CTET (Maths & Science) Official Paper-II Sep, 2014 (English-Hindi-Sanskrit) (Previous Year Paper)

A developmental perspective of teaching advocates that designing materials, making assignments, evaluating students' performance, counselling students (sometimes parents too), and maintaining discipline. 

As a teacher, you have to constantly make decisions about teaching materials and methods. These decisions should be based on several factors which include the subject matter to be covered, the needs of the students, and the overall goals to be achieved. 

Key Points

A developmental perspective of teaching-

• As an instructional expert, the teacher needs to devise practical and experiential methods for transacting the curriculum so that learners have a greater role and are more involved.
• Methods like debates, discussions, role play, simulation tasks, brainstorming are oriented towards discovery rather than passive learning and emphasize development and adaptation of instruction to learner needs.
• crate an open classroom where students experience the freedom to explore, experiment, share and express their needs, wishes, and desires
• The learning styles approach tries to develop profiles for individual students and attempts to match instructional methods, curriculum offerings, etc. to learners' personal styles, enhancing student input and making the class conducive to effective teaching and learning.
• have more elaborate systems of knowledge for analyzing problems in teaching
• arrange lessons to enable students to gain insight and a heightened sense of awareness, coupled with the creation of an encouraging learning atmosphere that helps to realize their potential.

Thus from the above-mentioned points, it is clear that the Developmental perspective of teaching demands teachers to adapt instructional strategies based on the knowledge of developmental factors.

Learning' means a relatively permanent change in behavior 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. 

• Psychological needs exist in the form of certain wants or desires that are unique to us.
• They are important since they influence what we want to learn and how much time, energy, and effort we are willing to learn.
• The dominant needs at any given point of time will determine what the individual is likely to leam and do.
• Learners cannot learn unless he is not motivated or does not have any psychological need.
• It is also very important to know the pattern of interests which individuals have for, it is a rich source of knowing them and understanding the nature of their learning.

Key Points 

• What we learn, why we learn and how well we learn are influenced by a number of factors. These include learner-centered factors like motivation, needs, self-concept, interests etc.,
• teacher and task-related factors such as teaching style, classroom ethos, transactional skills, and methodology, etc., and environmental factors such as the physical and psychological structures in which learning occurs.

Important 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

Thus from the above-mentioned points, it is clear that Learners cannot Learn unless they are prepared to learn.

Bandura’s Social Learning Theory (also known as Social Cognitive theory) of Personality is based on the premise that human behaviour is largely acquired and that the principles of learning are sufficient to account for the development and maintenance of behaviour. 

• Bandura theory of social learning can be explained under the following three headings:

1. Reciprocal determinism
2. Self-system
3. Principles of observational learning

• Bandura’s stated that children and adults learned behaviour by observing and imitating others.
• Nurture defines a process in which the individual grows up in the environment and cultural context.
• His theory also explains that human behaviour is an interaction that is continuous and reciprocal with the influences through cognitive, behavioural, and environmental sources.
• Bandura's famous Bobo doll experiment's findings support the argument for nurture in that our environment influences our behaviour.

Key Points 

Principles of observational learning-

• Children learn most of the social behaviours by observing and emulating adults.
• The way to put on clothes, dress one’s hair, and conduct oneself in society are learned through observing others.
• It has also been shown that children learn and develop various personality characteristics through observational learning.
• Aggressiveness, prosocial behaviour, courtesy, politeness, diligence, and indolence are acquired by this method of learning.

These points reflect the factors like environment, culture, society, etc. nurture the development of a child. 

Thus from the above-mentioned points, it is clear that the Theory of social learning emphasizes nurture. 

Additional Information

Reciprocal Determinism- Reciprocal causation reflects the interaction between thought, affect, and action. Expectations, beliefs, self-perceptions, goals, and intentions give shape and direction to behaviour. What people think, believe, and feel, affects how they behave.

Self-System- Bandura found that an individual’s self-efficacy plays a major role in how goals, tasks, and challenges are approached.

Erik Erikson’s theory of psychosocial development is one of the best-known theories of personality in psychology. 

• Erikson’s theory describes the impact of social experience across the whole lifespan.
• He felt the course of development is determined by the interaction of the body (genetic biological programming), mind (psychological), and cultural (ethos) influences.
• the psychosocial theory basically asserts that people experience eight ‘psychosocial crisis stages’ which significantly affect each person’s development and personality.
• Each crisis stage relates to a corresponding life stage and its inherent challenges.
• Erikson used the words ‘syntonic’ for the first listed ‘positive’ disposition in each crisis (example trust) and ‘dystonic’ for the second listed ‘negative’ disposition (example, Mistrust)

Important Points

Industry vs. Inferiority ( Latency 6-12 yrs)

• At this stage, If the child is encouraged and praised by parents and teachers then he/she develops a feeling of competence and belief in their skills.
• Feelings of inferiority are likely to develop and this might lead the child to become an underachiever.

Key Points

Erikson’s Eight Stages of development-

 

Thus from the above-mentioned points, it is clear that Erik Erikson’s theory of psychosocial development emphasizes on Industry versus Inferiority stage. 

Additional Information

• Stimuli and Response and Operant Conditioning are theories related to learning.
• Ophallic and Latency stages are the stages related to Psychosexual Stages of Development proposed by Freud.

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 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 children require culturally relevant knowledge and skills.

Important Points

Some central-concepts of Vygotsky's theory is-

Lawrence Kohlberg, an American psychologist, has propounded the 'Theory of Moral Development'.

• He has made a systematic study of moral development in his theory that is categorized into 3 levels and 6 stages.
• He has studied moral development by posing moral dilemmas to groups of children as well as adolescents and adults.

Key Points

The three-level of Moral Development is-

• Pre-conventional Level:
• At this level, the child is not responsive to cultural rules and labels of good and bad, right or wrong but interprets these labels in terms of physical or hedonistic consequences of actions or in terms of physical powers of those who communicate the rules and labels.
• Conventional level:
• At this level maintaining the expectations of the individual, family, group, or nation is perceived of value in its own right regardless of the immediate and obvious consequences.
• Post-conventional Level:
• At this level, there is a clear effort to define moral values and principles that have validity and application apart from the authority of the groups or persons.
• If young adolescents who join their teacher with strong beliefs in saying no to ragging and bullying are at the post-conventional level. As he believes in morals and values.
• In this stage, the social rules and laws get in conflict with moral principles.
• They agree to obey laws and social rules of conduct that promote respect and acknowledges their moral value.
• They obey laws and social rules that fall in line with these universal principles.

Thus from the above-mentioned points, it is clear that the young adolescent is at a post-conventional level. 

Additional Information

All the levels with their stages are mentioned in the following table-

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

On this basis progress in education is represented by those activities or undertakings or changes that are harmonious with and lead to eternal verities and ultimate values and as a practical matter, preparation for living, the essential aspects of it.

• Based on the belief that education should primarily serve the needs of children and focus on understanding, direct action and experience rather than rote knowledge and memorization.
• A free and democratic atmosphere should be provided in the classroom for the proper development of an individual.
• Democratic climate provides the child gets maximum opportunities for interaction with other children (i.e, collaboration) in the class, with the teacher and with a variety of teaching-learning material.
• A democratic atmosphere in the class encourages the students to actively participate in the learning process.
• In the democratic approach, peer tutors require some orientation to provide positive feedback to other students.

Thus from above-mentioned points, it is clear that in progressive education, knowledge is generated through direct experience and collaboration.

Howard Gardner proposed the theory of multiple intelligences. According to him, intelligence is not a single entity; rather distinct types of intelligence exist.

• Each of these intelligence is independent of each other. This means that, if a person exhibits one type of intelligence, it does not necessarily indicate being high or low on other types of intelligence.
• Gardner also put forth that different types of intelligence interact and work together to find a solution to a problem.
• Gardner studied extremely talented persons, who had shown exceptional abilities in their respective areas, and described eight types of intelligence.

Key Points

Bodily-kinesthetic intelligence is one of the types of intelligence given by Gardner. 

Bodily-kinesthetic Intelligence- 

• It entails the potential of using one’s whole body or parts of the body to solve problems. It is the ability to use mental abilities to coordinate bodily movements.
• people who have bodily-kinesthetic intelligence should learn better by involving muscular movement and are generally good at physical activities.
• Careers that suit those with this intelligence include athletes, dancers, musicians, actors, surgeons, doctors, builders, police officers, and soldiers.

Thus from above-mentioned points, it is clear that Bodily-kinesthetic intelligence is required for an airforce pilot. 

Additional Information

Following are types of intelligence-

Charles Spearman’s theory of intelligence is known as the two-factor theory. Spearman noticed that children who perform well in one subject tend to have good marks in other subjects also. This observation led him to propose that there is a common factor that affects all of your activities.

• Using a statistical method called “factor analysis”, he proposed that all cognitive activity or mental activity consists of two factors namely, “general” or “g” factor and “specific” or “s” factor.
• So, intelligence is a sum of the “g” factor and the “s” factor.
• The g-factor theory or general factor theory states that intelligence is composed of general intelligence.
• The g factor refers to the broad spectrum of mental faculties that influences the performance on a wide variety of cognitive abilities.
• The s factor is the single or unique factor. It proposes that all cognitive abilities are related to one another.

