making special provisions for their needs.

The learner-centred approach of teaching puts learners in the centre and gives primacy to children's experiences and needs.

It strongly believes that when children are given the freedom to work at their own pace, they develop the ability to assimilate the concepts efficiently.

Important Points

Characteristics of the learner-centred approach of teaching:

• It stresses the importance of enquiry, observation and investigation.
• It takes into account learner's capabilities, capacities and learning styles.
• It uses methods like experiential learning, problem-solving, concept mapping and creative writing.
• It emphasizes to provide ample opportunities to the children to foster their own strategy of learning to perform a task.

Role of teacher in learner-centred teaching:

• In this method**, teachers facilitate students as a facilitator** by providing with proper environment and materials to learn at their own pace.
• Teachers foster children’s learning and development best by building on the existing knowledge, abilities, interests, needs, styles of learning and strengths of the children in the class.
• In this approach, the role of the teacher will be that of a friend, facilitator and a guide who create a conducive learning environment for every child through planned activities.

Hence, it could be concluded that Learner-centred teaching means that learners are given an opportunity to construct knowledge and teacher is a guide in the learning process.

Additional Information

'Learning' means a relatively permanent change in behaviour that occurs as a result of experience with the environment. Learning is a process of acquiring knowledge and remembering information so that it may be applied to life situations.

Learning is fostered when the learner has opportunities to practice the new information, receive feedback and apply the knowledge or skill in familiar and unfamiliar situations, with less and less assistance from others.  Some general guidelines to help the children learn effectively are as follows-

• Give the child ample time for practice and repetition
• Use a variety of teaching materials concrete, pictorial, auditory and visual
• Provide a feedback immediately-i.e., tell the child whether he is correct or not
• by giving ample opportunities to the learner to apply a previously learnt skill in a new area of the application without direct instruction or guidance (adaptation) i.e, connecting new materials with something the child already knows
• let the child continue doing the activities which he already knows. He will become better at them and get the confidence to learn new things.

Thus from above-mentioned points, it is clear that learning can be facilitated by connecting new materials with something the child already knows.

Key Points

Principles of Learning-

• Children Learn by Doing
• Learning Proceeds from Simple to Complex
• Learning Proceeds from Known to Unknown
• Learning Proceeds from Concrete to Abstract
• Learning Proceeds from Whole to Part

In Constructivist teaching-learning, we promote learning for the construction of knowledge by learners themselves.  

• Learning for construction of knowledge is the basic presumption of constructivism.
• The emphasis is on such a learning environment where children can construct their own knowledge, develop their capacities and remain an active learner.

Piaget’s Cognitive Constructivism-

• Piaget has a firm belief that learning is a constructive process.
• Piaget emphasized an active learner who can observe, act, modify, manipulate, transform and construct own meaning of an object or event.
• In Piaget’s constructivism, a child’s language was an ecocentric and nonsocial speech

Vygotsky’s Social Constructivism-

• Vygotsky is known as the proposer of social constructivism. Social Constructivism approach talks about the importance of social interaction and context in learning. He believes that learning is social in nature.
• it emphasized on social context; knowledge is mutually built and constructed.
• Vygotsky is of the view that teacher should provide an environment to children to construct knowledge with peers and teacher i.e. co-construction of knowledge.
• for Vygotsky, children use a lot of private speech not only from social communication but also to plan, guide and regulate their behaviour in self-regulatory fashion.

Thus it is clear that in a constructivist classroom as envisioned by Piaget and Vygotsky, the teacher provides an opportunity for the students to engage in inquiry and problem-solving. Such that they construct their knowledge through organization, observation, adaptation and by the help of peers.

Piaget’s views indicate that there is no knowledge that is pre-existing in the world such that it can be ‘taught to a child. Nor does knowledge comes innately (on its own) to the child. Knowledge develops when she acts in the world. His theory also helps in understanding how children ‘construct’ knowledge. Thus, it is also known as a theory in ‘Constructivism.

Key Points

Cognitive development is the process in which cognition (thinking) develops. It is the orderly development of mental and intellectual processes, like logical thinking, making sense of new ideas, solving the problem and the like, that takes place over a period of time.

Therefore teachers ideally would engage in- following for cognitive development in child- 

• facilitates learning by creating opportunities for the children to engage with the world around them and act on it, this enables children to make sense of the world around them and constructs knowledge.
• the teacher is visualized to be a facilitator of children’s learning. The main role of the teacher is understood as being enabling children to construct knowledge.
• observing and engaging with children
• communicating with and relating to children
• understanding their socio-cultural contexts, their paces, styles of learning, and their interests
• developing in themselves the capacity for self-analysis, self-evaluation, adaptability, flexibility, creativity and innovation
• engage with subject content, examine disciplinary knowledge and social realities, relate subject matter with the social milieu of learners

Here it is clear that according to the theory of cognitive development given by Piaget no because the teacher supports and facilitates the active explorations of the children this statement is not correct because the teacher supports and facilitates the active explorations of the children.

Important Points

 According to Piaget, there are four stages of cognitive development:

• Stage I - The Sensory-Motor Stage (birth to 2 years)
• Stage II - The Pre-Operational Stage (2 to 7 years)
• Stage III - The Concrete-Operational Stage (7 to 12 years) and
• Stage IV - The Formal Operational Stage

The correct answer is: "Using a variety of ways to assess children over a period of time"

Key Points

• Continuous and Comprehensive Evaluation (CCE):
• CCE aims to assess all aspects of a child's development, including cognitive, emotional, and social growth, rather than focusing solely on academic achievements.
• It emphasizes the use of diverse methods of assessment to ensure a holistic understanding of a student's progress.
• Importance of Variety in Assessment:
• Assessing children using multiple methods such as projects, oral presentations, group activities, and observations helps in evaluating different skill sets, including creativity, critical thinking, communication, and collaboration.
• This approach provides a more accurate and well-rounded picture of the child's abilities and areas for improvement.
• Using varied assessment techniques over time reduces stress and anxiety in students by avoiding a one-size-fits-all approach.
• It allows teachers to track progress consistently and intervene early if there are areas where the child is struggling.
• Promoting Active Learning:
• Through diverse assessment methods, students are encouraged to engage actively in the learning process rather than passively memorizing content.
• It fosters a deeper understanding of concepts and builds lifelong learning skills.
• Flexibility in Teaching and Learning:
• Using varied assessment techniques provides flexibility to teachers to adapt their teaching strategies to meet the needs of individual learners.
• It also allows students to demonstrate their learning in ways that suit their unique strengths and preferences.

Additional Information

• Conducting assessment at the beginning and end of the session:
• While pre- and post-assessments provide useful information about a student's baseline and end-of-term performance, they do not offer a continuous understanding of the student's progress during the session.
• This approach does not align with the core idea of CCE, which emphasizes ongoing and regular evaluation throughout the academic year.
• Giving written tests to children periodically:
• Periodic written tests are a traditional method of assessment that primarily focuses on rote learning and memory recall.
• While useful for evaluating academic knowledge, this method does not assess other important aspects such as creativity, problem-solving abilities, or emotional and social skills.
• Having only multiple-choice questions in tests:
• Multiple-choice questions are limited in scope and primarily evaluate factual knowledge rather than higher-order thinking skills like analysis, synthesis, or application.
• Using only this method restricts the ability to assess a student's comprehensive understanding and limits opportunities for holistic evaluation.

Teachers are the implementers of education who foster the potential of young seedlings to grow and bloom. They carry a huge responsibility to shape and mould students' future.

• Teachers are the most important resources in educational settings. They are the key figures for any changes required in the educational field.

Key Points

It is important to appreciate children's work rather than criticize it as:

• it boosts their confidence to explore their knowledge and helps to foster creativity in children.
• creative expression provides the richest opportunities for individual expression and growth.
• it helps them to connect to the teacher in a better way and to don't hesitate to ask for any kind of help.
• students are curious in nature and they feel good when someone appreciates and shows interest in their work.

​

Important Points

**The teacher should keep the following points in view while teaching-**​

• Encourage individuality and originality.
• Encourage the child to freely express his/her ideas.
• Encourage the child to experience creative activities.
• Allow the child to experiment and to make “mistakes”.
• Encourage the child to discover things and to be resourceful.

Hence, it is clear that the above-mentioned statement is correct since it helps to foster creativity in children.

Hint

• Criticizing children's work could lead to low-self esteem and anxiety in them.

Science refers to the study of structure and behaviour of the physical and natural things through observation and experimentation. In other words, science is a classified knowledge gained from a systematic study of the behaviour of nature.

Key Points

• Teaching method is a way to put theory in practice with the help of principles, pedagogy and management strategies. It helps the teachers to plan and present the lesson in a coherent way.
• For a Science teacher, conducting experiments and doing projects will be the most preferred method as at secondary level, Science should be evolved from natural contexts of the learners.
• Scientific concepts are learnt better if learners explore them through activities and experiments.

