CTET (Maths & Science) Official Paper-II September 2015 (English-Hindi-Sanskrit) (Previous Year Paper)

Development and learning are not synonymous rather they both are different. Let's understand in brief:

• Development: It refers to a progressive and systematic series of changes that occur in the life of an individual he/she grows from infancy to old age.
• Learning: The process by which a person alters his responses and behavior in order to adjust himself to the changing environment is called learning.

Lev Vygotsky:

• A Russian psychologist and social constructivist.
• He had worked in the fields of educational and cognitive psychology.
• He believed that learning is an essential process and is necessary for development.
• He focussed on socio-cultural aspects and emphasized the role of society and culture in the development of a child.
• According to Vygotsky, learning is a process that occurs anytime in everyday life and that isn't just an external phenomenon.
• His theory of Zone of Proximal Development (ZPD) expanded learning and development, which posits that learning precedes development processes.

Hence, it could be concluded that the statement 'development process lags behind the learning process' best summarizes the relationship between development and learning as proposed by Vygotsky.

Important Points

• Zone of Proximal Development (ZPD) is the difference between what a learner can do by himself (or without help) and what he/she can do with help.
• So, ZPD is the area of proximal development in which guidance should be given so that a child can reach the maximum potential.

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 six culturally universal stages.

• Kohlberg adopts a cognitive theory of moral development and sets out to show that principles of moral judgment gradually develop as children grow older, but this development is highly dependent on environmental and social conditions.
• Kohlberg assumes that children have a morality that is distinct and different from adult morality.
• According to Kohlberg's scheme of things, there can be six stages of moral development. In such a way the development of a higher stage logically depends upon the development of the preceding stage. Each stage of moral development reveals a different kind of motivation for acting morally, or for forming a moral judgment.

Important Points

• A major criticism of Kohlberg’s theory is that Kohlberg did not account for cultural differences in moral reasoning of men and women.
• Criticism of Kohlberg’s theory regards justice concerns as developmentally more advanced than reciprocal considerations.
• Men tend to score as more morally developed than women on existing measures.
• This is because women rely more on 'care' considerations in moral dilemmas, whereas men rely more on 'justice' issues.

Hence, it becomes clear that not accounting for cultural differences in moral reasoning of men and women was a major criticism of Kohlberg's theory.

Learner-centred Classroom: Students and teachers participate equally in the teaching-learning process. The teacher is the facilitator and students actively engage in the activities. The needs of individual students form the basis.

• ‘Child-centred’ classroom means giving primacy to children’s experiences, their voices, and their active participation. This kind of classroom requires us to plan to learn in keeping with children’s psychological development and interests.

Role of the Teacher in a Learner-Centred Classroom are:-

• To make the active engagement of a child involves inquiry, exploration, questioning, debates, application, and reflection, leading to theory building and the creation of ideas.
• The teacher would employ such methods in which the learners are encouraged to take initiative for their own learning.
• The teacher will have to be sensitive to tribal cultures and practices and be able to incorporate local knowledge in the curriculum and textbooks.
• The teacher should provide space for individual children to express themselves freely in the classroom without fear of being judged or stereotyped. Children need to be aware that their experiences and perceptions are important and need to be encouraged to think and reason independently.
• To plan the teaching and learning process to suit the needs of the students.
• To promote learning by providing a conducive environment.
• To encourage learners to become active learners.

Hence, it becomes clear that in a learner-centred classroom, the teacher would employ such methods in which the learners are encouraged to take initiative for their own learning.

Intelligence refers to a set of different cognitive abilities to think rationally, act purposefully, resolve problems and deal with the demands of the environment.

The Theory of Multiple Intelligence:

Howard Gardner proposed this theory wherein he formulated eight categories of intelligence. He defined intelligence as “Intelligence is a bio-psychological potential to process information that can be activated in a cultural setting to solve problems or create products that are of value in a culture”.

• In one of his most influential books, Frames of Mind: Theory of Multiple Intelligences (1983).

Howard Gardner formulated the following types of intelligence:

• Intra Personal Intelligence (Self Smart): Individuals inclined to this intelligence tend to be more introverts as they have the ability to understand their own emotions, drives, desires, strengths, and vulnerabilities.
• They rely upon self-knowledge and self-motivation. This intelligence is instrumental in an individual's pursuit of the hobby, area of interest, the branch of study, and choice of career.

Hence, according to Gardner's theory of Multiple Intelligence, the factor that would contribute most for being a 'self-aware' individual would be "Intrapersonal".

Piaget and Vygotsky were notable contributors to the cognitive development components of psychology.

Let's understand in brief:

• Jean Piaget: He was a Swiss psychologist and known as the father of Child Psychology. He made a systematic study of cognitive development in his theory that is categorized in four stages.
• Lev Vygotsky: He was a Russian psychologist and a social constructivist. He has propounded 'Socio-cultural Theory' which emphasizes the role of social interaction in cognitive development.

Key Points 

They considered that acquisition of speech is the major activity in cognitive development. However, they differ from each other in this matter.

Piaget's and Vygotsky's view on 'Language and Thought':

Hence, it could be concluded that a major difference between the perspectives of Vygotsky and Piaget pertains to their views about language and thought.

Genetic materials refer to the passing of habits or attitudes from one generation to the next generation. Specific sets of abilities are passed to both girls and boys from their parents. Different people inherent different abilities or qualities from their families.

The statement that 'girls are socialized to be caring while boys are discouraged to show emotions such as crying' is most likely to agree with in this context as in our society: 

• girls are socialized to be caring. They are supposed to take care of the household works, family members, and other responsibilities regarding home.
• boys are supposed to be rough and tough. They are not allowed to show any kind of emotions like crying as it is considered as a sign of weakness for them.

Heredity contributes too many individual differences in temperament and personality, especially differences in emotionality, activity level, and sociability. 

Hence, it could be concluded that the statement that 'girls are socialized to be caring while boys are discouraged to show emotions such as crying' is most likely to agree with in this context.

Motivation is simply the reason for an action and that which gives purpose and direction to behaviour. It is a general term applied to the entire class of drives, desires, needs, wishes, and similar forces. Motivation can be considered the state of having encouragement to do something.

Three Important Aspects:-

• Needs- Biological and Sociogenic
• Drives- keep you activated
• Incentives- Rewards

Motivation is the best way to empower your students. By following ways teacher ensures that her student are motivated intrinsically:-

• Always motivate them to set a greater goal. A teacher must focus on the processes of learning of individual children rather than on the final outcome.
• By showing them how knowledge applies in real life.
• By group work and competition.
• By introducing then the system of rewards.

Hence, if a teacher wants to ensure that her students are motivated intrinsically. She would focus on the processes of learning of individual children rather than on the final outcome.

Assessment of the child’s abilities can only be done through feedback. It helps us to know whether the child has learned what you have taught and whether your teaching is effective. Giving and receiving feedback is a difficult undertaking as it requires the ability to deal with the feelings that arise. The assessment helps in finding the reason behind the failure of a child.

• Failure of a child to perform well in class tests leads us to believe that there is a need to reflect upon the syllabus, pedagogy, and assessment processes.
• The system of Comprehensive and Continous Evaluation (CCE) recommended to identify the learning needs, difficulties, and conceptual gaps to provide timely and appropriate interventions to reduce stress and anxiety and enhance learning to help all children progress.
• It was also intended to reduce rote learning, help teachers reflect, review and improve their teaching and provide all children, including those with special needs and those belonging to the marginalized groups, with the feedback to improve their learning to bloom their potential fully.

Hence, it becomes clear that the failure of a child to perform well in class tests leads us to believe that there is a need to reflect upon the syllabus, pedagogy, and assessment processes.

Children’s errors:

• are necessary in the learning process to give insight into children's thinking.
• help the teacher to be aware of learners' learning styles, and to cater to them according to their needs.

In the above-mentioned situation, 'the children have not yet gained conceptual clarity and there is a need for the teacher to reflect on his/her pedagogy' is most likely to be the analysis of the situation as:

• every student differs from others on psychological aspects such as intelligence, personality, etc.
• every child has a different pace of learning and a single method cannot be applicable to all children.
• pedagogy helps teachers to involve children in constructing their own knowledge through experiences.

