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

Lawrence Kohlberg, an American psychologist, has propounded the Theory of Moral Development. Kohlberg proposed three levels of moral development wherein each level comprised of two stages as depicted in the table below:-

• During the pre-conventional level, a child’s sense of morality is externally controlled. Children accept and believe the rules of authority figures, such as parents and teachers, and they judge an action based on its consequences. i.e. individualism exchange or tit for tat stage.
• During the conventional level, an individual’s sense of morality is tied to personal and societal relationships. Children continue to accept the rules of authority figures, but this is now because they believe that this is necessary to ensure positive relationships and societal order.
• During the post-conventional level, a person’s sense of morality is defined in terms of more abstract principles and values. People now believe that some laws are unjust and should be changed or eliminated.

Therefore, it becomes clear that Noor's statements represent exchange orientation typical at the pre-conventional level.

Gender refers to the socially constructed differences between men and women. It refers to the masculine and feminine qualities, behaviour, roles, and responsibilities that society upholds. Gender can be changed / re-oriented.

Gender stereotype an oversimplified and unfair belief or idea that groups of people have particular characteristics or that all people in a group are the same.

• Gender stereotyping can limit the development of the natural talents and abilities of girls and boys, women and men, as well as their educational and professional experiences and life opportunities in general.
• It referred to beliefs about typified characteristics deemed appropriate for different sexes in society.
• Stereotypes about women both result from and are the cause of, deeply engrained attitudes, values, norms, and prejudices against women.
• They are used to justify and maintain the historical relations of power of men over women as well as sexist attitudes that hold back the advancement of women.

Therefore, the widely held beliefs about characteristics for different sexes in society are referred to as gender stereotypes.

Additional Information

• Gender discrimination describes the situation in which people are treated differently simply because they are male or female, rather than on the basis of their individual skills or capabilities.
• A gender role, also known as a sex role, is a social role encompassing a range of behaviors and attitudes that are generally considered acceptable, appropriate, or desirable for a person based on that person's biological or perceived sex.
• Gender identity is the personal sense of one's own gender. Gender identity can correlate with a person's assigned sex at birth or can differ from it.

Gender refers to the socially constructed differences between men and women. It refers to the masculine and feminine qualities, behaviour, roles, and responsibilities that society upholds. Gender can be changed / re-oriented.

Gender Stereotyping refers to the relatively fixed and overgeneralized attitudes and behaviors that are considered normal and appropriate for a person in a particular culture based on his or her biological sex.

• Gender stereotyping can limit the development of the natural talents and abilities of girls and boys, women and men, as well as their educational and professional experiences and life opportunities in general.
• To eliminate the gender stereotyping, there have been conscious efforts to include stories in the curriculum where the father is involved in household works and the mother is doing adventure activities.
• Stereotypes about women both result from and are the cause of, deeply engrained attitudes, values, norms, and prejudices against women.

Strategies to Promote Gender Equity:

• Closing the gender gap in education at all levels
• Giving the equal opportunity to boys and girls in the classroom
• Teach both genders equally and ensure participation of both genders
• Assume that both genders have similar potential for developing physical and motor skills
• Build coalitions to advocate for gender equality in the planning stages

NOTE

• Gender bias is the tendency to prefer one gender over another. It is a form of unconscious bias, or implicit bias, which occurs when one individual unconsciously attributes certain attitudes and stereotypes to another person or group of people.
• Gender constancy refers to the theory that children develop a sense of gender over time and eventually come to understand that their biological sex is fixed and permanent.
• Gender discrimination describes the situation in which people are treated differently simply because they are male or female, rather than on the basis of their individual skills or capabilities.

Hence, the conscious efforts to include stories in the curriculum where the father is involved in household works and mother is doing adventure activities, is a move to eliminate gender stereotyping.

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 asserted that the cognitive development of children is enhanced through social interaction with other people, particularly those who are more skilled.
• 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.

Scaffolding is a teaching method that enables a student to solve a problem, carry out a task, or achieve a goal through a gradual shedding of outside assistance. Scaffolding literally means the structure which is made to support the work crew while a building is constructed or repaired.

• Scaffolding is when adults adjust the support to extend the child's current level of performance
• 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.
• In other words, it isa 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.
• 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.

NOTE:

• Discovery learning is a technique of inquiry-based learning and is considered a constructivist based approach to education. It can occur whenever the student is not provided with an exact answer but rather the materials in order to find the answer themselves.
• Inter-subjectivity is the process where two participants begin a task with a different understanding and arrive at a shared understanding. It is essential that participants work towards the same goal.

Hence, according to Vygotsky, when adults adjust the support to extend the child's current level of performance, it is called Scaffolding.

According to Piaget’s Cognitive Development Theory:

• Cognitive development takes place at different rates at different stages of development.
• Cognition develops through the interaction between the child and the environment.​
• Piaget’s theory focuses not only on understanding how children acquire knowledge but also on understanding the nature of the child’s intelligence.

Cognitive development is not a continuous process, it occurs in the following 4 stages:-

Stage 1: Sensorimotor Stage (Birth – 2 years)

• During this stage, babies up to 2 years learn through their senses. During this stage, they develop the motor function.
• They learn about their environment and who belongs to it. They also learn how to solve problems through trial and error.
• One of the primary lessons learned in the sensorimotor stage is object permanence. Object permanence is the concept that things do not vanish from existence if they are no longer in plain sight.

Stage 2: Preoperational Stage (2 – 7 years)  

• In this stage, children learn through symbolic learning.
• Symbolic learning is stimulated through language development and imitative or imaginative play. A child may give human characteristics to inanimate objects.
• During the preoperational stage, the child has egocentric thinking. This means that they lack the ability to see outside of their own perspective without being prompted by reward.
• The child also tends to not be able to understand that situations, actions, or issues can be altered or reversed.

Stage 3: Concrete Operational Stage (7 – 11 years)

• In this stage, a child has begun to develop logic and concrete reasoning skills. Children in the concrete operational stage are able to quantify and organize.
• Their egocentric thinking diminishes. They are able to understand the perspective of another person.
• Children in the concrete stage are able to understand and relate to relational terms. Relational terms, like time, size, space, and distance, are more easily understood and conceptualized in this stage.

Stage 4: Formal Operational Stage (11 – 15 years )

• The formal operational stage is the final stage of Piaget’s theory of development. In this stage, a child develops the ability to utilize abstract thinking.
• They are able to consider different perspectives, opinions, and concepts to draw conclusions.
• Children in the formal operational stage are able to use abstract thought. They use abstract thought to solve problems. In the formal operational stage, a child’s skills are fine-tuned.
• This makes the following forms of thought easy to use for drawing conclusions and solving problems:
• Deductive logic
• Hypothetical situations
• Problem-solving through the organization of information
• Drawing conclusions from information, thoughts, and opinions
• The ability to create informed opinions

Therefore, according to Jean Piaget's theory of cognitive development, hypothetico-deductive reasoning develops during the formal operational stage.

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.
• Vygotsky believed that it is important to understand the social processes and influence of the cultural context on children's thinking.
• Lawrence Kohlberg expanded on the earlier work of cognitive theorist Jean Piaget to explain the moral development of children, which he believed follows a series of stages. He defined three levels (pre-conventional level, conventional level, post-conventional level ) of moral development (each level has two distinct stages)
• Jean Piaget stressed that children actively construct their understanding of the world. The information does not simply enter their minds from the environment.
• Piaget believed that a child’s mind passes through a series of stages of thought from infancy to adolescence.
• In his theory of cognitive development, Jean Piaget proposed that humans progress through four developmental stages: the Sensorimotor, Pre-operational, Concrete Operational, and Formal Operational period.
• Albert Bandura is known for his Social Learning Theory which emphasizes the importance of observing and modeling the behaviors, attitudes, and emotional reactions of others.

Hence, according to Lev Vygotsky, It is important to understand the social processes and influence of the cultural context on children's thinking.

Jean Piaget’s Theory of Cognitive Development:

• Jean Piaget 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.
• According to him, cognitive structures are the basic mental patterns people use to process any information.

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

Applying Jean Piaget’s Theory In the Classroom of grade 6-8​: It has the following steps to structure preoperational development.

• It has the following steps to structure preoperational development.
• Use concrete props and visual aids whenever possible.
• Present problems with students that require reasoning based solutions.
• Make instructions relatively short, using actions as well as words.
• Do not expect the students to consistently see the world from someone else’s point of view.
• Be sensitive to the possibility that students may have different meanings for the same word or different words for the same meaning. Students may also expect everyone to understand the words they have invented.
• Give children a great deal of hands-on practice with the skills that serve as building blocks for more complex skills like reading comprehension.
• Provide a wide range of experiences in order to build a foundation for concept learning and language.

 Hence, it becomes clear that drawing implication from Piaget's theory of cognitive development, a teacher of grade 6-8 in his classroom should present problems that require reasoning based solutions.

The theory of Multiple Intelligences was introduced in 1983 by Howard Gardner in his book 'Frames of Mind'.

• According to Howard Gardner, “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”.
• The essence of Gardner’s Multiple Intelligences (MI) is that each person has eight types of intelligence.

Key Points 

Howard Gardner formulated the following types of intelligence:

 

Gardner’s Theory of Multiple Intelligence can be Understood Briefly by the Following Diagram:-

Hence, according to Howard Gardner's theory of multiple intelligence, the sensitivity to and capacity to detect patterns, handle long chains of reasoning are the characteristics of a person with Logico-mathematical intelligence.

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. It is the process of learning how to become part of a culture. Through socialization, one learns the culture’s language, their role in life, and what is expected from them.

Key Points Aims of Socialization in Education:-

• To make new members of society familiar with social traditions, manners, customs, etc.
• To prepare the members of the society to adapt to the constantly changing environment.
• To preserve the traditions, values, and customs of a society.
• To develop habits, skills, values, and motives that make them responsible, productive members of society.
• To study the various types of social relationships and their impact on individual development.
• To control the teaching-learning process to achieve the personality development of every single child.

NOTE

• Inclusion in education refers to a model wherein students with special needs spend most or all of their time with non-special (general education) needs students
• Mainstreaming: Many students with special needs are placed into a self-contained classroom or multi-classroom program in which they learn alongside peers who have disabilities as well.
• Differentiated learning or, simply, Differentiation, is a framework or philosophy for effective teaching that involves providing all students within their diverse classroom community of learners a range of different avenues for understanding new information in terms of acquiring content; processing, constructing, or making sense of ideas; and developing teaching materials and assessment measures so that all students within a classroom can learn effectively, regardless of differences in ability.