Hence, general intelligence is responsible for acquiring knowledge, abstract reasoning, and adapting to novel situations.

Key Points

• This “g”, or general factor, was postulated to be important in every mental act, although some acts were thought to depend upon it more than others.
• The difference between people in intelligence was a matter of how much “g” they possessed.
• Spearman called this general factor “mental energy.”

Thus from the above-mentioned points, it is clear that the factor 'g' in the Spearman definition of intelligence stands for general intelligence.

Jean Piaget, a Swiss psychologist, has made a systematic study of cognitive development in his theory that is categorized into four stages.

Sensorimotor stage: By the end of the sensorimotor stage (birth-2 years), a child has developed what Piaget referred to as, 'object permanence'.

• Object permanence is the realization that objects continue to exist even though they are not presently seen.
• Thus even in the absence of the actual object, the child can form mental images of its presence.
• However, gradually, the child learns to focus her/his vision and also learns that the object that moves out of her/his vision in fact does exist.
• Achievement of object permanence marks the transition of a child to the next stage of cognitive development.

Key Points

Other characteristics of the sensorimotor stage-

• child's behavior appears to be determined by stimulus-response (sensor = S, motor = R) arrangements.
• smoother and more coordinated reflex activities,
• prominent self-investigative behavior,
• reaching out reactions and the emergence of more goal-directed behavior
• representational thought
• learns that the objects in the environment are permanent

Thus from the above-mentioned points, it is clear that retrieving hidden objects is evidence that infants have begun to master in Object-permanence. 

Additional Information

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

Gender is a social construct that impacts attitudes, roles, responsibilities, and behaviour patterns of boys and girls, men, and women in all societies. 

Key Points

Gender Parity refers-

• to a statical representation of boy and girl data in a group.
• to assess the state of gender equality within a group or organization.
• when we divide the number of female students at a given level of education by the number of male students at the same level, the resulting value is called a gender parity score.

Thus from the above-mentioned points, it is clear that a comparison of the number of boys and girls who survive in Class 12 shows the criteria of gender parity in society. 

Additional Information 

Let us learn about some of the major interventions done in the Constitution for the rights of women for gender equality.

• Article 14: Equality before Law
• Article 15: Prohibition of discrimination on grounds of religion, race, caste, sex, or place of birth
• Article 16: Equality of opportunity in matters of public employment
• Article 17: Abolition of untouchability
• Article 19: Protection of certain rights regarding freedom of speech, etc
• Article 21: Protection of life and personal liberty

Individual differences, as the term suggests, refer to how individuals differ from each other.

• Different people have different interests; and their behavior is influenced by these interests, likings, dislikings, values and beliefs, etc.

Key Points

• Understanding of individual differences helps in planning course material and training programmes.
• Understanding of individual differences of the teachers and the taught can help in matching teaching and learning styles for better- academic results.
• To take care of individual differences you should design your instructional activities to suit the mental level of each student.

Important Points 

Some of the instructional strategies are discussed below-

• Organize instruction for the development of the cognitive process
• Use an existing cognitive level as a base
• Strengthen memory
• Formulate a level-specific instructional strategy
• Use individual meeting
• Provide instructions to overcome a learning disability

By giving different activities, observing the way the student answers in each, you will gain insights into the student's difficulties and will be able to help him/her overcome the difficulties. 

Thus from the above-mentioned points, it is clear that the knowledge of individual differences helps teachers in assessing the individual needs of all students and teaching them accordingly.

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. 

• From the assessment, it is revealed that if the desired level of mastery has not been attained by learners, the teaching-learning process may be repeated and certain remediation may be provided to them.
• It helps students to know their progress in learning and learning difficulties in different subject areas.
• The quality in assessment decides the quality of learning.
• If you carry out the assessment effectively, learning will be enhanced otherwise learning will not match the expectation of assessment.

Key Points

• Assessment of performance of learners helps a teacher to make academic decisions but also provides feedback on the teaching strategies and motivate them for learning.
• The goal is to increase student’s motivation and learning which requires productive feedback that will tell what they are doing right, pinpointing their strengths and helping them to develop their strength even further.
• Constant motivation and encouragement help children form a balanced personality

Thus from above-mentioned points, it is clear that assessment for learning fosters motivation. 

Hint

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

The term School-Based Assessment (SBA) may be defined as:

• Assessment that facilitates the attainment of competencies specified in terms of learning outcomes in a holistic manner during the teaching-learning process
• Assessment embedded in the teaching and learning process within the broader educational philosophy of ‘assessment for learning’
• Assessment of school students by school teachers in the schools

Important Points

Salient features of SBA-

• Integrate teaching-learning and assessment
• No-load on teachers of documentation- recording, reporting
• Child-centred and activity-based pedagogy
• Focus on (learning-outcome based) competency development rather than content memorisation
• Broadening the scope of assessment by way of including selfassessment, peer-assessment besides teacher assessment
• Non-threatening, stress-free and enhanced participation/ interaction
• Focus on an assessment of/and/as learning rather than an evaluation of achievement
• Reposing faith in the teacher and the system
• Enhancing self confidence in children

Thus from above-mentioned points, it is clear that School-Based Assessments improve learning by providing constructive (i.e, to provide child-centred and active instruction environment) feedback.

Portfolio assessment is a systematic and organized collection of evidence used by the teacher and student to monitor the growth of the student's knowledge, skills, and attitudes in a specific subject area. 

• It requires students to collect and reflect on examples of their work providing both instructional components to the curriculum and offering the opportunity for authentic assessment.
• The portfolio is a collection of students' work representing a selection of performances.
• It often documents a student's best work.

Key Points

• Portfolios are systematic, purposeful, and meaningful collections of students' work in one or more subject areas.
• In all cases, portfolios should reflect the actual day-to-day learning activities of students.
• Portfolios should be ongoing so that they show the students' efforts, progress, and achievements over a period of time.
• Portfolios are useful as a support to the new instructional approaches that emphasize the student's role in' constructing understanding and the teacher's role in promoting understanding.

Thus from the above-mentioned points, it is clear that if students in a class are asked to assemble various artifacts of their work in a notebook, to demonstrate what they can do for their society it is a portfolio assessment. 

Additional Information

The least restricted school environment is a type of arrangement in which disabled children learn in the regular classroom along with peers. 

• A special school is less restrictive than a residential institution, the child still misses out on normal school life.
• The special school limits the child's opportunities to participate in regular activities with non-disabled children.
• Integrated education in a regular school provides more freedom and opportunity for the child to interact with others compared to the special school. It is less restrictive than the special school.
• Full inclusion is the least restrictive setting for the child.

Important Points

• All disabled children (as well as disabled adults) should have the opportunity to live as normally as possible, in conditions that are as close as possible to the rest of society.
• In other words, they should have the opportunity to live in the least restrictive environment.
• Apart from the disabled child, a non-disabled child also gets sensitized to not bully the disadvantaged children. They also play a supportive role for disabled students.

Thus from the above-mentioned points, it is clear that by placing students in the least restricted school environment, the school sensitizes other children not to bully or to put the disadvantaged children down. 

Additional Information

Two principles can guide you in selecting the educational setting for the disabled child. These are-

1. All disabled children (as well as disabled adults) should have the opportunity to live as normally as possible, in conditions that are as close as possible to the rest of society. In other words, they should have the opportunity to live in the least restrictive environment.
2. All children should get the facility for education in keeping with their abilities.

Attention deficit hyperactivity disorder (ADHD) is one of the most common childhood disorders and can continue through adolescence and adulthood.

• symptoms include difficulty staying focused and paying attention,
• difficulty controlling behavior, and hyperactivity (over-activity). Inattention,
• hyperactivity, and impulsivity are the key behaviors of ADHD
• tend to fall down more, tip over more things accidentally, and have worse fine motor skills than other children
• ADHD have difficulty getting along with peers and establishing a friendship, perhaps because their behavior is often aggressive and generally annoying and intrusive to others.

Important Points

Treatment of ADHD-

• the most promising treatments of ADHD children involve parent training and changes in classroom management based on operant conditioning principles.
• In this treatment, children’s behavior is monitored at home and in school, and they are reinforced for behaving appropriately, for example, for remaining in their seats and working on assignments.
• Reducing the time allotted to complete an assignment.
• These programs have demonstrated at least short-term success in improving both social and academic behavior.

Thus from the above-mentioned points, it is clear that the best-suited strategy to deal with Attention deficit hyperactivity disorder (ADHD) is reducing the time allotted to complete an assignment to make it coincide with a time of attention and increasing this time in a phased manner.

Child behaviour problems or behaviour disorders are when children show a permanent pattern of hostile, destructive or disruptive behaviour towards self or towards the society. 

• Disruptive behavioural disorders are complicated and may include many different factors working in combination.
• For example, a child who exhibits delinquent behaviours of CD may also have ADHD (Attention Deficit Hyperactivity Disorder), anxiety, depression, a drug use problem and difficult home life.

Key Points

• Ecology emphasizes the totality of relationship among organisms and between them and their physical environment.
• From an ecological perspective, we can see one’s health as a dynamic function of one’s heredity and the current and accumulated effects of one’s material and non-material environment i.e, the interaction with people around him.
• This is what has been described as a type of ecological balance that mental health provides an individual to cope with the surroundings.
• In most cases, the family members create the behavioural ecology or a setting for the behaviour problems to occur and also to sustain it over a long time.