Hence, it could be concluded that 'the children have not yet gained conceptual clarity and there is a need for the teacher to reflect on his/her pedagogy' is most likely to be the analysis of the situation.

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

In the above-mentioned situation, the student is trying to regulate her own thinking by the organization of ideas as the organization of ideas refers to the arrangement of ideas in a systematic manner by an individual.

Key Points

Here the student is:

• highlighting the main points which show that the child is aware of the main points and is able to identify them.
• drawing visual representation which shows that the child is able to do abstract thinking on the basis of her understanding.
• posing questions which shows her curiosity & inquisitiveness and enables her to make the best of her educational experiences.

Hence, it could be concluded that in the above-mentioned situation, he is trying to regulate her own thinking by the organization of ideas. 

Additional Information

• Observational learning: It is a learning method which implies that student learns by observing and analyzing. Here, the child learns through watching others, keeping information, and then later recreating the behaviors that were observed.
• Strategy maintenance rehearsal: It involves the repetition of items in order to memorize them. It is also called as the rote rehearsal. For example, When we have a speech in our school, we continuously and repeatedly rehearse the speech in order to memorize it.
• Method of loci: It is used to recall a piece of information. It is a strategy for memory enhancement. The Loci system was used by Greek and Roman orators to remember the content and sequence of long speeches.

Problem-Solving Approach: Problem-solving is a learner-centred approach that emphasizes learner's active involvement in the learning process. It helps the children to learn better by catering totality of their experiences that occur in the educational process.

Teachers can model different aspects of problem-solving and engage students in activities and discussions around the concept. These are some ways by which teacher help children to become better problem solver-

• By providing multiple potential solutions for any problem
• By giving children a variety of problems to solve and support while solving them
• By 'do-it-yourself' projects
• By teaching basic problem-solving steps
• By Continous and Comprehensive Evaluation

Hence, from the above-mentioned points, it becomes clear that a teacher help children become better problem solvers by giving children a variety of problems to solve and support while solving them.

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.

• Socio-cultural changes in society impact the content and objectives of education. It is a relationship between education and social change.
• Learning activities in such social contexts may be cooperative, collaborative, planned or unplanned, and they can be led by one or more individuals, or be completely self-organizing.
• Learning in the social context refers to all learning that occurs in and among groups of people. So, learning takes place in a socio-cultural context.
• However, education is also influenced by the socio-cultural changes that take place in society, it responds to the socio-cultural changes by re-organizing its content and process and by reinterpreting its goals and objectives.
• During the past few decades, acculturation, and living together have been emphasized as desirable goals of education.

Hence, from the above-mentioned points, it becomes clear that learning takes place in a socio-cultural context.

Development is a process by which an individual grows and changes throughout the life cycle. The term development applies to the changes that have a direction and hold a definite relationship with what precedes it. ​

Key Points Facts about Development:

• The development process passes through different stages. Each stage of development has certain distinct and specific characteristics.
• When any process once gets complete on the basis of which learner can learn a new skill is called Maturation.
• Maturation refers to the changes that follow an orderly sequence and are largely dictated by the genetic blueprint which produces Growth, Development, and Evolution commonalities in our growth and development.
• Maturity comes from learning and experiences and hence the development of a person occurs.
• Development occurs due to the interaction between maturation and experience.
• Development is a progressive series of qualitative changes that occur as a result of maturity and experience.

Therefore, it becomes clear that development occurs due to the interaction between maturation and experiences.

Debates are a great way to exchange ideas. They can help you improve your knowledge and your reasoning skills. Debates always help to develop essential critical thinking skills about any topics that help the learner to look at any issues from different angles.

Key Points

• The term ‘nature’ stands for what comes to children through genetic influences and heredity, i.e. it denotes the influence of factors inherent in the child himself from the time he is conceived.
• On the other hand, the term ‘nurture’ stands for the influence of the environment on child development, i.e. all the contextual factors that influence who we are, including our perceptions of early childhood, our social relationships, and the society around us.
• There is a relationship between heredity and environment factors in determining development. Nature refers to heredity, influenced by inherited characteristics of personality, physical growth, intellectual growth and social interaction. Nurture refers to the influence of the environment of all of those same things and includes parenting style, physical surroundings, economic factor and anything that can have an influence and development that does not come from within the person.
• Development is a product of the complex interaction of heredity (nature) and environment (nurture). Heredity gave us the abilities for development, which are used by the environment. Heredity can best be viewed as something that sets a range within which an individual’s development is actually shaped by the support and opportunities of the environment.

Therefore, In the context of the 'nature-nurture' debate, we can say that heredity and environment are inseparably interwoven and both influence development.

Socialization: It refers to the process which transforms a quite helpless human infant into a self-aware, knowledgeable person who is skilled in the ways of their society’s culture. Socialization is a Life-Long process that continues throughout life from birth to adulthood. 

Key Points

• Socialization is a process of acquiring values, beliefs, and expectations.
• Socialization is a process in which a person adapts all the social behaviour as-
• Adaptation of social values and principles.
• Adaptation of cultural rituals
• Adaptation of skills
• Socialization is a combination of personality development and cultural development.

Types of Socialization:

• Primary Socialization: It happens during infancy and childhood, during this phase, infants learn language and certain basic Socialization behavior forms of the family and the society in which she/he lives. Agents of primary socialization are parents and family. For children, their families are the primary agent of socialization since they are in immediate contact with their family members, who in turn introduce them to the outside world.​
• Secondary Socialization: It occurs once the infant passes into the childhood phase and continues into maturity. During this phase more than the family some other agents of socialization like the school and friends.

Therefore, from the above-mentioned points, it becomes clear that Socialization is a process of acquiring values, beliefs, and expectations.

Jean Piaget, a Swiss psychologist, has made a systematic study of cognitive development in his theory that is categorized in four stages. Each stage is characterized by a distinct way of thinking and is age-related.

• He observed his children and their process of making sense of the world around them and developed a model of how the mind processes new information encountered.
• Piaget’s Pre-operational stage is from 2 - 7 years. In this stage, the child faces problems with the irreversibility of thought, concept of conservation, and struggles with the idea of centration.
• Due to the Irreversibility of thought, the child can focus his attention only on one aspect of the situation at a time and cannot reverse the direction of his thought.

Important Points

The Four Stages of Cognitive Development:

Therefore from the above-mentioned points, it is clear that Piaget attributed the above-mentioned inability to the Irreversibility of Thought.

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 Key Concepts:

• Schema: A representation in the mind of a set of ideas or actions which go together.
• Assimilation: The process of taking in information into our previously existing schemas.
• Accommodation: Involves altering existing ideas or schemas as a result of new experiences.
• Equilibration: A mechanism that assists children in achieving a balance between assimilation and accommodation.
• Piaget says learning starts with an adaptation that can be achieved through assimilation and accommodation.
• He believed that learning is a lasting change in behaviour due to the acquisitions that result from experience and this learning process occurs at gradual levels, as the existence of previous mental structures built through individual (assimilation and accommodation) are necessary for the adaptation of a coherent system through a balancing self-regulating. So, for the learning process of adaptation is necessary.

Hence, from the above-mentioned points, it becomes clear that according to Piaget's theory, children learn by processes of adaptation.

'Lev Vygotsky', a Soviet psychologist, has propounded the "Socio-cultural Theory". This theory implies the idea that social interaction plays a crucial role in the development of learners' cognitive ability. 

According to Vygotsky, 'zone of proximal development' or 'ZPD' refers to the:

• the gap between what the child can do independently and with assistance.
• difference between what a learner can do on his/her own and what he/she can do with someone's help.
• range of tasks too difficult for the child to do alone, but possible with the help of adults and more skilled peer.
• distance between learners' actual development level and his/her level of development under someone's guidance.

Additional Information

Other Important Terms Proposed by Vygotsky in his 'Socio-cultural Theory':

• Scaffolding: It refers to a process through which temporary support is imparted to the learners to enhance learning to achieve goals.
• More Knowledgeable Other(MKO): It refers to a person with a higher skill level and a better understanding of the concepts than the learners.

