CTET Paper 2 Maths & Science July 2019 (English-Hindi-Sanskrit) (Previous Year Paper)

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 in 3 levels and 6 stages.

Key Points

The above-mentioned description is related to 'The Universal Ethical Principle Orientation' stage of moral reasoning of Kohlberg as it is a stage of morality in which:

• values act as a guiding force that defines the right action based on one’s own conscience.
• universal and abstract moral values including equality, respect, etc. guide one's behavior.
• personality development is highly governed by ethical-moral thinking and internal moral principles.

Hence, it could be concluded that the above-mentioned description is related to 'The Universal Ethical Principle Orientation' stage of moral reasoning of Kohlberg.

Important Points

Refer to the table to be familiar with all the levels of Kohlberg's theory:

Piaget explained that children progress through four stages and in the same order. The Four Stages of Cognitive Development are as follows:-

1. The Sensorimotor Stage (0 to 2yrs)
2. The Preoperational Stage (2 to 7)
3. The Concrete Operational Stage (7 to 12)
4. The Formal Operational Stage (12 to adulthood)

The concrete operational stage is the third stage in Piaget's theory of Cognitive Development.

• In this stage, Children gain the abilities of conservation of number, area, volume, and orientation.
• Children can conserve numbers (age 6), mass (age 7), and weight (age 9). Conservation is the understanding that something stays the same in quantity even when its appearance changes.
• Children enjoy the company of friends in this stage so, this stage is also referred to as gang age, where the feeling of class inclusion dominates in a child.
• Reversibility, seriation, transitivity also developed in this stage
• Ability to conserve is one of the major accomplishments of the concrete operational stage.

Conservation is the understanding that a child develops to know that a thing remains the same even if it changes in shape or appearance.

NOTE:

• Hypothetic - Deductive Reasoning ⇒ Formal Operational Stage
• Secondary Circular Reactions ⇒ Sensorimotor Stage
• Animistic Thinking ⇒ Pre-Operational Stage

Hence, it becomes clear that major accomplishments of the concrete operational stage is Ability to conserve.

Constructivism is a theory based on observation and scientific study about how people learn. It says that people construct their understanding and knowledge of the world, through experiencing things and reflecting on those experiences.

Views of Constructivist: The constructivist approach to learning suggests that people actively construct or make their own knowledge and that reality is determined by the experiences of the learner.

• Constructivists such as Jean Piaget and Lev Vygotsky view learning as a continuous process of meaning-making by active engagement.
• Constructivists believe that a learner's ability to learn relies to a large extent on what he already knows and understands, and the acquisition of knowledge should be an individually tailored process of construction.
• Constructivism was based on cognitive development through mental construction where the learner constructs his/her own knowledge through meaning-making of concepts and experience.

Principles of Constructivism:

• Knowledge is constructed by the learner. The learner accommodates new information through the assimilation of previous information.
• Learning happens through meaning-making.
• Learning is an active process involving the learner’s active engagement in the process as well as with the world

Piaget’s constructivism theory was based on cognitive development and Vygotsky was based on social development.

NOTE:

Hence, it becomes clear that constructivists such as Jean Piaget and Lev Vygotsky view learning as the process of meaning-making by active engagement.

Gender stereotypes typecast a particular gender with a particular behaviour, nature, dressing, attitude, etc.

Examples of gender stereotypes:-

• Usually in stories and magazine articles, clippings from newspapers, gender role models are often attired in traditional dresses.
• A gown or frocks for girls, saree for older women, shirt for men, etc
• Girls asked to be neat, polite, talk softly
• Acceptable to boys behaving roughly, talking loud, or doing a shabby work;
• Girls asked to do a drawing, fine arts, and boys pushed to stronger martial arts, etc

.

• Fixing certain jobs to a particular gender

Hence, to dress in non-traditional attire helps to break this stereotyping and spread equality among everyone.

Gender bias is the differential treatment of individuals based on gender; gender roles define gender-specific roles; gender constancy is developing a constant idea of a particular gender over time.

Therefore, selecting and presenting stories and clippings from the newspaper that portray both men and women in non-traditional roles is an effective strategy to counter gender stereotypes.

Socialization is a process by which an individual becomes a member of society through a mechanism of interaction. 

• Its purpose is to prepare individuals for future roles.
• Socialization is a process of moulding an individual’s brain, attitude, behavior, etc to become a perfect human being in society.
• The important agents of socialization include media, day-care centres, peer groups, school, and religion.

Key Points Media, school, family, and neighbourhood play an important role in the child’s socialization.

• Media helps the child to interact with the society through social standards.
• Social media helps a lot to express one’s views and ideas to others commonly in society and thereby develops communicating and socializing skills.
• Family is the primary agents of socialization for a child.
• School plays a very important role next to family in the social development of a child.
• The school imparts socialization through various interactions with teachers, peers, other students, and other staffs of the school.
• The neighbourhood has a definite role in the socialization process of a child. The child is part of a society or a community and has to live in common among the neighbourhood.
• By communicating, interacting and sharing with neighbours, a child can develop social skills.
• Neighbours act as supporting pillars who can mentor and guide a child along with family members and teachers.

Hence, from the above-mentioned points, it becomes clear that given all the agents play an important role in a child’s socialization.

The theory of Multiple Intelligence which consists of eight different kinds of intelligence is propounded by an American psychologist 'Howard Gardner'. 

This theory emphasizes that:

• intelligence is of several kinds rather than dominated by a general factor.
• intelligence can't be tied to a single domain as each individual has his/her own abilities.

Key Points

The above-mentioned characteristic is related to the Interpersonal Intelligence of Howard Gardner’s theory as:

• Interpersonal intelligence deals with understanding and relating to other’s feelings.
• A person with interpersonal intelligence can understand various emotional states of other people.
• Interpersonal intelligence is the ability to respond appropriately to moods, temperaments, and intentions of others.

Hence, it could be concluded that the above-mentioned characteristic is related to the Interpersonal Intelligence of Howard Gardner’s theory.

NOTE: Refer to the diagram to know the category of intelligence suggested by Howard Gardner:

An assessment is done to provide valuable critical information about a child’s performance which reflects its development and growth. It is conducted in different phases of the teaching-learning process.

Some assessments are conducted before the beginning of the teaching-learning process, some are carried out during the process, and others conducted at the end of the instructional process.

Assessment:

• guides a teacher to plan and improve teaching-learning processes in the classroom
• provides information regarding the changes and progress that a child has developed in a learning process over a period of time which can be used for evaluating the quality of teaching-learning processes
• provides details about student’s milestones’ - individual capabilities, potential, strengths and challenging areas which can be discussed with the parents to work together and support the student’s growth and development.

Hence, it could be concluded that except statement (1), the remaining statements are correct in the context of the question.

John Dewey, an American philosopher has proposed the concept of 'Progressive Education' which emphasizes that learning takes place only through 'hands-on' approach so the students must interact with their environment to adapt and learn.

Belief in the capability and potential of every child is central to the concept of progressive education as it promotes: 

• emphasizes to enhance skills and understanding of the learners by engaging with the contents and experiences.
• promotes 'learning by doing' to make children self-reliant and productive to use their knowledge and talents effectively.
• ensures the active participation of students by working in a group and applying practical knowledge to complete an activity.

Hence, it could be concluded that belief in the capability and potential of every child is central to the concept of progressive education.

Additional Information

'Progressive Education' Promotes:

• Critical thinking
• Problem-solving skills
• Active engagement of students
• Development of social and communicative skills

Individual difference refers to the difference which distinguishes an individual from another on the basis of psychological characteristics.

Key Points

To understand individual differences in development it is important to consider both inherited characteristics as well as environmental factors and their interplay. 'Hereditary and Environment' are complementary in determining the development of an individual as:

• all the mental and social traits depend on the environment.
• all the potential inputs for growth and development depend on heredity.
• all the inborn traits, instincts, potentials, and I. Q. depends on the heredity.
• heredity places limit on IQ and environment determines the numeric position of IQ within these limits.

Hence, it could be concluded that to understand individual differences in development it is important to consider both inherited characteristics as well as environmental factors and their interplay.​

Important Points

• Heredity: It refers to the traits that pass down from the parents to their offspring. It is the most important personality and intelligence determinant.
• Environment: It refers to the circumstances in which an individual lives. Child's immediate environment strongly influenced their personality and intelligence.

Additional Information

Required steps to meet individual differences:

• Ability grouping.
• Enrichment of curriculum.
• Individualization of instruction.
• Identification of special talents.
• Adoption of modern method of teaching.

Development includes a series of qualitative and progressive change. Development can be defined as the changes in the structure, thought or behaviour, of a person that occurs as a function of both biological and environmental influences.