Important Points

• Experiments:
• It is a process of observation under controlled conditions by using a range of apparatus and methods.
• It refers to an approach to learning in which learning takes place through inquiry, observation, inferring, and testing of a hypothesis.
• Projects
• It is a method which emphasizes the voluntary participation of students by working in a group to complete a specific project.
• It ensures the transmission of practical knowledge to students and active learning by mutual co-operation of a group of peers.

Hence, it is clear that conducting experiments and doing projects will be the most preferred method in the context of the question.​

Motivation inspires people to work, individually or in groups such as to produce the best of results. Pires people to work, individually or in groups such as to produce the best of results.

It is the will to act by exerting a high level of efforts towards the achievement of organizational goals, conditioned by smart and efficient working. 

• The reward is a type of extrinsic motivation. The motivating factors are external, or outside, rewards such as money or grades. These rewards provide satisfaction and pleasure that the task itself may not provide.
• An extrinsically motivated person will work on a task even when they have little interest in it because of the anticipated satisfaction they will get from some reward.
• The rewards can be something as minor as a smiley face to something major like fame or fortune.
• It just means that the pleasure they anticipate from some external reward will continue to be a motivator even when the task to be done holds little or no interest. That is why rewards alone cannot ensure interest and long-term learning.

Thus it is clear that despite giving stars for every work, a teacher finds that the students are not motivated to learn. This is because rewards alone cannot ensure interest and long-term learning. 

Additional Information

Intrinsic Motivation-

• Intrinsic motivation refers to motivation that comes from inside an individual rather than from any external or outside rewards, such as money or grades.
• The motivation comes from the pleasure one gets from the task itself or from the sense of satisfaction in completing or even working on a task.

Vygotsky, a Russian psychologist, has argued that culture provides a social context in which people live, grow, and understand the world around them. This is an understanding which the socio-cultural perspective argues- 

• Vygotsky writes, every function in a child’s cultural development appears twice: first, on the social level and then inside the child.
• Vygotsky believed that cultures, like individuals, have a life of their own; they grow and change, and in the process specify what will be the end-product of successful intellectual development.
• His works say that people live and are located in a culture. They develop from childhood to adulthood in that culture.
• They perform all activities and think within the framework of their socio-cultural environment.
• He understood learning and development as processes that happen during interactions of a child with adults and peers.
• Therefore, their developmental processes can be only understood by studying children’s (or people’s) interactions with their culture.

Thus from the above-mentioned points, it is clear that sociocultural context plays a very important role in learning​. 

Important Points

Some central-concepts of Vygotsky's theory is-

One of the important characteristics of learning is that the acquisition of skills, habits, knowledge, and attitudes, influences the acquisition of new learning due to some kind of carry-over effect. 

Transfer of learning- It implies

• that training is one faculty of the mind that may help in the functioning of older faculties as well various faculties of mind - memory, reasoning, judgment, observation, etc. - are directed or trained through various academic subjects.
• problem-solving, in which experience in one task influences the performance of another.
• comes from the similarity of contents, the similarity of techniques, the similarity of principles, or a combination of these
• take place and effective when the children are encouraged to observe and interact with objects and people

Types of Transfer of Learning-

 

Thus from the above-mentioned points, it is clear that what the child learns, can apply that learning to various situations depends on opportunities she has to observe and interact with objects and people.

Motor development refers to the development of control over body movements. The child’s capacity to sit, stand, walk, hold an object, eat, write, climb stairs, run, etc. is included in motor development. 

Motor development makes the child mobile, increases his/her range of activity, and helps him/her to explore the surroundings. This also helps in cognitive development.

The physiological development of the human being manifests itself in a universal and orderly process of structural change marked by two interrelated kinds of sequence: (i) The Cephalocaudal and (ii) The Proximodistal

The Proximodistal- In this,

• The middle part of the body develops quicker than the outer part of the body.
• The growth of tissue and structure that is closer to the center of the body is a little faster than the maturation of tissues and systems that are located in its periphery.
• First, whole arm or leg movements are seen, then elbow and knee joint control, and finally the specialized reaching movements of the fingers.

Cephalocandal sequence- 

• As the name indicates, is a progression of differentiation and structural maturation from the head, through the trunk, to the extreme parts of the body.
• This means that the infant’s brain and head grow faster and reach maturity earlier than visceral organs.

Thus from the above-mentioned points, it is clear that the Proximodistal principle of motor development means that development proceeds from the center of the organism to its periphery.

The period of childhood is from two to twelve years of age. Development at this stage is not as rapid as during infancy. During this period the child refines the skills she has acquired during infancy and learns new skills as well. This is the period when coordination of the parts of the body improves.

The characteristics of childhood are- 

• During this period a child becomes more independent though adult guidance is constantly needed.
• The period of childhood is divided into two stages: the period of early childhood (2-6 years) and middle childhood (6-12 years).
• At this stage, the child comes in contact with other children and adults she finds out how to behave in a manner that is acceptable to them.
• A child learns the ways of eating, dressing, talking to elders, and other things that are a part of her culture.
• The social and cultural contexts in which children grow up exert influences in making sense of the social world of the child.
• Childhood is experienced differently by children within a context such as a family, orphanage, school, peer groups, cities, neighborhoods, and so on.
• There are variations in childhood when we compare two different individuals who grow up in different parts of the world with different cultural traditions.
• For example, the behavior of a child reared in a dysfunctional family is different from that of a child grown up in a normal family.

Thus from the above-mentioned points, it Is clear that childhood is experienced differently by children in different social and cultural contexts.

By individual differences-

• we mean physical and behavioural variations, seen in all species including human beings, some of us are tall, some short, some bright and some dull.
• Behavioural variations such as some being aggressive and some being polite.
• Different people have different interests; and their behaviour is influenced by these interests, likings, dislikings, values, beliefs, etc.
• While dealing with heredity and environment in the context of individual differences, one has to be cautioned against the misuse of terms like inborn. acquired. resemblance, maternal impressions. etc.

Key Points

• These differences are caused by heredity and environment. Heredity is determined by genes, chromosomes, and cytoplasm. The environment is determined by family, school neighbourhood, and place of work.
• Individual differences are generally measured through psychological tests such as intelligence or personality.

Factors to cause individual differences- 

 

Thus from the above-mentioned points, it is clear that Individual differences can be attributed to the complex interplay between hereditary factors and the environment.

Socialization is the process by which we acquire the culture of the society into which we are born - the process by which we acquire our social characteristics and learn the ways of thought and behaviour considered appropriate in our society. During the process of socialization

• children learn about their family traditions from their elders and preserve them and pass them on to the next generation as they grow older.
• helps children to learn and perform the different roles and responsibilities which they have learnt from their elders.

Agents of Socialization- 

Thus from above-mentioned points, it is clear that physical Infrastructure does not play a role in the socialization of children.

According to Piaget, cognitive development takes place at different rates at different stages of development. At the elementary level, there is not only an increase in children's capacity to learn but also a qualitative change in their thinking process. 

• The child actively selects and interprets environmental information in the construction of his/her own knowledge rather than passively copying the information as presented to the senses.
• In fact, the child ‘reconstructs’ and ‘reinterprets’ the environment to make it fit in the existing mental structures. The process of reconstructing and reinterpreting involves two mental processes assimilation and accommodation.​

​

 

This constant process of assimilation and accommodation in human beings is the way of interacting with the environment and gradually progressing towards cognitive development. It is the way in which they reconstruct and reinterpret reality.

Thus it is clear that according to Piaget, Assimilation and Accommodation pairs is essential for cognitive development of the child. 

Important Points

According to Piaget, there are four stages of cognitive development-

• Stage I - The Sensory-Motor Stage (birth to 2 years)
• Stage II - The Pre-Operational Stage (2 to 7 years)
• Stage III - The Concrete-Operational Stage (7 to 12 years) and
• Stage IV - The Formal Operational Stage

Schemas: Schemas are categories of knowledge that help us to interpret and understand the world.

Concentration is the cognitive process of selectively focusing on one aspect of the environment while ignoring other things. It is also referred to as the allocation of processing resources.

Piaget in his theory of cognitive development talks about cognition (thinking). According to him, the learners acquire knowledge through the interaction of innate power (heredity), environment and maturation.

Piaget has classified the whole continuum into four stages to elaborate on the process of cognitive development:

1. The Sensory-Motor Stage (birth to 2 years)
2. The Pre-Operational Stage (2 to 7 years)
3. The Concrete-Operational Stage (7 to 12 years)
4. The Formal Operational Stage (11-15 years)

The pre-operational stage defines that-

• Pre-operational thinking tends to be egocentric
• Pre-operational thinking tends to focus on only one aspect or dimension of a problem at a time. For example, while looking at the height of an object, the child is unable to consider any changes undergone in its width. The child is unable to handle multiple characteristics
• The pre-operational child cannot understand relational terms such as larger than, darker than
• The child at this stage is not able to understand how things operate internally or how things relate to one another.