Hence it could be concluded that according to Vygotsky, the zone of proximal development is the gap between what the child can do independently and with assistance.

A multi-cultural classroom is a classroom with learners having more than one culture and from different backgrounds. It incorporates values, beliefs, perspectives, the identity of learners from different cultural backgrounds**.**

• Assessment is a process of collecting, receiving, and using data for the purpose of improvement in the learning process. It determines the effectiveness of the learning process or program.

Key Points

A teacher in a multi-cultural classroom would ensure that the assessment considers the Socio-cultural context of her student as:

• Social interaction and cultural context play a crucial role in the development of learners' cognitive ability.
• In a multi-cultural classroom, the way students respond to assessment is subject to social and cultural influences.
• Assessment is a social activity and we can understand it only by taking account of the social-cultural context in which it operates.
• Education responds to the socio-cultural changes by re-organizing its content and process and by reinterpreting its goals and objectives
• There is a relationship between education and social change because socio-cultural changes in society impact the content and objectives of education.

Hence, it could be concluded that a teacher in a multi-cultural classroom would ensure that the assessment in the Socio-cultural context of her students.

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

An upper primary school constructivist classroom would foresee the student's active involvement in their own assessment plan with the teacher as 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.

Constructivist classroom gives primacy to:

• peer tutoring.
• group activity.
• Self-assessment.
• dignified discussion.
• cooperative learning.
• face to face interaction.

Hence, it could be concluded that an upper primary school constructivist classroom would foresee students' active involvement in planning for their own assessment with the teacher.

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

• A heterogeneous society refers to a society that includes all individuals with different abilities, interests, educational level, skills, cultural backgrounds, beliefs, values, sexes, ages, ethnicities, etc.

Important Points

The rationale behind inclusive education is that society is heterogeneous and schools need to be inclusive to cater to heterogeneous society as:

• It values the diversity, each child brings to the classroom and facilitates all with equal opportunities to learn and grow.
• Inclusive education improves the quality and making provisions of education for all.
• It provides a provision to include disabled children along with normal children in a regular classroom environment.
• It refers to an education system that accommodates all children regardless of their physical, intellectual, social, emotional, linguistic, or other conditions.
• It is a process where diversity in a group with respect to any aspect is appreciated and in which everyone is recognized and respected for his/her worth.
• It is an effort to make sure that diverse learners – those with disabilities, different languages and cultures, different homes and family lives, different interests and ways of learning - are taught using teaching-learning strategies adapted to individual learning needs.
• It is a process that allows every individual to feel accepted, valued, and safe. An inclusive community consciously evolves to meet the changing needs of its members.

Therefore, we can conclude that the rationale behind inclusive education is that society is heterogeneous and schools need to be inclusive to cater to heterogeneous society.

Creativity refers to a cognitive ability to produce something original by offering a fresh perspective. Creativity is goal-directed thinking which is unusual, novel, and useful. 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 create or produce something. They have the ability to solve problems or tasks in a creative way by means of generating many original ideas.

Signs of Creativity:

• High levels of creativity and the ability to create original and imaginative ideas
• A heightened sense of awareness
• Good skills in problem-solving
• Curious and impulsive nature
• Fast learners with good memories
• Innovators and good problem solvers
• Fluency of ideas

NOTE: Giving objective type tests, intelligence tests, and observing how the child interacts with peers in team tasks, are not effective ways to identify a creative child by the teacher.

Hence, it becomes clear that detailed observation of the child especially when she solves problems would be the most effective way to identify a creative child by the teacher.

The term 'underprivileged' refers to the disadvantaged section of people who are economically, socially, and vocationally in an unfavorable situation compared to the rest of the population of the society. 

• The disadvantaged section/background refers to not just low income, but also encompasses lower educational achievement, poverty, poor health, financial insecurity, etc.

Key Points

A teacher can effectively respond to the needs of children from 'disadvantaged sections' of society by:

• reflecting on the school system and herself about various ways in which biases and stereotypes surface.
• relating their local knowledge with the classroom environment to make them feel comfortable and participate in learning.
• awaking the consciousness of students to take responsibility for their selves and develop a quest for personal improvement.
• understanding the mental conditions of disadvantaged children and by celebrating unity in diversity in school or classroom programs.
• valuing their cultural and linguistic knowledge as disadvantaged children lack good cognitive development, phonological awareness, etc.

Hence, it could be concluded that a teacher can effectively respond to the needs of children from 'disadvantaged sections' of society by reflecting on the school system and herself about various ways in which biases and stereotypes surface.

Additional Information

Characteristic of children belonging from Disadvantaged Sections:

• Poor academic performance, high drop-out rates
• Emotional Deprivation and lack of adequate nurturance
• Reading and other learning disabilities and adjustment problems
• They are not exposed to a wide variety of experiences and facilities
• They have separation anxiety and face difficulty in adjusting to society

Discrimination is an act of making a difference between human beings based on group, classes, colour and communities. In the context of school or classroom, it refers to the process of treating learners unfairly on the basis of their characteristics.

Here, many teachers use only the lecture method to teach is not an example of discrimination at upper primary level as Lecture method is an old & traditional method of teaching.

• This method is helpful in imparting a large amount of factual information within a short period.
• In the lecture method, the teacher is an active participant and the students are passive listeners.
• The class listens, writes, and notes facts and the ideas for remembering and to think them over later.
• The lecture method is a one-way method thus only relevant in concepts dealing with theoretical understanding.
• In practical implementation of concepts dealing with learning by doing, the lecture methods become inconsequential.

​Hence, it could be concluded that many teachers use only the lecture method to teach is not an example of discrimination at the upper primary level.

Learning Disability: It is a neurological disorder that affects the way one receives and processes information. It has nothing to do with the intelligence of an individual.

• Learning disabilities can be lifelong conditions that can affect one's experience at school, work, daily routine and social situations.
• A learning disability is not a problem with intelligence or motivation.

A few of the Learning Disabilities are:

Characteristics of a Child with Learning Disability: Children with learning disabilities experience difficulty in learning and using certain skills namely reading, writing, listening, and mathematics calculations. Children can also face difficulty in reading fluently and reversing words because of learning disabilities.

Hence, from the above-mentioned points, it becomes clear that difficulty in reading fluently and reversing words is a characteristic of a child with a learning disability.

Questioning refers to the most effective strategy to arise curiosity and inquisitiveness too. Asking questions makes the classroom's ambiance more interactive.

Key Points

In the class, questioning by students should be encouraged as it could enhance their cognitive competencies in the following ways:

• Questions take learning forward by interactions and lead to conceptual clarity.
• Questions inspire learners to look out for information that aligns with their pursuits and might consequently promote lifelong learning.
• Asking questions allows learners to link between various pieces of information which can assist them in structuring essays and debates.
• Questioning boosts their confidence-up, makes them able to put forth their views, and helps the children to make the best of their educational experiences.​

​Hence, it could be concluded that children should be encouraged to ask questions in the class as questions take learning forward by interactions and lead to conceptual clarity.

Assessment is a process of collecting, receiving, and using data for the purpose of improvement in the learning process. It is integral to the teaching-learning process which helps in facilitating student learning and improving instructions.

Assessment facilitates mapping different dimensions of a child’s development holistically to provide a more authentic picture to help the child, teacher, and hence the system.

Assessing conceptual change and students' alternative solutions through several different methods of assessment will be a suitable practice to bring out the best in students as it will help the teacher in:

• collecting relevant information on student learning.
• making reliable decisions about educational planning.
• determining the effectiveness of the learning process or program.
• promoting a learner-friendly environment to optimize student learning.
• assessing both scholastic and co-scholastic aspects of students' growth.
• laying emphasis on thought processes and de-emphasizing memorization.

Therefore, from the above-mentioned points, it is clear that assessing conceptual change and students' alternative solutions through several different methods of assessment will be a suitable practice to bring out the best in students.

Vygotsky’s Sociocultural Theory of Learning:

• Vygotsky was a Russian psychologist who believed that social interactions play a key role in development. According to him, learning occurs when children interact with people and the environment.
• 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.
• Vygotsky embedded in this theory, the concept of 'private speech' which is a kind of speech directed to self with no communicative function. Children use private speech to guide their actions by speaking themselves.