Hence, the process by which children develop habits, skills, values, and motives that make them responsible, productive members of society is called socialization.

Heredity and environment are the elements that play a vital role in determining the personality development of an individual. How a person will develop depends on the environment but how far a person can develop depends on heredity. 

Each individual has a different pattern of behaviors and personality. This difference is seen due to the influence of heredity and environment.

• Heredity and environment play an important role in the development of the personality and other qualities in the individual.
• From the earliest moments of life, the interaction of heredity and the environment works to shape who children are and who they will become.
• While the genetic instructions a child inherits from his parents may set out a road map for development, the environment can impact how these directions are expressed, shaped or event silenced.
• In order to understand child development, it is important to look at the biological influences that help shape child development, how experiences interact with genetics and some of the genetic disorders that can have an impact on child psychology and development.
• The complex interaction of Heredity and the environment does not just occur at certain moments or at certain periods instead it is persistent and lifelong.

Hence, it becomes clear that heredity and environment both influence human development in a complex interplay.

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

• The progressive education philosophy says that educators should teach children how to think rather than relying on rote memorization.
• It promotes co-operative learning, children gain socially and academically knowledge from co-operative learning endeavors.
• Progressive classroom is the best way for students to experience real-world situations.
• The process of learning by doing is at the heart of this style of teaching.
• The concept, known as experiential learning, uses hands-on projects that allow students to learn by actively engaging in activities that put their knowledge to use.
• A reaction to didactic approaches such as behaviorism and programmed instruction, constructivism states that learning is an active, contextualized process of constructing knowledge.
• A progressive teacher is an effective one when he is able to stimulate the students to initiate, plan, and carry out their projects on their own. He encourages students to communicate in solving problems as a group not only within the context of the lesson.
• Knowledge is constructed based on personal experiences and hypotheses of the environment.
• For example, the workplace is a collaborative environment that requires teamwork, critical thinking, creativity, and the ability to work independently.
• Experiential learning, by helping students develop these skills, better prepares them for college and life as productive members of the workplace.

Therefore, from the above-mentioned points, it becomes clear that in a progressive classroom, knowledge is constructed by the learner.

Continuous and Comprehensive Evaluation (CCE) refers to a system of school-based evaluation of students that covers all aspects of students' development.

• CCE was introduced by the Central Board of Secondary Education (CBSE) in India to evaluate the student’s development in all aspects throughout the academic year on a continuous basis.
• The objective of CCE is to make evaluation an integral part of learning through diagnostic and remedial teaching.
• CCE helps in improving student’s performance by identifying his/her learning difficulties at regular time intervals right from the beginning of the academic session and employing suitable remedial measures for enhancing their learning performance.

CCE describes two different types of evaluations which include summative and formative assessment/evaluation.

• "Summative Evaluation", commonly known as  "Assessment of Learning" is a type of evaluation which:
• measures, certifies, and reports the level of students' learning by assessing them at the end of the term.
• produces an accurate description of students' potential and achievement to promote them to the next grades.
• "Formative evaluation", commonly known as "Assessment for Learning" is a type of evaluation which: 
• monitor the child's progress throughout the teaching-learning process and improves students' academic achievements.
• diagnoses and removes the learning difficulties of students with appropriate strategies.

Hence, it becomes clear that Continuous and Comprehensive Evaluation includes both formative and summative assessments using a wide variety of strategies.

Stereotype threat is a phenomenon in which a person’s concern about confirming a negative stereotype can lead that person to underperform on a challenging assessment or test. It occurs when a person is worried about behaving in a way that confirms negative stereotypes about members of their group. It is socially premised psychological threat that arises when one is in a situation or doing something for which a negative stereotype.

• Foster a 'growth mindset' by conveying the idea that intelligence is not fixed, but can change and grow incrementally, with practice and “exercise.”
• Create a learning environment in which mistakes and missteps are valued as opportunities for learning.
• Encourage students to 'think out loud', to ask questions, to embrace difficult problems, and to take intellectual risks.
• Describing the situations of role models from different social groups in which their mistakes, missteps, and wrong turns have led to discovery and innovation.
• Hong and Lin-Seigler have found that learning about struggles faced by famous physicists increased students’ interest in science and problem-solving.

Therefore, to reduce the impact of stereotype threat, a teacher's initial step can be presenting stories and examples of role models from different social groups.

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.

• An 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.

Key Points

Role of Teacher in an Inclusive classroom:

• Inclusion requires teachers to accept the responsibility for creating schools in which all children can learn and feel they belong.
• The teacher should believe that every child has the potential to learn as per their abilities and strength.
• Labeling students as ‘handicapped child’ or ‘disabled child’ and paying attention to only gifted or talented children will create an environment of discrimination among students.
• The factor of secondary socialization (i.e. learning from friends and peer group) will also get severely affected, which will be an obstacle in achieving the full potential of the children.

Therefore, in an Inclusive classroom, a teacher’s most important role is to believe that every child has the potential to learn as per their abilities and strength.

Learning disability includes those skill deficits which are confined to scholastic performance in subjects like reading, writing, and arithmetic even though having average or above-average intelligence.

• Learning Disabilities are due to genetic and/or neurobiological factors that alter brain functioning in a manner that affects one or more cognitive processes related to learning.
• A learning disability is not a problem with intelligence or motivation.

Signs of Learning Disability:-

• Difficulty in recognizing words or letters
• Poor vocabulary skills
• Difficulty in writing letters
• Anxiety around reading
• Difficulty with understanding or remembering what was read
• Difficulty in calculations

Some other common learning disabilities in children:-

 

• Autism is a developmental disorder of variable severity that is characterized by difficulty in social interaction and communication and by restricted or repetitive patterns of thought and behavior.
• Creative student refers to abilities to solve problems or tasks in a creative way by means of generating many original ideas.
• Mental impairment is a mental or psychological disorder.

Hence, from the above-mentioned points, it becomes clear that all the given indications are related to a student with a learning disability.

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.

Key Points

• The primary objective of inclusive education is to educate disabled students in the regular classroom and still meet their individual needs.
• Inclusive education allows children with special needs to receive a free and appropriate education along with non-disabled students in the regular classroom.
• Students with specific learning difficulties may require resource support for meeting their individual needs.
• This support can be provided in the form of developing specific learning objectives based on an analysis of each student's learning strengths and weaknesses during their class or after school hours or if possible, in another small room during school hours.
• The support can be provided on a one-to-one basis or in a small group.

Therefore, a teacher can address the needs of specially-abled learners in an inclusive classroom by developing specific learning objectives based on an analysis of each student's learning strengths and weaknesses.

The meaning of creativity is to think or do something differently. Creativity is considered as the ability to produce something original.

Key Points

• The creative learner has a highly developed problem-solving ability, a curious and impulsive nature, an ability to create original and imaginative ideas.
• Creative learning encourages diversity of ideas, opinions, and perspectives and helps to think laterally and approach problems from multiple perspectives.
• Flexibility and originality help to think differently/challenge the old assumption, try out new ways, create resources without many facilities, ponder over the mystery of things with an open mind.
• Teachers must develop in our students' creative thinking skills for successful adaptability to change and fulfilling social and moral responsibilities for the improvement of social situations.
• A teacher can encourage creative learners in her classroom by encouraging multiple perspectives and appreciating original ideas.

Convergent thinking refers to thinking that is required to solve problems that have only one correct answer. The mind converges to the correct solution.

Divergent thinking is open-ended thinking where the individual can think of different answers to the questions or problems in terms of her/his experiences. Such kind of thinking helps in producing novel and original ideas.

Hence, a teacher can encourage creative learners in her classroom by encouraging multiple perspectives and appreciating original ideas.

Meaningful learning is an active, constructive, and durable process. It implies understanding i.e a child must feel that the information is useful and not limit them to only memorizing it. It requires active learning techniques. It also implies linking new information to existing knowledge.

• Meaningful learning is a generative process of representing and manipulating concrete things and mental representations, rather than storage and retrieval of information.
• Showing genuine interest in the content matter and having concern for children's overall well-being and learning, supports meaningful learning.
• The most important measure of curriculum development is meaningful learning.
• Only if the child finds the activity or knowledge being learned meaningful, then only will its inclusion in the curriculum be justified.

 NOTE:

• Children find it difficult to cope with several tests and assignments that give them anxiety and the fear of others being judgmental about their performance.
• The lecture method is an age-old and widely used method of teaching that helps teachers to present logically organized facts and is a direct source of information.
• Lectures are especially useful for teaching large groups. However, the learners are passive as there is usually one-way communication and it is difficult to assess whether learners have actually learned.

Therefore the factor of Showing genuine interest in the content matter and having concern for children's overall well-being and learning supports meaningful learning in the classroom.

Problem-solving is a learner-centred approach that emphasizes learner's active involvement in the learning process. In this approach, teachers create a problematic situation for students and then assist them in perceiving, defining, and stating the problems in a fear-free classroom environment. 

An effective problem-solving strategy is a plan of action used to find a solution. Different strategies have different action plans associated with them For example, a well-known strategy is the trial and error principle.

• In the means-ends analysis, it is possible to control the entire process of problem-solving. In the means-end analysis, a problem is solved by dividing the in into a number of sub-goals. It is an example of an effective problem-solving strategy.
• the problem solver begins by envisioning the end, our ultimate goal, and then determines the best strategy for attaining the goal in his current situation.
• It starts from a predetermined goal, in which actions are chosen that lead to that goal.
• Each action that is executed leads to the next action; everything is connected together in order to reach the end-goal.
• In the meantime, however, problems may arise. It is often hard to determine where exactly the crux is.
• With the help of Means-End Analysis, both forward and backward research can be done to determine where the stagnation is occurring. This enables the larger parts of a problem to be solved first, to subsequently return to the smaller problems afterward.

NOTE:

• The concept of functional fixedness is a cognitive bias that limits a person to use an object only in the way it is traditionally used. Functional fixedness is the inability to realize that something known to have a particular use may also be used to perform other functions.
• A response set is a human tendency to answer questions in ways that are the most complimentary, or flattering, to the respondent rather than telling the absolute truth.

Hence, it becomes clear that means-end analysis is an effective problem-solving strategy.