Thus from above-mentioned points, it is clear that Ecological approach suggests the interaction of the child with the people around him and with social institutions to deal with a disruptive behaviour disorder.

Hint

Renzulli’s Three-ring (circle) conception of giftedness has been widely used in schools and educational institutions around the world since its inception. It is based on the interaction between three basic clusters of three human traits, being above average ability, a high level of task commitment, and a high level of creativity. 

Key Points

• While various compositions of these traits can usually be applied to one or two performance areas, there is no ‘ideal’ combination.
• ‘General’ performance areas include mathematics, music, languages, and so on,
• whereas ‘specific’ performance areas may include film making, electronics, sculpture, and so on.
• Ultimately, Renzulli views giftedness as a behaviour, rather than an attribute

Additional Information

• This model has found support amongst teachers whose ‘gut instinct’ leads them to believe that a particular student is gifted, despite them not necessarily scoring well on formal tests and assessments.
• Children who appear to be intrinsically motivated and with highly developed special interests and ability in particular areas typify those gifted students encompassed by Renzulli’s model.
• It is also particularly applicable to cultural models of giftedness as it acknowledges the integral and interwoven roles that creativity and task commitment play in addition to above-average ability in culturally valued activities.

Thus from above-mentioned points, it is clear that Renzulli is known for his three-circle definition of giftedness.

Giftedness is an exceptional general ability shown in superior performance in a wide variety of areas, that is why gifted students do not excel in the single domain but in multiple-domain. These individuals have special learning needs in areas requiring the functional use of intelligence and artistic ability and creativity.  

Key Points

Gifted students can be guided through-

• the teacher should identify the gifted children on the basis of observation of their characteristics, interaction styles, quality of assignment and participation project work
• The teacher has to adapt teaching to the needs of all his/her students. This flexibility makes a smooth connection between teacher and child as the teacher will understand easily what the child demands.
• Administer intelligence test
• Segregation of gifted children and arranging classes exclusively for them.
• Acceleration through which the gifted children may be allowed to complete the prescribed course of study in a shorter period
• Enrichment programme through prescribing enriched content and suggesting additional books and journals for their study.

Thus from the above-mentioned points, it is clear that for gifted students, the teacher should adapt as the student changes. 

Additional Information

Some important characteristics of gifted children are-

• Advanced logical thinking, questioning and problem-solving behaviour.
• High speed in processing information
• Superior generalisation and discrimination ability
• Advanced level of original and creative thinking
• High level of intrinsic motivation and self-esteem

Learning disability can be defined as an imperfect ability to listen, think, speak, read, write, spell, or do mathematical calculations. Learning disability is believed to be present if there is a substantial difference between expected and actual performance based on intelligence. 

Key Points

For monitoring the progress of learning disabled child we use Structured behavioural observation in which-

• The information of disabled child must be recorded,
• Selection of data and standardization of conditions of observation of their learning process
• The teacher is supposed to be knowing the situation and therefore need to prepare a specific plan for collection and recording the data of a disabled child
• In this type, the categories of observation have to be developed. It is subjected to high levels of control and differentiation.
• Other ways are-
• Task description
• Formulation of strategy
• Modeling
• Guided practice
• Verbalisation
• Self-monitoring

Thus from the above-mentioned points, it is clear that Structured behavioral observation is the most appropriate method to monitor the progress of children with learning disabilities. 

Hint

Advantages of the Structured Behavioural Observation Method-

• It provides direct information about the behavior of individuals and groups.
• It helps to gather data when the situation is real and not artificially set up.
• It helps to develop a holistic perspective

Additional Information

Children with learning disability experience difficulty in learning and using certain skills namely reading, writing, listening, reasoning and mathematics. Learning disability is an invisible disability. The child usually appears normal in every aspect except that his learning difficulties limit his progress in school. 

Key Points

Ways to increase the chances of learning-disabled students are-

• Students with specific learning difficulties may require resource support for meeting their individual needs.
• This support can be provided in their classroom after school hours or if possible, in another small room during school hours.
• The support can be provided on a one-to-one basis or in a small group.
• providing adequate space in the classroom for keeping learning aids etc
• promoting success by making use of appropriate tasks and strategies
• resource support in language, mathematics and for teaching them learning strategies on weekly basis. The skills of these children can improve significantly with appropriate interventions.
• giving extra time for tests, taking shorter tests learning spellings of different words than their peers

Thus from above-mentioned points, it is clear that the best way to increase the chances of learning disabled students is by teaching a variety of skills and strategies that can be applied across a range of contexts. 

Important Points 

Some learning disabilities are-

Vygotsky, a Russian psychologist, has argued that culture and language provides a social context in which people live, grow, and understand the world around them. 

Key Points

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.
• a language that people around us speak, it also becomes the language of a child's thinking
• 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 above-mentioned points, it is clear that According to Socio-cultural theory of Vygotsky culture and language play a crucial role in development. 

Important Points

Some central-concepts of Vygotsky's theory is-

The scientific method is defined by the Random House Dictionary as a method in which a problem is identified, relevant data is gathered, a hypothesis is formulated, which is empirically tested. 

The scientific method is an empirical method of acquiring knowledge that has characterized the development of science since at least the 17th century.

• It involves careful observation, explain, predict, and/or control phenomena.
• It involves formulating hypotheses, via induction, based on such observations; experimental and measurement-based testing of deductions drawn from the hypotheses; and refinement (or elimination) of the hypotheses based on the experimental findings.

Key Points

Some steps in this logical procedure are-

• Observation and description (explanation) of a phenomenon
• Formulation of a hypothesis to explain the phenomenon.
• In the classical scientific method of which physics is the paradigmatic example, it takes the form of a causal mechanism or mathematical relation.
• Using the hypothesis to predict the existence of other phenomenon or the results of new observations
• Performance of experiments to test the hypothesis (see Glossary) by several impendent researchers. If all the researchers come to the same results, then the hypothesis will become a theory or law.
• Experimental verification is the key to the success of the scientific method.
• Dissemination for peer review.

Thus from the above-mentioned points, it is clear that to explain, predict, and/or control phenomena are the goals of the scientific method. 

Important Points

An error can be understood as the difference between the computed and correct answers. Errors may be due to mistakes, false negatives, lack of knowledge, and misconceptions among students.  

Key Points

As a teacher, you should do- 

• The process of discussing in the class which 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 if a student makes errors in Mathematics. As a teacher, you would ask the student to use an alternative method or redo it to find out errors on his/her own. 

Additional Information

Innovative Remedial Measures are adopted according to the type of errors committed by the students in their Formative Assessments. For example- 

• For computational errors:- drill work is practiced.
• For careless errors:- common misconceptions are listed out from the past experience so that students recall them while solving questions.
• For incorrect formulae error: handouts with correct formulae & figures are provided and wherever possible explained through activities
• Suitable innovative and interesting activities are carried out in the classroom

Emotional intelligence: The notion of emotional intelligence broadens the concept of intelligence beyond the intellectual sphere/domain and considers that intelligence includes emotions. Emotional intelligence is a set of skills that underlie accurate appraisal, expression, and regulation of emotions. It is the feeling side of intelligence. Emotional intelligence is often described as the capacity to be aware of, control, and express one’s emotions, and to handle Intrapersonal​ and interpersonal relationships empathetically.

Howard Gardner proposed the theory of multiple intelligences. According to him, intelligence is not a single entity; rather distinct types of intelligence exist.

• Each of this intelligence is independent of each other. This means that, if a person exhibits one type of intelligence, it does not necessarily indicate being high or low on other types of intelligence. That is why different intelligence demands different methods for different students.
• Gardner also put forth that different types of intelligence interact and work together to find a solution to a problem.
• Gardner studied extremely talented persons, who had shown exceptional abilities in their respective areas, and described eight types of intelligence.

​

Important Points

• Interpersonal Intelligence- 
• This intelligence is concerned with the capacity to understand the intentions, motivations, and desires of other people.
• It allows people to work effectively with others
• This area has to do with interaction with others.
• In theory, people who have a high interpersonal intelligence tend to be extrovert, characterized by their sensitivity to others’ moods, feelings, temperaments, and motivations, and their ability to cooperate to work as part of a group
• Intrapersonal Intelligence- 
• This entails the capacity to understand oneself, to appreciate one’s feelings, fears, and motivations.
• People with intrapersonal intelligence are intuitive and typically introverted.
• They are skillful at deciphering their own feelings and motivations.
• This refers to having a deep understanding of the self; what are your strengths/ weaknesses, what makes you unique, you can predict your own reactions/ emotions

Thus from the above-mentioned points, it is clear that Emotional intelligence may be associated with Intrapersonal and interpersonal intelligence.

Hint

Following are types of intelligence-

The emotion is defined as a strong mental or instinctive feeling such as love or fear' involving many bodily processes, and mental states. 