• The exact course and nature of development is constantly influenced by environmental factors and keeps changing accordingly.
• Development is relatively ordered and takes place gradually over a period of time.
• Development involves the physical, cognitive, emotional, social, and language development of an individual which are influenced by maturation and learning over the period of time.
• It is a continuous process that happens throughout the lifetime, takes place even after attaining maturity of physical growth and not a predetermined factor.
• Every individual develops at different rates.
• Hereditary growth factors like the colour of the eyes or hair, facial features, etc are determined at the time of birth itself.

Hence, from the above-mentioned points, it becomes clear that the exact course and nature of development are not determined at the time of birth itself.

Gender refers to the socially and culturally constructed system that attributes meaning to what it means to be a male or a female in a particular society.

Gender bias in teaching leads to differential learning experiences, even though the girls and boys of a class sit in the same classroom and attended by the same teacher.

• It refers to the belief when someone prioritize one gender more than the other one.
• The result of the research studies about teachers interacting more with boys than girls is an example of gender bias in teaching.

Examples of Gender Bias in Teaching and at school:-

• Girls being given lesser opportunities to participate in school and classroom events
• Applying gender stereotypes like femininity norms among girls to behave quiet, being neat, calm etc., and masculine norms among boys to be loud, bold, strong, etc.
• Stereotypical expressions of male and female characters in textbook content.
• Assigning work differentially to boys and girls​.

Methods to Avoid Gender Bias in Teaching:-

• Allow for equal participation in activities by girls and boys.
• Treating both boys and girls equally.
• Following gender bias-free teaching and learning methods.

Hence, from the above-mentioned points, it becomes clear that teachers interacting more with boys than girls is an example of gender bias in teaching.

Divergent thinking is an open point of thinking which produces multiple possible solutions to a single problem.

Creativity is considered as the ability to produce something original or to find the solution to a problem by themselves.

Creative children have the ability to come up with original and divergent solutions to a problem.

General Traits of a Creative Child:

• Think and act independently
• Curious and active learner
• Deep thinkers and visionary
• Ability to come up with divergent solutions
• Open-minded and Intuitive
• Interesting, fun-filled, vibrant
• Ambitious and likes challenges
• Self-occupied and self-disciplined
• Like to take risks and experiment

Curious children can provide original and divergent solutions to the problem because of their experimental, curious, deep and divergent thinking nature.

They try to think deep into the problem, tackle it, and find multiple solutions to solve it. They mostly think and work independently and hence their solutions are unique and original.

NOTE:

• Impaired and children with a learning disability cannot provide original divergent solutions because of their impairment or disability which might hinder their thinking and learning process.
• Egocentric children fail to think on their own. They face difficulty in thinking outside of their own viewpoints.

Hence, it becomes clear that the ability to come up with original and divergent solutions to a problem is a primary characteristic of a creative child.

In the teaching-learning process, visually challenged learners suffer from an issue with sight or vision but when they are facilitated with the right training and tools, they develop a good literacy ability.

Key Points

Instructional adaptations that a teacher should make while working with visually challenged learners include:

• using a lot of touches and feel materials.
• giving verbal clues to create opportunities to imagine.
• introducing tactile materials during classroom discussions.
• speaking clearly and loudly with appropriate pauses and reiterations.
• providing learning with the help of auditory systems such as an audio CD of the textbook, radio, etc.
• using braille system to make them read-write as it's raised dots will help the child to study the words through the pattern.

Hint

• A teacher should not use a variety of visual presentations and written tasks especially worksheets for visually challenged learners as it could lead to low self-esteem and feeling of failures in them.

Hence, it could be concluded that a teacher should speak clearly and use a lot of touches and feel materials while working with visually challenged learners.

Important Points

• Tactile materials: It refers to the inputs which children receive through the receptive sensors of their skins.
• Braille system: It refers to a pattern of raised dots called "Braille" to represent letters, numbers, and punctuation marks, that can be felt with a finger.

Inclusive Education refers to the inclusion of all children in the education system, regardless of their differences and disabilities.

• It values the diversity, each child brings to the classroom and facilitates all with equal opportunities to learn and grow.
• It provides a provision to include disabled children along with normal children in a regular classroom environment.

Key Points 

Cooperative learning and peer tutoring should be actively promoted in an inclusive classroom as these both strategies will:

• boost up the confidence of special children while learning with normal children.
• help the special child to gain quality experience by engaging them in active learning.

Let's Understand in Brief:

Hence, it could be concluded that 'cooperative learning and peer tutoring**'** should be actively promoted in an inclusive classroom.

Inclusive education refers to the practice of educating students with special needs in regular classes for all. It provides a provision to include disabled children along with normal children in a regular classroom environment.

• Inclusive classroom refers to an education system that includes children regardless of physical, intellectual, social, linguistic, or other differently-abled conditions.
• An inclusive classroom is not limited to children with a disability but also gifted children, economically disadvantaged children, children from remote populations, children belonging to ethnic, linguistic, or cultural minorities or children from other marginalized groups.

Important Points

Providing an individual education plan (IEP) is most important in an inclusive classroom.

Need for IEP in an inclusive classroom

• In an inclusive classroom, students with a diverse background, varied skills, diverse abilities, and challenges are grouped in a single classroom.
• So the individual learning capacities will be highly different from each other physically, cognitively, academically, socially, and emotionally.
• To balance these individual differences, an appropriate individual education plan is highly necessary for an inclusive classroom.

IEP advantages:

• Aids in attending to the individual needs of a student so that he/she can be a part of an inclusive classroom.
• Provide extra attention
• Evaluate independently
• Motivate in learning

IEP strategies:

Hint

• The testing, competitive learning, and uniform instruction are not applicable in an inclusive classroom because it comprises of students with mixed abilities.

Hence, from the above-mentioned points, it becomes clear that an individualized education plan is most important in an inclusive classroom.

Dyslexia is a learning difficulty based on language processing disorder. Dyslexic learners has-

1. Lack of reading skills
2. Face difficulties with spelling and pronunciation of words
3. Lack of writing fluency

Key PointsDyslexic learners lack reading and writing fluency because they lack executive function, cannot process phonological information, or decode words.

To correct this lack in reading and writing fluency, dyslexics should be provided

• Awareness in phonology, recognizing letters, correspondence of sound and letter, orthography, morphology, syllable, syntax, semantics, etc
• Practice continuous repeated reading and writing to increase fluency

Additional Information

• The creative learner has a highly developed problem-solving ability, a curious and impulsive nature, and the ability to create original and imaginative ideas.
• Attention-Deficit Hyperactivity Disorder (ADHD) is a type of developmental or behavioural disorder whose essential feature is a persistent pattern of inattention, hyperactivity, and impulsivity.

Learning is the acquisition of new behaviour or the strengthening or weakening of old behaviour as a result of experience. It represents progressive changes in behaviour. It also involves the acquisition of knowledge, habits, and attitude. The term learning covers every modification in behaviour to meet environmental requirements.

In Facilation of Meaningful Learning:-

• The learner takes control of the learning process and the teacher acts as the facilitator or the resource provider.
• The learner is responsible for developing and achieving his/her own learning goals
• Makes sure that the learner understands the facts and information provided and relates it with already existing information.
• Long-lasting, durable, coherent, organized, problem solving
• Using examples and non-examples, encouraging multiple ways to look at a problem, and connecting new knowledge to a pre-existing knowledge will facilitate meaningful learning.

Hint

• Repetition learning helps to practice a skill repeatedly until the learner masters the skill. Recall helps to bring out stored information.
• These are rhetoric processes of rote learning which cannot promote meaningful learning.

Hence, from the above-mentioned points, it becomes clear that promoting repetition and recalls does not result in meaningful facilitation of learning.

The constructivist environment is related to the constructivist approach of education which gives primacy to collaborative learning by involving learners in discussions and projects.

Constructivist environment:

• emphasizes on collaboration with others for learning.

• ensures the active involvement of learners and promotes peer tutoring.

• allows learners to foster their own strategy of learning to perform a task.

• provides ample opportunities to learners to make them work at their own pace.

• views learners as makers of meaning and creators of knowledge through social interaction.

• NOTE: In the constructivist learning environment teachers assess learners during the teaching-learning process and gives feedback on the learning process rather than the products.

Hence, it could be concluded that teachers employ a specific end of the term assessment strategies and give feedback on products rather than processes that would not be consistent with a constructivist environment.

Teachers play the most crucial role in **moulding the behaviour of learners.**his shaping of behaviour is achieved through planning and dedication. 

• The benefits of teaching are maximized when teachers act as a facilitator for the students.
• A teacher should encourage students to set learning goals rather than performance goals.
• The role of the teachers is considered to view learners as active participants in their learning and not as recipients of knowledge.
• A teacher has to play an interactive role with patience and perseverance to foster the potential of young seedlings to grow and bloom.

NOTE: Setting performance, marking seeking, or failure avoiding goals will pressurize the learner.