Teaching effectively involves not only the use of tools, techniques, and strategies to optimize student learning but an understanding of context, in particular how your students learn, how they process information, what motivates them to learn more, and what impedes the learning process. There are different kinds of teaching-learning methods in a fashion which makes learning a fruitful process.

• Focusing on the reproduction of knowledge as given by the teacher is not an effective method since it is limiting the opportunities for active exploration and learning through the environment. Rather It is more focused on rote learning and memorization is not an effective strategy for teaching-learning.
• The experimentation and exploration are essential for teaching because it allows the practical activities to integrate teachers and students, to provide joint planning in which teacher and student construct the process of the activity), and the use of teaching techniques that can lead to a better understanding of the subject.
• Encouraging children to make intuitive guesses is an effective strategy for teaching-learning.
• A dialogue and discussion sparks engaged learning through an open exchange of perspectives that deepens students' understanding of an issue or topic.
• The dialogue process promotes analysis of course content and encourages reflection.

Hence, focusing on the reproduction of knowledge as given cannot be an effective strategy for teaching-learning.

For the non-attentiveness of the child, there can be various reasons such as the curriculum may be repetitive or boring, the class environment is not interactive and maybe the child is suffering from ADHD.

• Not paying attention is a mental disorder of the neurodevelopmental type.  It is also called attention deficit hyperactivity disorder (ADHD).
• It is characterized by problems of paying attention, excessive activity, or difficulty controlling behavior, all of which are not appropriate for the learner’s age**.**

To Address such Disadvantaged Learners Teachers Should:-

• Seat a child with ADHD away from windows
• Creating a distraction-free space
• Giving one instruction at a time
• Talk to them and find out the reasons for their disinterest
• Keeping instructions simple and structured
• Using audio-visual aids and charts while explaining

NOTE: Scolding them or asking them to go out or giving a lot of worksheets, won't solve the problem, rather it will burden the child.

Hence, talking to the child and finding out reasons for their disinterest can be an effective way of removing the non-attentiveness of the child.

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.

Constructionism seeks to understand how children and childhood knowledge is constructed, by whom, why, and most substantially what purpose it would serve.

• 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.
• It emphasizes the diversity of situations and circumstances in which childhood is experienced.
• Constructivists believe that prior knowledge impacts the learning process and it is crucial for constructing knowledge.
• Asking students what they already know about a topic and what puzzles them affords an opportunity to assess children's prior knowledge and the processes by which they will make sense of phenomena.
• Constructivist learning is based on the active participation of learners in problem-solving and critical thinking–given real and authentic problems.

NOTE:

• Conditioning in behavioral psychology is a theory that the reaction (response) to an object or event (stimulus) by a person or animal can be modified by 'learning', or conditioning. The most well-known form of this is Classical Conditioning, B.F. Skinner built on it to produce Operant Conditioning.
• Rote memory allows for the memorization of base information, but it doesn't put that information into any sort of context. The lack of context for complex subjects means that the student has not learned anything about what they are studying.

Hence, it becomes clear that the Constructivist approach suggested that prior knowledge of the learner is crucial for constructing knowledge.

It is assumed that young children actively construct naive theories about phenomena (such as birth, disease, death, and growth) that they encounter in their world.

• A naive theory (also referred to as commonsense theory or folk theory) is a coherent set of knowledge and beliefs about a specific content domain (such as physics or psychology), which entails ontological commitments, attention to domain‐specific causal principles, and appeal to unobservable entities.
• Conceptual change often takes the form of theory change and examples, because concepts are considered to be embedded in theories and their practical demonstration through examples and counter-evidence that help in clearing the misconceptions that arise in a child's mind, often regarded as 'naive theories'.
• Forming a theory of mind is critical in our ability to understand ourselves and others.
• So, it is important to clear each and every doubt raised in a child’s mind by giving a practical demonstration and building up permanent concepts.

NOTE: Scolding and dismissing or ignoring children’s ideas will completely discourage their active exploration and learning approach and that will hinder their all-around development.

Therefore, challenging the conceptions of the naive theories through dialogue will help in the proper construction of the knowledge in the child.

Emotion is a mental state associated with fear, anger, love, etc. Cognition is the process of acquiring knowledge through experiences and senses. 

Cognition describes how mental processes i.e. learning, remembering, problem-solving, and thinking develop from birth until adulthood. Understanding cognitive development is useful in determining the kind of thinking children are capable of at different age levels.

• The relationship between cognition and emotion has fascinated important thinkers within the intellectual tradition. Physical, cognitive, emotional, and social development in a child is the development of an integrated and holistic fashion.
• Cognition is closely intertwined with emotions and language. Mind states are a powerful determinants of one’s current judgments and decision making, that often effect once performance outcome in a task both in social and non-social context.
• Emotions or emotional approach is a psychological construct that involves the use of emotional processing and emotional expression in response to a different situation.
• The relationship between cognition and emotions is bi-directional - a dynamic interplay.
• Emotions are experienced as positive feelings, negative feelings, undesired reactions to any stressful situation, these often impact decision making i.e. cognition.
• The Emotional Approach involves the conscious use of emotional expression and processing to better deal with stressful situations.

Hence, the relationship between cognition and emotions is bi-directional i.e. a dynamic interplay between both cognition and emotions.

Learning is the acquisition of new behaviour or the strengthening or weakening of old behaviour as the 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.

It has been found out that the child’s difficulty in learning may be due to many factors within the child himself. These are-

• The Interest of the Student - The factor of interest is very closely related in nature to that of symbolic drive and reward.  A favorable mental attitude facilitates learning.
• The Emotional Health of the Student - Concentration needs emotional and mental poise and absence of mental conflict or complex. Some children find it difficult to prepare for the examinations, simply because of fear of the examination and anxiety neurosis. A calm, serene, and balanced mind has the power to concentrate and learn better.
• Pedagogical Strategies - The strategies or steps taken by the teacher to make the class environment interactive and that also engrave interest among students regarding the topic.
• The Social and Cultural Context of the Student -  Regardless of the differences, most students learn best when they live in a culture that values not just education but understanding the material well. So students should be encouraged to question and test concepts when they are learning and not on cultural backgrounds.

Hence, from the above-mentioned points, it becomes clear that all the given factors will affect learning.

Knowledge is not absorbed but rather constructed through a person’s experiences with his or her environment. This knowledge may be constructed individually or collaboratively is termed as the construction of knowledge.

Key Points

• Meaningful construction of knowledge is a collaborative process that aims to produce new understanding or knowledge which exceeds something that anyone alone could not achieve.
• It is also essential that knowledge construction is based on each others’ ideas and thoughts.
• The association of response to the stimulus or vice-versa in remembering either of the two with the help of the other.
• '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 learner's cognitive development.
• According to Vygotsky, social interaction is the primary cause of learners' development as his theory emphasizes that children learn through interaction and collaboration with skilled and knowledgeable people.

Hence, Social interaction is an important aspect of the process of meaningful construction of knowledge.

Additional Information

• Reinforcement is simply defined as an effect that increases the probability of a response. It is the process of giving reward and punishments to the children. It is, therefore, discussed in terms of observable or measurable events. We reward people, we reinforce the behaviour.
• In operant conditioning, infants act or operate, on the environment, and stimuli that follow their behavior change the probability that the behavior will occur again. A stimulus that increases the occurrence of a response is called a reinforcer. For example, sweet liquid reinforces the sucking response in newborns. Removing a desirable stimulus or presenting an unpleasant one to decrease the occurrence of a response is called punishment. A sour-tasting fluid punishes newborns’ sucking response. It causes them to purse their lips and stop sucking entirely.

The learning attitude of students determines how well they think, prioritize, choose a career, pursue your goal, perform in work, etc. Attitude can alter every aspect of a students’ life, including their education and attitude on learning and it determines their ability and willingness to learn.

• Learning is determined by the child’s level of consciousness, the results obtained by statistical analysis of the data show that there is a statistically significant interrelationship between attitude, performance, and other factors.
• Research has shown that when students repeatedly engage in an activity (designing, experimenting, etc.) to earn a reward (like a 'star' or 'badge') that is not directly related to that activity are likely to develop a materialistic attitude towards learning.
• The statistical analysis showed that students who have positive ways of thinking about learning and get involved in activities achieve higher academic performance than those who make minimal efforts in this regard.
• Students with good results believe that learning provides satisfaction, and just being a student is not enough to feel fulfilled. They are willing to take on additional tasks and condemn superficiality in school tasks.
• They set specific goals for learning, aiming at acquiring new knowledge and not just completing a routine activity and strive for excellent school performance.
• In addition to this, students with good performance consider learning a way towards personal development. This ensures their personal achievement and success in life.

Hence, it becomes clear that when students repeatedly engage in an activity to earn a reward that is not directly related to that activity, they are likely to develop a materialistic attitude towards learning.

Childhood is generally considered to be either a natural biological stage of development or a modern idea or invention. It is generally referred to as the pre-school or school period.

• Social Constructionism seeks to understand how children and childhood knowledge is constructed, by whom, why and most substantially what purpose it would serve.
• It emphasizes on the diversity of situations and circumstances in which childhood is experienced.
• According to contemporary socio-constructivist theorists, the concept of childhood is a social construction because it is a theory of knowledge in sociology and communication that evaluates the development of the child on the basis of assumptions of reality.
• Social constructivism is an approach that tells about importance of social interaction and context in learning. It approaches to learning that holds that people actively construct or make their own knowledge and that reality is determined by the experiences of the learner.
• Constructivism's central idea is that human learning is constructed, that learners build new knowledge upon the foundation of previous learning. This prior knowledge influences what new or modified knowledge an individual will construct from new learning experiences.
• A child-centred constructivist approach to early childhood education is applicable to various classroom scenarios.
• Children benefit from group problem-solving. By working together to find solutions, students experience cognitive growth.

Hence, it becomes clear that according to contemporary socio-constructivist theorists the concept of childhood is a social construction.

During middle childhood, the growth rate is slow but steady. The child's thinking develops rapidly and his/her store of information grows at a fast pace. They are better at recognizing emotions in others and empathizing with them. It is considered to be a transitional period between childhood and adulthood.

Key Points The Development of a Child is divided into Different Stages: 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Therefore, it becomes clear that during period of middle childhood children begin to think logically but concretely.

Socialization is the process where the child learns to associate and relate with others. 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.