Key Points

Emotion can be defined as the-

• a subjective feeling and the experience of emotions varies from person to person
• “feeling” aspect of consciousness, characterized by certain physical arousal, certain behavior that reveals the feeling to the outside world, and an inner awareness of feelings.
• Emotion is a complex pattern associated with mood, temperament, personality and disposition, and motivation.
• Interest, enthusiasm, boredom, laughter, empathy, action, curiosity are examples of positive emotions.
• Apathy, grief, fear, hatred, shame, blame, regret, resentment, anger, hostility are examples of negative emotions.
• Emotions, as we experience them, move us internally, and this process involves physiological as well as psychological reactions.

Thus from the above-mentioned points, it is clear that 'emotions may not only occur within individual students but also the entire class' has been least discussed in the psychology of emotion. 

Additional Information

• Physiological emotions- increase in heart rate, throbbing temples, increased perspiration, and trembling in your limbs when you are angry or excited about something
• Psychological emotion- the need for achievement, affiliation, power, curiosity and exploration, and self-actualization motives.

Motives are a hypothetical state that activates behaviour and propels one towards goals. Meaning of motive is the reason for doing something or behaving in a specific way. 

Basically, there are two types of motives: biological and psychosocial.

• Biological motives are also known as physiological motives as they are guided mostly by the physiological mechanisms of the body.
• Psychosocial motives, on the other hand, are primarily learned from the individual’s interactions with the various environmental factors.

Key Points 

Psychosocial Motives- These are complex forms of motives mainly resulting from the individual’s interaction with her/his social environment. Need for Affiliation, Need for Power, Need for Achievement etc are its type.

• Need for Achievement-
• Some students work very hard and compete with others for good marks/grades in the examination, as good marks/grades will create opportunities for higher studies and better job prospects.
• It is the achievement motivation, which refers to the desire of a person to meet standards of excellence.
• Need for achievement, also known as n-Ach, energises and directs behaviour as well as influences the perception of situations.

Thus from above-mentioned points, it is clear that if Rajesh is struggling to solve the problem of Mathematics completely. The inner force compelling him to search for a way to solve it completely is known as a motive.

Motivation refers to how urges, drives, desires, aspirations, strivings, or needs, direct, control or explain the behavior of human beings. Motivation is something that makes the person to action and continues him in the course of action already initiated. 

There is a motivational cycle that helps us to understand behavior.

• This motivational cycle starts with a need, a state of lack or deficit of some necessity
• The state of need leads to a driving state. Drives can be stimulated due to internal factors or external factors. Internal factors could be thoughts and memories while external factors could be environmental factors.
• This driving state arouses you and pushes you to perform some goal-directed behaviour. For example, if we are thirsty there is a need for water, this need will drive us towards attaining water and once we have consumed water, the need is satisfied and the drive is reduced or diminished.
• once the performed behaviour leads to the achievement of the desired goal, it reduces the drive and the organism returns to a balanced state. the motivational cycle ends here.

Refer to the image:

Thus from the above-mentioned points, it is clear that properly sequenced in the context of motivation-cycle is Need, Drive, Arousal, Goal-directed behaviour, Achievement, Reduction of arousal.

Albert Bandura’s Social Learning Theory states that people learn by observing, imitating, and modeling behavior. It premises that human behavior is largely acquired and that the principles of learning are sufficient to account for the development and maintenance of behavior. 

Bandura theory of social learning can be explained under the following three headings:

1. Reciprocal determinism
2. Self-system
3. Principles of observational learning

Key Points

Social Observational Learning- Observational learning refers -

• In this kind of learning, human beings learn social behaviors, therefore, it is sometimes called social learning.
• In many situations, individuals do not know how to behave. They observe others and emulate their behavior, called modeling.
• Modeling, according to Bandura, refers to the behavior of the observed person and not to the behavior of the person who follows.
• there were certain steps involved in the modeling process-
• Attentional Processes
• Retentional Processes
• Reproduction Processes
• Motivational Processes

Refers to the table:

Hint

• Retention is the ability to store information as an important part of the learning process.
• Self-System- Bandura found that an individual’s self-efficacy plays a major role in how goals, tasks, and challenges are approached.
• Reciprocal Determinism- Reciprocal causation reflects the interaction between thought, affect, and action. What people think, believe, and feel, affects how they behave.

Thus from the above-mentioned points, it is clear that Retentional is a process in the social observational learning theory of Bandura.

Concept:

First, find the LCM (Lowest Common Factor) of the given fraction.

Then arranged it according to the given question.

Given:

$[ - \frac{{11}}{{20}},;\frac{7}{{ - 15}},;\frac{{17}}{{ - 30}};and - \frac{3}{{10}}]$

Calculation:

LMC of the (20, 15, 30, 10) = 60

Multiply each fraction with the LCM i.e. 60

⇒ - 11/20 × 60 = - 33

⇒ - 7/15 × 60 = - 28

⇒ - 17/30 × 60 = - 34

⇒ - 3/10 × 60 = - 18

After arrange in decreasing order (descending order), We find that

$- \frac{3}{{10}}; > ;\frac{7}{{ - 15}}; > ; - \frac{{11}}{{20}}; > ;\frac{{17}}{{ - 30}}$

Given:

Let,

x is subtracted from the -5/7 to get -1.

Calculation:

$\frac{-5}{7}$ - x = -1

Then, 

⇒ x = $\frac{-5}{7}$ +1 

= $\frac{2}{7}$

Concept:

(a + b)² = a² + b² + 2ab

Given:

a = $\sqrt {{{\left( {2013} \right)}^2} + 2013 + 2014}$

Calculation:

After rearranging the given question,

a = $\sqrt {{{\left( {2013} \right)}^2} + 2013 + {(2013~+~1)}}$

a = $\sqrt {{{\left( {2013} \right)}^2} + 2 \times 2013 + 1}$

a = \(\sqrt {{{\left( {2013} \right)}^2} +1^2+~ 2 \times 1 \times 2013} \)

a = $\sqrt {{{\left( {2013~+~1} \right)}^2}}$

a = 2014

Given:

a < b < c < 0 

Where,

a, b, c are the integers.

Calculation:

Let,

c = -1, b = -2, a = -3 

Then,

a + c < b = (-1) + (-3) < (-2)

-4 < -2 

So, 

We can say that statements (1) is correct.

Given:

The number 829030000 is expressed as k × 10n

Calculation:

 829030000 = k × 10n

8.2903 × 10⁸ = k × 10n

Then comparing both side,

k = 8.2903 And n = 8

So, 

k + n = 8.2903 + 8 = 16.2903

Given:

LCM of two prime number x and y is 161

where x > y

Concept:

Prime number: 

• The numbers other than 1 whose only factors are 1 and the number itself are called Prime numbers.
• 2 is the smallest prime number which is even.
• Every prime number except 2 is odd.

The least common multiple (LCM): 

• It is the “smallest non-zero common number” which is a multiple of both the numbers.
• For example, consider two numbers x and y, whose prime factors are,

x = a × a × b × c

y = a × b × b × b 

Then,

LCM of x and y will be = a × a × b × b × b × c

Calculation:

Prime factors of 161 are 7 and 23 only. Therefore we can say that LCM of 7 and 23 will be 161.

Hence, we can write,

161 = 7 × 23 

Hence,

x = 23 and y = 7 (as x > y)

Now the value of 3y - x is

3 × 7 - 23 = -2

Hence, the value of 3y -x is -2.

Additional Information

Composite number: 

• Numbers having more than two factors are called Composite numbers.
• 1 is neither a prime nor a composite number.
• Two numbers having only 1 as a common factor are called co-prime numbers.

Highest Common Factor:

• The Highest Common Factor (HCF) of two or more given numbers is the highest of their common factors.
• The product of the HCF and LCM of two numbers is equal to the product of the two numbers.​

Concept:

Probability:

• The probability represents the chance that something will happen.
• the sum of the probabilities of all the elementary events of
  

an experiment is 1.

The theoretical probability (also called classical probability) of an event E,

written as P(E), is defined as,

$_{P\left( E \right) = ;\frac{{{\rm{Number;of;outcomes;favourable;to;E}}}}{{{\rm{Number;of;all;possible;outcomes;of;the;experiment}}}}}$

The number of prime factors:

If a composite number 'P' is divided into its prime factors a, b and c. Let, x, y and z represent the number of prime factors a, b and c respectively

Now we can write 'P' as

P = a^x × b^y × c^z

Then the total number of prime factors, 

N = (x + 1)(y + 1)(z + 1)

Calculation:

Given composite number is 72.

According to the above discussion, we can write 72 as

72 = 2³ × 3²

Total number of factors of 72 are

N = (2 + 1)(3 + 1) = 12

So the factors are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72.

Therefore, the total number of possible outcomes 12.

The number of factors less than 11 is 

1, 2, 3, 4, 6, 8, 9

So, the total number of favorable outcomes are 7.

Therefore, the required probability will be,

$_{P\left( E \right) = ;\frac{{{\rm{Number;of;outcomes;favourable;to;E}}}}{{{\rm{Number;of;all;possible;outcomes;of;the;experiment}}}}}$

$\Rightarrow P(E) = \frac{7}{12}$

Hence, the probability that a randomly selected factor from positive factors of 72 is less than 11 will be 7/12.

Concept:

• If the power of two numbers is the same, then we can multiply the base. i.e.

a^m × b^m = (a × b)^m

• If any number have multiple powers then we can multiply the power. i.e.