Scaffolding:

• It 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.
• In other words, it is a means by which a child's 'zone width' (or potential for new learning) can be assessed. i.e. scaffolding helps with providing support to learners in their initial phase of learning, which is in the right amount and gradually decreases as the learner progresses.
• Scaffolding to a child would change depending on the level of the child's performance.
• As children are given assistance or shown how to perform certain tasks, they use this information as a guide on how to perform these tasks and eventually learn to perform them independently.
• Scaffolding helps a learner to move from a Zone of Actual Development to Zone of Proximal Development and finally reach to Zone of Desired Development, with the help of a more experienced person like peers, elders in the family, or teachers.

Hence, from the above-mentioned points, it becomes clear that amount and type of scaffolding to a child would change depending on the level of the child's performance.

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

As an upper primary school mathematics teacher one should believe that students' errors provide insights into their thinking as student’s errors:

• are a significant step in the teaching-learning process.
• give insight into students' conceptual mistakes and basic knowledge.
• are considered as a part of the teaching-learning process as it helps to understand the child.
• help the teacher to be aware of learners' learning styles, to cater to them according to their needs.

Hence, it could be concluded that as an upper primary school mathematics teacher one should believe that students' errors provide insights into their thinking.

Reasons 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​

Failure is the state or condition of not meeting a desirable aim and may be viewed as the opposite of success. There are many cognitive, physical, intellectual, scholastical, emotional, and cultural causes for the failure of students.

A child's failure is a reflection on the system and its inability to respond to the child as:

• children are like clay, the way the system mold them the shape they acquire.
• children fail because teaching is not done in a way that is meaningful to them
• every child has the potential to excel provided that they are given proper guidance.
• the school system does not take care of the needs and interests of every student.

Other Reasons for the Failure of Students in Schools are:

• lack of adequate practice
• Teaching through incorrect teaching methods
• Non-coordination between teaching and learning
• Not being compatible with the school environment

Hence, it becomes clear that a child's failure is a reflection on the system and its inability to respond to the child.

Mathematics, we found its applicability in various areas. The learner-centred curriculum will help to inculcate values by incorporating appropriate contents and activities. 

• It is certainly true that most of the skills taught at the primary stage are useful in everyday life. It will make better use of the time children spend in schools in terms of the problem solving and analytical skills it builds in children, and prepare them better to encounter a wide variety of problems in life.
• Our reflections on the place of mathematics teaching in the curricular framework are positioned on these twin concerns: what mathematics education can do to engage the mind of every student, and how it can strengthen the student’s resources.
• We describe our vision of mathematics in school, attempt to delineate the core areas of concern and offer recommendations that address the concerns, based on these twin perspectives.

Hence, we conclude that the twin concerns are what mathematics education can do to engage the mind of every student and how it can strengthen the student's resources.

Concept:

LCM is lowest common multiple which can be found using prime factorization method.In this we find the prime factors of the given numbers individually and LCM of two numbers is the  product of prime factors counted the maximum number of times they occur in any of the numbers.

Calculation:

22 = 2 × 11

54 = 2 × 3³

135 = 3³ × 5

198 = 2 × 3 × 3 × 11

∴ LCM of 22, 54, 135 and 198 = 2 × 3³ × 5 × 11

Van-Hiele (The Netherlands) geometrical thought describes the different level of learning geometry on the basis of understanding. In the Informal Deduction, the child understands the Properties of shapes and Relation among properties. 

Following are the steps of all the five levels-

• Visualization-
• Shapes
• Classes of Shapes
• Analysis-
• Classes of Shapes
• Properties of Shapes
• Informal Deduction-.
• Properties of shapes
• Relation among properties
• Deduction-
• Relation among properties
• Deductive symptoms of properties
• Rigour- 
• Deductive symptoms of properties
• Analysis of deductive symptoms

Hence, we conclude that the above situation is of informal deduction.

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.

• Mathematics reveals hidden patterns that help us to understand the world around us. In mathematics, we deal with numbers, calculations, measurement of shapes and structures, establishing relationships among variables, etc.
• The goal of mathematics education in school is to develop a child’s thinking, clarity of thought, and pursuing assumptions to logical conclusions.
• Mathematics is the science of all sciences and art of all arts.
• Mathematics tools consist of all types of materials including language, written symbols, meaningful instructions to establish their purpose.
• The presence of Mathematics can be seen anywhere including subjects like sciences, agriculture, psychology, history, geography, drawing, arts, and commerce. So, Mathematics correlates with all other subjects.
• Mathematical tools play an ever-more important role in today’s mathematics.
• Students use calculators, computers, manipulatives, and other mathematical tools to enhance mathematical thinking, understanding, and power.

All other options are also included in Mathematical tools. But the given correct option is the best choice among all.

Hence, it becomes clear that 'Mathematical tools' refer to all types of materials including language, written symbols, meaningful instructions to establish their purpose.

Mathematics is a man-made, well-disciplined subject, which deals with abstract concepts and things. It has its own language, its own tools and mode of operation to help people in a proper understanding of nature’s work and complicated problems of life. 

• In math, however, their language problem is confounded by the inherently difficult terminology, some of which they hear nowhere outside of the math classroom.

Key Points

The four stages of language development in the mathematics classroom in order are as follows;

• Everyday language: This stage begins with everyday language, which is acquired naturally through social interaction. Mathematized language is similar to everyday language but makes the mathematical concepts that are present in the everyday language explicit.
• Mathematized situation language: Language in mathematics is an essential component to make it more “real” to learners, and this can be done through the context in which mathematics is taught. At this stage S=students, through language, can think and talk mathematics and in this way, the relevance and application of mathematics to real-life situations can be facilitated.
• Language of Mathematics problem solving: The language used in the problem is often more complex than it needs to be in order to do the math. At this stage, language is used to describe the situation in a word problem, they will have difficulty connecting the mathematical operations to the situation.
• Symbolic language: At this stage, the learner learns the symbols that are used in mathematics. Mathematics is viewed as symbolic in nature and thus not hindering its comprehension by second or third language speakers. The language of mathematics then allows the child to verbalize the fact that she has to add some unknown amount to the money she has ($15) so it equals the price of the doll ($22), and finally, move to symbolic language: 15 + x = 22. At each step in this process, the language of math must be more consciously taught and learned; if this does not happen, children will have difficulty reaching the stage of symbolic language.

Hence, we conclude that the correct order is Everyday language →  Mathematized situation language → Language of Mathematics problem solving → Symbolic language.

Some students have disturbances in the visual-spatial-motor organization, which may result in weak or lacking understanding of concepts, very poor "number sense," specific difficulty with pictorial representations and/or poorly controlled handwriting and confused arrangements of numerals and symbols. Students with profoundly impaired conceptual understanding often have substantial perceptual-motor deficits and are presumed to have right hemisphere dysfunction.

• A learner exhibiting difficulty in sorting, recognizing patterns, orienting numbers and shapes, telling time and measurement may have dyscalculia with difficulty in visual-spatial skills. visual-spatial learners would share the disadvantage of missing the underlying mathematical concepts.
• If the task at hand is presented in a meaningful way so that the visual-spatial learner sees a real-world application for finding a solution to the problem, he will arrive at a solution by constructing and synthesizing a larger conceptual framework that incorporates the concepts to be learned.

Hence, we conclude that the above situation is of disturbance in visual-spatial skills.

Central Board of Secondary Education (CBSE) was formed officially in 1962 with the sole purpose to make a common standard and platform for every student in the country. CBSE is one of the most preferred boards in the country and the reasons are many.

The Prime Focus of CBSE is on:-

• Innovations in teaching-learning methodologies by devising students friendly and students centered paradigms.
• Skill learning by adding job-oriented and job-linked inputs.
• To fulfill the educational requirements of those students whose parents were employed in transferable jobs.
• To affiliate institutions for the purpose of examination and uplifting of the academic standards of the country.

About `GANIT Week':-

CBSE has decided to celebrate a 'GANIT' Week in schools to commemorate the birth anniversary of the legendary mathematician, Srinivasa Ramanujan.