• Socialisation is also considered as the passing of culture from one generation to the next.
• Watching children play together provides valuable insight into how socialization affects child development, and during their formative years, children will acquire most of their social skills through group interactions with other children.

Primary Socialization: It happens during infancy and childhood. It refers to the process where the child becomes socialized through the family or neighbourhood in the early childhood years. 

• This highlights that the key agent in the process of primary socialization is the family.
• For example, a very young child in a family has little knowledge of his culture. He is unaware of the values, social norms, practices, etc. It is through the family that the child gets to know what is accepted and what is not in a particular society.
• Two specific processes are conducted by the family when speaking of primary socialization. They are-
• Internalization of the society’s culture
• Structuring of the personality

Secondary Socialization: It occurs once the infant passes into the childhood phase and continues into maturity. It refers to the process that begins in the later years through agencies such as education and peer groups. 

• During this phase more than the family, some other agents of socialisation like the school and friends’ group begin to play a role in socialising the child.
• Friends and peer groups are some examples for secondary social agents.

 Hence, from the above-mentioned points, it becomes clear that family and neighbourhood are primary socializing agencies.

Concept:

If x and y are twin primes then both x and y must be individually prime and they should differ by 2

Calculation:

Twin Prime between 1 and 100

3, 5

5, 7

11, 13

17, 19

29, 31

41, 43

59, 61

71, 73

∴ There are eight pairs of twin prime between 1 and 100.

Given:

21168 = 2^a × 3^b × 7^c

Calculation:

Factors of 21168 = 2⁴ × 3³ × 7²

∴ a = 4

⇒ b = 3

⇒ c = 2

According to the question:

⇒ (4a - 5b + c) = {(4 × 4) - (5 × 3) + (2)}

⇒ 16 – 15 + 2

⇒ 3

Given:

x is the least number which when divided by 8, 12, 20, 28, and 35 always leaves the remainder 5

Concept used:

Required number = LCM of given number + Equal remainder

Calculation:

LCM of 8, 12, 20, 28, and 35 be 840

840 is the least factor which is divisible by 8, 12, 20, 28, and 35 leaves remainder 0

According to question,

There is always remainder = 5

Required number = 840 + 5 = 845

Sum of the digits of the number = 8 + 4 + 5 = 17

Given:

Number is subtracted from each of 50, 61, 92, and 117 to make it in proportion

Calculation:

Let the number be x

⇒ (50 – x)/(61 – x) = (92 – x)/(117 – x)

⇒ (50 – x) × (117 – x) = (92 – x) × (61 – x)

⇒ 5850 – 50x - 117x + x² = 5612 - 92x - 61x + x²

⇒ 238 = 14x

⇒ x = 17

Given:

Sum = Rs.1710

4 times of A = 6 times of B = 9 times of C

Calculation:

Let the LCM of 4, 6 and 9 be 36

According to question:

⇒ 4 × A = 6 × B = 9 × C = 36

⇒ A = 9

⇒ B = 6

⇒ C = 4

9 + 6 + 4 = 1710

⇒ 19 units = 90

Difference between A and C = 9 – 4 = 5

⇒ 5 × 90 = 450

Given:

Fruits in basket A and B  = 7 : 9

after putting six fruits from basket A to B ratio will become = 1 : 3

Calculation:

Let the constant be x

Fruits in basket A and B initially = 7x and 9x

According to question:

⇒ (7x - 6)/(9x + 6)= 1/3

⇒ 21x - 18 = 9x + 6

⇒ 12x = 24

⇒ 12x = 24

⇒ x = 2

Total number of fruits = 7 × 2 + 9 × 2 = 32

Given:

DA⊥AB, CB⊥AB and AC = BD

Concept:

Property of congruent triangle: (SAS) A pair of corresponding sides and the included angle are equal.

Calculation:

AB = BA, BC = AD and ∠ABC = ∠BAD

∴ ΔABC ≅ ​ΔBAD

Formula Used:

By Pythagoras theorem:

⇒ (Hypogenous)² = (Perpendicular)² + (height)²

Calculation:

Option1:

20 cm, 22 cm, 24 cm

⇒ (24)² = (22)² + (20)²

⇒ 576 = 484 + 400

⇒ 576 not equal 884

Not satisfied

Option2

15 cm, 32 cm, 37 cm

 ⇒ (37)² = (15)² + (32)²

⇒ 1369 = 225 + 1024

⇒ 1369 not equal 1249

Not satisfied

Option3

11 cm, 60 cm, 61 cm

⇒ (61)² = (60)² + (11)²

⇒ 3721 = 3600 + 121

⇒ 3721 = 3721

Hence satisfied

Option4

19 cm, 40 cm, 41 cm

⇒ (41)² = (40)² + (19)²  

⇒ 1681 = 1600 + 361

⇒ 1681 not equal 1961

Not satisfied

Given:

Sides of quadrilateral is ratio = 3: 5: 7: 9

Concept:

Sum of all the angles in quadrilateral = 360°

Calculation:

Let the constant be x

⇒ 3x + 5x +7x +9x =360°

⇒ 24x = 360°

⇒ x = 15°

According to question:

Difference between the highest and the lowest angle = 9x – 3x = 6x

∴ 6 × 15° = 90°

Concept:

Sum of any two sides of triangle > third side

Calculation:

⇒ Sum of two side > 6

Only possible combinations are as below:

⇒ 2, 5, 5

⇒ 3, 4, 5    

⇒ 4, 4, 4

3 Different triangles are possible

Given:

Length, breathe and height of cuboidal godown = 56 m, 42 m, 10 m respectively

Dimensions of boxes = 2.8 m × 2.5 m × 70 cm

Formula used:

The volume of the cuboid = Length × breadth × height

Number of boxes = Volume of the godown/Volume of the Boxes

Concept:

1 m = 100 cm

Calculation:

The volume of the godown = 56 m × 42 m × 10 m

The volume of the boxes = 2.8 m × 2.5 m × 70 cm = 2.8 m × 2.5 m × 0.70 m

Now, Number of boxes = (56 × 42 × 10)/(2.8 × 2.5 × 0.70)

⇒ 4800

∴ The total number of boxes that can be stored in the godown = 4800

Given:

Circumference of base of cylinder = 528 cm

Height of cylinder= 2 m = 200 cm

Formula Used:

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

Cicumference of circle = 2π × radius

Calculation:

Circumference of circle = 528 cm

⇒ 2πr = 528

⇒ radius = 84 cm = 0.84 m

Volume of cylinder = π (0.84)² × 2

⇒ 4.4352 m³

∴ The volume of the cylinder is 4.4352 m3

Formula used:

Area of a quadrilateral when one diagonal and the lengths of the perpendiculars from its opposite vertices to this diagonal are given = (1/2 × sum of the lengths of the perpendiculars)

Calculation:

Area of quadrilateral = [1/2 × AC × (DF + BE)]

⇒ 227.2 = [1/2 × AC × (8.8 + 7.2)]

⇒ 454.4 = AC × 16

⇒ AC = 28.4cm

Given:

5(3x + 4) - 8(6x + 7) = 9x – 8

Calculation:

⇒ 15x + 20 – 48x – 56 = 9x – 8

⇒ -36 -33x = 9x – 8

⇒ 42x + 28 = 0

⇒ x = - 2/3

According to question:

(x² - 2x + 1) = {(-2/3)² – 2 (-2/3) +1}

⇒ 4/9 + 4/3 + 1

⇒ 25/9

Given:

a(a + b² + c) + b²(a² + b² + c²) - c(a + b²) and a = 1, b = -3 and c = -2

Calculation:

Putting the value a, b. c in the equation

{1(1 + (-3)² + (-2)} + (-3)² {1 + (-3)² + (-2)²} – (-2) {1 + (-3)²}

⇒ 8 + 126 + 20

⇒ 154

Given:

(x – y)(x2 + xy + y2) + (x + y)(x2 – xy + y2) – (x + y)(x2 – y2)

Concept used:

Dividing the above expression in three parts for easy calculation

Calculation:

First part

(x – y)(x² + xy + y²) = x³ +x² y + xy² – x² y – xy² – y³ = (x³ – y³)

Second part

(x + y)(x² – xy + y²) = x³ – x² y + xy² + yx² – xy² + y³ = (x³ + y³)

Third part

(x + y) (x² – y²) = (x³ – xy² + yx² – y³)

Now, adding all the three parts

(x³ – y³) + (x³ + y³) – (x³ – xy² + yx² – y³)

⇒ x³ + y³ + xy(y - x)

∴ The value of the given expression is x3 + y3 + xy(y - x)

Given Data:

11, 25, 0, 8, 25, 30, 44, 50, 30, 18, 20, 17, 11, 9, 24, 25, 29

Number of terms = 17

Formula:

Mean = (sum of terms) / (number of terms)

Range = difference between the highest and the lowest number in the data.

Median = [(n + 1)/2]th term of the series

 

Calculation:

Median:

Arranging the terms in ascending order:

0, 8, 9, 11, 11, 17, 18, 20, 24, 25, 25, 25, 29, 30, 30, 44, 50

Since the number of terms is odd

 

Median = [(n + 1)/2]th term of the series = [(17 + 1)/2]th term = 9^th term = 24

 

Mode:

Mode in the term which occurs with the highest frequency

 

 

 

Mode = 25

Range of the data =  difference between the highest and lowest number in the data.

the highest number in the data = 50

the lowest number in the data = 0 

range of data = 50 - 0 = 50

 

Median = 24

Mode = 25

Range = 50

Mean of range, median and mode = (50 + 24 +25) / 3 = 33

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

Mathematical Theorem: A statement that has been proven with the help of logical arguments is referred to as a Mathematical Theorem.

• It is a statement that has been proven by logical arguments based on axioms.
• A result that has been proven to be true using operations and facts that were already known.
• It is proven based on pre-established statements that require no proof, such as axioms, which are self-evident.

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).

According to NCERT -

 

Hence, it becomes clear that a mathematical theorem is a statement that has been proven by logical arguments based on axioms.

Euclid around 300 B.C. collected all known work in the field of mathematics and arranged it in his famous treatise called Elements.

• Euclid assumed certain properties, which were not to be proved. These assumptions are actually “obvious universal truths”.
• He divided them into two types: Axioms and Postulates.