$(a^m)^n = a^{m\times n}$

Calculation:

From the above discussion, we can write the given number as,

$\sqrt[3]{{500}} \times \sqrt[3]{{16}} = (500)^\frac{1}{3}\times (16)^\frac{1}{3}$

$= (500\times 16)^\frac{1}{3}$

$= (8000)^\frac{1}{3}$

$= (20^3)^\frac{1}{3}$

= 20

Hence, the value of $\sqrt[3]{{500}} \times \sqrt[3]{{16}}$ will be 20.

Additional Information 

Some important properties are:

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

$\frac{a^m}{a^n} = a^{m-n}$

$(a\times b\times c)^m = a^m\times b^m\times c^m$

Concept:

Any composite number can be broken into its prime factors and the number is always divisible by its factors. 

Some useful results are:

a² - b² = (a + b)(a - b)

(a + b)² = a² + 2(a × b) + b²

(a - b)2 = a2 - 2(a × b) + b2

Calculation:

Let,

Y = (x + 1)4 - (x - 1)4

∵ a2 - b2 = (a + b)(a - b)

⇒ Y = [{( x + 1 )²}² - {( x - 1 )²}²]

⇒ Y = [(x + 1)2 - (x - 1)2] × [(x + 1)2 + (x - 1)2]

⇒  Y = 4x( 2x² + 2 )

⇒ Y = 8x( x² + 2 )

We can see that 8 is the factor of a given function, therefore 8 will always be divisible by a given function.

Given:

The hundreds digit of a three-digit number = 7 + units digit.

Concept:

Place value: The digit of any number is called its place value.

For example, in the number 256, the place value of 5 is 5.

Face value: It is the actual value of any digit in a particular number.

For example, in the number 256, the face value of 5 is 50.

Any number can be written as the sum of, a product of the face value and place value.

for three digit number, 

abc = 100a + 10b + c

Calculation:

Let the three-digit number is 'abc'

according to question,

a = 7 + c    

⇒ a - c = 7       .......(1)

Now, according to above discussion 'abc' can be written as,

abc = 100a + 10b + c    ......(2)

on reversing the number, we get the new number 'cba'

⇒ cba = 100c + 10b + a      ......(3)

Substracting equation (2) from (1)

abc - cba = ( 100a + 10b + c ) - ( 100c + 10b + a ) 

abc - cba = 99( a - c )

abc - cba = 99 × 7 = 693     [ from equation (1) ]

Hence, unit digit of final number will be 3.

Given:

Money of 'A' = 20% more than Money of B and, 

Money of 'C' = 20% less than Money of B.

Concept Used:

Percentage: A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the per cent sign, '%'.

If P is x per cent more than Q, then

P = Q{1 + (x/100)}

If P is x per cent less than Q, then

P = Q{1 - (x/100)}

Percentage of P more than Q

= {(P - Q)/Q} × 100%

Calculation:

Let, B have x money, then according to the question,

Money of 'A' = 20% more than Money of B 

A = B{1 + (20/100)}

⇒ A = (6/5) × B      ----(1)

Money of 'C' = 20% less than Money of B, i.e

C = B{1 - (20/100)}

⇒ C = (4/5) × B             ......(2)

So, the amount of money of A, more than C will be

A - C = (6/5 - 4/5) × B

⇒ A - C = (2/5) × B 

Percentage of money, A has more than C 

\(%age = \frac{\frac{2B}{5}}{4B}{5}}\){(A - C)/C} × 100%

⇒ {(2/5) × B}/{(4/5) × B} × 100%

= (1/2) × 100%

⇒ 50%

∴ A has 50% more money than C.

Alternate Method 

Let, B has 100 rupees

Then, according to the question, 

Money of A = 120 rupees, and

Money of C = 80 rupees

Therefore, the difference in money between A and C

= 40 rupees

Percentage of money, A have more than C = {(A - C)/C} × 100%

⇒ (40/80) × 100%

⇒ (1/2) × 100%

⇒ 50%

∴ A has 50% more money than C.

Given:

The present age of Rani = y

Rani is x year older than Hamid

Fifteen years ago, Hamid's age was 1/4 of the age of Rani

Calculation:

Age of Hamid + x years = age of Rani

Age of Hamid = age of Rani - x = y - x

According to the question:

Fifteen years ago, the age of Hamid = y - x - 15

Fifteen years ago, the age of Rani = y - 15

Hence, y - x - 15 = 1/4 × (y - 15)

⇒ 4y - 4x - 60 = y - 15

⇒ 3y - 4x = 45

Hence option 1 is correct i.e. 3y - 4x = 45

Given:

20 CP = x SP

profit = 25 %

CP = cost price of article

SP = selling price of the article

Formula used:

Profit % = (Profit/CP) × 100

Here, SP → Selling price, CP → Cost price

Calculation:

20 CP = x SP

⇒ SP/CP = 20/x

Profit = (20 - x)/x

Given profit = 1/4

equating both

(20 - x)/x = 1/4

⇒ 80 = 5 x

⇒ x = 16

Concept:

Amount = P$\left ( 1 - \frac{r}{100} \right )^n$

Where,

P = Principal Value, n = time, r = Rate of depreciates

Given:

Amount (Present value) = Rs 1,45,800, Time = 3 years, r = 10%.

Calculation: 

Let the purchase value is x.

Amount = P$\left ( 1 - \frac{r}{100} \right )^n$

1,45,800 = x$\left ( 1 - \frac{10}{100} \right )^3$

1,45,800 = x$\left (\frac{9}{10} \right )^3$

9³ x = 1,45,800 × 1000

x = $\frac{1,45,800 \times 1000}{729}$

x = Rs 2,00,000

Given:

b = 48 cm

A = 168 cm²

Where,

b = The base of an isosceles triangle ABC

A = Area of an isosceles triangle ABC

Concept:

An isosceles triangle has the property that if altitude is drawn on the unequal side then it divides the triangle into two small congruent triangles and altitude is the perpendicular bisector of a triangle

So, altitude divides the base of the isosceles triangle into two parts of equal length.

area of triangle = (1 / 2) × base × height

Pythagoras theorem states that, in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

Calculation:

A = (1 / 2) × 48 × h

⇒168 = (1 / 2) × 48 × h (given)

⇒h = 7 cm

 

AC = √ AD² + CD² (By pythagoras theorem)

⇒AC = √ 7² + 24² 

⇒AC = 25 cm

Given:

Area of square = $\frac{16}{π}$(area of the circle).

Concept:

Square:

It is a shape that has four straight sides of the same length and four angles of 90^∘.

Area of a square having side s 

A_s = length × width

A_s = S²

Circle:

• It is a round-shaped figure that has no corners or edges.
• All the points on the surface of the circle are equidistant from the centre point.

For a circle of radius r,

Diameter (d) of circle = 2r

Circumference = 2πr

Area A_c = πr²

​

Calculation:

According to the question,

$A_s = \frac{16}{\pi}A_c$

$⇒ S^2 = \frac{16}{\pi}\pi r^2$

⇒ S = 4r

⇒ S = 2d

$\Rightarrow \frac{S}{d} = \frac{2}{1}$

Hence, the ratio of the side of the square to the diameter of the circle is 2:1.

Given:

The Sum of all interior angles of a polygon is 1400°

Formula used:

Sum of interior angles of a regular polygon of side 'n' = (n - 2) × 180° 

Calculation:

Let number of sides of the polygon is n

(n - 2) × 180 = 1440

⇒ n - 2 = 8

⇒ n = 10

∴ number of sides of the polygon is 10

Concept:

The pentagonal pyramid 

Calculation:

a = 6, b = 10, c = 6 (From the diagram)

Where,

a = the number of faces of a pentagonal pyramid

b = the number of edges of a pentagonal pyramid

c = the number of vertices of a pentagonal pyramid

${\left( {\frac{{a - b + c}}{2}} \right)^2} - 2$

= \()[(6 - 10 +6 ) / 2 ]² - 2

= 1 - 2

= -1

Given:

One angle of a triangle is 130°

Concept:

The Sum of all internal angles of the triangle is 180° 

Calculation:

Consider an △ABC, such that ∠BAC = 130° and bisectors of ∠B and ∠C meet at O.

To find: ∠BOC

Now, in △ABC,

∠BAC + ∠ABC + ∠ACB = 180° 

⇒ 130° + ∠ABC + ∠ACB =180      ----(Angle sum property)

⇒ ∠ABC + ∠ACB = 50° ​

⇒ ∠OBC + ∠OCB = 25°    ----(OB and OC bisect ∠ABC and ∠ACB)

Now, in △OBC,

∠OBC + ∠OCB + ∠BOC = 180° 

⇒ 25° +∠BOC = 180° 

⇒ ∠BOC = 155°

Given:

4 (A) = 6 (B)

h = 12 cm

Where,

A = Area of CSA of cylinder

B = Sum of the area of its base

h = height of cylinder

Formula used:

Curved surface area of cylinder = 2π × radius × height

Volume of cylinder = π × (radius)2 × height

Area of base = π × (radius)2

Calculation:

4 (A) = 6 (B)

⇒4 (2 π r h) = 6 (2 π r²)

⇒ 8 h = 12 r

⇒ 8 × 12 = 12 r (given h= 12 cm)

⇒ r = 8 cm

Volume of cylinder = π × 8² × 12

= 768 π

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

Important Points

Explanation: The statement "It is more useful to know how to mathematize than to know a lot of Mathematics." is given by David Wheeler.