Hence, from the above-mentioned points, it becomes clear that a teacher should encourage students to set learning goals rather than performance goals.

Learning strategies refer to the various approaches, processes, and actions that the learner applies to learn a concept. These are the learner’s own way of organizing and using specific sets of skills to achieve expected learning outcomes.

Here, all the above-mentioned activities are examples of effective learning strategies. 

Let's Understand in Brief:

Hence, it could be concluded that all the above-mentioned activities are the examples of effective learning strategies.

Motivation refers to the process that guides an individual to achieve a goal. There are two main types of motivation which include extrinsic and intrinsic motivation.

Let's Understand in Brief:

Hence, it could be concluded that the sentence “I complete my homework because the teacher gives us marks for each assignment" is an example of extrinsic motivation.

Teaching involves the use of varieties of techniques in order to make teaching-learning a fruitful and meaningful process.

A primary classroom teacher should use both examples and non-examples as a teaching tool to facilitate productive learning.

• Examples:
• It utilizes similar situations, ideas, or concepts to learn new information or concept easily.
• Examples help to understand an unclear concept by relating to another similar concept.
• Nonexamples:
• It utilizes contrasting situations, ideas, or concepts to learn new information.
• Non-examples help students to understand concepts by stretching their thinking effectively.

Hence, it could be concluded that in a primary classroom, a teacher should give both examples and non-examples.

Additional Information

Examples and Non-examples Enhance:

• Self-awareness
• Critical thinking
• Interest in learning
• Active engagement
• Understanding of concept

Meaning-making is an important process in meaningful learning which aims in learning through conceptual understanding to impart valuable knowledge to the learner.

• Exploration and discussion are the best strategies to promote meaning-making in children.
• This is facilitated by various learning attributes like observation, exploration, analysis, discussion, inference, etc.
• Meaning-making helps the children to relate the current information with already existing information and make an understanding of the whole concept.

For efficient meaning-making in learning concepts, children need to:

• Engage actively in the learning process
• Follow an inquiry-based approach and analyze every concept
• Apply curiosity and critical thinking and ask questions like ‘why’, ‘how’ to understand how and why things happen
• Develop hypothetical analysis through diverse ideas and relate the cause and effect and other relationships in a concept
• Discuss the same with the teacher and peers to brainstorm ideas and come to a meaningful conclusion about the concept
• Learning concepts learned with a meaningful understanding will stay for a lifetime than rote learning

NOTE: Transmission of information, using punitive measures, uniform, and standardized testing; although, might promote learning but will not create meaningful learning.

Hence, it becomes clear that exploration and discussion strategies would promote meaning-making in children.

Error**:** When a learner can’t master a topic, he/she is vulnerable to making errors. Errors are nothing but incorrectness made by a child during learning. 

• Misconceptions: These take place due to the mismatch in previously assimilated and newly accommodated knowledge.

Key Points Children’s errors and misconceptions:

• are significant steps in the teaching-learning process.
• are necessary for the learning process to give insight into children's thinking.
• help the teacher to be aware of learners' learning styles, to cater to them according to their needs.
• are considered a part of the teaching-learning process as it helps to understand the child.

Hence, it could be concluded that children’s errors and misconceptions are significant steps in the teaching-learning process.

Additional InformationReasons for errors and misconceptions:

• Lack of interest & knowledge
• Misunderstanding of concept
• Missing out on important points or steps
• Inability to grasp the central idea or concept
• Forgetting related previously assimilated knowledge

The constructivist frame/perspective is based on the idea that meaningful learning takes place when learners actively construct their own knowledge.

Key Points

The central idea of the constructivist frame is that learners learn through experiencing things and reflecting on those experiences.

In the constructivist frame, the child is viewed as:

• imaginative on the basis of sources.
• little scientists and markers of meaning.
• problem solver and a scientific investigator.
• creator of knowledge through social interaction.
• builder of new knowledge by activating the previous one.

Important Points

• As a problem solver, the child learns by exploring, investigating, experimenting, and inquiring about the facts and information provided.
• As a scientific investigator, the child actively takes part in the learning activity and tends to be – reflective, analytical, creative, etc.

Hence, it could be concluded that in the constructivist frame, the child is viewed as a problem solver and a scientific investigator.

co-operative learning refers to a heterogeneous group where students work collaboratively but each member is also accountable for his/her share of work to achieve the expected goal.

Key Points

A teacher’s role while using co-operative learning in her class should be supporting and monitoring each group as the teacher's role in co-operative learning includes:

• Selecting and arranging the group setting
• Setting goals to be met by the group members
• Providing necessary materials and other resources
• Supporting each student throughout the learning process
• Observing and monitoring each student's understanding of the task
• Evaluating each student’s performance based on how his/her performance.

Hence, it could be concluded that a teacher’s role while using co-operative learning in her class is to be supportive and monitor each group.

• Development: It refers to a qualitative change that results in an increase in structure for better and enhanced functioning of organs.
• Learning: It is a comprehensive process that refers to a change in behavior, knowledge, and skill as a result of practice and experience.

Key Points

Development and learning are inter-related and inter-dependent and contribute to each other.

• It should be noted that development is a product of maturity and learning.
• Maturity is more or less automatic, unfolding biological potential which is an irreversible sequence and entails biological changes.
• Such changes are relatively independent of environmental factors as long as environmental factors remain normal.
• There is a more or less permanent change in human behavior from the individual's experience in the environment.
• Learning occurs across the entire life span, which differs from maturity.
• However, learning depends on the process of maturing i.e. individual readiness (mental and physical) for certain activities.

Hence, we can conclude that the statement 'development and learning are inter-related and inter-dependent' denotes the relationship between development and learning correctly.

Swiss biologist and psychologist Jean Piaget observed his children and their process of making sense of the world around them and how the mind processes new information encountered.

Piaget's Theory of Cognitive Development, assimilation, accommodation, and equilibrium are the ways through which children integrate new experiences into already existing cognition structures (schema). 

Schema:

• Schemas are mental representations of how information is organized and interpreted.
• Schemas are specific psychological structures, these are constructed in organized ways to make sense of experience.
• It is a building block of knowledge and also called as rooms or packet of information in our mind.
• These are already existing mental models in mind to represents anything.

Assimilation: It is the addition of a new concept or experience into an existing schema. For example, the baby's sucking of thumb is an initial schema.

Accommodation: It is the revision of an existing schema to suit the new experience. For example, the baby modifies the way it sucks to include sucking on a new toy.

Equilibrium: The cognitive stability or balance arrived by the processes of assimilation and accommodation is the equilibrium obtained. Equilibration is the balancing act between ‘old’ and ‘new’ perceptions and experience.

NOTE: Images, mental map, and tools are also psychological structures but were not stressed by Piaget.

Hence, according to Piaget, specific psychological structures (organized ways of making sense of experience) are called schemas.

According to Vygotsky’s 'Social Constructivism Theory', the zone of proximal development tells the child can travel with the help of scaffolding from adults and others through questions or suggestions but yet act and learn independently and reach far beyond in the process.

• Scaffolding refers to a technique that provides the right kind of support in the right amount at the right time to increase a child’s competence.
• Proper guidance from a more knowledgeable other (MKO) along with encouragement and motivation makes a learner develop more skill and complete and excel in the learning process.
• Knowledge is constructed through scaffolding from the more knowledgeable other by means of social interaction.
• The term proximal refers to the skills which change to mastering the skill with assistance or scaffolding from MKO through social interaction.

The zone of proximal development changes the stage from ‘what I can’t do’ to ‘what I can do’ with some help.

NOTE:

• Equilibration balances assimilation and accommodation or information.
• Conservation speaks about how objects remain the same in certain qualities.
• Intelligence lies in acquiring and applying knowledge.

Hence, from the above-mentioned points, it becomes clear that the zone of proximal development constructs the given statement.

Lev Vygotsky’s theory is called the Socio-Cultural Theory which-

• States basic mental capacities are transformed into higher cognitive processes primarily through social interactions
• Recognizes social interaction and language** as key players of cognitive development**
• Emphasizes social and cultural interactions with the community through social activities

Additional Information

He explains this with the concept of the Zone of Proximal Development (ZPD), which refers to a range of tasks that a child can achieve only with assistance from a more skilled adult or peer called the More Knowledgeable Other (MKO). Adult assistance is provided wherever necessary which is called Scaffolding. 

Other terms are associated with:

• Stimulus-Response association – Skinner
• Adaptation – Piaget
• Rewards and Punishment – Skinner

Hence, according to Ley Vygotsky, basic mental capacities are transformed into higher cognitive processes primarily through Social interaction.

Concept used:

HCF:- The greatest common divisor of two or more positive integers happens to be; the largest positive integer that divides the numbers without leaving a remainder.