Axioms:

• The things which are equal to the same thing are equal to one another.
• If equals are added to the equals, the wholes are equal.
• If equals are subtracted from equals, the remainders are equals.
• Things which coincide with one another are equal to one another.
• The whole is greater than the part.
• Things which are double of the same thing are equal to one another.
• Things which are halves of the same thing are equal to one another

 NOTE:

• Pythagoras Theorem: It states that “ In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides “. The sides of this triangle have been named as Perpendicular, Base, and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
• Euler's theorem is a generalization of Fermat's little theorem dealing with powers of integers modulo positive integers. It arises in applications of elementary number theory.
• René Descartes has been dubbed the “Father of Modern Philosophy“, but he was also one of the key figures in the Scientific Revolution of the 17th Century, and is also considered behind the making of the first modern school of mathematics.

Hence, it becomes clear that Euclid gave the Axiom "Things which are equal to the same thing are equal to one another."

Inter-disciplinary approach not just the combination of two or more disciplines, but one discipline, which is facilitated by one or more disciplines.

Since in question it is asked about assessment strategy which would help in encouragement, hence we have to choose those points which can be categorized under formative assessment because formative assessment helps to improve performance and encourage to achieve goals.

Important Points

Assessment strategy to encourage interdisciplinary in Mathematics:

• Projects: While working on projects students get to know their weaknesses and strengths.
• Field trips: It will help the student assess their abilities and behaviors.

because it will enhance critical thinking, communication skill and it will help to analyze things at all the stages of life.

Additional Information

Also, Anecdotal records and Olympiad are important tools in mathematics and that can be used for assessment but not as an encouragement, as they are used for judging.

• Anecdotal records: A summary of an event in which a child or a group of children has taken part.
• Olympiad: An Examination conducted by various institution based on a different curriculum to compare the performance of the students with their peers.

Hence, we can conclude that projects and field tripscan be used as assessment strategy to encourage interdisciplinary 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.

Proof of a Mathematical Statement consists of a sequence of statements, each statement being justified with a definition or an axiom or a proposition that is previously established by the method of deduction using only the allowed logical rules. Thus, each proof is a chain of deductive arguments each of which has its premises and conclusions.

Direct Proof: It is the proof of a proposition in which we directly start the proof with what is given in the proposition. It is a kind of  Straight forward approach in which chain of arguments leads directly from what is given or assumed, with the help of axioms, definitions, or already proved theorems, to what is to be proved using rules of logic.

Example: In this preposition” The sum of two even integers is always even”. If we take any two even numbers i.e. 2 and 4 and add these, 2 + 4 = 6, we get 6 that is also an even number as it is divisible by 2.

NOTE:

• Proof by Induction: Mathematical induction, is a strategy, of proving a proposition that is deductive in nature.
• Proof by Contradiction: Here, we start with the assumption that the given statement is false. By rules of logic, we arrive at a conclusion contradicting the assumption, and hence it is inferred that the assumption is wrong and hence the given statement is true.
• Proof by using Contrapositive Statement: The contrapositive of a conditional can be formed by interchanging the conclusion and the hypothesis and then negating both of them.

Hence, it becomes clear that the direct proof method can be used to prove 'The sum of two even integers is always even'.

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.

Some Important Skills Promoted by Mathematics: 

• Visualization: On observing a mathematical problem first thing is to visualize in mind what methods or approaches one should take to arrive at a solution quickly and smoothly. It is often used when solving word problems in mathematics.
• Transposition: While solving algebraic equations one often needs to transfer values from one side to another. It is mathematically termed as transporting values from RHS to LHS or vice versa as per requirement.
• Generalization: It is usually referred to as something like the generalization of a concept, i.e. a version of the concept is provided that is less restrictive than the original from which it is derived. It typically becomes more general by dropping or weakening some of the original requirements or some of the original axioms.
• Estimation: Getting an estimated solution while solving a mathematical problem like 72.13 × 5 + 40 =?  While solving the above problem a student will think like 72.13 × 5 (i.e. 70 × 5) = 350 + 40 so the estimated value of the solution will be around 400. It is also referred to as the prediction of future projection observing the current pattern or statistics.

NOTE: Memorization is a passive process and can be done only where you know prior events and then memorize the answers accordingly. But this method cannot be opted in a situation where you don’t know exactly what the question will ask.

Hence, it becomes clear that skills like Visualization, Transposition, Generalization, Estimation are promoted by mathematics at the upper primary stage.

Critical Thinking: The ability to apply reasoning and logic to new or unfamiliar situations, ideas, and opinions. It refers to the process of judging or analysing facts, events, etc. It requires proper analysis, evaluation, inference and explanation.

• Thinking critically involves seeing and observing things in an open-minded way and examining an idea or concept in a way to form as many angles as possible.
• Reasoning tasks promote critical and creative thinking in mathematics.

Open-Ended questions: Open-ended questions are the questions which 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.

For example:- Following questions are open ended:-

• Evaluate 72 × 73 in three different ways and compare the result.
• Formulate any two situation to represent the equation 7x + 3 = 24.
• A students calculated the volume of a right circular cylinder of radius 3.5 cm and height 10 cm as 38.5 cm3. What did she go wrong?

Close Ended Questions: These allow a learner to choose one answer from a limited list of possible answers.

For example:- Calculate the volume of a right circular cylinder of radius 3.5 cm and height 10 cm.

Here calculating the volume of a right circular cylinder will not develop critical thinking among students, as it is just concern with putting up values into already deduced formula.

Ways to Develope Critical Thinking in a Child:

• Begin with a question
• Create a foundation
• Consult the classics
• Use information fluency
• Utilize peer groups
• Try one sentence at a time
• Problem-solving
• Return to role-playing

Hence, it becomes clear that the tasks like calculating the volume of a right circular cylinder will not develop critical thinking among students.

As Per NCF - 2005, the teaching of mathematics should enhance the child’s resources to think and reason, to visualize and handle abstractions, to formulate and solve problems. This broad spectrum of aims can be covered by teaching relevant and important mathematics embedded in the child’s experience. Succeeding in mathematics should be seen as the 'Right of every child'.

Key Points

Vision For School Mathematics:

• Children learn to enjoy mathematics rather than fear it.
• 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 who created history.
• Children learn mathematics is more than formulas and mechanical procedures.
• Children see mathematics as something to talk about, to communicate through, to discuss among themselves, to work together on. and relating it to other subjects is essential.
• The infrastructural challenge involved in making available computer hardware, and software and connectivity to every school should be pursued.
• Children pose and solve meaningful problems.
• Children use abstractions to perceive relationships, to see structures, to reason out things, to argue the truth or falsity of statements.
• Children understand the basic structure of Mathematics: Arithmetic, algebra, geometry, and trigonometry, the basic content areas of school mathematics, all offer a methodology for abstraction, structuration, and generalization.

Hence, contributions of mathematicians from different region and different social groups should be highlighted aligns with the overall objective of achieving 'Mathematics for All' as per NCF-2005.

Mathematics is a branch of science which deals with counting, calculating, and studying numbers, shapes, and structures. Effective Mathematics teaching should aim to promote students’ confidence in mathematics, curiosity, freedom, and belief in doing mathematics.

• 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.

Key Points

Professional Teaching Standard Defines the Role of Mathematics Teachers as:

• A mathematics teacher plays the role of philosopher, friend, and counsellor.
• Teach concepts, procedures, and convictions to the students.
• Promote mathematical problem solving, reasoning skills.
• Create a Learning Environment that promotes the development of a child’s mathematical power and encourages them to think of multiple ways of approaching a problem.
• Foster students’ mathematical dispositions.
• Assess students’ understanding of mathematics.

Hence, characteristics like multiple ways of approaching a problem is encouraged in an effective mathematics classroom.

In teaching Mathematics active involvement of students is very important, and teachers must provide opportunities to the students where they get hands-on practical experience. Mathematical concepts are abstract and helping learners construct these meaningfully has always been a challenge for teachers. 

• A teacher must act as a facilitator and encourage students to figure out ways to solve a particular problem, participate in an activity.
• Teachers play an interactive role in fostering the potential of young seedlings to grow and bloom.
• Teachers' patience and perseverance significantly impact a child's success in the classroom.
• A mathematics teacher plays the role of philosopher, friend, and counsellor.

For example: In calculating the volume of different objects, the teacher should encourage students to figure out ways.

NOTE: Just writing formulas and doing up calculations is a deductive approach that reduces the creative thinking ability of the child. So, it should never be used in the mathematics class.

Hence, encouraging students to figure out ways to calculate the volume of different objects is a desirable practice in the context of teaching and learning of measurement of volume.

Piaget believed that children in the concrete operational stage can incorporate inductive logic. a general principle to predict the outcome of a specific event. creatively, is that they always follow a logical order, and a child can use abstract reasoning to arrive at the solution.

Concrete Operational Stage (7 – 11 years)

• In this stage, a child has begun to develop logic and concrete reasoning skills. Children in the concrete operational stage are able to quantify and organize.
• Their egocentric thinking diminishes and is able to understand the perspective of another person.
• Piaget says co-ordination of different visual and tactile experiences is required for understanding projective space and the progression of geometric ideas follows a definite order.
• Children in the concrete stage are able to understand and relate to relational terms. Relational terms like time, size**, space**, and distance, are more easily understood and conceptualized in this stage.

NOTE:

Piaget’s Four Stages of Cognitive Development:

 

Hence, from the above points, we can infer that the Progression of Geometric ideas follows a historical rather than a logical order is NOT true according to Piaget's view of children's understanding of space.

Calculation:

⇒ -12 × -3 + [20 ÷ (-4) + 24 ÷ 8] – [16 ÷ (-2)] = (- 4) + x

⇒ 36 + [(- 5) + 3] – [-8] = (-4) + x

⇒ 36 + (-2) + 8 = (-4) + x

⇒ x = 46

Given:

30x0867y is divisible by 88

Concept:

Divisibility rule of 11 = Sum of odd terms – sum of even terms = 0 or multiple of 11

Divisibility of 8 = last three digits of number must be divisible of 8

Calculation:

Factors of 88 = 2³ × 11

Divisibility for 8

⇒ 30x0867y = 67y must be divisible by 8

⇒ it is possible when y = 2

Divisibility for 11

⇒ 30x08672 = 3 + x + 8 + 7 = 18+x

⇒ 30x08672 = 0 + 0 + 6 + 2 = 8

⇒ 18+ x – 8 = 10 +x

∴ x = 1

According to question:

⇒ (3x + y) = 3 × 1 + 2 = 5

Concept used:

⇒ (20/3) + (5/2) × (15/4) - (11/2) × (17/4) + (5/3)(7/8 +3/4 × 2/3)

⇒ (20/3) + (5/2) × (15/4) - (11/2) × (17/4) + (5/3)(7/8 + 1/2)

⇒ (20/3) + (5/2) × (15/4) - (11/2) × (17/4) + (5/3)(11/8)

⇒ (20/3) + (75/8) - (187/8) + (55/24)

⇒ (160 + 225 - 561 + 55)/24 

⇒ -121/24

⇒ $-5 \frac{1}{24}$

The main chemicals inside the stomach are pepsin, gastric juice, and hydrochloric acid. These chemicals present in our stomach and are necessary for the digestion of food.