• “Mathematics” is hard to define. One definition is “the body of knowledge centered on concepts such as quantity, structure, space, and change, and also the academic discipline that studies them.” It's more than just a set of tricks – it's a way of understanding and solving problems.
• Wheeler developed the idea of mathematics as an activity rather than a body of knowledge.
• He saw children as embryo mathematicians rather than mere learners of techniques.
• "Because mathematics is made by men and exists only in their minds, it must be made or remade in the mind of each person who learns it. In this sense, mathematics can only be learned by being created."

Additional Information

• George Polya, in his book Mathematical Discovery, defines problem-solving as the conscious search for some action appropriate to attain some clearly conceived, but not immediately attainable aim.
• Van Hiele theory describes how young people learn geometry. It postulates five levels of geometric thinking which are labeled visualization, analysis, abstraction, formal deduction, and rigor.

Hence, we can conclude that the above statement is given by David Wheeler.

According to the National Curriculum Framework (NCF) 2005, the main goal of Mathematics education in schools is the 'mathematization' of a child's thinking. Clarity of thought and pursuing assumptions to logical conclusions is central to the mathematical enterprise.

• While there are many ways of thinking, the kind of thinking one learns in Mathematics is an ability to handle abstractions and an approach to problem-solving.
• The goal of mathematics education in school is the mathematization of the child’s thought processes. Mathematization refers to the ability to regard something mathematically i.e., logically.

Important Points

Aims of Mathematics education in school: 

• NCF 2005 recommends that the main goal of mathematics education is the development of children's thinking ability in mathematization.
• Basically, it means that children should learn to think about any situation using the language of mathematics. They can use the tools and techniques of mathematics in real life.

Key Points

There are two kinds of aims for mathematics education in school.

The narrow aim: Turning out employable adults who will contribute to social and economic development

• Building numeracy in children
• numbers and operations on them
• measurement of quantities
• fractions
• percentages and ratios

​Higher aims of mathematics: Developing the ability of mathematization which is regarded as constituting the higher aims of mathematics, includes developing such abilities as:

• The role that mathematics plays is mostly about thinking
• Clarity of thought and pursuing assumptions to logical conclusions is crucial to the mathematics
• The kind of thinking one learns in mathematics is an ability to handle abstractions
• Developing the right attitude for problem-solving and tackling all problems in a systematic manner

Hence, we can conclude that As per NCF 2005, one main goal of Mathematics education in schools is to mathematize the child's thought process.

The aim of teaching Mathematics at school is to develop useful capabilities, particularly those relating to numeracy- numbers, number operations, measurements, decimal, and percentage. 

The broader aim is to develop the child to think and reason mathematically, to pursue assumptions to their logical conclusions, and to handle abstractions.

Important Points

As per NCF 2005, the Mathematics curriculum is ambitious, coherent, and teaches important Mathematics. Here ‘ambitious’ refers to seek higher aims of teaching Mathematics in school. Developing the ability of mathematization which is regarded as constituting the higher aims of mathematics, includes developing such abilities as:

• problem-solving
• use of heuristics
• estimation and approximation
• optimization
• use of patterns
• visualization
• representation
• reasoning and proof
• making connections
• mathematical communication including developing aesthetic feeling.

Such a higher aim in mathematics “is to develop the child’s inner resources, to think and reason mathematically, to pursue assumptions to their logical conclusion and to handle abstraction. It includes a way of doing things, and the ability and the attitude to formulate and solve problems” 

Key Points

Mathematics (NCF 2005)

• It should be based on the practical knowledge of content, provide through problem-solving and rational pedagogies.
• Mathematics makes learners systematic, confidential, self-evaluated, self-esteem, self-reliable, etc.

Visions for School Mathematics:

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

• Children learn to enjoy mathematics:
• This is an important goal, based on the premise that mathematics can be both used and enjoyed life-long, and school is the best place to create such a taste for mathematics. On the other hand, creating (or not removing) a fear of mathematics can deprive children of an important faculty for life.
• Children learn important mathematics:
• ​Equating mathematics with formulas and mechanical procedures does great harm. Understanding when and how a mathematical technique is to be used is always more important than recalling the technique from memory (which may easily be done using books or browsing appropriate websites), and the school needs to create such understanding.
• Children see mathematics as something to talk about, to communicate, to discuss among themselves, to work together on. Making mathematics a part of children’s life experience is the best mathematics education possible.
• Children pose and solve meaningful problems:
• ​In school, mathematics is the domain that formally addresses problem-solving as a skill.
• Considering that this is an ability to use in all of one’s life, techniques and approaches learned in school have great value.
• 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.

Hence, we can conclude that As NCF 2005, the Mathematics curriculum is ambitious, coherent, and teaches important Mathematics. Here 'ambitious' refers to seek higher aims of teaching Mathematics in school.

Remedial instruction is the process of providing help to students who are experiencing difficulties so they can understand and master the concept with which they are struggling.

• Providing him with a worksheet with partially solved problems to complete the missing gaps. By providing the partially solved worksheets will enable the learner to see his gaps himself and identify his problematic areas.
• Each pupil is different in terms of learning ability, academic standards, classroom learning, and academic performance, and each has his own in learning.
• By adapting school curricula and teaching strategies, teachers can provide learning activities and practical experiences to students according to their abilities and needs.

Key Points

Students mistakes in expressive writing include-

• illegible handwriting,
• Incomplete sentences, and
• Errors in syntax, grammar, and spelling.

Through the primary level, children are taught how to form words, build sentences, and construct paragraphs. By class 4, it is usually clear which students are still having difficulty. The number of referrals of students with expressive writing difficulties typically spikes in class 4. 

Hence, we can conclude that the best remedial strategy to remove errors in his writing is providing him with a worksheet with partially solved problems to complete the missing gaps.

Mathematics is commonly perceived as the most difficult subject at all stages in the school curriculum. Further, its abstractness is highlighted in the textbooks and classroom transactions, although all the concepts included in the mathematics curriculum are related to the real-life experiences of the child. It is a common belief that mathematics concepts cannot be learned without being taught.

Explanation:

• A teacher asked the students to collect leaves and to identify symmetry patterns. This task reflects the teacher’s efforts to relate a real-life experience with mathematical concepts.
• We can connect mathematics in our daily life. There are many activities and maths exercises which are directly or indirectly connected with our daily routine life.
• Certain qualities that are nurtured by mathematics are the power of reasoning, creativity, abstract or spatial thinking, critical thinking, problem-solving ability, and even effective communication skills.
• Maths puzzles and riddles encourage and attract an alert and open-minded attitude among students and help them develop clarity in their thinking. 
  

Emphasis should be laid on the development of the clear concept in mathematics which reflects daily life experience in a child, right from the primary classes

Additional Information

Mathematics in Everyday Life

• Making Routine Budgets
• Construction Purpose
• Exercising and Training
• Shopping at Grocery Stores and Supermarkets
• Cooking and Baking
• Sports
• Management of Time
• Driving
• Weather Forecasting
• The base of Other Subjects
• Problem-solving skills
• Marketing​

Hence, we can conclude that through the above activity or task, the teacher wants to relate a real-life experience with mathematical concepts.

Mathematics is commonly perceived as the most difficult subject at all stages in the school curriculum. Further, its abstractness is highlighted in the textbooks and classroom transactions, although all the concepts included in the mathematics curriculum are related to the real-life experiences of the child. It is a common belief that mathematics concepts cannot be learned without being taught.

Explanation:

• The twin premises to fix the place of Mathematics teaching in our school curriculum are How to engage the mind of every student” and “how to strengthen the student’s resources.”
• Mathematics is the most feared subject among the students, so one of the challenges is to engage every student so that the fear among them is reduced. Also, another challenge is how to strengthen the students' resources so that the learning outcomes can be maximized.
• Mathematics is a subject, where a pupil needs to develop various skills and this requires a meticulous plan to accommodate all the areas of mathematical skill development. And to achieve all this, the principle of curriculum construction needs to be thoroughly followed.

Principles of Curriculum Construction (Mathematics)

• Principle of Child-Centeredness
• The curriculum should provide a fullness of experience for the students
• The curriculum should be dynamic and not static
• The curriculum should be related to everyday life
• It must take into account the economic aspect of the life of the people to whom an educational institution belongs
• The curriculum should be real and rationalistic
• The curriculum should lay emphasis on learning to live rather than living to learn
• The curriculum should help in preserving and transmitting our cultural traditions.
• The curriculum should be flexible and elastic
• The curriculum should emphasize attitudes rather than the acquisition of knowledge
• The curriculum should be well integrated
• The curriculum should provide both for uniformity and variety

Additional Information

Organization of the Curriculum

After selecting the topics, the curriculum has to be organized, maintaining the mathematical sequence and continuity

• Principle of Curriculum Organization
• Principle of Correlation
• Principles of Logical and Psychological Order
• Principle of Activity
• Principle of Vertical Correlation
• The Criterion of Difficulty
• Principle of Motivation
• Adaptation to Individual Differences

Hence, we can conclude that The twin premises to fix the place of Mathematics teaching in our school curriculum are "how to engage the mind of every student" and "how to strengthen the student's resources".