Calculation:

x = 2³ × 3² × 5³ × 7³

y = 2² × 3³ × 5⁴ × 7³

z = 2⁴ × 3⁴ × 5² × 7⁵

HCF = 2² × 3² × 5² × 7³

HCF = (2 × 3 × 5)² × 7³

HCF = 30² × 7³

Diagram

52272 = 2⁴ × 3³ × 11²

p² × q³ × r⁴ = 52272

p² × q³ × r⁴ = 11² × 3³ × 2⁴

On comparing

p = 11, q = 3 and r = 2, then

⇒ (2p + q - r)

⇒ (2 × 11 + 3 - 2)

⇒ 22 + 3 - 2

⇒ 25 - 2

⇒ 23

7-digit number 134x58y is divisible by 72, so we can say number also divisible by 8 and 9.

Divisibility law of 8 ⇒ A number divisible by 8 if its last three-digit is divisible by 8

Divisibility law of 9 ⇒ A number is divisible by 9 if the sum of its digit is divisible by 9.

7-digit number 134x58y is divisible by 8 if its last digit will be y = 4.

7- digit number 134x584 divisible by 9 if x = 2

⇒ 1 + 3 + 4 + x + 5 + 8 + 4

⇒ 25 + x

If we put x = 2, then number become 27 which is divisible by 9.

Now, (2x + y)

⇒ (2 × 2 + 4)

⇒ 4 + 4

⇒ 8

Let’s check which not a Pythagorean triplet using Pythagoras theorem is

Taking option (1) 8, 15, 17

⇒ 17² = 8² + 15²

⇒ 289 = 64 + 225

⇒ 289 = 289

So, option (1) is a Pythagorean triplet.

Taking option (2) 11, 60, 63

⇒ 63² = 11² + 60²

⇒ 3969 = 121 + 3600

⇒ 3969 ≠ 3721

So, option (2) is not a Pythagorean triplet.

Taking option (3) 13, 84, 85

⇒ 85² = 13² + 84²

⇒ 7225 = 169 + 7056

⇒ 7225 = 7225

So, option (3) is a Pythagorean triplet.

Taking option (4) 7, 24, 25

⇒ 25² = 7² + 24²

⇒ 625 = 49 + 576

⇒ 625 = 625

So, option (4) is a Pythagorean triplet.

Concept used:

Supplementary angle: Two Angles are Supplementary when they add up to 180 degrees.

Calculation:

Let the angle be x

So its complement angle will be = 90° - x

So, its supplement angle will be = 180° - x

Given, that the supplement is 4 times its complement

According to the question

⇒ 180° - x = 4 (90° - x)

⇒ 180 - x = 360° - 4x

⇒ 4x - x = 360° - 180°

⇒ 3x = 180°

⇒ x = 180°/3

⇒ x = 60°

Concept used:

Obtuse angled triangle: A triangle in which one angle is greater than 90° is called an obtuse angle triangle.

Sum of all the angles of the triangle is 180°

Calculation:

As we know,

Sum of all three angles of triangles is 180.

According to the question

⇒ x + 3x + 20 + 6x = 180

⇒ 10x + 20 = 180

⇒ 10x = 180 – 20

⇒ 10x = 160

⇒ x = 160/10

⇒ x = 16

First angle = x = 16°

Second angle = 3x + 20 = 3 × 16 + 20 = 48 + 20 = 68°

Third angle = 6x = 6 × 16 = 96°

So, this is the obtuse angled triangle.

Diagram

In triangles ABC and DEF, ∠C = ∠F, AC = DF, and BC = EF

So, we can say ΔABC ≅ ΔDEF

AB = DE

⇒ 2x - 1 = 5x - 4

⇒ 5x - 2x = 4 - 1

⇒ 3x = 3

⇒ x = 3/3

⇒ x = 1

As we know,

The sum of the length of any two sides of a triangle is greater than the length of the third side.

Given,

One side of the triangle is 5 and other is 10 cm and its perimeter is P cm

Let third side of the triangle be x, then

From option (1) taking least value of p = 20

Perimeter of the triangle = p

⇒ 5 + 10 + x = 20

⇒ x = 20 - 15

⇒ x = 5

So, the side of the triangle are 5, 5 and 10

⇒ 5 + 5 = 10

⇒10 = 10 (can’t formed the triangle)

From option (2) taking least value of p = 21

⇒ 5 + 10 + x = 21

⇒ x = 21 - 15

⇒ x = 6

So, side of the triangle are 5, 6 and 10.

⇒ 5 + 6 = 10

⇒ 11 > 10

Now, we can say with side of 5, 6 and 10 we can form a triangle.

Taking largest possible value of p = 29

⇒ 5 + 10 + x = 29

⇒ 15 + x = 29

⇒ x = 29 - 15

⇒ x = 14

So, side of the triangle are 5, 10 and 14

⇒ 5 + 10 = 14

⇒ 15 > 14

Now we can say with side of 5, 10 and 14 we can form a triangle.

So, the correct option is 2.

13, 8, 15, 14, 17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14

First of all, we arrange the data in ascending order, then

8, 9, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17

Total number (n) = 15

As we know,

Median = [(n + 1)/2]^th = [(15 + 1)/2]^th = [16/2]^th = 8^th number

8^th number is 14

So, x = 14

If 8 is replaced by 18 then,

13, 18, 15, 14, 17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14

Again, we arrange the data in ascending order, then

9, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 18

Total number (n) = 15

Median = [(n + 1)/2]^th = [(15 + 1)/2]^th = [16/2]^th = 8^th number

8^th number is 15

So, y = 14

x + y

⇒ 14 + 15

⇒ 29

Calculation:

A bag contains 3 white, 2 blue and 5 red balls.

Total number of balls = 3 + 2 + 5 = 10

Number of balls that are not red = 10 - 5 = 5

Probability of balls drawn is not red = (number of balls which are not red)/(total number of balls) = 5/10 = 1/2

Given, l = 8 m and b = 6 m

As we know,

Volume of cuboid = lbh

Total surface area of cuboid = 2 (lb + bh + hl)

⇒ 2 (8 × 6 + 6 × h + h × 8) = 194

⇒ 48 + 6h + 8h = 194/2

⇒ 14h = 97 - 48

⇒ h = 49/14

⇒ h = 3.5

Volume of cuboid = 8 × 6 × 3.5 = 168 m³

Given, height of the trapezium h = 7 cm

Let length of smaller parallel side be x

Then, length of bigger parallel side = x + 6 cm

As we know,

Area of trapezium of = (1/2) × (sum of parallel side) × height

⇒ 105 = (1/2) × (x + x + 6) × 7

⇒ 2x + 6 = (105 × 2)/7

⇒ 2x = 30 - 6

⇒ x = 24/2

⇒ x = 12 cm

Length of longer parallel side = x + 6 = 12 + 6 = 18 cm

Given:

Radius of cylinder r = 3 cm

Formula used:

Curved surface area of cylinder = 2πrh

Calculation:

As we know,

Curved surface area of cylinder = 2πrh

⇒ 94.2 = 2 × 3.14 × 3 × h

⇒ h = 94.3/(2 × 3 × 3.14)

⇒ h = 5 cm

Volume of cylinder = πr²h = 3.14 × 3 × 3 × 5 = 141.3 cm³

Let x be added to each of 14, 12 and 34 and 30 so, the numbers become in proportion.

⇒ (14 + x)/(12 + x) = (34 + x)/(30 + x)

Using dividiendo and componendo

⇒ (14 + x + 12 + x)/(14 + x - 12 - x) = (34 + x + 30 + x)(34 + x - 30 - x)

⇒ (26 + 2x)/2 = (64 + 2x)/4

⇒ 26 + 2x = 32 + x

⇒ 2x - x = 32 - 26

⇒ x = 6

Now, put the value of x in √(12x + 9)

⇒ √(12 × 6 + 9)

⇒ √(72 + 9

⇒ √81

⇒ √(9 × 9)

⇒ 9

Concept used:

There are n lines of symmetry for a regular polygon with 'n' sides.

For example:-

Line of Symmetry is the imaginary line where you can fold the image so that both halves match exactly.

Similarly,

A regular polygon of 10 sides has 10 lines of symmetry.

⇒ 10 (x + 6) + 8(x - 3) = 5(5x - 4)

⇒ 10x + 60 + 8x - 24 = 25x - 20

⇒ 25x - 18x = 36 + 20

⇒ 7x = 56

⇒ x = 56/7

⇒ x = 8

Taking option (1)

⇒ 3(3x - 5) = 2x + 1

⇒ 3 (3 × 8 - 5) = 2 × 8 + 1

⇒ 3 (24 - 5) = 16 + 1

⇒ 3 × 19 = 17

⇒ 57 ≠ 17

So, option (1) is false.