Thus it is clear that a child focuses on one aspect of a situation and ignores the others, this is due to concentration. 

Key Points

Lawrence Kohlberg studied moral development by posing moral dilemmas to groups of children as well as adolescents and adults. 

When people are confronted with moral dilemmas, it is their reasoning that is important and not their final decision, Kohlberg theorized that people progress through three levels (comprising six stages) as they develop abilities of moral reasoning.

Key Points

The initial level is the pre-conventional level. People at this level (primarily children) conceive of rules and social expectations as being external to the self. It includes two stages-

Stage-1 Punishment-obedience orientation- 

• At the first stage, the physical consequences of an action determine whether it is good or bad.
• The right is defined by literal obedience to authority and the avoidance of punishment and physical damage.

Stage-2 Instrumental-exchange orientation-

• What's right satisfies one's own needs and occasionally the needs of others.
• the right is defined as serving one's own interests and desires and as letting others do likewise
• cooperative interaction is based on terms of simple exchange

​Thus it is clear that in pre-conventional morality rules are external to the self.

Important Points

The other two levels are-

Vygotsky, a Russian psychologist, has argued that culture provides a social context in which people live, grow, and understand the world around them. This is an understanding which the socio-cultural perspective argues- 

• Vygotsky writes, every function in a child’s cultural development appears twice: first, on the social level and then inside the child.
• Vygotsky believed that cultures, like individuals, have a life of their own; they grow and change, and in the process specify what will be the end-product of successful intellectual development.
• His works say that people live and are located in a culture. They develop from childhood to adulthood in that culture.
• They perform all activities and think within the framework of their socio-cultural environment.
• He understood learning and development as processes that happen during interactions of a child with adults and peers.
• Therefore, their developmental processes can be only understood by studying children’s (or people’s) interactions with their culture.

Thus it is clear that Vygotsky believed that cognitive development occurs in a sociocultural context and evolves out of the child's social interaction. 

Important Points

Some central-concepts of Vygotsky's theory is-

Lev Vygotsky was a Russian psychologist and a social constructivist. He has propounded 'Socio-cultural Theory' which emphasizes the role of social interaction in cognitive development.

Lev Vygotsky emphasized that the acquisition of speech is the major activity in cognitive development. He believed that cognitive skills and patterns of thinking are the product of the interaction between the individual and the socio-cultural institution where the individual grows up.

Vygotsky's view on 'Language and Thought':

• Private speech gives direction to children.
• Language is essential for cognitive development.
• Language plays a powerful role in shaping individuals' thoughts.
• By acquiring language, the child modifies its higher mental functions.
• In the initial stage, thought & language are independent but merge at around three years of age.

Hence, it could be concluded that according to Vygotsky, language plays a crucial role in the development of cognitive ability.

Additional Information

In his "Socio-cultural Theory", Vygotsky also proposed three stages of language that a child progresses while developing language functions.

These stages are:

If a teacher believes that each child is unique and a special individual, and therefore actively involves them in their own education and development.

The teacher is adopting a child-centric education. In this approach, the ‘learner’ or ‘child’ is the main focus of the educational programme. It emphasizes ‘learning’ rather than ‘teaching’.

Child-centric education advocates that-

• accommodate the individual difference and unique character of each individual learner
• each individual’s growth presents a different range of problems and requirements,
• at every stage from the womb to tomb” implying that the child’s individuality and dignity should be respected and his/her needs, interests, aptitude. So that two individual provided opportunities to grow and realise their potentials in the same class.
• Teacher adopts a variety of teaching-learning strategies to address the needs of all children at the same time.
• Varieties of activities/opportunities are available in the classroom, which enables each child to learn at her/his own pace and in tune with her/his own learning style.

Here it is clear that if a teacher believes that each child is unique and a special individual, and therefore actively involves them in their own education and development. The teacher is adopting a child-centric approach to learning. 

Additional Information

In a child-centred classroom-

• The child is not a passive but an active participant in the classroom process.
• Reflects planning of teaching-learning and its monitoring jointly by teacher and children
• Evaluation of the child’s attainment is done to ensure the child’s progress and not as a means of passing judgement on the child’s abilities and achievement. it is diagnostic as well as remedial.

Intelligence is a capacity to understand the world, think rationally, and use available resources effectively when faced with challenges. 

Multidimensional' means intelligence consisting of different aspects derived from experiential, environmental and genetic influences. Intelligence is conceived in terms of multiple abilities.

Howard Gardner, an American Psychologist, proposed the theory of multiple intelligences. 

• There are multiple intelligences with autonomous intelligence capacities.” So, intelligence cannot be viewed as a single entity.
• Gardner initially proposed eight types of intelligence which later on he increased to nine.
• Thus Gardner views each individual as a unique combination of various intelligence.

​Thus from above-mentioned points, it is clear that **Intelligence is a multi-dimensional concept.**​

Key Points

According to linguistic relativity hypothesis or Whorfian theory, our language shapes our thought. 

Key Points

• Whorf proposed that the available words of the language influence our thinking.
• our language does not determine all aspects of our thinking. It only influences the way people think about the relationship between objects.
• Language influences perception, a fundamental aspect of cognition (thinking).
• Language is the main vehicle by which we know about other people’s thoughts, and the two must be intimated.
• people think not just in words but in images and abstract logical propositions.
• Language development is an essential aspect of cognitive development

Thus from above-mentioned points, it is clear that language influences thought.

Additional Information

Theories of language acquisition-

The gender division is something which can be understood as natural and unchangeable and based on social expectations and stereotypes.  Boys and girls are brought up to believe that the main responsibility of girl is housework and bringing up children and boy is to earn for livelihood, do the work of power, driving etc. 

Key Points

Parents tend to buy their children gender-stereotypical toys. They also, intentionally or otherwise, tend to reinforce certain ‘appropriate’ behaviours. Even today girls are discouraged from playing sports like football or from playing ‘rough and tumble’ games and forces to play with a doll. 

• A gender stereotype is an assignment of roles, tasks and responsibilities to a particular gender on the basis of preconceived prejudices.
• It is also the assumptions made about a particular gender that may be positive or negative.
• the cultural expectations are formed around the children, based on gender
• for boy toys like cars, lions, guns and elephants are bought for him preferably blue and never pink
• the girl child is often considered inferior to a boy child and would be encouraged to learn cooking, dancing, singing, housekeeping and the like and she may have restrictions on going out.

Thus from above-mentioned points, it is clear that When parents buy dolls for their daughters and football for their sons, their decision reflects gender stereotyping. 

Additional Information

• gender stereotypes are dynamic and not static.
• Both men and women carry out their responsibilities according to the division of the innate characteristics of gender.
• Gender stereotypes are reflected in marriage, family and community**.**

We know that children with mental retardation have difficulty in understanding, learning and remembering as compared to non-disabled children of their age, which is called individual differences in a child.

Here is a need for an educational and training programme specially designed for each child, based on his individual needs and abilities. This education and training plan is called the Individualized Education Programme (IEP).

• The purpose of the Individualized Education Program is to provide appropriate education and training to every child with a disability, including those with mental retardation.
• 'Individualized' means that the teaching-learning must be developed to meet the educational and learning needs of a single person rather than a group of persons.
• which means that the education and training are devised on the basis of: (i) what are his needs, and (ii) what are his abilities?
• Developing individualized teaching-learning for a particular child is a team effort. The most important persons in this team are the parents of the child.

Thus it is clear from the above-mentioned points, in a classroom, teaching-learning needs to be individualized since there are individual differences among learners.

Additional Information

• Teaching and training of the child should be done in the appropriate context. This means that we should train the child to do a particular activity in the situation in which he needs to show it.
• Evaluation helps to know whether the child is learning what we are teaching and also helps us to evaluate the training programme itself.

Given:

$3x + \frac{1}{3x} = 6$ and x ≠ 0,

Formula Used:

(a + b)² = a² + b² + 2ab

Calculation:

$3x + \frac{1}{3x} = 6$

On diving whole equation by 3 we get 

$x + {1\over9x} = 2$

On squaring both sides we get,

$(x + {1\over9x})^2 = 4$

⇒ $x^2 + {1\over81x^2} + {2\over9} = 4$

∴ $x^2 + \frac{1}{81x^2} = 4 - {2\over9} = {34\over9} = 3{7\over9}$

Given 

(2x + 5y)2 - 5(2x + 5y) - 14

Calculation

In order to make factors -5(2x + 5y) can be written as (-7 + 2)(2x + 5y) = -7(2x + 5y) + 2(2x + 5y)

Rewriting the given equation as  

(2x + 5y)² - 7(2x + 5y) + 2(2x + 5y) -14

= (2x + 5y)(2x + 5y -7) + 2(2x + 5y -7)

= (2x + 5y - 7)(2x + 5y + 2)

So, 2x + 5y - 7 is a factor.

Shortcut Trick

Sort the runs scored: 5, 9, 14, 15, 16, 18, 20, 50, 80, 100, 102.

Range (x) = Max − Min = 102 − 5 = 97.