Mathematics is commonly perceived as the most difficult subject at all stages in the school curriculum. Further, its abstractness is highlighted in the textbooks and classroom transactions, although all the concepts included in the mathematics curriculum are related to the real-life experiences of the child. It is a common belief that mathematics concepts cannot be learned without being taught.

Explanation:

• The above activities given in the question are the types of activities that help the child to identify the relation between number patterns and shapes.
• For a long, geometry and trigonometry have wisely been regarded as the arena wherein students can learn to appreciate this pattern and shape best. In the elementary stage, if students have learned many shapes and know how to associate quantities and formulas with them, here they start reasoning about these shapes using the defined quantities and formulas.

Additional Information

The objective of teaching Geometry

• To enable the learner to acquire the knowledge of geometrical facts.
• To implement geometrical principles like equality, symmetry similarity in every nature of things.
• To develop the ability to draw accurate figures.
• To demonstrate the nature and the power of pure reason.
• To systematize the information received by the pupils in the pre-school stage.
• To aid the pupils in becoming familiar with the basic geometrical concepts and space perceptions and in understanding the fundamental techniques such as the use of a set square, protractor, compass, etc.
• To acquaint the pupil with the geometrical notations

Note:

• A pentomino (or 5-omino) is a polyomino of order 5, that is, a polygon in the plane made of 5 equal-sized squares connected edge-to-edge.
• A hexomino (or 6-omino) is a polyomino of order 6, that is, a polygon in the plane made of 6 equal-sized squares connected edge-to-edge.

Hence, we can conclude that option 2nd is correct.

As per NCF-2005, the main goal of mathematics education is the development of children's ability to mathematization. Basically, it means that children should learn to think about any situation using the language of mathematics so that the tools and techniques of mathematics can be used. This typically involves só drawing pictures (representations), choosing variables, framing equations, and arriving at a conclusion logically.

Important Points

• As per the vision statement of NCF 2005, School Mathematics does not take place in a situation, where children memorize formulae and algorithms. They should enjoy mathematics.
• Mathematics is regarded as a powerful tool for interpreting the world and therefore should be rooted in real experience across the whole curriculum.
• Problems arising through imaginative stories and plays can often be even more vivid for young children than genuinely real-life problems. The use of fairy tales, adventure stories, comic strips is some of the exemplars of materials that can fire the imagination in children.

Key Points

NCF 2005 & Mathematics

• To ensure a good start to the students in learning mathematics.
• To give clarity on fundamental concepts and processes of the subject.
• To create love, faith, and interest in learning mathematics.
• To develop in them a taste and confidence in mathematics.
• To develop an appreciation for accuracy.
• To acquaint them with the relation of mathematics with their present as well as
• future life.
• To see aesthetics in mathematics.
• To develop in them the habits like regularity, practice, patience, self-reliance and
• hard work.
• To apply mathematics in other subjects.
• To acquaint them with mathematical language and symbolism.
• To prepare them for the learning of mathematics of higher classes.
• To prepare them for mathematical exhibitions.

Additional Information

Visions for School Mathematics:

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

• Children learn to enjoy mathematics: This is an important goal, based on the premise that mathematics can be both used and enjoyed life-long, and school is the best place to create such a taste for mathematics. On the other hand, creating (or not removing) a fear of mathematics can deprive children of an important faculty for life.
• Children learn important mathematics: ​Equating mathematics with formulas and mechanical procedures does great harm. Understanding when and how a mathematical technique is to be used is always more important than recalling the technique from memory (which may easily be done using books or browsing appropriate websites), and the school needs to create such understanding.
• Children see mathematics as something to talk about, to communicate, to discuss among themselves, to work together on. Making mathematics a part of children’s life experience is the best mathematics education possible.
• Children pose and solve meaningful problems: ​In school, mathematics is the domain that formally addresses problem-solving as a skill. Considering that this is an ability to use in all of one’s life, techniques and approaches learned in school have great value.
• Not only confined to the development of problem-solving skills, but mathematics also provides an opportunity to make up interesting problems, and create new dialogues thereby. Posing problems reflects the levels and quality of learning besides developing the ability of creative inquiry in the children.
• 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. Appreciating the scope and power of mathematics uniquely refines our instincts.

Hence, we can conclude that option 4 is correct regarding NCF 2005.

GeoGebra is one of the most innovative, open-code math software. It is an interactive geometry, algebra, statistics, and calculus application.

• It includes both commercial and not-for-profit entities.
• GeoGebra uses an exploratory approach to teach concepts of geometry.
• It is a free suite of software used to explore mathematics concepts.
• It links visual geometry with algebraic expressions of things.

Key Points

The advantages of using GeoGebra are:

• In comparison to a graphing calculator, GeoGebra is more user-friendly. GeoGebra offers an easy-to-use interface, multilingual menus, commands, and help.
• There are several ways to use GeoGebra for teaching and learning, mainly for demonstration, exploration and modeling, creation, and experimental work.
• Students can personalize their own creations through the adaptation of interface (e.g. font size, language, quality of graphics, color, coordinates, line thickness, line style, and other features).
• GeoGebra was created to help students gain a better understanding of mathematics. Students can manipulate variables easily by simply dragging “free” objects around the plane of the drawing, or by using sliders. Students can generate changes using a technique of manipulating free objects, and then they can learn how the dependent objects will be affected. In this way, students have the opportunity to solve problems by investigating mathematical relations dynamically.
• Cooperative learning is the right context for a mathematics course. Lecturing should be replaced by a task-oriented interactive classroom.
• The algebra input allows the user to generate new objects or to modify those already existing, by the command line. The worksheet files can easily be published as Web pages.
• GeoGebra stimulates teachers to use and assess technology in the visualization of mathematics.

Hence, we can conclude that with the help of 'Geogebra' software, students can learn all concepts of geometry through an exploratory approach.

The literal meaning of the verb ‘mathematize’ is ‘to reduce to or as if to mathematical formulas.’ In general, the term “mathematization” refers to the application of concepts, procedures, and methods developed in mathematics to the objects of other disciplines or at least of other fields of knowledge. According to the National Curriculum Framework (NCF) 2005, the main goal of Mathematics education in schools is the 'mathematization' of a child's thinking.

Important Points

Equating mathematics with formulas and mechanical procedures does great harm. Understanding when and how a mathematical technique is to be used is always more important than recalling the technique from memory (which may easily be done using books or browsing appropriate websites), and the school needs to create such understanding. 

Key Points

The major reasons for student's failure in Mathematics at the school level are-

• Fear and Failure: Lack of awareness of objectives is also another cause of fear and failure. Failure to recognize place value leads to failure in four operations in mathematics.
• Disappointing Curriculum: Unattractive and Loaded mathematics curriculum created disappointment among the students. Most of the mathematics curriculum emphasizes procedure, formulas, mathematical facts, and memorization of concepts. The textbook and syllabi on mathematics are rigidly prescribed. The mathematics curriculum is far away from real life.
• Inadequate Learning Materials: For the majority of children in elementary schools textbook in mathematics is the only resource material available to them. The student finds very little scope for pleasure and fun in learning mathematics from the textbooks. There is hardly any other materials available to the children especially those who are in rural and remote areas.
• Crude Assessment: Most of our mathematics curriculum emphasized on memorization of formulas. Our classroom teaching process is also examination-oriented. For example students free to answer — + — = 8 than 2 + 6 = —? Moreover, similar types of assessment procedure are applied in formative
• Inadequate teacher preparation: As there is an acute dearth of mathematics teachers, it forced other teachers to teach mathematics in the classes in compulsion. They are mostly depending on the textbooks. Most of the teachers also assume that they know all the mathematics required for the elementary level. So there is a lack of teacher preparation in the teaching of mathematics.
• The teaching-learning process: The teaching-learning process in mathematics at the elementary level are not attractive because Bookish knowledge in the class creates dissatisfaction, School mathematics learning becomes charmless, dull, uninteresting, and stereotype, with emphasis on rote learning, Emphasis on teaching, not on learning, Development of Understanding, Application, and skill are ignored
• Lack of interest: Most school children find learning mathematics difficult and lose their confidence in mathematics. The teaching-learning process in mathematics is not joyful and attractive. So students lack their interest and attitude towards mathematics.

Hence, we can conclude that one of the major reasons for student's failure in Mathematics at the school level is that our assessment process emphasizes on testing of procedural knowledge than mathematization of abilities.

Concept:

Pinhole Camera

• A pinhole camera is a simple camera that does not have any lens.
• Light is made to pass through a very small pin size hole which is made lightproof by proper covering around it.
• A real and inverted image is formed on the screen.
• A real image is formed when real light rays form images.
• When light rays are not real, then a virtual image is formed. Example: Image formation by plane mirror.
• Rectilinear propagation of light means light travels in a straight line. This is clearly visible as light passes straight through the hole and forms images.
• The size of the image may change upon the distance of the object from the camera.
• As the distance between camera and object changes, the image size increases.

Explanation:

• The image formation can be understood by the above diagram.
• A ray of light coming from the top of the object or tree forms its image on the screen at the bottom.
• So, the image formed is inverted.
• The size of the image formed in such a case will be less than an object, thus the image is said to be diminished.
• The image is coloured as per the object.