• In order to commemorate the 128^th birth anniversary of Dr. Srinivasa Aiyangar Ramanujan on 22^nd December 2015, the CBSE invites schools affiliated to it to celebrate GANIT.
• GANIT stands for Growing Aptitude in Numerical Innovations and Training.
• 'GANIT' Week in schools will help students to overcome the fear of mathematics by joyfully learning the subject.
• The spirit behind the GANIT week is to make the study of mathematics more interesting and reduce the fear of learning the subject.

The Schools shall Conduct the Following Activities During the GANIT Week:-

• December 16: Lecture on Mathematics by eminent scientists
• December 17: Essay writing competitions
• December 18: Quiz competitions
• December 19: Experience sharing on innovation by teachers and students
• December 20: Screening of films produced by Vigyan Prasar
• December 22: Origami and poster competition to be followed by a formal culmination function

Hence, from the above-mentioned points, it becomes clear that GANIT stands for Growing Aptitude in Numerical Innovations and Training.

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. 

Mathematics at Upper Primary Level: Mathematics is a subject where the active participation of a child is necessary. So those skills which target in the direction of involving students actively, need to be promoted in the upper primary stage.

• Visualization, transposition, generalization, and estimation are the skills that are promoted by mathematics at the upper primary stage.
• Mathematics at upper primary level focus on acquiring knowledge and understanding of concepts, facts, principles, etc. related to commercial mathematics, mensuration, elementary statistic.
• Gaining an understanding of mathematical concepts and their applications in solving problems logically.
• To develop abilities to read and interpret data from statistical graphs, charts, etc.
• To acquire knowledge and understanding of the properties of geometrical figures through activities, experimentation, verification, etc. in mathematical contexts.

Hence, learning mathematics at upper primary level is about gaining an understanding of mathematical concepts and their applications in solving problems logically.

Open-Ended Questions: Open-ended questions are the questions that can't be answered in yes or no, rather requires a detailed answer with proper explanation. These are a useful tool for primary teachers to help students to discover new ideas and develop critical thinking.

• These types of questions give tremendous freedom to the respondents to answer according to their interpretation.
• An open-ended question permits the respondents to answer in their own words.
• Open-ended questions are used to opine self-reflection of a subject or topic. Checklists, ranking orders, alternate responses are other types of self-reporting modalities used.

For example, Write a pair of integers whose sum gives a negative integer. There are many possible pairs of integers whose sum gives a negative integer. So, this question has multiple answers. Hence, it is an open-ended question.

NOTE:

• Close-Ended Questions: These allow a learner to choose one answer from a limited list of possible answers.  They are easier and quicker for the respondents as well as for the researcher.
• Reflection question is what we call any question that makes a student look back over what or how they have learned. Reflective questioning is a technique in which the mentor asks questions designed to encourage the beginning teacher to discuss and analyze her or his practice.
• Reflection questions often assess metacognitive skills, otherwise known as thinking about how we think and learn.

Hence, from the above-mentioned points, it becomes clear that the given question is Open-ended question.

Concept:

An integer is a whole number (not a fraction) and can be positive, negative, or zero.

Calculation:

Integers between -7 and - 3 are: -6, -5, -4

⇒ - 6 × -5 × -4 = -120

Concept: A whole number that can be made by multiplying other whole numbers is called a composite number

Calculation:

9 can be made by 3 × 3 so, 9 is a composite number, and also 9 is an odd number.

∴ A composite number can be odd

To assess the progress of students towards the Mathematics accepted goals, a variety of assessment strategies are applied.

The teacher can assess the knowledge of basic concepts, terms, processes, and relationships in mathematics, the application of mathematical knowledge and skills in problem-solving, skills of computation, of using instruments, of drawing figures, graphs, etc., and analytical thinking as well.

Important Points

In geometry class of VI grade students, the teacher explained the construction of angles measuring 30°, 60° and 90°, with the help of demonstration of construction and bisector of an angle. Then she asked the students to construct an angle of 15° and an angle of 45°. In this situation, the teacher wants to assess the students' understanding and ability to combine two skills learnt, to accomplish the given task.

Key Points

In a math class, a teacher follows a proper sequence in teaching which is usually practically followed in any classroom. This is known as classroom operations. 

• It plays a major role in Mathematics learning and one of the challenges that teacher face in a classroom depending on different factors i.e., nature of the content, the learning style of the students, knowledge of teaching methods and also depends on the ability to use mathematical tools.

Additional Information

Purposes or reasons for assessment taken by the teacher in the classroom is:

• to find out how much mathematics our student has learnt.
• to identify which students are weak in mathematics.
• to keep a record of their progress for reporting to the principal and to parents.
• to recommend promotion to the next class or detention in the same class.

Hence, we conclude that in the above situation, the teacher wanted to assess the student's understanding and ability to combine two skills learnt, to accomplish the given task.

Solution:

Calculation: taking LCM and calculating

⇒ (10000 + 11000 + 1100 + 1110 + 111)/10000

⇒ 2.3321

Converting all the fractional numbers to the decimal form

$1+ \frac{11}{10}+\frac{11}{100}+ \frac{111}{1000}+ \frac{111}{10000}$

⇒ 1 + 1.1 + 0.11 + 0.111 + 0.0111

2.3321

Given:

Numbers are 4, 3, 2, 2, 7, 2, 2, 0, 3, 4, 4.

Calculation:

Arranging numbers in ascending order, we get

0, 2, 2, 2, 2, 3, 3, 4, 4, 4, 7

Here, Total numbers are 11, which is odd.

⇒ Median will be 6^th number. [ ∵ (11 + 1)/2 = 6^th ]

∴ Median = 3.

Now, Mode will be the most repeated number i.e. 2.

Now, Range = Highest Value - Lowest Value

⇒ 7 - 0 = 7.

∴ Required mean = (3 + 2 + 7)/3 = 12/3 = 4

Solution:

Given: The sum of all interior angles of a regular convex polygon is 1080°.

Formula Used: The sum of all interior angles of the regular polygon is (n - 2) × 180; where n is the number of sides.

Calculation: using the above formulae, we get

⇒ (n - 2) × 180 = 1080°

⇒ n = 8

∴ measure of each of its interior angles = 1080°/8 = 135°

Solution:

Given: ∠D = 60° and ∠C = 100°, The bisectors of ∠A and ∠B meet at point P.

Calculation: 

∠A + ∠B + ∠C + ∠D = 360°

⇒ ∠A + ∠B = 200°; ∠PAB + ∠ABP = 100°

also, bisectors of ∠A and ∠B meet at the point P

so in ΔABP

⇒ ∠PAB + ∠ABP + ∠APB = 180°

⇒ ∠APB = 80°

Solution:

Given: PQ = DE, EF = PR and FD = QR

In this type of question, if two triangles are congruent then their corresponding angles and corresponding sides are equal.

∴ ΔDEF ≅ ΔQPR

Solution:

Given: the perimeter of a trapezium is 104 cm, the lengths of its non-parallel sides are 18 cm and 22 cm, and its altitude is 16 cm.

Formula Used: A = 1/2(a + b) × h; P = (a + b + c + d); here A = area of trapezium, P = perimeter; a,b are length of parallel sides, c,d are length of non-parallel sides; h = altitude of trapezium

Calculation: using the above formulae, we get

⇒ 104 = a + b + 18 + 22

⇒ (a + b) = 64

∴ required area = 1/2 × 64 × 16 = 512 cm²

Formula Used:

Total surface area = 6a²; a = edge of a solid cube

Calculation: 

Using the above formulae, we get, also initial surface area = 6a²

Increased edge of the cube = a + 150% of a = 2.5 a

New surface area = 6 × (2.5a)² = 37.5a²

∴ Percentage increase in the surface area = (37.5a² - 6a²) × 100/6a² = 525%

Given: The radii of the bases of two cylinders are in the ratio of 2 ∶ 3 and their heights are in the ratio of 5 ∶ 3.