• Pepsin: It is an enzyme found in gastric juice that helps digest and breakdowns protein into smaller pieces called polypeptides.
• Gastric Juice: It is a thin, clear, practically colorless acidic fluid produced by stomach glands and help promote digestion.
• Hydrochloric Acid:
• It creates the acidic conditions necessary for the action of the enzyme pepsin. The function of hydrochloric acid is to kill bacteria and pathogens.
• When hydrochloric acid is secreted in excess, it causes health problems like indigestion. Excessive secretion of stomach acid can also lead to the formation of peptic ulcers.
• Milk of magnesia is also used to treat symptoms caused by too much stomach acid such as heartburn, indigestion.
• Milk of magnesia is a laxative that is thought to work by drawing water into the intestines, an effect that helps to cause movement of the intestines.
• It is also s used for a short time to treat occasional constipation.

Hence, from the above-mentioned points, it becomes clear that X is hydrochloric acid & Y is milk of magnesia.

The correct answer is Baking bread

Key Points

• Bacteria are microscopic, single-celled organisms that thrive in diverse environments. Bacteria was discovered by AV Leeuwenhoek. Bacteria are organisms that exist in their millions, in every environment, both inside and outside other organisms. 
• Bacteria are found almost everywhere on Earth and are vital to the planet's ecosystems.
• Some bacteria are harmful but must serve a useful purpose. They support many forms of life, both plant, and animal, and they are used in industrial and medicinal processes.
• Bacteria can use most organic and some inorganic compounds as food and some can survive extreme conditions.

Additional Information

• Some Uses of Bacteria:
• Bacteria are used in the manufacture of foods and the production of antibiotics, probiotics, drugs, vaccines, etc.
• Bacteria are used in the formation of curd.
• lactic acid bacteria such as Lactobacillus, Lactococcus, and Streptococcus are used in the manufacture of dairy products.
• Bacteria convert milk into useful dairy products, such as buttermilk, yoghurt, and cheese.
• Bacteria are used in the fermentation of Sugarcane juice.
• Coliform bacteria are used to measure the level of contamination of a water body.
• Bacteria are present in the nodules of the legumes where the process of nitrogen fixation is done by the bacteria and the NH3 produced is absorbed by the plant. Rhizobium bacterium is responsible for nitrogen fixation.

Mistake Points

• Baking soda and baking powder help in baking bread.
• The microbe responsible for baking bread is a fungus named Saccharomyces cerevisiae for this reason it is also called baker's yeast.
• Hence, from the above-mentioned points, it becomes clear that bacteria are not used in the baking of bread.

• The forest is a complex ecosystem consisting mainly of trees that buffer the Earth.
• Forest is a dense growth of trees, together with other plants, covering a large area of land.
• Trees are an important component of the environment.
• They clean the air, cool it on hot days, conserve heat at night, and act as excellent sound absorbers.

Key Points

Deforestation: 

• Humans have taken land from the forest to cultivate in order to feed the ever-increasing population and to build houses, industries, etc.
• Cutting down of trees on a large scale for these purposes is known as deforestation.
• Deforestation comes in many forms, including fires, clear-cutting for agriculture, ranching and development, unsustainable logging for timber, and degradation due to climate change.

Desertification:

• It refers to the persistent degradation of dryland ecosystems by climatic variations and human activities.
• Desertification occurs as a result of a long-term failure to balance human demand for ecosystem services.
• Desertification is one of the greatest environmental challenges today and a major barrier to meeting basic human needs in drylands.

Erosion:

• It is the process in which earthen materials are worn away and transported by natural forces.
• Erosion is the process by which soil and rock particles are worn away and moved elsewhere by gravity, or erosion can also perform by wind, water, etc.
• Erosion is the opposite of deposition, the geological process in which earthen materials are deposited, or built up, on a landform.

 Important Points

• Conservation is the care and protection of resources so that they can persist for future generations.
• It includes maintaining the diversity of species, genes, and ecosystems, as well as functions of the environment, such as nutrient cycling.
• The main function of conservation is protecting or restoring the structure, function, and species compilation within the system.
• Conservation is not a process where anything gets erode, degrade, etc. like Deforestation, Desertification, and Erosion.

Hence, from the above-mentioned points, it becomes clear that the Conservation process is different from the other given processes.

• Digestion: It is the complex process of turning the food you eat into nutrients, which the body uses for energy, growth, and cell repair needed to survive. The digestive system uses mechanical and chemical activities to break food down into absorbable substances during its journey through the digestive system. The processes of digestion include six activities: ingestion, propulsion, mechanical or physical digestion, chemical digestion, absorption, and defecation.
• Photosynthesis: It is the process of harnessing energy from sunlight and turns it into chemical energy. During photosynthesis, molecules in leaves capture sunlight and energize electrons, which are then stored in the covalent bonds of carbohydrate molecules. Plants, algae, and a group of bacteria called cyanobacteria are the only organisms capable of performing photosynthesis. Because they use light to manufacture their own food, they are called photoautotrophs.
• Respiration: It is the process in which organisms exchange gases between their body cells and the environment. Respiration is the process of chemical breakdown i.e. oxidation of food materials to provide energy for life. Respiration is the process of gas exchange between the air and an organism's cells. Three types of respiration include internal, external, and cellular respiration.

NOTE: 

Crystallisation: Crystal is a solid particle in which the constituent molecules, atoms, or ions are arranged in some fixed and rigid, repeating three-dimensional pattern or lattice. Crystallisation is a process of atoms arranging into a well defined, rigid crystal lattice in order to minimize their energetic state.  is a process whereby solid crystals are formed from another phase, typically a liquid solution or melt.

Hence, from the above-mentioned points, it becomes clear that crystallisation is not a chemical change.

Sediment is material eroded off other particles that are then worn down into pieces ranging in size from microscopic particles to pebbles to boulders. Soil is a complex mixture of living organisms, organic matter, minerals, water, and air. Soil is formed by different particles such as gravel, rock, sand, silt, clay, etc.

• Clay is a very fine-grained material composed mainly of flakes from a variety of mineral deposits. Clay particles are microscopic in size, they are less than 1/256 mm, or 0.00015 inches, in diameter.
• Silt is a sediment material with an intermediate size between sand and clay. Carried by water during the flood it forms a fertile deposit on valleys floor. The particle size of silt ranges from 0.002 and 0.06 mm in diameter.
• Sand fragments or mineral particles that range in diameter from about 1/16 to 2 mm (from 0.002 to 0.08 inches).
• Gravel chipped or rounded fragments that typically range in diameter from about 3 to 75 mm (0.125 to 3 inches).
• Rock: When rocks (igneous, sedimentary, or metamorphic) are at or near the surface of the earth they are exposed to the processes of weathering.
• Ascending order as per the size of all the above particles is Clay, Silt, Sand, Gravel, Rock.
• Weathering of rocks forms pieces of rock-like Clay, Silt, Sand, and Gravel. These types of rock are of various sizes and shapes.
• In mechanical weathering rocks are broken up into smaller pieces by frost-wedging, root-wedging, etc.

Hence, from the above-mentioned points, it becomes clear that ascending order as per the size of particles is Clay, Silt, Sand, Gravel, Rock.

Concept:

• Respiration is a metabolic process common to all living things. It refers to one's breathing and the movement of air into and out of the lungs. The respiratory system provides oxygen to body tissues for cellular respiration, removes the waste product carbon dioxide, and helps maintain acid-base balance.

Different animals use different organs for their respiration. Some examples are:-

Explanation:

Respiratory System of Fish:

• Most fishes absorbed dissolved oxygen in water by means of the gills.
• Water taken in continuously through the mouth passes backwards between the gill bars and over the gill filaments, where the exchange of gases takes place.
• Each filament contains lamellae, which are discs supplied with capillaries.
• In fishes, gills are tissues made up of feathery structures called gill filaments that provide a large surface area for gas exchange.

Hence, from the above-mentioned points, it becomes clear that the function of gills in the fish is to absorb dissolved oxygen from water.

Electric Circuit: An electric circuit is a closed-loop through which electric charge flows as a result of a driving voltage. It may also be an open circuit where the electron flow is cut short because the path is broken.

• An open circuit does not allow electrical current to flow. A simple circuit has conductors, a switch, a load, and a power source.
• An electric circuit includes a device that gives energy to the charged particles constituting the current, such as a battery or a generator, devices that use current, such as lamps, electric motors, and the connecting wires or transmission lines.

Electrical Conductors: Those materials that can conduct electricity as its electrons can move freely from one atom to another. For example Seawater, iron blade, gold, silver, copper, aluminum, and graphite, etc. All these are good conductors of electricity.

• Through the conductor, electric current can flow easily or electrons can move freely from one atom to another. So, a blade can be used to complete an electric circuit if one runs out of connecting wire.
• Bad conductors of electricity- plastic, rubber, glass, air, wooden stick, paper strip, charcoal, and diamond.
• Electric current can not flow through bad conductors of electricity.

Hence, from the above-mentioned points, it becomes clear that a blade can be used to complete an electric circuit if one runs out of connecting wire.

Plane mirrors are simply flat mirrors without curves. These are polished surfaces coated with mercury such that they reflect most of the light falling on them. 

• The image formed by a plane mirror is always virtual and erect.
• The image formed is ‘virtual’ because it is a copy of an object formed at the location from which the light rays appear to come.
• The distance of the image ‘behind’ the mirror is the same as the distance of the object in front of the mirror.
• The image and object are the equal distance from a plane mirror.
• The image size formed by the Plane mirror is the same as the object size.
• The distance of the image ‘behind’ the mirror is the same as the distance of the object in front of the mirror.