Taking option (2)

⇒ 2(x + 3) = 5(x - 5) + 4

⇒ 2 (8 + 3) = 5 (8 - 5) + 4

⇒ 2 × 11 = 5 × 3 + 4

⇒ 22 = 15 + 4

⇒ 22 ≠ 19

So, option (2) is also false.

Taking option (3)

⇒ 5(x - 5) = 2(x - 3) + 5

⇒ 5 (8 - 5) = 2 (8 - 3) + 5

⇒ 5 × 3 = 2 × 5 + 5

⇒ 15 = 10 + 5

⇒ 15 = 15 (satisfied)

So, option (3) satisfies the equation.

Let P be subtracted from 5y - 13x - 8x to obtain 11x - 16y + 7a

According to the equation

⇒ 5y - 13x - 8a - P = 11x - 16y + 7a

⇒ P = 5y - 13x - 8a - 11x + 16y - 7a

⇒ P = 21y - 24x - 15a

Mathematics is the science which deals with quantitative calculations, measurement, arrangement, logical reasoning, and relationships of quantities. Mathematics reveals hidden patterns that help us to understand the world around us.

• In mathematics, we deal also with numbers, calculations, measurement of shapes and structures, establishing relationships among variables, etc.
• Teaching mathematics requires thinking about concepts, learner-centred pedagogy, and diversified creative assessment.
• Mathematical concepts are abstract and helping learners construct these meaningfully has always been a challenge for teachers.

Children Coming to School from Rural Areas: They have sound knowledge about mathematics. They use mathematics in their daily activities. They may have rich oral mathematical traditions and knowledge. 

NOTE: Given other options are not appropriate according to the question.

Hence, from the above-mentioned points, it becomes clear that children coming to school from rural areas may have rich oral mathematical traditions and knowledge.

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

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

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

An axiom is a statement that is assumed to be true and need not be proved. These are propositions that are assumed. Different axioms are used for different mathematical reasoning and proving theorems. They are used as the starting point of any mathematical reasoning.

Additional Information

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

Hence, it becomes clear that the statement, 'Axioms are propositions which are assumed' is correct.

Error: When a learner can’t master on a topic, he is vulnerable to make errors. Errors are nothing but incorrectness made by a child knowingly unknowingly. 

Key Points

So, the following should be noted:

• Errors are necessary in the learning process to give insight into children's thinking.
• It helps the teacher to be aware of their learning styles, to cater them according to their needs, hence, they are the rich source of information about children's learning.
• Children’s error should be accepted as a feature of motivation for teachers because it can guide the teacher in planning her classes.
• It is considered as a part of the teaching-learning process as it helps to understand a child.
• Student’s error help teacher to take various pedagogy method as the teacher uses different pedagogy according to the need of students.

Hence, we conclude that "They should be overlooked" is not true in context to children's error in mathematics.

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

The Nature of Mathematics is Logical as it relies on:

• Mathematics relies on the evaluation of truth or the likelihood of statements.
• Mathematics is a language.
• It visualized as the vehicle to train a child to think, reason, analyze, and articulate logically.
• Mathematics relies on the development of skills like speed, accuracy, estimation.
• Mathematics is a tool. 
• Using mathematics as a tool provides new opportunities for taking advantage of mathematical methods.
• Using mathematics as a tool is in no way meant in a pejorative sense. It rather emphasizes the productivity of mathematics in coping with structures of arbitrary nature.
• Mathematics deals with structures and such structures can be found at various places.
• It relies on the improvement of reasoning power, analytical and, critical thinking.
• Mathematics is a form of art.
• Mathematicians often use aesthetic terms in describing the work they do.
• It consists of beautiful theorems, elegant proofs, cute short cuts, powerful symmetries.
• It relies on the enhancement of scientific attitudes like estimating, finding, and verifying results.

Hence, from the above-mentioned points, it becomes clear that all the given points regarding Mathematics are true.

Contradiction Method-

• We explore ‘indirect’ arguments, in particular, a very powerful tool in mathematics known as ‘proof by contradiction’.
• In this method, we assume that something is true and later it comes out as false.
• To prove √2 is an irrational number, a teacher firstly assumes that it is a rational number and then proceeds to show how this assumption becomes false and not feasible. So this is an example of the Contradiction method.

Additional Information

• Proof by Induction Method: Social Science induction, is a strategy, of proving a proposition that is deductive in nature.
• Proof by Deductive Method: It is based on deduction. At first, the rules are given and then students are asked to apply these rules to solve more problems.

Hence, it becomes clear that the given statement is an example of proof by the Contradiction method.

Mathematics is the study of numbers, shape, quantity, and patterns. The nature of mathematics is logical and it relies on logic and connects learning with childrens' day to day life.

• Assessment in mathematics refers to the process of collecting, receiving, and using data for the purpose of improvement of the mathematical learning process.

Key Points

Holding conversations and one to one discussion with children would be a desirable assessment practice in the context of mathematics learning as it will help teachers in assessing children by:

• involving them in actively in the learning process.
• making them learn to look at any issue from different angles.
• providing them an opportunity to share their ideas and experiences.
• ensuring maximum participation of learners in learning through conversation.

Hence, it could be concluded that holding conversations and one to one discussion with children can also be helpful in assessing them in the context of mathematics learning.

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

Key Points

The Nature of Mathematics:

• It helps students to connect classroom learning with everyday life.
• Mathematics is an important subject and is not hard in comparison to other subjects.
• It is just a myth that girls need extra attention because they are weaker in mathematics.
• Everyone can learn and succeed in mathematics.
• Mathematics visualized as the vehicle to train a child to think, reason, analyze, and articulate logically.
• It is also a myth that mathematics takes a lot of time to be understood in comparison to other subjects.
• Development of skills like speed, accuracy, estimation.
• Improvement of reasoning power, analytical and, critical thinking.
• Enhancement of scientific attitude like estimating, finding, and verifying results.

Hence, from the above-mentioned points, it becomes clear that everyone can learn and succeed in mathematics.

Proportional Reasoning: It involves understanding the multiplicative relationships between rational quantities (a/b = c/d), and is a form of reasoning that characterizes important structural relationships in mathematics and science.

• Proportional reasoning is the ability to compare ratios or the ability to make statements of equality between ratios.
• Proportional reasoning is foundational to understanding fractions.
• Proportional reasoning involves, detecting, expressing, analyzing, explaining, and providing evidence in support of assertions about, proportional relationships.
• It involves thinking about the relations among relations.

Jean Piaget's Views:

• Proportional reasoning represents a cornerstone in the development of children’s mathematical thinking.
• Piaget considers the ability to reason proportionally to be a primary indicator of formal operational thought, and this stage is viewed as the highest level of cognitive development.
• Proportional reasoning helps in understanding the concept related to ratio and proportion.
• Ratio and proportion are critical ideas for students to understand.

Piaget’s Concept of Formal Operational Thought:

• It is associated with one’s ability to reason proportionally.
• The attainment of proportional reasoning is considered a milestone in students’ cognitive development.
• Piaget described the development of proportional reasoning in three stages:-

1. Students are not aware of ratio dependence and seek solutions by guessing.
2. Students are aware of objective dependence.
3. Proportionality is discovered and applied to obtain correct solutions.

NOTE:

• Van Hiele describes how people learn geometry. According to his theory, there are five levels of thinking in geometry.
• Zoltan Dienes stands with those of Jean Piaget and Jerome Bruner as a legendary figure whose theories of learning have left a lasting impression on the field of mathematics education.
• Lev Vygotsky propounded the 'Socio-Cultural Theory'.

Hence, it becomes clear that the role of proportional reasoning in understanding the concept related to ratio and proportion was highlighted by Jean Piaget.

During the teaching-learning process, a child makes mistakes willingly-unwillingly or due to some alternative conceptions. It is the job of the teacher to help students to correct those mistakes after diagnosing them.

• Remedial strategy refers to the method of teaching that helps the teacher to provide learners with the necessary help and guidance to overcome the problems which are determined through diagnosing them.

Key Points

In the above-mentioned phenomenon, the best remedial strategy is to explain the concept of equality using alternate methods as it will help learners in:

• gaining a better and clear understanding of the concept.
• developing a basic sense regarding the general idea of the topic.
• changing their misconceptions about the topic with the correct knowledge.

Hence, it could be concluded that explaining the concept of equality using alternate methods will be the best remedial strategy in the above-mentioned concept.

Pedagogy refers to the set of principles that influence the approaches to the teaching-learning process. It consists of learning environment, teaching-learning arrangements, methods, general educational principles, etc.

Mathematics is the study of numbers, shape, quantity, and patterns. The nature of mathematics is logical and it relies on logic and connects learning with learners' day to day life.

Key Points

Contemporary understanding of Mathematics Pedagogy is necessary for every teacher as it encourages them to:

• initiate mathematical talk in the classroom.
• encourage the ability to approximate solutions.
• encourage children to develop mathematical thinking.
• develop the skill of systematic reasoning in students.
• enable children to recognize and employ pattern of mathematical thought.
• create opportunities for students to guess-and-verify the solutions to problems.