So, the correct option is  Real, inverted, coloured and diminished

Concept:

Mode of Reproduction in Plant

• There are two modes of reproduction in plants: Sexual and Asexual.
• The sexual mode of reproduction takes place through flowers by transfer of pollen grains.
• The asexual mode of reproduction includes vegetative propagation, spore formation, fragmentation, etc.

Flower as Reproductive Part

• The flower is considered the reproductive part of the plant in case of sexual reproduction.
• The flower contains a male part and a female part.
• The male part is known as stamen and the female part is known as the pistil.
• The male part or stamen consists of anther and filament. 
• The anther produces pollen grains while the stamen supports the anther.
• Pollen grains contain male gametes.
• The female part or pistil consists of Ovary, stigma, style. 
• The ovary contains female gametes or ovules.
• Male and a female gamete fuse to form a zygote.
• This happens through the process of pollination.
• In pollination, the pollen grains from the anther go to stigma and fertilization happens in the ovary.
• The transfer of pollen grains from stamen to pistill takes place through insects, air, water or other mediums.

Conclusion:

• Anther and Filament is the part of stamen and Ovary, stigma, style are part of pistil.
• This is represented in section A, so it the correct answer.

Additional Information

Pollination

• The pollen grains by different means like wind, insects, or other methods get transferred to stigma.
• From stigma, the pollen grains reach to ovary.
• The ovary contains one or more ovules.
• The female gamete or the egg is formed in an ovule In sexual reproduction a male and a female gamete fuse to form a zygote.
• If pollination happens in the same flower it is termed self-pollination.
• If pollination happens from one flower to another it is called cross-pollination.

Unisexual and BIsexual Flower

• Flowers that contain either only pistils or only stamens are called unisexual flowers. Examples: Corn, papaya
• Flowers that contain both stamens and pistil are called bisexual flowers. Examples: mustard, rose.

The correct option is ''fibrous roots and parallel venation''.

Concept:

• Roots are the underground structures that help in the absorption of water and minerals, provide a proper anchorage to the plant parts, storage of reserve food material, and synthesis of plant growth regulators.
• Roots are mainly of two types: taproot and fibrous roots.

 

 

​

                        (a) Taproot, (b) Fibrous root

Venation:

• The arrangement of veins and the veinlets in the lamina of the leaf is termed venation.
• When the veinlets form a network, the venation is termed as reticulate.
• When the veins run parallel to each other within a lamina, the venation is termed parallel.

​

Explanation:

• Plants having leaves with reticulate venation have tap roots while plants having leaves with parallel venation have fibrous roots.
• The grass is a monocot having parallel venation & fibrous roots.

The correct option is starfish.

Key Points

Scientific classification - 

Kingdom: Animalia

Phylum: Echinodermata

Class: Asteroidea

Order: Forcipulatida

Family: Asteriidae

Genus: Asterias

Species: A. rubens

 

• Starfish possess a very unique system of digestion.
• The mouth of starfish is present on the ventral surface (underside) while the anus is present on the dorsal surface (Upper surface).
• The starfish catches its prey with the mouth, then it pops out its cardiac stomach through its mouth to eat the soft material of those animals which are covered by hard shells of calcium carbonate.
• After opening the shell and eating the soft material the stomach goes back into the body of the animal to slowly digest the food with the help of digesting enzymes.

Concept:

Small Intestine

• Food after being processed in the stomach reaches the small intestine.
• The length of the small intestine is 7.5 m and it is highly coiled.
• It receives secretions from the liver and the pancreas.
• It has villi which are a finger-like projection.
• Villi ensure the maximum surface area for maximum absorption.

Large Intestine

• Undigested and unabsorbed enters into the large intestine.
• The length of the large intestine is 1.5 m.
• It is wider and shorter as the compared small intestine.
• It absorbs water and salt from the undigested food and provides passage for egestion for it through the anus.

Calculation:

The length of small intestine = 7.5 m

The length of the large intestine = 1.5 m

Required ratio

$R = {7.5 \space m \over 1.5 \space m} = {5 \over 1}$

So, the required ratio is 5 : 1

Concept:

Heat and Temperature

• Temperature is the degree of hotness of any object.
• Higher the temperature, the hotter the object.
• Temperature is measured in  Celsius scale, Fahrenheit scale, and Kelvin.
• Kelvin is the SI unit of temperature.
• Celsius scale is based on the freezing point of water at 0°C and the boiling point of water at 100°C.
• The region between these two temperatures is divided into 100 equal parts i.e. each part equals 1°C.
• The absolute zero value is at -273.15°C.
• Fahrenheit scale is a temperature scale that is based on the freezing point of water at 32°F and the boiling point of water at 212°F.
• The region between these two temperatures is divided into 180 equal parts i.e. each part equals 1°F.
• The absolute zero value is at -459.67°F.
• The relation between the three scales is given as,

​$\frac{C}{5}=\frac{F-32}{9}$

Explanation:

The normal body temperature is 37°C.

Putting this in 

$\frac{C}{5}=\frac{F-32}{9}$

$\implies \frac{37}{5}=\frac{F-32}{9}$

⇒ F = 98.6°F

So, the normal body temperature is 37°C and 98.6°F respectively in celsius and Fahrenheit.

The correct option is 37°C and 98.6°F. 

Additional Information

• Temperature is measured using a thermometer.
• A clinical thermometer is used to measure body temperature while a laboratory thermometer is used in scientific experiments.
• Kelvin is the SI unit of measuring temperature. K = 273 + X ° C, X is temperature in Celsius.

Concept:

Conduction: 

• The heat transfer through direct physical contact is known as conduction.
• The heat is transfer takes place from the hotter end to the colder end. 
• Heat transferred from the electric burner of a stove to the bottom of a pan is transferred by conduction.
• Good conductors of heat allow the transfer of heat across them through conduction. 
• Most of the metals are conductors of heat.
• Poor conductors of heat do not allow heat to pass through them. 
• Examples of poor conductors of heat include air, water, plastic, wood, etc.

Explanation:

Considering the different options:

• Air, water, plastic: All are poor conductors of heat. So, this is the correct option.
• Wool, wood, iron: Iron is metal and a good conductor. Wool and wood are poor conductors. So, this option is incorrect.
• Water, copper, wood: Water, wood are poor conductors, but copper is a good conductor.
• Air, aluminium, wool: Air and wool are poor conductors while aluminium is a good conductor.

Correct answer Air, water, plastic

Additional Information

Transfer of heat in water takes place through convection.

Convection

• It is heat transfer by the movement of its molecules.
• It occurs only in fluids (liquid and gas) not in solids because solid particles can not move from one place to another.
• For example, in a pot boiling water on the stove, or in thunderstorms, where hot air rises up to the base of the clouds.
• Sea breeze and land breeze occurs due to convection.

​Air is a poor conductor and vacuum is in space. The heat from the sun raches to us through radiation. 

Radiation: 

• When electromagnetic radiation is emitted or absorbed to transfer the heat or When heat is transferred in the form of electromagnetic waves is known as radiation.
• Electromagnetic radiation includes microwaves, radio waves, infrared radiation, visible light, ultraviolet radiation, gamma rays, and X-rays.

Concept:

• Warmer air is lighter than cooler air.
• There are three methods of heat transfer, conduction, Convection, and Radiation.
• In conduction, heat transfer takes place from the hotter end of the body to the cooler one. 
• Conduction takes place in good conductors of heat like metal.
• Poor conductors like wood, water, wool etc do not allow heat to pass through them.
• This process of heat transfer takes place in air or water is generally convection. 
• Process of convection: If water is heated on a flame, the hot water goes above and cold water comes down.
• Convection is the phenomenon responsible for the sea breeze.

Explanation:

• The sea breeze can be observed in coastal areas.
• During the day, the land gets heated faster than the seawater
• The air over the land becomes hotter and rises up.
• The cooler air from the sea moves toward the land.
• So, a cool breeze can be felt at sea beaches which is known as a sea breeze.
• At night, water cools slower than land.
• Land becomes cooler and water becomes hot.
• So, the cool air from land rushes toward the sea.
• This is called land breeze.

So, 'During the day, the land gets heated faster than the sea water' is the correct option as it is the reason for sea breeze. 

Additional Information

 Radiation: 

• When electromagnetic radiation is emitted or absorbed to transfer the heat or When heat is transferred in the form of electromagnetic waves is known as radiation.
• Electromagnetic radiation includes microwaves, radio waves, infrared radiation, visible light, ultraviolet radiation, gamma rays, and X-rays.
• It does not require any medium.
• Sun heats earth by radiation.

Concept:

Acid and Base

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Indicators

• The indicators are chemicals or natural substances which change their colour in presence of acid or base.
• Litmus paper is an indicator that is obtained from lichens.
• Other indicators include turmeric, china rose, phenolphthalein, and several others.

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Explanation:

• In A, we have hydrochloric acid. Phenolphthalein remains colorless in acid, So, A is colorless.
• In B, we have a solution of sodium hydroxide.
• Sodium hydroxide is a base. Phenolphthalein turns pink in the base.
• So, B becomes pink.
• Phenolphthalein has no effect on neutral substances like distilled water.
• So, the C will remain colourless.

The correct option is A is colourless, in B pink and in C colourless.