 

Given that, the distance between Manjula and the mirror is 5 m. Manjula moves 1 m towards the mirror. Now the distance between Manjula and the mirror is 4 m.

In the below image, point 'O' denotes Manjula and point 'I' denotes Manjula's image. 

As we know, the distance of the image ‘behind’ the mirror is the same as the distance of the object in front of the mirror. Therefore, the distance between herself and her image now is 4 m + 4 m = 8 m.

Hence, from the above-mentioned points, it becomes clear that The distance between Manjula and her image now is 8 m.

Frequency (f) is the number of oscillations per second. It is measured in cycles per second or Hertz (Hz). The time for one oscillation is called the Time Period (T) it is measured in seconds.  The time to complete one oscillation remains constant. 

The relationship between frequency and time period is $T=\frac{1}{f}$

Given that,

A pendulum oscillates 30 times in 3 seconds.

∴ the pendulum oscillates 10 times in 1 second. There is 10 number of oscillations per second. The frequency of the pendulum is 10 Hz.

As we know  $T=\frac{1}{f}$. Therefore, the time period is $\frac{1}{10}$= 0.1 seconds.

Hence, from the above-mentioned points, it becomes clear that pendulum's time period is 0.1 s and frequency is 10 Hz.

Bearings: 

• Bearings are mechanical assemblies that consist of rolling elements and usually inner and outer races which are used for rotating or linear shaft applications. There are several different types of bearings, including ball and roller bearings.
• A ball bearing is a type of rolling-element bearing that uses balls to maintain the separation between the bearing races.
• The purpose of a ball bearing is to reduce rotational friction and support radial and axial loads.

Friction:  

• It is a kind of resisting force that acts between two contact bodies to avoid relative motion between them.
• It is formed due to the close interaction of charged particles at the surface of the bodies due to electromagnetic forces.
• Friction between two surfaces in contact can never be eliminated on earth.
• Frictional forces are of three kinds:-
• Static friction (fs): When two bodies do not slip on each other, the force of friction is static friction. It can change its value until its max. Fmax ≥ fs
• Kinetic friction (fk): When two bodies slip over each other the force of friction is called kinetic friction.
• Rolling friction (fr): Friction caused because of the rolling surface is termed as rolling friction.
• Rolling friction is less than sliding friction.

Object Moving in a Fluid: When an object moves through a fluid, it pushes the molecules of the fluid out of the way. At the same time, the molecules of the fluid exert an equal and opposite force on the object. This force resisting motion through a fluid is a type of friction that is often called drag. The friction force on an object moving through a fluid depends upon its shape.

Hence, from the above-mentioned points, it becomes clear that Ball bearings are used to 'reduce' friction between parts of a machine.

Copper is an element with the symbol Cu and atomic number 29. Copper is a major industrial metal because of its high ductility, malleability, thermal and electrical conductivity and resistance to corrosion. Copper sulphate is used as an agricultural poison, and water purifier.

Zinc metal is used for dry batteries, roof cladding, and to protect iron structures from corrosion by attaching zinc as sacrificial anodes. Zinc is used in alloys with copper to create a harder metal known as brass.

• If Zinc metal is dipped in the Copper sulphate solution the reaction will take place because zinc is more reactive than copper and it will displace the copper from copper sulphate solution to form Copper and Zinc sulphate.

Zn + CuSO₄ →  Cu + ZnSO₄

On the other hand, Cu + ZnSO4 →  No Reaction 

• Another name for Copper sulphate is Blue Vitriol.
• Water is present in the form of crystals in Copper Sulphate.

Hence, from the above-mentioned points, it becomes clear that Zinc can replace copper with copper sulphate solution.

Additional Information

Thermometer:

• It is a device that is used to measure the temperature. A thermometer is calibrated by using two objects of known temperatures.
• The typical process involves using the freezing point and the boiling point.
• Thermometer works on the zeroth law of thermodynamics.
• Common types of thermometers are Room thermometers, Clinical thermometers, Mercury thermometers, thermocouple thermometers, laboratory thermometers.

Clinical Thermometer: It is a medical thermometer that is used to measure body temperature. They are sensitive and accurate, having a narrow place where the level of mercury rises very fast. It is used to measure human body temperature in the range of 35°C to 42°C.

Room Thermometer: A thermometer to monitor room temperature. Room thermometers have a range from 20°C to 50°C.

Laboratory Thermometer: It is used to measure temperatures or temperature changes with a high degree of precision. They are generally a liquid in a glass device, a bimetallic strip, an electronic thermistor thermometer, or an infrared device. It ranges from -10˚C to 110˚C.

Hence, from the above-mentioned points, it becomes clear that the range of a Laboratory Thermometer is greater than that of a Clinical Thermometer.

Calorific Value or Energy Value is defined as the amount of energy liberated by the complete combustion of a unit quantity of fuel. It is expressed in Joule per kg (J/kg).

• The calorific value is the measurement of heat or energy produced and is measured either as gross calorific value or net calorific value.
• The efficiency of fuel mainly depends on the calorific value.
• If the value is high, its efficiency will also be high. If the value is low, its efficiency would also decrease. The calorific value is directly proportional to its efficiency.

Calorific Value of Different Fuels:-

Hence, from the above-mentioned points, it becomes clear that the calorific value of LPG is more than that of Biogas.

Given: Speed of bus is 50 km/h for 12 minutes or $\frac{12}{60}$ hour. 

The speed of the bus is 40 km/h for 18 minutes or $\frac{18}{60}$ hour. 

Concept: Distance = Speed × Time

Calculation: Let Distances D₁ and D₂ for different speeds.

∴ D₁ = 50 × $\frac{12}{60}$ = 10 km

Similarly, D₂ = 40 × $\frac{18}{60}$ = 12 km

Total distance covered by the bus is D₁ + D₂ = 10 + 12 = 22 km

Hence, from the above calculation, it becomes clear that total distance covered by the bus during this time is 22 km.

Circular Motion: The motion in which a particle moves on a circular path is called circular motion.

Periodic Motion**:**

• The motion which repeats in an equal interval of time is called periodic motion.
• For example, Earth revolving around the sun, swing in motion, bouncing ball, the motion of the Earth around its axis, etc.
• For periodic motion, motion does not have to be circular.

Oscillatory Motion**:** The to and fro motion of a body about its mean position is called oscillatory motion. For example, Simple pendulum, the motion of plucked string of a sitar, etc.

Rectilinear Motion: It is a linear motion in which the direction of the velocity remains constant and the path is a straight line. Rectilinear motion is a motion in a straight line. For example, car moving on a straight road, motion of light, elevator movement, etc.

Hence, from the above-mentioned points, it becomes clear that for periodic motion, motion does not have to be circular.

EXPLANATION:

Plane mirrors are simply flat mirrors without curves. These are polished surfaces coated with mercury such that they reflect most of the light falling on them. 

• The image formed by a plane mirror is always virtual and erect.
• The image formed is ‘virtual’ because it is a copy of an object formed at the location from which the light rays appear to come.
• The distance of the image ‘behind’ the mirror is the same as the distance of the object in front of the mirror.
• The image and object are the equal distance from a plane mirror.
• Image is laterally Inverted means is inverted from left to right, like an image seen in a mirror. The right side of the object appears as its left side, and vice versa.

The image size formed by the plane mirror is the same as the object size. 

• The distance of the image ‘behind’ the mirror is the same as the distance of the object in front of the mirror.

Hence, from the above-mentioned points, it becomes clear that the image formation in the plane mirror is not real.

The nature of science considers the special characteristics, values, and assumptions that scientific knowledge is based on and how scientific knowledge is developed.

Key Points

The Basic Understandings about the Nature of Science:

• Scientific investigations use a variety of methods.
• Scientific knowledge is based on empirical evidence.
• Science is tentative i.e. scientific knowledge is open to revision in light of new evidence.
• Science promotes scepticism, scepticism is the act of suspending judgment (the opposite of jumping to conclusions) when evaluating an explanation or claims.
• Scientific models, laws, mechanisms, and theories and explain natural phenomena.
• Scientific knowledge assumes order and consistency in natural systems.
• Science is a human endeavor and a way of knowing.
• Science is interdisciplinary, i.e., it addresses questions about the natural and material world.

Hint

• Science is not about facts instead it focuses on developing the understanding of the concepts and to explore the reasoning behind a fact.

Hence, from the above-mentioned points, it can be inferred that science is not equivalent to a set of facts.

According to NCF 2005, science is a dynamic, expanding body of knowledge, covering ever-new domains of experience. In a progressive forward-looking society, science can play a truly liberating role, helping people escape from the vicious cycle of poverty, ignorance, and superstition. These different imperatives have to be kept in mind in shaping science education.

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

Basic Criteria of the Validity of a Science Curriculum: 

1. 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.
2. Content Validity requires that the curriculum must convey significant and correct scientific information. Simplification of content, which is necessary for adapting the curriculum to the cognitive level of the learner, must not be so trivialized as to convey something basically flawed and/or meaningless.
3. Process Validity requires that the curriculum should engage the learner in acquiring the methods and processes that lead to the 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.
4. Historical Validity requires that the science curriculum be informed by a historical perspective, enabling the learner to appreciate how the concepts of science evolve over time. It also helps the learner to view science as a social enterprise and to understand how social factors influence the development of science.
5. 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 equipping him/her with the requisite knowledge and skills to enter the world of work.
6. Ethical Validity requires that the curriculum promotes the values of honesty, objectivity, cooperation, and freedom from fear and prejudice, and inculcate in the learner a concern for life and preservation of the environment.

Therefore, it becomes clear that according to NCF 2005, good science education should be true to the child.

According to NCF 2005, science is a dynamic, expanding body of knowledge, covering ever-new domains of experience. In a progressive forward-looking society, science can play a truly liberating role, helping people escape from the vicious cycle of poverty, ignorance, and superstition.

• Science education cultivates students' curiosity about the world and enhances scientific thinking.
• This will prepare students to participate in public discourse in science-related issues and enable them to become life-long learners in science and technology.
• The advances in science and technology have transformed traditional fields of work such as agriculture and industry and led to the emergence of wholly new fields of work.
• People today are faced with an increasingly fast-changing world where the most important skills are flexibility, innovation, and creativity. These different imperatives have to be kept in mind in shaping science education.
• These different imperatives have to be kept in mind in shaping science education. Good science education is true to the child, true to life, and true to science.
• Process Validity requires that the curriculum should engage the learner in acquiring the methods and processes that lead to the 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 and satisfied by activities and experiments.