Hence, it could be concluded that the contemporary understanding of Mathematics Pedagogy doesn't encourage teachers to introduce the computation of problems before the development of conceptual understanding.

Follow BODMAS rule to solve this question, as per the order given below:

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

⇒ [(-4) + 2] × (-3) - (-3) [(-3) × (-7) - 8] + (4) [(-48) ÷ 6]

⇒ (-2) × (-3) + 3 [21 - 8] + (4) (-8)

⇒ 6 + 3 × 13 - 32

⇒ 6 + 39 - 32

⇒ 45 - 32

⇒ 13

Shortcut Trick

Note: This question can also be solved by simply converting the fractions in decimal forms and then comparing. 

⇒ 44/49 = 0.89

⇒ 33/38 = 0.86

⇒ 22/25 = 0.88

⇒ 24/29 = 0.82

So correct descending order is 44/49, 22/25, 33/38, 24/29.

So the correct option is (2).

Additional Information

One of the ways to do this question is to make the denominator of every fraction equal by taking L.C.M of 49, 38, 25, 29 and then comparing the numerator. A fraction with higher value of numerator will be greater.

L.C.M of  49, 38, 25, 29 = 1,349,950

This is very long approach so we will follow short trick approach.

From option (1)

The division is not commutative. That means usually a ÷ b is not equal to b ÷ a, 

For example

20 ÷ 5 ≠ 5 ÷ 20

So, option (1) is not true.

From option (2).

1 is the multiplicative identity

a × 1 = a × 1

So, option (2) also is true.

From option (3)

Subtraction is not commutative. that means usually a - b is not equal to b - a.

For example

10 - 5 ≠ 5 - 10.

So, option (3) is True.

From option (4)

Multiplication is associative:

Associative property of integers stated that for any three elements or numbers a, b and c.

For example,

a × (b × c) = (a × b) × c

abc = abc

Hence associative property is true for multiplication.

Concept:

Speed:

• The distance traveled by the body in unit time is called speed.

$Speed = \frac{{Distance}}{{Time}}$

 $\implies Time= \frac{{Distance}}{{Speed}}$

• Average Speed: Since the body does not always have the same speed, So we use the concept of average speed. It is the ratio of total distance covered to total time taken by the body.

$Average;Speed = \frac{{Total;Distance}}{{Total;Time}}$

Calculation:

Total Distance = 5 km + 5 km = 10 km

Total time = Time taken to reach + Time taken to return

$⇒ Total;Time = \frac{{Distance}}{{Spee{d_1}}} + \frac{{Distance}}{{Spee{d_2}}}$

$⇒ Total;Time = \frac{{5;Km}}{{12;km/hr}} + \frac{{5;Km}}{{8;km/hr}} = \frac{5}{{12}} + \frac{5}{8} = \frac{{25}}{{24}};hr$

We know that,

$Average;Speed = \frac{{Total;Distance}}{{Total;Time}}$

$⇒ Average;Speed = \frac{{10;km}}{{25/24;hr}}$

⇒ Average Speed = 9.6 km/hr

Explanation:

Unit:

• Measurement means the comparison of an unknown quantity with some known quantity. This known fixed quantity is called a unit.
• In ancient times, people used a length of a foot, the width of a finger, the distance of a step as units of measurement. This caused confusion and a need to develop a uniform system of measurement arose.
• Now, we use the International System of Units (SI units). This is accepted all over the world.
• The metre is the unit of length in the SI unit.
• Distance is measured in length.

Some Commonly used units of measurement  

Ancient measurement:

• Cubit (Arm length) is an ancient system of measurement.
• 1 cubit = 45.72 centimetres (or 1 cubit = 18 inches)

Measuring Very long distances:

• Light year: It is equal to the distance travelled by light in one year
• 1 Light year = 5.88 trillion miles

So, the units of measurement of length are cubit, metre, light year.

Additional Information

• Hertz is the unit of frequency i.e number of repetition in one second.
• It is not the unit of Length.

The correct answer is Cellophane sheet, Newspaper, Carpet.

Concept:

Friction: Friction opposes the relative motion between two surfaces in contact. It acts on both the surfaces.

• Friction depends on the nature of surfaces in contact.
• For a given pair of surfaces, friction depends upon the state of the smoothness of those surfaces.
• This means if the surface is more smooth then the friction over there is very less.
• Friction depends on how hard the two surfaces pressed together.
• Static friction comes into play when we try to move an object at rest.
• Sliding friction comes into play when an object is sliding over another. Sliding friction is smaller than static friction.
• Friction can be increased by making a surface rough.

Explanation:

• Cellophane is a plastic sheet with a high degree of smoothness so very less friction over there.
• A newspaper on a microscopic level has little roughness with respect to cellophane.
• Carpet on the other hand has more roughness and creates more friction.
• The increasing order of roughness is Carpet > Newspaper > Cellophane

⇒ Friction in increasing order (Cellophane < Newspaper < Carpet)

Concept: 

• Motion: If the position of a body changes with respect to time then the body is considered as in motion.
• Uniform motion: If an object covers equal distances in equal intervals of time, it is said to be in uniform motion.
• The distance-time graph of uniform velocity is straight line.
• Non-Uniform motion: Motions where objects cover unequal distances in equal intervals of time, for example, when a car is moving on a crowded street or a person is jogging in a park.

Explanation:

• If a body is moving with uniform velocity, means the velocity over time is constant (not changing).
• The below graph represents the velocity-time graph.

The velocity-time graph of the motion will be a straight line parallel to X-axis.

Fuel: The sources of energy for domestic and industrial purposes are mainly wood, charcoal, petrol, kerosene, etc. These substances are called fuels.

• A good fuel is one that is readily available, cheap, burns easily in the air at a moderate rate, and produces a large amount of heat.
• Petroleum is extracted from crude oil.
• With the help of fractional distillation of crude oil, not just petroleum but also a large number of by-products are extracted.
• Byproducts of petroleum are Paraffin wax, Bitumen, Lubricating oil, etc.
• Like Petroleum, gasoline, Naptha, paraffin, Diesel, Fuel oil, Lubricating oils, Bitumen, and some solid carbons.

All the given options are the by-product of petroleum while Coke is a byproduct of Metallurgical Coal and not petroleum.

Concept:

Heat is transferred by three modes:

• Conduction: The process by which heat is transferred from the hotter end to the colder end of an object is known as conduction. 
• Conductors: The materials which allow heat to pass through them easily are conductors of heat. For examples, aluminium, iron and copper.
• Insulators: The materials which do not allow heat to pass through them easily are poor conductors of heat such as plastic and wood. Poor conductors are known as insulators. The water and air are poor conductors.
• Convection: When water is heated, the water near the flame gets hot. Hot water rises up. The cold water from the sides moves down towards the source of heat. This water also gets hot and rises and water from the sides moves down. This process continues till the whole water gets heated. This mode of heat transfer is known as convection.
• Radiation: From the sun the heat comes to us by another process known as radiation. The transfer of heat by radiation does not require any medium. It can take place whether a medium is present or not.

Explanation:

When all the materials are kept at 30° C, then all the materials will be at equilibrium temperature after some as this is closed room.

The Metallic Spoon get heated to 30° C (Say T₃)

The plastic bottle and wooden spoon are kept (T₁ = T₂).

⇒  T₁ = T₂ = T₃ = T Room Temp.

Concept:

Photosynthesis is the process through which plants utilize sunlight to make food and it takes place inside the green part (chloroplasts) of the plant.

Modes of Nutrition:

• Autotrophs:
• The mode of nutrition in which organisms make food themselves from simple substances is called autotrophic (auto = self; Trophos = nourishment) nutrition.
• Photosynthesis: The leaves have a green pigment called chlorophyll. It helps leaves to capture the energy of the sunlight. This energy is used to synthesize (prepare) food from carbon dioxide and water. Since the synthesis of food occurs in the presence of sunlight, it is called photosynthesis.
• In the presence of sunlight Carbon dioxide + water → Carbohydrate + oxygen.
• Some plants, green algae, and cyanobacteria can perform photosynthesis.
• Heterotrophs: Animals and most other organisms take in food prepared by plants. They are called heterotrophs (heteros = other).
• They are dependents on the one who produce food ex- animals, insects, reptiles, etc.
• Rhizobium: The nutrients replenished in the soil by these bacteria. This bacteria helps in fix nitrogen after becoming established inside the root nodules of legumes (Pulses crops).
• Virus: Its mode of nutrition is heterotrophs, as it takes food from the host (the body where it lives).

Explanation:

Only green algae out of the four options are able to perform photosynthesis while the others are dependent on the other sources of food.