Formula Used: π × r² × h

Calculation: using the above formulae, we get

⇒ ratio of their volumes = (π × 2² × 5) ∶ (π × 3² × 3)

⇒ required ratio = 20 ∶ 27

Rewriting the polynomial as

4x² + y² - 4xy + 14x - 7y + 12

⇒ (2x - y)² + 7(2x - y) + 12          ----(1)

Let 2x - y = a, then polynomial (1) becomes

⇒ a² + 7a + 12

⇒ a² + 4a + 3a + 12

⇒ (a + 4)(a + 3)

Substituting the value of a in the above polynomial

(2x - y + 4)(2x - y + 3) are the two factors of the given polynomial

looking at the options

∴ The required answer is 2x - y + 3

Let x be the number subtracted from -5/7

Thus,

(-5/7) - x = -2/3

x = (-5/7) + (2/3)

∴ x =  -1/21

The number given in the question can be written as

0.00001278 = 1.278 × 10^-5      ----(1)

Comparing equation (1) with k × 10n

⇒ k = 1.278

⇒ n = -5

⇒ Required value = k + n = 1.278 + (-5)

∴ Required value = -3.722

On calculating square root of 893304 by long division we get 

√893304 = 945.147

⇒ The number to be added = 946² – 893304

⇒ The number to be added = 894916 – 894916

∴ The number to be added = 1612

Given expression is $\sqrt[3]{-91125}-\sqrt[3]{512}$

⇒$\sqrt[3]{-91125}$ = -45

⇒ $\sqrt[3]{512}$ = 8

⇒ $\sqrt[3]{-91125}-\sqrt[3]{512}$ = – 45 – 8

∴ $\sqrt[3]{-91125}-\sqrt[3]{512}$ = – 53

GIVEN:

51y3 is divisible by 9

CONCEPT:

Divisibility of 9 = Sum of all digits will be divisible by 9

CALCULATION:

5 + 1 + y + 3 = 9 + y

∴ y = 0 or 9

Solution:

(x² - 2)(1 - 3x + 2x²) 

⇒ x² - 3x³ + 2x⁴ - 2 + 6x - 4x²

⇒ 2x⁴ - 3x³ - 3x² + 6x - 2

Coefficients of x² = -3

Coefficient of x = 6

Sum of coefficients = -3 + 6 = 3

∴ Sum of coefficients is 3

GIVEN:

1 cm (map) = 3 × 10⁶ cm (actual)

CONCEPT:

1 km = 100000 cm = 1 × 10⁵ cm

CALCULATION:

9 cm (map) = 9 × 3 × 10⁶ cm = 270 × 10⁵ cm

Converting cm to km

Actual distance = (270 × 105 )/(1 × 105)

∴ Actual distance = 270 km

GIVEN:

Rate of depreciation (R) = 12%

Present value of machine (A) = 9680

Time (n) = 2 years

FORMULAE USED:

Let P be the value of the machine when purchased two years ago

A = P (1 + (R/100))n

CALCULATION:

9680 = P (1 – (12/100))2

P = 9680/(0.882) = 12500

∴ The value of the machine when purchased two years ago = Rs. 12500

While solving a question using depreciation value then the Rate of depreciation is taken negative, because the value of the article is decreasing.

The National Council for Educational Research and Training (NCERT) published a document called the National Curriculum Framework (NCF). NCF 2005 has been translated into 22 languages and influenced the syllabi in 17 states.

In a mathematics class, students at the primary level enjoy learning, solving problems, develop mathematical curiosity, and become confident in using mathematics to analyze and solve problems.

Role of Mathematics in School Curriculum:  National Curriculum framework, 2005 recommends that teaching of mathematics at the primary level should focus on-

• Children understand the basic structure of Mathematics like Arithmetic, algebra, geometry, and trigonometry, the basic content areas of school mathematics, all offer a methodology for abstraction, structuration, and generalization.
• Mathematics implies understanding of the appropriate use of learned mathematical techniques.
• Teachers engage every child in the class with the conviction that everyone can learn mathematics and enrich them with examples of achievements and contributions of mathematicians from different regions and different social groups.
• Helping students to connect classroom learning with everyday life.
• Children learn to enjoy Mathematics rather than fear it.
• Children pose and solve meaningful problems.

NOTE: Mathematics does not imply learning only geometrical theorems, mathematical procedures, algorithms, and solving mathematical games and puzzles. So, other options are not appropriate.

Hence, from the above-mentioned points, it becomes clear that important Mathematics implies understanding the appropriate use of learned mathematical techniques.

Concept:

• Frequency: It is the number of occurrences of a repeating event per unit of time. It is denoted by f and its SI unit is Hertz (Hz)
• Mathematically, $frequency (f) = \frac{1}{{Time;Period ;(T)}}$
• 1 Hertz means 1 cycle in 1 sec
• Time Period: It is the time taken by an object to complete one cycle passes through a point. Its SI unit is Sec.
• Mathematically, $Time;Period;\left( T \right) = \frac{1}{{frequency;\left( f \right)}}$

Calculation:

Given,

An object is vibrating at 5000 Hz. 

That means,

Frequency = 5000 Hz

Time period = 1/ 5000 = 0.0002 sec ⇒ Option 2 is correct.

Concept:

• Earthquake: It is a sudden violent shaking of the ground, it causes great destruction over the ground surface.
• It is mainly due to the movement of tectonic plates of earth crust or volcanic action.

Explanation:

• Earthquakes are able to initiate landslides over mountainous regions or wet regions.
• If the earthquakes are under the sea bed, this sudden shake can create extreme pressure outwards and might take a shape of a Tsunami.
• Sometimes the earthquakes can break the dams and overflows of water can create the situation of floods.

The earthquake has no direct effect on Lightning & thunder as these processes are happening in the atmosphere and the earthquake mostly covers the ground impact.

Hence, landslides, Tsunami, and Floods can be caused by earthquakes.

Explanation:

The lens present in our eyes forms an image on the Retina. 

Retina has optic nerves which carry this information to the brain. 

On the Retina there are two types of photoreceptors cells -

1. Rod cells: These cells are responsible for vision in low lights, they are sensitive to dim light, can detect shapes and movement of the objects but can not perceive colour.
2. Cone cells: These cells can detect the colours of the body and sensitive to bright light.

The best option for this question is 'Cones are sensitive to bright light.'

Additional Information

Blind Spot

• The optic nerves are made up of two cells, cones, and rods.
• Cones are sensitive to bright light and rods are sensitive to dim light.
• Cones sense color. At the junction of the optic nerve and the retina, there are no sensory cells.

Concept:

• Satellite: Anything that goes around a planet is called a satellite. Ex - Moon, sputnik -1 etc.
• Natural Satellite: A natural satellite is an object that orbits a planet or other body larger than itself and which is not man-made. Ex- Earth has a moon as a natural satellite.

Explanation:

This is the chart of the planet with their natural satellite number-

Hence, Venus has no natural satellite of its own.

Good science education is true to the child, true to life and true to science. This simple observation leads to the following basic criteria of validity of a science curriculum-

• Cognitive validity requires that the content, process, language and pedagogical practices of the curriculum are age-appropriate, and within the cognitive reach of the child. Simply, at this stage learner know the facts and principles of science and its applications, consistent with the stage of cognitive development. Thus the concept of Shadow formation at the upper primary level fulfilled by the concept of cognitive validity.
• Content validity requires that the curriculum must convey significant and correct scientific content. Simplification of content, which is necessary to adapt the curriculum to the cognitive level of the learner, must not be so trivialized as to convey something basically flawed and/or meaningless.
• Process validity requires that the curriculum engage the learner in acquiring the methods and processes that lead to generation and validation of scientific knowledge, and nurture the natural curiosity and creativity of the child in science. Process validity is an important criterion since it helps the student in ‘learning to learn’ science.
• Environmental validity requires that science be placed in the wider context of the learner’s environment, local and global, enabling him/her to appreciate the issues at the interface of science, technology and society and preparing him/her with the requisite knowledge and skills to enter the world of work.

Hence, we conclude that Cognitive validity is most appropriately fulfilled by the concept of 'shadow formation' in class VI syllabus at upper primary level.

Cognitive skills play a major role to construct mind mapping and concept mapping while studying self-learning materials. When learners read the self-learning materials it is expected that they should understand, conceptualize and relate the information to their experiences for better and effective learning.