Mean (y) = Sum ÷ Count = 429 ÷ 11 = 39.

Median (z) = Middle term (6^th) = 18.

Given x = y + z + p ⇒ 97 = 39 + 18 + p ⇒ p = 40.

∴ The correct answer is 40.

Alternate Method

Given: Runs of 11 players = 16, 9, 15, 18, 50, 100, 102, 14, 20, 80, 5.

Formula: Range (x) = Max − Min | Mean (y) = Σx ÷ n | Median (z) = ((n+1)÷2)^th term.

⇒ Arranging data in ascending order: 5, 9, 14, 15, 16, 18, 20, 50, 80, 100, 102.

⇒ Range (x) = 102 − 5 = 97.

⇒ Mean (y) = (5 + 9 + 14 + 15 + 16 + 18 + 20 + 50 + 80 + 100 + 102) ÷ 11 = 429 ÷ 11 = 39.

⇒ Median (z) = 6^th term = 18.

⇒ Given equation: x = y + z + p.

⇒ 97 = 39 + 18 + p.

&

Given:

The number of red balls in a bag  = 5

The number of white balls in a bag = 8

The number of green balls in a bag = 4

Concept used:

The probability formula is used to compute the probability of an event to occur. To recall, the likelihood of an event happening is called probability.

Formula required:

P(A) = Number of favorable outcomes/Total number of outcomes

Calculations:

Total number of out comes = the bag contains number of balls

⇒ 5 + 8 + 4 = 17

The number of favorable outcomes = total number of outcomes - the number of not favorable outcomes

⇒ 17 - 4 = 13

P(A) = 13/17 

∴ The probability that it is not green, is 13/17

Concept used:

Any number can be written as digit × place value

For example:- 354 = 3 × 100 + 5 × 10 + 4 × 1 = 300 + 50 + 4

Solution:

abc + bca + cab = 3 × (a + b + c) × k

⇒ (100a + 10b + c) + (100b + 10c + a) + (100c + 10a + b) = 3 × (a + b + c) × k

⇒ (100a + 10 a + a) + (100b + 10b + b) + (100c + 10c + c) = 3 × (a + b + c) × k

⇒ 111a + 111b + 111c = 3 × (a + b + c) × k

⇒ 111 × (a + b + c) = 3 × (a + b + c) × k

⇒ k = 111/3

⇒ k = 37

Concept

A square-based pyramid has 5 faces, 4 equal triangles and a square.

 A square-based pyramid has 8 edges.

A square-based pyramid has 5 vertices.

Calculation

Number of faces = F = 5

Number of edges = E = 8

Number of vertices = V = 5

So, 3F + 2V + E = 3(5) + 2(5) + 8 = 15 + 10 + 8 = 33.

If a person sells two articles at the same selling price, one at a gain of a% and another at a loss of a%, then the seller always incurs a loss given by 

Loss% = (a/10)2

Where a = 12%

Loss% = (12/10)2

⇒ 144/100 = 1.44%

∴ The loss percent in the whole transaction is 1.44%

Detailed explanation:

Given:

Priya sold two watches Each watch = Rs. 1232

Gain on one watch1 = 12%

Loss on watch 2 = 12%

Formulae required:

Profit = selling price - cost price 

The selling price of watch = cost price + profit

Loss = cost price - selling price 

The selling price of watch = cost price - loss

Loss% = (Loss/Cost Price) × 100

Calculations:

Watch 1: when gain = 12%

Selling price = Cost price + gain 

⇒ 1232 = 12% of cost price + cost price

⇒ 1232 =  (1 + 12/100) cost price 

⇒ 1232 =  (112/100) cost price

⇒ Cost price = 1232 × 100/112

⇒ Cost price =1100

Watch 1: when loss = 12%

Selling price = Cost price - loss 

⇒ 1232 = cost price - 12% of cost price

⇒ 1232 =  (1 - 12/100) cost price 

⇒ 1232 =  (88/100) cost price

⇒ Cost price = 1232 × 100/88

⇒ Cost price = 1400

The total cost price = 1400 + 1100

⇒ 2500

The total selling price =1232 + 1232

⇒ 2464

Total transaction loss = Cost price - selling price   (∵ Selling price < Cost price)

⇒ 2500 - 2464 = 36

Loss % = (36/2500) × 100

⇒ 1.44%

∴ The loss percent in the whole transaction is 

1.44%

Concept:

1. Four sides and one Diagonal. 2. Three sides and both diagonals. 3. Two adjacent sides and 3 angles. 4. Three sides and two included angles. 5. Four sides and one angle.

Constructing all cases one by one : 

1) AB = 5.5 cm, BC = 4 cm, ∠ A = 60°, ∠ B = 105° and ∠ C = 105°

2) AB = BC = 3 cm, AD = 5 cm, ∠ A = 90° and ∠ B = 105°

3) AB = 5 cm, BC = 3.5 cm, CD = 5 cm, AD = 3 cm and AC = 8.5 cm

Here, AB + BC = AC which can not be possible in a quadrilateral

Points A, B and C lie in a straight line so, no quadrilateral can be formed.

4) AB = 4.5 cm, BC = 4 cm, CD = 6.5 cm, AD = 3 cm and BD = 6.5 CM

So, a quadrilateral cannot be constructed in case 3.

Concept 

Complementary angles are those angles whose sum is 90°

Supplementary angles are those whose sum is 180° 

Calculation

x = 180° - x - 32°

⇒ 2x = 180° - 32° = 148°

So, x = 74°

y = 90° - y + 24°

⇒ 2y = 90° + 24° = 114°

So, y = 57°

Then, x + y = 74° + 57° = 131°

Given 

In ΔABC, D is the mid-point of BC and ∠C = 40°. A is joined to D and AD = BD.

Concept Used:

Angles opposite to the equal sides of a triangle are equal

Sum of all angles of a triangle = 180º

Calculation

BD = DC = AD

⇒ ∠ ABD = ∠ BAD and ∠ ACD = ∠ CAD [Angles opposite to the equal sides of a triangle are equal]

∠ ACD = ∠ CAD = 40º

And, ∠ A = ∠ BAD + ∠ CAD

Now,

In Δ ABC, ∠ A + ∠ B + ∠ C = 180º  [Sum of all angles of a triangle = 180º]

∠BAD + ∠ ABD + 40º + 40º = 180°

 

⇒ 2 × ∠ BAD = 180º - 80º = 100º (∵ ∠ ABD = ∠ BAD)

∠BAD = 50º

So, ∠ BAC = 50º + 40º = 90º

Let the side of the square be 'a'

Area of square = side × side or side²

Area of square = a²

Side of square side increased by 25% = a + a × 25/100

⇒ a (1 + 25/100) = a(125/100)

⇒ 5a/4

Area of new square = (5a/4) × 5a/4

⇒ 25a²/16

Change in area of square if side increased by 25% = (25a²/16) - a²

⇒ [(25a² - 16a²) ÷ 16] × 100 = 9a²/16

Percentage change in area = [(9a2/16) ÷ a²] × 100

⇒ 9× 100/16 = 56.25%

∴ The area will increase by 56.25%

 

Let the side of square be '100 cm'

Area of square = side × side 

⇒ 100 × 100 = 10000 cm²

After increasing each side 25% = 100 + 100 × 25/100

⇒ 100(1 + 25/100) = 100 × (1 + 0.25)

⇒ 100× 1.25 = 125

Area of the square after increasing side by 25% = 125 × 125

⇒ 15625

The difference between old area and new area of square = 15625 - 10000

⇒ 5625

Percentage = (5625/10000) × 100

⇒ 56.25%

∴ The area will increase by 56.25%

 

If each side of a Square or any two-dimensional shape is increased by x %, its area is increased by [(x² /100) + 2x]%

⇒ [(25 × 25)/100] + 2 × 25 = 6.25 + 50

⇒ 56.25%

Given:

A rectangular paper piece = 22 cm × 8 cm

height of a cylinder = 8 cm

Concept used:

Circumference of the circle(one face of the cylinder) = length of the rectangle (∵ length is rolled as a cylinder)

Formula required:

The volume of a cylinder = πr2h

Circumference of a circle = 2πr

where π = 22/7

Calculations:

Circumference of a circle(one face of the cylinder) = length of the rectangle

 2 π r ⇒ 22

⇒ 2 × (22/7) × r = 22

⇒ r = 7/2 cm

The volume of a cylinder = πr²h 

⇒ (22/7) × (7/2) × (7/2) × 8 =  308 cm³

∴ The volume of a cylinder is 308 cm³

Given:

There are two pieces of wire each of length = 30 cm

Sides of triangle = 5 cm, 12 cm, and 13 cm 

Square perimeter = 30 cm

Concept used:

Pythagorean triplets are a² + b² = c² where a, b and c are the three positive integers. These triplets are represented as (a, b, c). ... He is famous for a property of triangles with a right angle i.e 90° angles, and the property is known as Pythagoras Theorem.