Explanation:

• Climate has a profound effect on all living organisms. Animals are adapted to survive in the conditions in which they live.
• Adaptation of animals to climatic conditions is essential for their survival.

Polar regions: Polar regions are situated near the poles, i.e. north pole and south pole. Animals living there have adapted to these severe conditions. Considering the examples of polar bears and penguins.

Polar Bears Adaptation to Climate:

• Polar bears have white fur so that they are not easily visible in the snowy white background.
• To protect them from extreme cold, they have two thick layers of white fur.
• They also have a layer of fat under their skin.
• On warm days, the polar bear goes for swimming. They are good swimmers.
• Their paws are wide and large, which helps to swim when overheated.

The correct option for this question will be white fur, flat feet, fat under the skin which helps the polar bear to survive in extreme cold.

Nutrients are an essential part of the food they provide us energy and help us to grow. The major nutrients in our food are named carbohydrates, proteins, fats, vitamins, and minerals.

In addition, food contains dietary fibers and water which are also needed by our body. 

• The combination of different nutrients is present in food.
• Milk contains the fat-soluble vitamins A, D, E, and K.
• Milk is a good source of calcium, magnesium, phosphorus, potassium, selenium, and zinc.
• Milk is considered a good source of these nutrients-
• Calcium, vitamin D, protein, phosphorus, magnesium, potassium, vitamin B12, and zinc are majorly found in milk.

Therefore, the combination set of Protein, calcium, and vitamin D is correct.

The correct answer is Iodine.

Key Points

• Iodine is a non-metal that is widely used as an antiseptic.
• The purple-colored solution containing iodine is called Tincture of Iodine.
• Tincture of iodine is primarily used to sterilize wounds and prevent microbial infections.
• Iodine plays a crucial role in maintaining hygiene and health due to its antimicrobial properties.
• This solution is applied to wounds to ensure they are free from harmful bacteria, thus preventing infections.
• Iodine is essential for various biological processes, including the production of thyroid hormones.
• It is also used in other medical preparations and diagnostic procedures.

 Additional Information

• Chlorine
• Chlorine is a non-metal used primarily in the purification of water.
• It is also used in the production of plastics, disinfectants, and bleaching agents.
• Chlorine has strong oxidizing properties, which make it effective in killing germs and bacteria.
• Although chlorine is a powerful disinfectant, it is not used for wound sterilization.
• Bromine
• Bromine is a non-metal used mainly in the manufacture of flame retardants.
• It is utilized in industries for producing photographic chemicals, water treatment agents, and dyes.
• Bromine compounds are toxic and not suitable for direct application on wounds.
• Sulphur
• Sulphur is a non-metal used in the production of crackers, fertilizers, and rubber products.
• It is also employed in making sulfuric acid, which is an important industrial chemical.
• Sulphur is not used in antiseptic solutions for wounds.

Explanation:

• Air: It is a mixture of different gases. The major constituents of air are nitrogen, oxygen, carbon dioxide and argon. Other components of air are water vapour and dust particles.
• There are some properties:
• Air has weight.
• It does not have shape and size.
• Air occupies space.
• Air can exert pressure.
• Air is present in soil and water. In the soil, they reside in the small gaps between the particles while in the water they are dissolved and comes out with bubbles.

Water cycle: The water from the ocean and surface of the earth goes into the air as vapour; returns as rain, hail or snow and finally goes back to the oceans. The circulation of water in this manner is known as the water cycle. So, Air plays an important role in the water cycle.

The process of continuous movement of water over different places of the earth, the water vapour in the air moves all around and form cycle.

Hence, it becomes clear that Air is present in the soil.

Explanation:

Human Digestive System:

• The process of digestion starts when the food is in the mouth.
• Mouth releases saliva which brokes down food into sugar.
• Through the oesophagus or the food pipe food flowed down to stomach.
• In the stomach- the gastric juices containing HCl and pepsin get mixed to kill bacteria and break down protein.
• Protein digestion starts here. 
• Liver is the largest gland of the body and secretes bile juice. Bile juice is stored in the gall bladder and has a significant role in the digestion of fats.
• Pancreas has enzymes that help in total digestion of all food components
• The pancreatic juices contains three enzymes and helps in digestion of protein -
• Trypsin
• Amylase
• Lipase
• The digestive tract and associated glands together constitute the digestive system.

From the above discussion, we now know the different parts of the digestive system.

• Liver - Largest gland
• Stomach - helps in the digestion of protein.
• Gall bladder - Where bile juice is stored
• Pancreas -  Releases digestive juice into the small intestine​

Additional Information

• Protein digesting enzyme called pepsin is released in stomach.
• The pancreas secretes pancreatic juice which contains enzymes like trypsin for digesting proteins and lipase for breaking down fats.

The correct answer is Cells of a tissue have similar Structure.

Explanation:

Cells: The cell is the basic structural, functional, and biological unit of all known organisms.

• There are different shapes of the cells.
• The size and shape of the cells might be different in different organism.
• Some cells have a nucleus (Eukaryotic cells) while the other does not have a defined nucleus (prokaryotic cells).

Tissues:  A tissue is a group of similar cells performing a specific function. These tissues further made organs and later organ system

⇒ The correct option in the above statements are - cells of tissue have a similar Structure.

Concept:

Reproduction: The production of new individuals from their parents is known as reproduction.

Modes of reproduction -

Asexual Reproduction: In asexual reproduction, plants can give rise to new plants without seeds

1. Fragmentation: Where the body of the organism breaks into smaller pieces, called fragments and each segment grows into an adult individual. like Algae etc.
2. Vegetative propagation: It is a type of asexual reproduction in which new plants are produced from roots, stems, leaves, and buds. Since reproduction is through the vegetative parts of the plant, it is known as vegetative propagation. Ex- sweet potato, ginger, grass, etc.
3. Spore formation: Reproduction in fungus/fungi and Chlamydomonas.
4. Budding: The small bulb-like projection coming out from the yeast cell is called a bud. The bud gradually grows and gets detached from the parent cell and forms a new yeast cell. Ex-yeast, sponges, and hydra.

Sexual Reproduction: When two individuals are involved in the reproduction process, where male and female gametes fuse for their offsprings termed as sexual reproduction.​

• Sexual reproduction in plants
• Sexual reproduction in animals.

Explanation:

As described above we can clearly figure out the asexual reproduction modes in different organizations.

• Yeast (a) - Budding (iv)
• Potato (b) - Vegetative propagation (i)
• Algae (c) - Fragmentation (ii)
• Fungi (d) - Spore Formation (iii)

Concept:

• Ozone layer: It is a thin layer of Earth atmosphere, which protects us from ultra-violet rays resides at the stratosphere. Ozone is made of three molecules of oxygen (O₃).
• Ozone depletion i.e. gradual thinning of Earth’s ozone layer in the upper atmosphere caused by the release of chemical compounds containing gaseous chlorine or bromine from industry and other human activities.
• The depletion of the ozone layer results in an increase in the earth's atmospheric temperature.
• Chlorofluoro Carbons (CFCs) and some Halogens are the chemicals that break the ozone into simple oxygen.
• CFCs are found in aerosols, paints, and refrigerants. Nowadays government bans CFCs compounds.
• Ozone gas is a poisonous gas.

Explanation:

Therefore, Pollutants that are responsible for the depletion of the ozone layer are chlorofluorocarbons.

Concept:

• Illness/Diseases: It is a state of experience by the body when one or more of the control systems of the body are not functioning normally.
• Communicable disease: The diseases which are infectious or transmissible from a body to body through biological agents in humans and animals. Ex- Influenza, Ebola, Covid-19, etc.
• Non-communicable disease: The disease that is not transmissible directly from one person to another through biological agents, Ex- Astana, Diabetes, etc.

Explanation:

Some common communicable diseases are:

Hence, Typhoid, Swine flu, Malaria, Polio are communicable diseases.

Mistake Points Polio is also a communicable disease.

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

Nature of science:

• Science is always tentative.
• Science promotes scepticism.
• Science as an approach to investigation.
• Science is an interdisciplinary area of learning.
• Science is a particular way of looking at nature.
• Science is a process of constructing knowledge.
• Science demands perseverance from its practitioners

NOTE: Science is not static, but rather dynamic in nature because science is a field of new research and inventions.

Hence, it can be concluded that the statement 'science is static in nature is not true in the context of the question.

Science aims at enabling students to develop their communication skills to be able to understand scientific information, such as data, ideas, arguments, and investigations, and communicate it using appropriate scientific language in a variety of communication modes.