• Creating is putting elements together to form a coherent or functional whole, recognizing elements into a new pattern or structure through generating, planning, or producing.
• For example, making a device using a simple electric circuit is a learning objective matching with creating process.
• Thus, by making a device using a simple electric circuit., one does not simply experience the arrangement but one is engaged in a series of events in which mental representations of the arrangement are created and manipulated by processes operating overtime.
• These processes are identified which help to understand the various aspects and unique features of the circuit and help in making a decision regarding the process of the simple electric circuit.

Hence, we conclude that the above cognitive process is about creating.

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.

Scientific Knowledge: It is the nature of science and scientific knowledge that gave confidence, and understanding. The difference between scientific knowledge and other types of knowledge is critical to understanding science itself.

• Scientific knowledge comes in different forms, which vary in their explanatory and predictive power.
• Scientific knowledge is socially and culturally embedded.
• Scientific knowledge varies in certainty and it is theory-laden.
• The development of scientific knowledge involves imagination and creativity.

Hence, from the above-mentioned points, it becomes clear that Scientific knowledge is not absolute, certain, and eternal.

Science education strengthens students 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 teaching of science also helps students to develop desirable attitudes, values, and behaviour pattern necessary for an environment-friendly lifestyle. 

• Values constitute an important aspect of self-concept and serve as guiding principles for an individual.
• Values indirectly influence behaviour through their influence on attitudes.
• Values can shape attitudes, it does not however mean that values shape all attitudes.

Assessment of Attitude and Values: Assessing Learner attitudes and values helps to understand the constructivist approach of assessing learner attitudes, values, and self-awareness. Attitude and values assessment can be done in several ways or techniques. These techniques include behavioral observation, direct questions, and personal statements.

• Behavioral Observation technique of assessment of attitude and values development among students by science education. Observation of performance needs to be done in a variety of contexts to establish the level of achievement of specific skills.
• Observations can also be used as feedback.

• Check-list: By using a check-list, students scored mastery criteria when certain competencies can be observed by the assessor. If it cannot be observed, the students are not getting the value.
• Rating Scale: Rating of performance using a rating scale allows the appraiser gives the mean of the control of a particular competency because the provision of a continuum in which the value of the option value is more than two categories.
• Paper-Pencil Test: It is used to measure relevant factors of participants' visuospatial ability.

Hence, it becomes clear that observation is the most appropriate technique of assessment of attitude and values development among students by science education.

The correct answer is: A and D

Different parts of plants are considered as food like roots, stems, leaves, flowers, fruit, seeds, etc.

Key Points

• Banana and Pumpkin are the plants in which two or more than two edible parts.
• Banana - All the parts of the banana plant is edible. Humans usually eat the fruit and the flower.
• Pumpkin - Most of the parts of the pumpkin are edible flowers, leaves, stems, seeds, and flesh (including pumpkin skin) are all edible.
• Lady's finger - This velvety green fruit which is again mistaken to be a vegetable is a fruit. Only the flowering part of it is edible.
• Brinjal - We eat the fruit of the brinjal plant, as a vegetable.

Therefore, the correct option is Banana & Pumpkin.

Concept:

Human digestive system-

In the whole digestive system, 

• Oesophagus pushes the food downwards and it is not involved in any digestive functions.
• The large intestine absorbs water and some salts from the undigested food material and it is not involved in the digestion process.
• In rectum remaining waste passes and remains there as semi-solid faeces. It is not involved in any digestive function.

⇒ Option 1 is correct

Explanation:

• The Villi are found inside the small intestine to absorption of nutrients from the digested food.
• They are finger-like projection inside the small intestine to increase their surface area to absorb essential nutrients from the food.
• They have thin walls and mostly covered with a thin channel of blood capillaries so, the nutrients can be absorbed by blood and easily transport

∴ Option 2 is correct 

These small pores are not able to pass food through it.

Explanation:

• Ruminants: The mammals that are able to acquire nutrients from plant-based food by fermenting it in a specialized stomach prior to digestion, principally through microbial actions.
• There is a special chamber inside their digestive system called rumen where microbial fermentation takes place

For example - Cow, Sheep, Deer, Buffalo etc.

Hence, it becomes clear that Buffalo, cow, deer are ruminants.

Concept:

• Muscle cramps happen when anaerobic respiration takes place in our muscle cells.
• When we are doing heavy physical work/exercise then there is a lack of oxygen as demanded by the muscles cause this.

Explanation:

The below figure explains the flow of conversion of glucose to energy -

• When the Pyruvate converted into lactic acid instead of CO₂ + Energy + H₂O
• Muscle cramps occur.
• A hot water bath or a massage can help in getting relief from muscle cramps. These two things improve blood circulation, thereby increasing the supply of oxygen to the muscles.

Hence, after doing physical work we get muscle cramps are due to the conversion of pyruvate to lactic acid.

Explanation:

• The human excretory system includes certain organs that eliminate the wastes such as salts, carbon dioxide, urea, uric acid and water produced by the body.
• The path of the urine in the human excretory system is -

• After filtering from kidney → The urine through Ureter → Stored in Urinary bladder → Exit through urethra.

⇒ Option 4 is correct

Concept:

• Speed: The distance travelled by the body in unit time.
• $Speed = \frac{{Distance}}{{Time}}$
• Also, $Time= \frac{{Distance}}{{Speed}}$
• 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 = 10 km + 45 km = 55 km

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

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

$⇒ Total;Time = \frac{{10;Km}}{{40;km/hr}} + \frac{{45;Km}}{{60;km/hr}} = \frac{10}{{40}} + \frac{45}{60} = \frac{{120}}{{120}};hr=1;hr$

We know that,

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

$⇒ Average;Speed = \frac{{55;km}}{{1;hr}}$

⇒ Average Speed = 55 km/hr

Explanation:

• Concave Mirror: It is a converging mirror and it's recessed inward.
• When Object is placed between Focus (F) and Pole (P) the image produced is erect virtual and magnified.
• 
• In all other case image is real.
• In Convex lens again when an object is placed between Focus (F) and Center of curvature the image produced is erect virtual and magnified.
• In All other cases, a real image is formed
• 

⇒ Option 2 is correct

Concept:

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, polio etc.

Non-communicable disease: The disease that is not transmissible directly from one person to another through biological agents, Ex- Astana, Diabetes, etc.

Explanation:

Polio: Polio or Poliomyelitis is an infectious disease caused by the polio virus. Polio is transmitted through contaminated water or food, or contact with an infected person. 

• Poliomyelitis, or simply Polio, is a highly contagious infectious disease caused by three types of Poliovirus. The Poliovirus is a virus that destroys the nervous system causing paralysis.
• Poliovirus is a highly contagious virus specific to humans.
• Jonas Salk discovered and developed the first polio vaccine.
• The first polio vaccine was the inactivated polio vaccine which came into use in 1955.

Hence, it becomes clear that Polio is caused by a Virus.

Alternative concepts are those ideas that are not congruent to generally accepted ideas. Children, at an early age usually have such concepts.

Important Points

Thus, in the above situation, the teacher should challenge the child's idea by presenting pictures taken from space and helping her in understanding how large the radius of the Earth is. With the help of this strategy, we can do corrections in a child's previous knowledge.

Key Points

Purpose of Alternative Concepts:

• These concepts are a normal part of the learning process.
• Through this process, the teacher recognizes that children are capable of thinking and their thinking is different from that of adults.
• They naturally form ideas from our everyday experience, but not all the ideas we develop are correct concerning the most current evidence and scholarship in a given discipline.
• This helps the students to interpret new experiences through these erroneous understandings for being able to correctly grasp new information.
• The teacher used instructional strategies to be effective in achieving conceptual change and helping students leave their alternative conceptions.

Note that:

• Reviewing and revising former statements of students can help teachers to reflect on their growth and renew their dedication to the goals and knowledge that they hold.
• If children participate in statement-taking, it indicates one's thinking, actions, visions, and concrete thinking about the subject.

Hence, we can conclude from the above scenario option 1 is correct.