Formulae required:

Area of square = side²

The perimeter of square = 4 × side

Area of triangle = base × height × 1/2

Calculations:

Perimeter of a square = 4 × side 

⇒ 30 = 4 × side 

⇒ side = 30 ÷ 4

⇒ side = 7.5 cm

Area of square = 7.5 × 7.5 

⇒ 56.25 cm²

Area of triangle = (1/2) × 5 × 12  (∵ 5, 12, and 13 are Pythagorean triplets so, the triangle is a right-angled triangle

⇒ 30 cm²

The ratio of the area of the triangle to that of the square = 30 ∶ 56.25

⇒ 8 ∶ 15

∴  The ratio of the area of the triangle to that of the square is 8 ∶ 15

The teacher is using an inductive approach by asking the students to observe and analyze a pattern that emerges from their observations. The students are drawing circles of different radii and calculated the ratio of circumference to diameter for each circle. They find that this ratio is almost the same for each circle.

Key Points

• In the inductive approach, students are encouraged to gather specific observations or data and then draw general conclusions based on patterns or trends observed in the data.
• In this case, the students are observing a consistent pattern in the ratio of circumference to diameter across different circles.
• Based on the pattern, they can make a generalization that the ratio of circumference to diameter is constant for all circles.

Hint

• The project method involves engaging students in a long-term project or investigation. While the students are engaging in an activity related to circles, the given scenario does not involve a long-term project.
• The analytical approach typically involves breaking down a problem or concept into smaller parts and analyzing each part separately. While the students are calculating the ratio of circumference to diameter, the focus is on identifying a pattern rather than conducting a detailed analysis.
• The deductive approach involves starting with general principles or theories and applying them to specific situations. In this scenario, the students are not given any general principles or theories to apply. They are instead making observations and drawing conclusions based on those observations, which aligns with the inductive approach.

Hence, we can conclude that in the above scenario, the teacher is using an inductive approach.

CBSE recommendation**, Mathematics laboratory** is a unique room or place, with relevant and up-to-date equipment, known as instructional materials, designed for the teaching and learning of mathematics and other scientific or research work, whereby a trained and professionally qualified person (mathematics teacher) readily interacts with learners on a specified set of instructions. 

Key Points

Math lab is a place where learners get the opportunity to engage with mathematical objects, experiment with mathematical theories, solve mathematical puzzles and problems, play mathematical games, experience hands-on training, and so on.  

• The math labs/corners are important due to the following reasons: 
• It helps learners to comprehend mathematical concepts effectively by utilizing concrete objects and experiencing real situations.
• Learners can test and experience theoretical knowledge and discover different mathematical properties.
• It enhances the interest and motivation of learners to learn mathematics.
• Math labs provide objects and materials, which help learners to relate concepts with their daily life activities and nature.
• Individual learning is promoted while exploiting math labs as learners engage in an exploration of mathematical contents in their own way.
• The cognitive development is supported and enhanced as learners exercise both mind and body by engaging in learning activities.
• The teacher can demonstrate learning concepts by connecting with multiple learning resources present in the math labs.
• It helps in the development of the skill of inquiry and critical thinking.
• The principle of ‘learning by doing’ can be practiced by learners.

Thus from above-mentioned points, it is clear that the main purpose of the Mathematics Laboratory is to provide opportunities for hands-on learning.

Mathematics is a branch of science that deals with counting, calculating, and studying numbers, shapes, and structures. 

In Mathematics, mathematicians are concerned with arguments, instead of proofs. The truth of an argument can be acquired through two main processes i.e. Deduction and Induction.

• Arguments with logical processes are generally divided into two parts i.e. a Premise and a Conclusion.
• To prove an argument, one has to provide reasons to support it. To do so, one begins with plausible assumptions, the Premises (Axioms), and then show that those assumptions logically entail a Conclusion (Theorem).

Important Points

An axiom:

• is a statement that serves as a starting point from which other statements are logically derived.
• is a statement that is assumed to be true and need not be proved.
• is a mathematical statement that we assume to be true without proof.
• are the propositions that are assumed.
• are used for different mathematical reasoning and proving theorems.
• are used in the starting point of any mathematical reasoning.

NOTE: A theorem is a statement that has been proven by logical arguments based on axioms. 

Hence, we can conclude that Axioms are the same as propositions statement is true about 'axioms'.

In upper primary classes, most of the concepts in Mathematics are abstract in nature. One can reach this abstraction and learn higher and higher related concepts. Mathematics education deals with all issues at all levels related to Teaching-Learning of mathematics in the socio-cultural-economic contexts and is concerned with the development and of appropriate mathematics curricula.

Important Points

An essential aspect of mathematics planning in upper primary classes:

• Learners learn mathematical thinking most effectively through applying concepts and skills in interesting and realistic contexts which are personally meaningful to them.
• Encourage thinking rather than mere recall.
• The solutions to problems that are worth solving seldom involve only one item of mathematical understanding or only one skill.
• Design appropriate activities so that the learners can work on them and construct concepts with confidence and a feeling of success.
• The creation of a learning environment that is stimulating, interactive, and enlightening for the learners is the most challenging task of a constructivist teacher.

NOTE: Present Mathematical concepts in a hierarchical manner is essential at the primary level.

Hence, we can conclude that 'providing learning opportunities to allow learners to construct concepts' is the most essential aspect of mathematics planning in upper primary classes.

Mathematics is the study of patterns, numbers, geometrical objects, data, and information. It deals with data analysis, integration of various fields of knowledge, involves proofs, deductive and inductive reasoning, and generalizations

• It involves the mathematization of thoughts that develops through mathematical reasoning, consisting of abstract statements and their proofs.
• Any assumption, hypothesis, and argument in mathematics can be proved with the help of various methods of proof.
• A sentence is called a mathematically acceptable statement if it is either true or false but not both at the same time.
• If a statement is true, we say that it is a valid statement. A false statement is known as an invalid statement.

Key Points

Direct proof:

• It includes a logically valid argument that begins with the assumptions and hypotheses.
• It consists of various steps of detachment in order to prove the conclusion is true.
• Let's understand this by the example,
• Consider any two odd integers X and Y, with the hypothesis, p: x and y are odd.
• The conclusion we want to reach is q: XY is odd (product of two odd integers is odd).
• The essence of this direct proof lies in showing the following :
• ​p ⇒ q.
• So, if n² is odd, then n is also odd. Like (13)² = 169 and (7)² = 49 whereas 13 and 7 are the odd number so as 169 and 49 are.

Hint

 

 Hence, it is concluded that the above statement can be proved by using "direct proof".

Mathematics is the study of geometrical figures, their co-relation, and their dependency on each other. It deals with quantity, measurement, and spatial relationships.

• The teacher should use effective teaching methods of mathematics so that individualized discovery-oriented (or problem-solving) learning could be fostered.

Key Points

Mathematical theorem:

• The theorems in mathematics are dependent on the abstract nature of mathematics.
• Theorems are generally referred to as mathematical statements that can be proved with the use of logical reasoning.
• A theorem can be in the form of an implication i.e., any hint or suggestion as the theorem are general statements of mathematics that are proved using definite methods and logical reasoning.
• The theorem needs to be proved by logical arguments and properly organized in a step-wise manner.
• Firstly the hypothesis needs to be formed, then the statement is being proved with the use of logical reasoning. So, theorems have proof based on logical reasoning and hypothesis.
• A theorem can be bi-conditional as if one condition is true then the other condition of the theorem has to be true.
• For example, if the sum of two angles of a triangle is 90 degrees then the third angle of a triangle has to be 90 degrees. (The sum of all three angles of a triangle is 180 degrees).

Hint 

• A proved theorem does not become an axiom but it is said to be based on axioms and postulates because they are useful to prove and derive the complex theorems and abstract statements of mathematics.
• For example, Pythagoras theorem that states that the hypotenuse of a right-angle triangle will be equal to the sum of the other two sides of a right-angle triangle.

Hence, it is concluded that a theorem becomes an axiom if proved is not true about a Mathematical theorem.

During the Upper primary stage, slowly children must be given the opportunity to deal with abstract concepts. This is the stage at which algebra needs to be introduced. It should be introduced by connecting it to real-life situations and through its use in solving various life problems. In algebra, the emphasis has now been given to equations by broadening the base to include ideas such as mathematical sentences, replacement set and solution set.

Key Points

Keeping the above stated higher objectives of mathematics education in view, the NCF 2005 have spelt out the vision for school mathematics : 

• Children use abstractions to perceive relationships, to see structures, to reason about things, to argue the truth or falsity of statements. Logical thinking is a great gift of mathematics can offer us, inculcation, such habits of thought and communication in children is a principal goal of teaching mathematics.
• Children understand the basic structure of mathematics: Arithmetic, algebra, geometry and trigonometry, the basic content areas of school mathematics, all offer a methodology for abstraction, structuration and generalization.
• Children pose and solve meaningful problems: In school, mathematics is the domain which formally addresses problem-solving as a skill.
• Teachers engage every child in the class with the conviction that everyone can learn mathematics.