Key Points

Science develops: 

• Scientific Attitude: Scientific attitude is caring about evidence and being willing to change theories on the basis of new evidence. Scientific attitude is concerned and developed by science.
• The scientific attitude reveals why even a failed theory can help us to understand what is special about science.
• Scientific attitude helps to tackle problems objectively without bias promoting logical thinking.
• Scientific Temper is the attitude to search for new bodies of knowledge, not to accept anything without proof or a test, have the ability to change one’s stand in the light of new evidence, and not to rely on preconceived notions in lieu of observational evidence. It is developed by science.
• Science for Equity, Empowerment, and Development (SEED) Division has been set up under the Department of Science and Technology, established with the broad objectives of providing opportunities to motivated scientists.

Hence, from the above-mentioned points, it becomes clear that Equity, Scientific attitude, and Scientific temper are developed by Science.

Science aims at enabling students to develop their communication skills to be able to understand scientific information, such as data, ideas, arguments, and investigations, and communicate it using appropriate scientific language in a variety of communication modes. Science Teachers help middle and high school learners understand scientific phenomena.

Key Points

The Role of a Science Teacher:

• Design curriculum as per the needs of the students.
• Instruct students on the proper use of equipment, materials, aids, and textbooks.
• Provide a rich variety of learning experiences to learners.
• Establishing classroom, lab, and field trip rules and regulations and ensuring that all students understand what is expected of them.
• Grading papers, updating records, and handling various administrative tasks.
• Creating an environment where students feel comfortable asking questions.
• Participating in other school activities and regularly communicating with parents.
• Drawing up suitable assessments and delivering helpful feedback to students, parents, and other teachers.

Hence, from the above-mentioned points, it becomes clear that the role of a science teacher should be to provide rich variety of learning experiences to learners.

Physical-world is explored and understood with the help of science. Science is an ever-expanding knowledge sphere; many of the established universal laws are subject to change based on new observations and experiments. 

Science education is related to the environment of the students and prepares them for the world. It should promote concerns about the preservation of the environment among the students.

Science Education as recommended by NCF-2005: NCF 2005 provides ample scope for the holistic development of the learners.

• It recommends various initiatives and approaches such as activity-based learning, experiential learning, collaborative learning, and so on.
• Science in general is used to explain the environmental phenomenon and physical world around us.
• Science is also equated to technology; technology employs the various principles of science.
• According to NCF-2005, good science education is one that is true to the learner, true to life, true to the environment of the learner, and true to science.
• The relation between the ‘nature of science and technology helps us in formulating the ‘vision of science education.

Hence, from the above-mentioned points, it becomes clear that good science education should be true to the learner, true to the environment of the learner, and true to science.

Cognitive development of children is enhanced through social interaction with other people, particularly those who are more skilled.

Benjamin Bloom’s taxonomy is a hierarchical organization of cognitive objectives. Bloom classifies learning objectives into three domains, cognitive, affective, and sensory domain.

1. Cognitive Domain: mental skills
2. Affective Domain: growth in feelings or emotional areas
3. Psychomotor Domain: manual or physical skills

Key Points

The cognitive domain involves six categories of learning that serve in the development of intellectual skills.

According to Bloom, learning of concepts and identifying examples reflects one’s understanding level, recalling of previously learned information reflects one’s memory level, isolating and organizing information into parts involves analyzing and generation or construction of new ideas reflects one’s creative level, as understood from the diagram shown below:

The given statement is, Conducting a survey on the awareness of people about sources of air pollution in learners' localities. Here 'Creating' cognitive process will be most appropriate because, in the survey, new or original work will produce.

Hence, from the above-mentioned points, it becomes clear that 'Creating' cognitive process will be most associated with the given learning objective.

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

Important Points

Working on engaging the learners first can be the most appropriate strategy for involving learners in the teaching-learning of science as learning by doing and experiencing the consequences of one's own actions helps learners in:

• retaining information and concepts for a longer period.
• enhancing skills and better understanding of the concept.
• nurturing their curiosity and interest in the learning process.
• gaining concrete experience by actively engaging with content.
• assimilating practical knowledge by applying theoretical knowledge.

Hence, it could be concluded that working on engaging the learners first can be the most appropriate strategy for involving learners in the teaching-learning of science.

Reflection of Light may be defined as the bouncing back of the light ray by a smooth polished surface. It occurs through smooth polished surfaces like Plane mirrors, Spherical mirrors (concave and convex). We see objects around us due to this phenomenon of light.

Key Points

• By observing the reflection of light on a white paper screen by the learners and drawing conclusions, meaningful clarification on the concept of reflection of light can be given as one can learn a skill in an effective way by practicing that specific skill.

Here learners' engagement in observation and drawing conclusions will help learners in:

• retaining information and concepts for a longer period.
• enhancing skills and a better understanding of the concept.
• nurturing their curiosity and interest in the learning process.
• gaining concrete experience by actively engaging with content.
• assimilating practical knowledge by applying theoretical knowledge.

Hence, it could be concluded that observing the reflection of light on a white paper screen by the learners and drawing conclusions is the correct option in the context of the question.

Science Education should be strengthened so as to develop well-defined abilities and values such as the spirit of inquiry creativity, objectivity, the courage to question, and aesthetic sensibilities. 

• The objectives of science teaching are to make learners ‘scientifically literate' as science is a compulsory component of the curriculum up to the secondary level.
• Science teaching should focus on developing awareness among the learners about the interface of science, technology, and society, sensitizing them, especially to the issues of environment and health, and enabling them to acquire practical knowledge and skills to enter the world of work.
• According to NCF-2005, good science education is one that is true to the learner, true to life, true to the environment of the learner, and true to science.

Key Points

Co-curricular activities in Science Teaching: These activities are usually organized outside the classroom to provide opportunities for students to develop their special talents and to creatively express themselves through various forms. Some of the activities are:- 

• Participation in science fair and exhibitions.
• Involve is poster making and science dramas.
• Participation in science clubs and associations.
• Excursion and sports activities.
• Involve in social services, literary and cultural activities.
• Visit in science parks, fields, and museums. Field visit provides hands-on experiences to the learners.
• Aesthetic and cultural development activities.
• Social welfare activities.

Hence, from the above-mentioned points, it becomes clear that field visits important in science because it provides hands-on experiences to the learners.

Assessment is a process of collecting relevant information on student learning. It is an integral part of the teaching-learning process. Assessment is conducted in different phases of the teaching-learning process.

• In learner centered assessment the ‘learner’ or ‘child’ and not the ‘teacher’ is the main focus of the educational programme.
• The overall goal is the all-round development of the child and not only that of acquiring knowledge.

Key Points

Tool for Learner Centered Assessment: Portfolio, concept mapping, rating scale, Journal writing, and anecdotal records, etc. are the tools for learner centered assessment.

• Portfolio: It contains samples of the learner's work like project reports, assignments, etc to evaluate academic achievement and learning progress over time. It is used for learner centered assessment.
• Concept Mapping: It is a pedagogic technique to help students to check explicitly how new concepts can be related to previously learned concepts. Concept maps are graphical tools for organizing and representing knowledge. It can be in the form of flowcharts, tables, Venn diagrams, etc.
• Journal Writing: It refers to a form of writing, written by learners to record their insights, perceptions, experiences, etc on a specific topic. It helps them in organizing their thoughts and allows them to reflect on themselves. It is used for learner centered assessment.
• Field Trip: It refers to a learning approach that ensures the active involvement of learners in the learning process by taking them at a certain place where they earn knowledge by engaging with real situations.
• Project Work: It refers to a series of task that needs to be done by a group of learners to achieve a particular goal. It promotes the voluntary participation of learners and emphasizes active learning. It is used for learner centered assessment.

NOTE: Paper-Pencil test is used to measure relevant factors of participants' visuospatial ability.

Hence, from the above-mentioned points, it becomes clear that Portfolio, Concept mapping and Journal writing are the tools for learner centered assessment.

Assessment is a process of collecting relevant information on student learning. It is one of the crucial components of the teaching-learning process. Assessment does more than just measuring learning.

• Assessment process measures personality, attitude, cognitive, social functioning and intelligence.
• The primary purpose of assessment is to improve students learning and teachers' teaching as both respond to the information it provides and focuses on the areas to clear the confusion of a concept and improve understanding of the child.

Important Points

• Assessment for learning - during instruction
• Assessment of learning - after instruction
• Assessment as learning - self-assessment

Assessment as learning in Science means Self-assessment.

Self-assessment:- It is the ability of a person to accurately evaluate or assess his/her performance, and his/her strengths and weaknesses.

NOTE:

• Summative Assessment: Commonly known as "Assessment of learning" refers to measure, classify, certify and report the level of student learning by assessing them at the end of the term.
• Peer Assessment: It refers to one student or a group of students assessing other students. In peer assessment, a student’s work is evaluated by other students of his/her group.
• Formative Assessment: It is a type of assessment that refers to monitor the child's progress throughout the learning and teaching process. It provides feedback to the teachers regarding the effectiveness of their teaching.

Hence, from the above-mentioned points, it becomes clear that Assessment as learning in Science means Self-assessment.