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 education cultivates students' curiosity about the world and enhances scientific thinking.
• This will prepare students to participate in public discourse on science-related issues and enable them to become life-long learners in science and technology.

Important Points

Desirable Aims of Science Education at the Upper Primary Level:

• To provide practical knowledge of the subject matter content.
• To provide the latest knowledge to develop scientific knowledge scientific appreciation and scientific temper among the students.
• To know the facts and principles of science and its applications.
• To encourage them to learn about nature develop a love for nature and try to conserve natural resources and prevent pollution.
• To imbibe the values of honesty, integrity, and cooperation.
• To develop the scientific attitude and to use it for development works to have the open-mindedness for objective decision making and critical thinking.
• Students should be aware of the global dimension of science, as a universal activity with consequences for our lives and subject to social, economic, political, environmental, cultural, and ethical factors.
• To nurture natural curiosity, aesthetic sense, and creativity in science and technology.
• Students should be able to understand how science and technology are interdependent and assist each other in the development of knowledge and technological applications.

Hence, it becomes clear that gaining the knowledge available through memorizing is not a desirable aim of science education at the upper primary level.

The types of question that are intended to raise the responders’ spirits a complete and significant response by expending their own topic awareness and state of mind. An open-ended question is the contradictory of those closed-ended questions which has a single or a definite answer. It does not inspire a brief or single-worded response. These kinds of questions also have an inclination to be additional impartial and least prominent. However, open-ended questions are difficult to answer and still more difficult to analyse. For example, a teacher asks his students, 'suppose the moon emits light of its own, would it still have phases?'

Benefits of Open-Ended Questionnaires-

• Enables improved levels of collaboration and consideration.
• Inspires the respondents to deliver the information containing their worries, mental state and ideas.
• Supports in constructing an optimistic learning environment and sharing experiences.
• They give chances to answer an unrestricted amount of conceivable responses.
• Responders may give long responses. Responders are able to succeed and make clear answers
• Unexpected conclusions are able to be exposed.

Thus, "Suppose the moon emits light of its own, would it still have phases?" is the open-ended question.

Discovery learning or 'discover knowledge' emerged from the desire to give pupils the excitement by finding things out for themselves.  Discovery comprises of these elements, namely: collection of data or study of consequences and drawing inferences.

There is a modified version, known as ‘structured enquiries in which the pupils receive suggestions for the procedure to use how together data, organise it, and a series of questions which ‘lead’ to the solution of the problem. In the unstructured version, only the problem is posed and the pupils devise procedures for themselves.

• The inquiry curricula are based on inductivist conception, in which discoveries follow directly from unbiased observations.
• Students labelling the given materials as 'conductors' and 'non-conductors' by placing them in a self-assembled closed electric circuit gives the learners the best opportunity to 'discover knowledge'. Some other activities will promote discovery learning are-
• Of what materials are the doors and windows of your school made of?
• From where do we get wood for the windows and the doors?
• From where we do we get firewood?
• What will happen if all the trees are cut?

Hence, we conclude that students labelling the given materials as 'conductors' and 'non-conductors' by placing them in a self-assembled closed electric circuit gives the learners the best opportunity to 'discover knowledge'.

Note that: 

• Observation means watching carefully. We do see many things, situations in our routine life.  In the process of observing the observer uses all his sensory organs in an integrated manner. The observer obtains information about the World around him for a definite purpose. This is one of the best scientific tools to collect data for research.  On the basis of observation, the data is collected, analysed, processed and used for research purpose. Thus, 'I am able to hear the approaching train sooner through the track than through the air' is an observation since the observer is using his sense organs.
• We apprehend an event through perception and the intellect makes a judgment and “on the basis of the judgment previously made” we infer or draw a conclusion. This process of coming to new knowledge is called inference. This process can be related to the past, present or future events and occurrences. From above-mentioned points, we conclude about sound. We make a movement from the particular to make a larger conclusion.

Hence, we conclude that "I am able to hear the approaching train sooner through the track than through the air." is an observation and other statements are inferences.

Hypothesis: Hypothesis used in research and both require an examination of facts.

• The first approach is to gather appropriate factual data and examine them to see whether an answer to the research question can be formulated.
• The second approach uses prior research and thinking to come up with one or more hypothesized answers to the research question. This is called a hypothesis.

Key Points

• A hypothesis is a tentative answer to a research problem, expressed in the form of a clearly stated relation between the independent and the dependent variables. Hypotheses are tentative answers because they can be verified only after they have been tested empirically.
• In the above question 'distance traveled by a ball that is rolled on the inclined plane' and the 'angle of the plane by constructing a graph'  are two concepts, thus, a statement in a declaratory sentence form, about a relationship between two or more variables, which is taken for granted with the purpose of deciding on the basis of research, about the probable existence of the presumed relationship.

Additional Information

• A hypothesis is a formal affirmative statement predicting a single research outcome, a tentative explanation of the relationship between two or more variables.
• To give an example, “SDI services of an Information Centre, are used by students of research and junior research scholars much more than senior researchers.”
• One of the primary functions of a hypothesis is to state a specific relation between two or more variables in such a manner that it is possible to empirically test them.

Hence, we can conclude that describing the relationship between the distance travelled by a ball that is rolled on the inclined plane and the angle of the plane by constructing a graph is an example of a hypothesis.

Explanation:

Plastic is a polymer of ethene. A polymer is a substance made of many repeating units. 

• Plastic is a man-made substance.
• Plastics generally have these properties:-
• ​Resistance to corrosion and chemicals,
• High strength-to-weight ratio,
• Resistance to shock,
• Good durability, low cost,
• Easy to manufacture,
• Water-resistant
• Low toxicity,
• Light in weight and
• Non-reactive to chemicals and solutions.

Hence, it becomes clear that ​common characteristic properties of plastics are durable, light in weight, non-reactive.

Biodiversity is a term coined to describe the immense variety and richness of life on this planet. The word was coined in 1985 and during the 1990s has become very widely used in the scientific circles.

Every year, May 22 is observed as International Day for Biodiversity or World Biodiversity Day. This date commemorates the date of Adoption of the Agreed Text of the Convention on Biological Diversity at UNEP Headquarters, Nairobi on 22 May 1992.

• Biodiversity or Biological Diversity is immensely rich in wildlife and cultivated species, diverse in form and function but closely integrated into a system through multiple networks of interdependencies.
• Biodiversity refers to the different species of flora and fauna present in an area.
• The forest has a wide variety of flora and fauna which flourishes widely in the given area and area rich source of biodiversity.
• Biodiversity is not concerned with a particular species.

EXPLANATION:

A cell is the fundamental structural and functional unit of all living organisms. Anton van Leeuwenhoek discovered the first living cell in 1674.

• Inside each cell is a dense membrane-bound structure called the nucleus.
• The nucleus is the largest organelle in the cell that contains thread-like structures called chromosomes on which genes (DNA) are present.
• A gene is the basic physical and functional unit of heredity. Genes are made up of DNA.
• The nucleolus is the round irregular structures present inside the nucleus.
• The ribosome is not a part of the nucleus. They are found floating in the cytosol or attached to the endoplasmic reticulum.

​

• Gamete formation: These are cells used during sexual production. The male gamete is sperm while the female gamete is the egg or ova.
• Fertilization: This is the process where the male and female gametes fuse to form a single cell called a zygote.
• Zygote: This is the combination of the parent gene(male and female gene) formed during fertilization. It contains the necessary genetic information to form a new human being.
• Embryo: This is the early stage of development of the new individual.

The correct sequence of events is during reproduction in human beings.

Gamete formation → Fertilization → Zygote → Embryo

EXPLANATION:

• Thyroxin hormone is the hormone that is required for the growth of the tadpoles. Thyroxin hormone produces by the thyroid gland in the presence of Iodine. That’s why Iodine should be available in sufficient quantity in the water of the pond.
• If iodine is not available in the diet, then the thyroid may produce an insufficient hormone which will affect the process of metamorphosis.  If water is iodine-deficient, in which the frog lays an egg, then tadpoles hatched from these eggs will not grow into adult frogs.

So, Iodine elements must be available in sufficient quantity in the water of a pond in at tadpoles are growing.