Thus from above-mentioned points, it is clear that Generalisation is an important aspect of algebra in Class VI.

Errors:

• When a learner can’t master a topic, he/she is vulnerable to make errors. Errors are nothing but incorrectness made by a child during learning.
• It also takes place due to the mismatch in previously assimilated and newly accommodated knowledge.

Important Points

Children's errors are a window into how they think:

• Learning from mistakes and errors is a crucial and important part of learning new concepts.
• Committing errors in learning to show the thinking ability and capacity of a child.
• Errors are very helpful in developing the critical and creative thinking of the students.
• It is like a window into how the learner pounder on the errors and learns from the errors.
• The teachers should not deny the learner to committing errors, if the teacher does, he/she deteriorate the thinking capacity of a child.
• Imitating others while learning will also barrier to developing critical thinking.

Key Points 

As a teacher, you should adopt the following strategies- 

• The process of discussing in the class gives the students an opportunity to discover their sources of error and then proceed to correct misunderstandings of facts, concepts, mathematical principles as well as errors in computations, etc.
• Ask students to use an alternative method or redo it to find out errors on his/her own.
• A common practice is that students will justify the answer only when the teachers ask them to do so due to mistake or error.
• What is required is to build the process of justification as a habitual one in our students. The process of justification will help them to explain why their answer is correct and convince peers and teachers.
• always teach alternatives so that student can follow divergently thinking

Thus from the above-mentioned points, it is clear that the teacher should study the errors and their possible causes and design her teaching strategy.

• Mathematics is a science that involves dealing with numbers, different kinds of calculations, measurement of shapes and structures, organisation and interpretation of data and establishing relationship among variables, etc. Mathematics relies on logic, reasoning, problem-solving, creativity and mathematical way of thinking.
• Creative thinking has a major role in mathematical reasoning. It is creative thinking that has led to the invention of new ideas and knowledge.

Key Points

Below are given a few methods that you can think of in order to inculcate the skill of creative thinking in your students-

• Make your teaching more meaningful. Don’t allow children to act as passive listeners and ensure the active participation of children in the learning process.
• Start teaching with the concrete concept and slowly build up the difficulty level. Try to explain real-world problems with simple examples.
• Engage students in problem-solving situations by providing problems that have multiple solutions.
• Try to provide problems that involve divergent thinking and show the ways of reaching answers in multiple ways as-
• Quiz programmes
• Conduction of math fairs, field-trips, exhibitions, etc
• Exhibition of mathematical models, aids, charts, etc
• Seminars and workshops

Thus from above-mentioned points, it is clear that field-trips are best suited to assess the Mathematical creativity in learners.

Hint

• An investigatory project is basically a science experiment where you start with a problem and do research to decide what you think the outcome will be.
• Annual examinations are given to the student at the end of the year.
• Olympiad examination is exams at the same level in which students compete with each other.

Mathematics is a science that involves dealing with numbers, different kinds of calculations, measurement of shapes and structures, organization and interpretation of data, and establishing relationships among variables, etc. s. Various topics to be included at this stage may be numbers and their operations, shapes, spatial understanding, patterns, measurement, and data handling. In our day to day life, you must have seen several kinds of tables consisting of numbers, figures, names, etc. These tables provide ‘Data’. Data is a collection of numbers gathered to give some information. 

Key Points

Some activities of data-interpretation in the classroom are-

• A survey of 120 school students was done to find which activity they prefer to do in their free time. In this, we collect the data of students and interpret it in tablet form.
• A class which is preparing to go for a picnic. The teacher asked the students to give their choice of fruits out of banana, apple, orange, or guava and prepared a list of all the children and wrote the choice of fruit against each name.
• Similarly providing survey reports from newspapers also the activities related to data interpretation. In this students collect data and organize it in table form.

Thus from the above-mentioned points, it is clear that providing survey reports from newspapers is most appropriate in teaching-learning of data interpretation in Class VII

Concept used:

Rational number between two numbers a and b = (a + b)/2.

Calculation : 

x = -2/3 and y = -3/4

x + y = -2/3 - 3/4 = (-8 - 9)/12 = -17/12

(x + y)-1 = -12/17

x-1 = -3/2 and y-1 = -4/3

x-1 + y-1 = -3/2 - 4/3 = (-9 - 8)/6 = -17/6

Then, the rational number between (x + y)-1 and x-1 + y-1 = [(-12/17) + (-17/6)]/2

⇒ (-72 - 289)/204 

⇒ -361/204

Additional Information

A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero. For example : 2, 6/5, -9/12, etc.

Calculation

0.109 + 0.2 + 0.111 - x + (0.19 × 0.1) + (0.11 ÷ 0.2) = 8 × (10)^-1

0.420 - x + 0.019 + 0.55 = 0.8

0.989 - x = 0.8

x = 0.989 - 0.8 = 0.189

Given:

3x - 2(x + 3) = 2(2x - 5)

Claculations:

3x - 2x -  6 = 4x - 10

⇒ x - 6 = 4x -10 

⇒ x - 4x = -10 + 6

⇒ -3x = - 4

⇒ x  = 4/3

$\frac{5x - 2}{3x - 5} = \frac{5\times \frac{4}{3} - 2}{3\times\frac{4}{3} - 5}$

⇒ (20/3) - 2)/(4 - 5)

⇒ (14/3)/(-1)

⇒ (-14/3)

∴ The required value is (- 14/3)

Given:

 $√{768}$ × $√{3267}$ = 44 × y

Firmulae required:

(a^m)ⁿ = a^mn

√a = a^1/2

a^m ×  b^m = (a × b)^m

Calculations:

Factors of 768 = 256 × 3

⇒ 2⁸ × 3                  (∵ 256 = 2⁸)

Factors of 3267 = 121 × 27

⇒ 11² × 3³     (∵ 121 = 11² , 3³ = 27)

⇒ (768)^1/2 × (3267)^1/2 = 44 × y

⇒ (28 × 3 × 112 × 33)^1/2 = 44 × y

⇒ (2⁸ × 3⁴ × 11² )^1/2 = 44 × y

⇒ 2^{8 × 1/2} × 3^{4 × 1/2} × 11^2 ×1/2 = 44 × y

⇒ 2⁴ × 3² × 11 = 44 × y

⇒ 16 × 9 × 11 = 44 × y

⇒ y = 9 × 4 = 36

∴ The value of y is 36

Given: 

$\sqrt[3] {-2688} \times \sqrt[3]{1764} = 24 \times z$

Calculations:

Factors of 2688 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 7

⇒ 2⁷ × 3 × 7

Factors of 1764 = 2 × 2 × 3 × 3 × 7 × 7

⇒2² × 3² × 7²

$\sqrt[3]{2688} × \sqrt[3]{1764} = 24 × z$

$⇒ -1 × \sqrt[3]{2^7 × 3× 7} × \sqrt[3]{2^2 × 3^2 × 7^2} = 24 × z$

 $⇒ -1 × \sqrt[3] {2^7 × 3 × 7× 2^2 × 3^2 × 7^2} = 24 × z$

 $⇒-1(2^{7+2} × 3^{1 + 2} × 7^{1 + 2})^{1/3} = 24 \times z$

⇒ -1 × 2^{9 × 1/3} × 3^{3 × 1/3} × 7^{3 × 1/3} = 24 × z

⇒ -1 × 2³ × 3 × 7 = 24 × z

⇒ z = 24 ÷ (8 × 3 × 7 × -1)

⇒ z = -7

∴ The value of z is -7

Given:

$\frac{{{{\left[ {{{\left( {\frac{2}{3}} \right)}^2}} \right]}^3} × {{\left( {\frac{1}{3}} \right)}^{ - 4}} + {3^{ - 1}} × \frac{1}{6}}}{{{{\left( {\frac{5}{8}} \right)}^{ - 3}} × {{\left( {\frac{5}{4}} \right)}^2} × {2^{ - 1}}}}$

Formula required:

$\sqrt[2]{a} = a^{1/2}$

$\sqrt[3]{a} = a^{1/n}$

$a^m \times a^n = a^{m + n}$

a-m = 1/am

Calculations:

[(2/3)²]³ = (2/3)⁶

(1/3)^-4 = 3⁴

3^-1 = 1/3

(1/3) × (1/6) = 1/18

(5/8)^-3 = (8/5)³

2^-1 = 1/2

 $\Rightarrow \frac{{{{\left[ {{{\left( {\frac{2}{3}} \right)}^2}} \right]}^3} × {{\left( {\frac{1}{3}} \right)}^{ - 4}} + {3^{ - 1}} × \frac{1}{6}}}{{{{\left( {\frac{5}{8}} \right)}^{ - 3}} × {{\left( {\frac{5}{4}} \right)}^2} × {2^{ - 1}}}} = \frac{(\frac{2}{3})^6 × \ 3^4 + \frac{1}{3}× \frac{1}{6}}{(\frac{5}{8})^{-3}× (\frac{5}{4})^2 × \frac{1}{2}}$ 