Therefore, from the above-mentioned points, it becomes clear that process validities of a good science education curriculum are satisfied by activity and experiment.

Co-curricular activities organized outside the classroom allow students to develop their special talents and creatively express themselves through various forms. For example, participation in science clubs, field trips, involvement in science dramas, social welfare activities, etc.

Field trips for students are like an educational experience that they never could have had in the classroom. Field trips are considered fun, but the children learn as well, whether they realize it or not because they require significant planning and coordination for teachers and administrators to make a great combination of learning and fun together.

• Interactive Learning: Field trips help students interact with what they are learning. The experience goes beyond reading about a concept; students can see it, manipulate it, or participate in it physically.
• Field trip encourages interaction and enhances observation skills among children.
• Entertainment: Field trips provide entertainment for students. They often serve as a powerful motivator for students, stirring up excitement as the trip nears. Breaking away from the routine provides kids with a refresher that might make them more focused back in the classroom.
• Extension of Classroom Study: Field trips take the book learning from the classroom and extend it to life. Students often question the importance of topics they study in class. Field trips, particularly for older students, can answer the question of how learning can be applied in life.
• Social Interaction: Field trips place children in a different social environment.  Leaving the classroom for a field trip places the kids in a different social environment. They encounter a new set of adults and possibly other children during the course of the average field trip. These interactions teach them how to behave in different settings.
• New Experiences: Many children don't get to experience the typical field trip locations with their families. A school trip allows students to experience new venues and promotes process skills through concrete experiences. Field trips may help a child experience a zoo, even if their families have never taken them.

Hence, option D is the least appropriate.

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 in science-related issues and enable them to become life-long learners in science and technology.

Key Points

Objectives 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 encourage them to learn about nature to develop the love for nature and to try to conserve natural resources and prevent pollution.
• To develop the scientific attitude and to use it for the 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.
• Students should be able to understand how science and technology are interdependent and assist each other in the development of knowledge and technological applications.

Hint

• Science never focuses on mugging up exact definitions of the concepts, rather it always focuses on deep understanding and interlinking of the concepts.

Therefore, just emphasizing on the textbook definitions of concepts should not be an objective of science education at the upper primary level.

Critical Thinking is the ability to apply reasoning and logic to new or unfamiliar situations, ideas, and opinions. It refers to the process of judging or analyzing facts, events, etc. It requires proper analysis, evaluation, inference, and explanation.

• Critically thinking involves seeing and observing things in an open-minded way and examining an idea or concept in a way to form as many angles as possible.
• Open-ended questions can't be answered in yes or no, rather requires a detailed answer with proper explanation. These are useful tools for primary teachers to help students to discover new ideas and develop critical thinking.
• For Example: Asking children to discuss among themselves in groups followed by sharing in a large group. This activity can enhance critical thinking among children.

Key Points

Ways to Enhance Critical Thinking among Children:

• Using the scientific method approach to thinking and eliminating emotion.
• Asking children to discuss among themselves in groups followed by sharing in a large group.
• Develop your child’s critical thinking skills by challenging their minds with research.
• Encourage children to ask questions.
• Motivate the child to solve problems and listen to the solution.
• Give them problems and responsibilities that make them think.
• Playing games like puzzles, riddles, and board games helps children to navigate their experimentation and learning.

Hence, from the above-mentioned points, it becomes clear that asking children to discuss among themselves in groups can enhance critical thinking among children.

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

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, A teacher begins the class by 'demonstrating' the chemical test of starch in a given sample of food. Here the cognitive process associated with the 'demonstrating' is Applying. Because the teacher begins the class by demonstrating the chemical test, here he is able to use the knowledge or understanding of facts and principles.

Hence, from the above-mentioned points, it becomes clear that the cognitive process associated with the 'demonstrating' in the given statement is Applying.

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.
• Activities for learning are planned jointly by teachers and students. Activities for learning are planned jointly by teachers and students.

Key Points

Methods to Provide Active Learning:

• The more children are involved, the greater would be the possibility of their concentration.
• Participation in Science Clubs And Associations
• Approach should be centered on learner needs.
• Involve in social services, literary and cultural activities.
• Developing a science corner for children.
• Organization of field trip.

Hence, from the above-mentioned points, it becomes clear that listening to a lecture in class does not promote active learning among children.

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. 

According to NCF-2005: 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.

Key Points

To Find the Learning Gaps of Learners in Science: Learning gaps in learner can be found by using the followings-

• Concept Mapping: It refers to the visual representation of knowledge which helps the learners to connect concepts and ideas for better understanding. Concept mapping can be used for finding the learning gaps of learners. It can be in the form of flowcharts, tables, Venn diagrams, etc.
• Anecdotal Record: These are the short narrative summary of one or many events in which a child or a group of children has taken part that is written after the event has taken place. Anecdotal Records can be used for maintaining and finding the learning gaps of learners.
• Portfolio: A portfolio is a collection of documents and writing that you assemble in order to demonstrate that you have the appropriate prior and experiential learning to earn a course level credit. Portfolio used for finding the learning gaps of learners in subjects.

NOTE: An Achievement test is used to measure the relative accomplishment of pupils in specified areas of learning. The term-end achievement test is conducted at the end of the session. It is not useful for finding the learning gaps of learners in subjects.

Hence, from the above-mentioned points, it becomes clear that Concept Mapping, Anecdotal Records and Portfolios are used for finding the learning gaps of learners in science.

Observation is the action or process of carefully watching someone or something. It is the act of noticing something or judgment from something seen or experienced. Observation would seem to be an obvious method of carrying out research in psychology. 

Various Technique of Observation: 

• Assessment of students to know about their performance.
• Naturalistic observation involves observing involves studying the spontaneous behavior of participants in natural surroundings.
• In Participant observation, the observer becomes part of the group they are studying.
• Anecdotal Records: They are the short narrative summary of one or many events in which a child or a group of children has taken part that is written after the event has taken place. Anecdotal records can be a tool that is based on the technique of observation.

Key Points

Features and Applications of Anecdotal Records:

• Primarily involves observation of the child while participating in an event or many events and recording the observations.
• The record is centered on the learner and not the subject matter.
• Provides an understanding of the child’s uninhibited behavioral responses to various diverse situations.
• Aid the teacher to understand the child’s behavioral and personality patterns and how they change according to the situation.
• This knowledge helps the teacher to plan the teaching curriculum accordingly and allocate tasks depending upon the child’s behavior and skills.

Hence, from the above-mentioned points, it becomes clear that an Anecdotal record is a tool based on the technique of observation.

Key Points

• The wool comes from sheep, goat, yak, and some other animals. These wool-yielding animals bear hair on their body. Wool is the hair that covers the skin of some animals, isolates it from the cold and heat, maintaining constant its body temperature. There are many varieties of ovine breeds that produce wool with fibers different for their fineness, length, shininess, and resistance.
• Pashmina Fiber is blended with superfine merino wool. Pashmina, popularly known as ‘Cashmere’, is well known for its fineness, warmth, softness, desirable aesthetic value, elegance, and timelessness in fashion.
• Wool is also obtained from goat hair, the under the fur of Kashmiri goat is soft. It is woven into fine shawls called Pashmina shawls. That means Pashmina shawl is made from the hair of goats.
• Wool is also employed by Angora rabbit and merino sheep.
• Yak wool is common in Tibet and Ladakh.
• Mohair is obtained from angora goats, found in hilly regions such as Jammu and Kashmir.
• Camel wool is a type of fabric derived from the coats of camels. They can be found in Turkey, China and Siberia.
• The camel hair can be used for carpet backing as well as creating wool rugs, wool blankets, and knitting wool. Camel wool is used to make carpets.
• Camel hair in textiles is used pure or blended with wool only.

Hence, from the above-mentioned points, it becomes clear that Pashmina shawl is made from the hair of goats and Camel wool is used to make carpets.

Animal, any of a group of multicellular eukaryotic organisms i.e. distinct from bacteria, their deoxyribonucleic acid, or DNA, is contained in a membrane-bound nucleus. Animals differ from members of the two other kingdoms of multicellular eukaryotes, the plants, and the fungi, in fundamental variations in morphology and physiology. 

Snakes are an order of reptiles distinguished by their long, limbless body and elongated tails. They live in almost every ecological niche, except the polar regions, and are particularly plentiful in tropical regions and deserts.

Features of Snake:

• Snakes are carnivores. This means that they only eat meat. Snakes are often seen as pests, but they actually can help keep pests at bay by eating rodents.
• Their body curves into many loops for moving forward.
• Most snakes simply swallow their prey whole. Large snakes, such as the python, will strangle their prey to death and then swallow it whole.
• Snakes have many muscles. Snakes lack a diaphragm muscle to push their lungs.
• Their rib muscles which expand the chest during each breath also propel the body forward when the snake moves.
• Their skeleton consists of long flexible backbones and dozens of pairs of ribs. Their skins is covered by scales and is generally dry to the touch.
• Snakes don't smell with their noses like humans. They have a forked or split tongue that they use to smell and taste chemical compositions in the air.
• The skins from cobras, pythons, lizards, water snakes, and other snakes have beautiful texture and patterns.

Hence, from the above-mentioned points, it becomes clear that from all the given features, the identified animal is Snake.

Arteries are blood vessels that carry blood away from the heart. The arteries are a part of the circulatory system and are responsible for delivering oxygen and nutrients to all cells.

• All arteries do not carry oxygen from the heart to the tissues and organs.
• Most arteries carry oxygenated blood, but Pulmonary artery is the only artery that carries deoxygenated blood. It carries deoxygenated blood from the right ventricle to the lungs.
• Arteries have thick and elastic walls.
• The Pulmonary Artery carries blood from the right side of the heart to the lungs.
• Arteries typically have a thicker tunica media than veins, containing more smooth muscle cells and elastic tissue.
• Aorta carries oxygen-rich blood from the left side of the heart to the body and coronary arteries carry oxygen-rich blood from the aorta to the heart muscle. The aorta is the largest artery in the body.
• Veins carry deoxygenated blood from the body to the heart. The pulmonary vein carries oxygenated blood from the lungs to the heart.

Hence, from the above-mentioned points, it becomes clear that all arteries do not carry oxygen-rich blood.