⇒ [2⁶ × 3^-6 × 3⁴ + (1/3) × (1/6)] ÷ [8³ × 5^-3 × 5² × 4^-2 × 2^-1] = [2⁶ × 3^-6+4 + 1/18] ÷ [4³ × 2³ × 2^-1 ×  5^-3 × 5²× 4^-2]

⇒ [2⁶ × 3^-2 + 1/18] ÷ [2⁴ × 5^-1] = [64/9 + 1/18] ÷ 2⁴/5

⇒ (129/18) ÷ 16/5 = (129 × 5)/(18 × 16) 

⇒ 215/96

∴ The required value is 215/96

Given 

Gaurav has Rs. (72 × 104) in his account and his brother his Rs. (27 × 103) in his account

Calculation

Total amount in their accounts = (72 × 104) + (27 × 103) = 49 × 10⁴ + 128 × 10³

⇒ 490 × 10³ + 128 × 10³ 

⇒ (490 + 128) × 10³ 

⇒ 618 × 10³ = 6.18 × 10⁵

On comparing it with the standard form m × 10ⁿ we get, m = 6.18 and n = 5

So, m + n = 6.18 + 5 = 11.18

The correct match is (a) - (iv), (b) - (v), (c) - (ii), (d) - (i)

Explanation:

• Alexander Fleming - 
• In 1929, Alexander Fleming was working on a culture of disease-causing bacteria.
• Suddenly he found the spores of a little green mould in one of his culture plates.
• He observed that the presence of mould prevented the growth of bacteria.
• In fact, it also killed many of these bacteria. From this, the mould penicillin was prepared.
• Edward Jenner -
• Edward Jenner discovered the vaccine for smallpox in 1798.
• It is also considered to be the first vaccine ever.
• Small Pox is caused due to Variola Virus.
• Robert Köch  -
• Robert Köch (1876) discovered the bacterium (Bacillus anthracis) which causes anthrax disease
• Louis Pasteur -
• He discovered fermentation in 1857.

Concept:

• Endocrine glands lack ducts and are hence, also called ductless glands. Their secretions are called hormones which are directly released into the bloodstream.
• The adrenal cortex produces three main types of steroid hormones: mineralocorticoids, glucocorticoids, and androgens.
• Mineralocorticoids (aldosterone) -> zona glomerulosa ->blood pressure and electrolyte balance.
• Glucocorticoids cortisol and cortisone -> zona fasciculata -> metabolism and immune system suppression.
• Androgens -> zona reticularis -> converted to fully functional sex hormones in the gonads

Regulation:

• Glucocorticoids are under the regulatory influence of the hypothalamus-pituitary-adrenal HPA axis. Glucocorticoid synthesis is stimulated by the adrenocorticotropic hormone ACTH.
• Mineralocorticoid secretion is regulated mainly by the renin-angiotensin-aldosterone system RAAS. The juxtaglomerular apparatus of the kidneys release the enzyme renin into the blood, which starts reactions that lead to the formation of Angiotensin II. [Mineralocorticoids are not under influence of the pituitary so even if the adrenal gland is endocrine it does not answer]

Explanation:

• The pituitary gland is the master gland of the body as it controls the functioning of many other endocrine glands.
• The pituitary gland is located in a bony cavity called Sella tursica and is attached to the hypothalamus by a stalk.
• It secretes several hormones like growth hormone (GH), prolactin (PRL), thyroid-stimulating hormone (TSH), adrenocorticotrophic hormone (ACTH), and luteinizing hormone (LH), follicle-stimulating hormone, melanocyte-stimulating hormone (MSH), oxytocin and vasopressin.
• Thyroid-stimulating hormone (TSH) stimulates the synthesis and secretion of thyroid hormones from the thyroid gland.
• In males, Luteinizing hormone (LH) stimulates the synthesis and secretion of hormones called androgens from the testis.

Hence, the two endocrine glands which secrete their hormones when they receive orders from the pituitary through its hormones are the thyroid & testis.

 

Mistake Points In this Question the thyroid and testis are exclusively endocrine and receive their order from the pituitary gland to secrete their hormones. The adrenal gland and part of its secretion are independent of the pituitary.

The correct match is (i) - (B), (ii) - (C), (iii) - (D), (iv) - (A)

Explanation:

• Cell Wall:
• Plant cells, in a ddition to the plasma membrane, have another rigid outer covering called the cell wall. The cell wall lies outside the plasma membrane. The plant cell wall is mainly composed of cellulose.
• **The cell wall provides mechanical support to the cell.**​
• Cell membrane: 
• This is the outermost covering of the cell that separates the contents of the cell from its external environment.
• The cell membrane allows or permits the entry and exit of some materials in and out of the cell.
• It also prevents the movement of some other materials. The cell membrane, therefore, is called a selectively permeable membrane.
• Cytoplasm:
• The cytoplasm is the fluid content inside the plasma membrane.
• It is the arena of cellular activities i.e. cell reactions happen in it.
• It also contains many specialised cell organelles. Each of these organelles performs a specific function for the cell.
• Nucleus:
• The nucleus is called the brain of the cell as it controls all the cellular metabolism and encloses the genetic information of the cell.
• The nucleus has a double-layered covering called a nuclear membrane.
• The nuclear membrane has pores that allow the transfer of material from inside the nucleus to its outside, that is, to the cytoplasm

Concept:

• Cells are the structural & functional unit of life.
• Cells that have membrane-bound nuclei are called eukaryotic whereas cells that lack a membrane-bound nucleus are prokaryotic.
• In both prokaryotic and eukaryotic cells, a semi-fluid matrix called cytoplasm occupies the volume of the cell.
• Besides the nucleus, the eukaryotic cells have other membrane-bound distinct structures called organelles like the endoplasmic reticulum (ER), the Golgi complex, lysosomes, mitochondria, microbodies and vacuoles.
• The prokaryotic cells lack such membrane-bound organelles.
• Ribosomes are non-membrane bound organelles found in all cells – both eukaryotic as well as prokaryotic.
• The eukaryotic can be further classified into two types - Animal cells & Plant cells.

Explanation:

• All eukaryotic cells are not identical.
• Plant and animal cells are different as the former possess cell walls, plastids and a large central vacuole which are absent in animal cells.
• On the other hand, animal cells have centrioles which are absent in almost all plant cells.

Below is the table to compare animal & plant cells.

Hence, the combination of components of an animal cell is the Cell membrane, Cytoplasm, Nucleus, Vacuole.

Aspergillus, Penicillium, and Bread mold are fungi.

Concept:

• Fungi constitute a unique kingdom of heterotrophic organisms.
• Fungi show a great diversity in morphology and habitat.
• Fungi are cosmopolitan and occur in air, water, soil, animals, and plants.
• The study of fungi is Mycology.
• Fungi are categorized into 4  classes: Ascomycetes, basidiomycetes, Phycomycetes & Deuteromycetes

Explanation:

• Aspergillus:
• It is a Fungus genus that belongs to the class Ascomycetes or the sac fungi.
• It includes several species like A. Proliferans, A. Fumigatus, A.Flavus & A. Niger
• Rhizopus (the bread mold): 
• It is a Fungus genus that belongs to the class Phycomycetes.
• Members of Phycomycetes are found in aquatic habitats and on decaying wood in moist and damp places or as obligate parasites on plants.
• Penicillium:
• It is a Fungus genus that belongs to the class Ascomycetes or the sac fungi.
• Its mycelium is branched and septate.
• It has asexual spores are conidia produced exogenously on the special mycelium called conidiophores. Conidia on germination produce mycelium.

Additional Information 

• ​Lactobacillus: 
• Lactobacillus is a gram-negative bacteria.
• It promotes the formation of curd. It multiplies in milk and converts it into curd.
• Paramecium:
• The paramecium is a ciliated protozoan.
• It comprises a single cell only.
• Spirogyra:
• Spirogyra is a free-floating green alga. It belongs to the Chlorophyta kingdom.
• Spirogyras are filamentous algae that consist of thin unbranched chains of cylindrical cells
• Amoeba:
• The amoeba is amoeboid protozoan.
• It has false feet called pseudopodia that are used for locomotion And capturing prey.

Concept:

Breathing:

• Breathing refers to the process of air moving into and out of the lungs.
• Breathing, in other words, is a basic give-and-take activity or simply saying just exchange of gases.
• When we breathe, we take in oxygen-rich air from the environment and exhale carbon dioxide-rich air.
• This is a continual process that occurs throughout an organism's life.
• Inhalation is the process of taking in oxygen-rich air. Exhalation, on the other hand, refers to the process of exhaling carbon dioxide-rich air.
• One inhalation and one exhale makeup one breath.

​Respiration: 

• Breathing is not similar to respiration.
• Respiration is a chemical process whereas breathing is a physical process.
• In respiration, processes at the cellular level are taking place.
• Here, glucose (released by complete digestion of food) is broken down into water and carbon dioxide in the presence of oxygen.
• ATP which is the energy currency is also released.

Explanation:

• The given four statements are -
• A. It is a process that provides oxygen to the body - True for Breathing
• B. In this process water is produced in the cell. - True for Respiration
• C. This process helps the body to get rid of carbon dioxide. - True for Breathing
• D. In this process, food breaks down to release energy. - True for Respiration
• Out of these statements, B and D are a part of the process of respiration and not breathing.
• Only statements A and C are correct for breathing.

Hence the correct answer to this question is - statements A and C.

In the learner-centered approach, the need, interest, mental ability, and social context of the learner are taken into account.

• In the activity-based approach, importance is given to the learner who gets new knowledge by doing activity in his/her own environment.
• Activity is an objective-oriented task in which the learner gets spontaneously involved and derives pleasure in achieving the learning objectives.

Key Points

In the activity-based approach, we consider the following assumptions- 

• Pupils have different learning styles (that instruction should accommodate)
• Children’s innate curiosity and self-perpetuating exploratory behavior should form the basis of their learning in school.
• They should have the opportunity to pursue their interests as deeply and as long as they find the pursuit satisfying.
• The individual child often learn in unpredictable ways (and instruction should accommodate such eventualities)
• Children are capable of making intelligent decisions in significant areas of their own learning.
• The function of the school is to help children develop learning to learn in order to become lifelong learners.
• In activity-based science, the teacher least emphasizes the memorization of science facts because science is a practical approach.
• Children have adopted the skill of questioning by discussing among them.
• Learning is facilitated by the relationship of openness, trust, and mutual respect; and school should provide an accepting and warm emotional climate.

Thus from the above-mentioned points, it is clear that memorization is least developed among students by activity-based science education.

Science as a discipline has its unique perspective. Science is not limited to observation, experimentation, and analysis only; rather it is a way of life. Science is an expanding body of knowledge through the process of inquiry. 

Key Points

These characteristics define the nature of science-

• Science is a particular way of looking at nature- Scientist always considers eclipse a natural phenomenon, enjoys the sight and tries to understand what caused the event and investigates whether it could have any ill effects.
• Science is a rapidly expanding body of knowledge- Newer disciplines are being discovered and established every day and the older ones are being enriched by researches being carried out in institutes of higher learning
• Science is an interdisciplinary area of learning- It is then that knowledge was organized for convenience into disciplines like physics, chemistry, biology, geology, astronomy, etc. though no natural phenomenon falls completely under just any one of these disciplines
• Science is a truly international enterprise- Science does not belong to any single country or a group of countries, and it would be morally and ethically wrong to deny the fruits of scientific development to any country in the world.
• Science is always tentative- All theories, even the seemingly well-founded ones, can be revised or improved upon, or abandoned altogether whenever new evidence emerges, either as new experimental observations or as new theoretical developments

Thus from the above-mentioned points, it is clear that Scientific knowledge has a tentative character.

A science teacher has to plan and execute the assessment as an integrated part of his/her teaching-learning process. A teacher has to devise various tools and adopt different techniques for assessment depending upon nature of the content, type of skills, level of the learner, etc. In means, one can not use a similar kind of tool for assessing a variety of process skill, for different kind of content and activities. 

Key Points

Nature of assessment in science-

• Assessment in science promotes scientific enquiry-
• When a teacher plans assessment activities in science, its key focus is that it should promote scientific enquiry.
• If as a teacher, you plan and use such tools and techniques, which involve problem solving, investigation, active thinking and reasoning, your assessment will promote scientific enquiry
• Assessment is linked with cognitive levels of learner-
• assessment tool should be linked with every level of cognitive learning which are based on remembering, understanding, applying, analyzing, evaluating and creating
• Assessment in science is comprehensive in nature-
• Comprehensiveness is the key characteristic of assessment in science. A science teacher never assesses only one dimension, rather it assesses many dimensions during one assessment.
• Assessment in science facilitates the development of process skills-
• The major role of assessment is not grading or promoting. Its role in facilitating the development of scientific process skills.
• One cannot undermine the importance of informal observations that are constantly collected by the teachers whenever they are interacting with children.

HintNodoubt tests are helpful in assessing the knowledge of students but they do not test everything about the students.

Hence, we can conclude that we must realise that we have to test everything that the student knows using a variety of tools statement is the most impractical ideal about assessment of science.

An “open book examination” is one in which examinees are allowed to consult their class notes, textbooks, SLPMs, and other approved material while answering questions during the examination. In an open book examination, it is therefore meaningless to ask questions for which relevant information from the textbook or other relevant material can be directly copied into the answer book. Given the availability of textbooks or other material in the examination room, teachers will not ask questions that require the mere transfer of information from the textbook to the examination (answer) booklet. 

Key Points

Following are the advantages and disadvantages of the Open Book Examination.

• Advantages-
• It is less demanding on memory because it is no longer necessary for students to cram a lot of facts, figures, and numbers for open-book examination.
• It provides a chance for students to acquire knowledge during the preparation process of gathering suitable learning materials rather than simply recalling or rewriting it.
• It helps to gauge the conceptual understanding of the student.
• It promotes information retrieval skills of students through finding efficient ways to get the necessary information and data from books and various resources.
• It enhances the comprehension and synthesizing skills of students because they need to reduce the content of books and other study materials into simple and handy notes for examination.
• Open book questions reduce the fear of assessment.
• Disadvantages-
• It is difficult to ensure that all students are equally equipped regarding the books they bring into the exam with them because the stocks of library books may be limited and also some books may be expensive to students.
• It requires more desk space for students during the examination because students often need lots of desk space for their textbooks, notes, and other reference materials.
• Sometimes students may spend too much time finding out which parts of the books to look for answers to instead of applying the knowledge, practical skills, and reasoning ability.
• A lot of students are unfamiliar with open-book examinations. They must be provided with clear procedures and rules.

Thus from the above-mentioned points, it is clear that option a, c, d have embraced the spirit of open-book questions.

Science refers to the study of structure and behaviour of the physical and natural things through observation and experimentation. In other words, science is a classified knowledge gained from a systematic study of the behaviour of nature.

• Textbooks help teachers and learners in this regard. It is a tool to be used in the teaching-learning process to facilitate effective and meaningful learning.

Key Points

The purpose of including the above paragraph in a science textbook is-

• To develop a historical perspective: 
• ​The Silk Road was a vast trade network connecting Eurasia and North Africa via land and sea routes.
• The Silk Road may have formally opened up trade between the Far East and Europe during the Han Dynasty, which ruled China from 206 B.C. to 220 A.D.
• The Silk Road earned its name from Chinese silk.
• To develop an appreciation of how incidents/ideas give rise to the discovery of new things.
• According to an old Chinese legend, the empress Si-lung-Chi was asked by the emperor Huang-ti to find the cause of the damaged leaves of mulberry trees growing in their garden.
• The empress found white worms eating up mulberry leaves. She also noticed that they were spinning shiny cocoons around them.
• Accidentally a cocoon dropped into her cup of tea and a tangle of delicate threads separated from the cocoon.
• To develop a holistic understanding of science
• ​Art, religion, philosophy, technology, language, science, architecture, and every other element of civilization was exchanged along these routes.
• These were carried with the commercial goods the merchants traded from country to country.
• This paragraph also develops a holistic understanding of science related to silk and the silk route, that how scientifically it was traded in ancient times.

Hence we conclude that a, b & c statements are correct regarding the purpose of this paragraph to be given in the NCERT book of class 7.

In learning science, the activity approach is used for the extended learning process. In the activity-based approach, importance is given to the learner who gets new knowledge by doing activity in his/her own environment. Activity is an objective-oriented task in which the learner gets spontaneously involved and derives pleasure in achieving the learning objectives.

Explanation:

The above-given activities have the following advantages -

• This activity helps students to go beyond textbooks and find answers for themselves.
• ​In the above activity, a student will inquire about the families in his/her neighborhood.
• He Will make data about the consumption of coal, gas, electricity, petrol, and kerosene.
• Then by studying the statics based on the data they will conclude whether the consumption of these commodities has increased or decreased.
• It means they are not limited to the book data.
• So they will go beyond textbooks and find answers for themselves.
• ​​Such activities help students become confident and learn to enquire themselves.
• ​This activity is aimed at boosting learners’ confidence generally and creating a positive learning environment.
• By doing this activity students will invent their hidden strength.
• They will become confident while talking to others during the survey.
• Their Communication skill will be improved.
• They can work in pairs or teams if they find that easier.
• They will learn to enquire themselves.
• Such activity gives an authentic understanding to students of an issue.
• ​In this activity, students record several responses to the same task and then choose their best response as an average.
• So all data collected by the students will be based on the real facts.
• So students can easily understand the whole concept.
• They will also conceptualize the scientific side of the activity.

Hence, we can conclude that the option 4 is the least appropriate response.