Place of Mathematics in Curriculum MCQ Quiz - Objective Question with Answer for Place of Mathematics in Curriculum - Download Free PDF

Mathematical thinking goes beyond just following procedures; it involves reasoning, understanding concepts deeply, and being flexible in approaching problems. It requires explaining why solutions work and exploring different strategies rather than just memorizing steps.

 Key Points

• Statement (a) reflects mathematical thinking because reasoning about why a solution is valid is crucial to understanding mathematics deeply.
• Statement (c) also aligns with mathematical thinking since exploring multiple methods encourages creativity and a better grasp of concepts.
• Statement (b), which focuses on memorizing steps for routine problems, is more about rote learning than genuine mathematical thinking.

Hence, the correct answer is 'a and c'.

The topical approach in curriculum design is a method of structuring the content by dividing it into specific, manageable topics. This approach ensures that each topic is covered in depth, allowing students to master individual concepts before moving on to the next one. 

Key Points

•  In the context of the given question, the topical approach involves organizing content topic-wise and dealing with one topic thoroughly.
• This ensures that the teacher and students focus on mastering one concept at a time, which promotes better understanding and retention.
• By dedicating time to a specific topic, students can grasp the nuances of each idea without feeling overwhelmed by too many subjects at once.

Hint

• Dividing the syllabus into broader themes or teaching through stories, describe different approaches but not the topical approach.  While thematic approaches organize content around larger ideas, they don’t focus on in-depth exploration of individual topics.
• Teaching concepts through stories can be an engaging method, but it’s not specifically related to the topical structure of a curriculum.
• Repeating the same concept every year is more aligned with spiral curricula, where concepts are revisited at increasing levels of complexity over time, rather than focusing on one topic in detail.

Hence, the correct answer is organizing content topic-wise and dealing with one topic thoroughly.

The concept of a concentric approach in curriculum design refers to the way content is structured and delivered, particularly in mathematics education.

Key Points

•  In this context, the concentric approach in mathematics involves revisiting concepts with increasing depth.
• As learners progress through their studies, they are exposed to the same ideas multiple times, but each time with a more advanced perspective.
• This helps in reinforcing foundational knowledge while also promoting a deeper understanding of complex concepts.

Hint

• Teaching abstract concepts first is often not ideal in mathematics, as learners need a strong foundation of concrete ideas before progressing to abstract thinking.
• Teaching from known to unknown is more aligned with general teaching strategies, but it doesn't emphasize revisiting and deepening understanding like the concentric approach.
• Focusing only on real-life examples can be useful in some cases, but it doesn't capture the essence of revisiting and expanding on concepts in mathematics.

Hence, the correct answer is revisiting concepts with increasing depth.

The National Curriculum Framework (NCF), 2005, emphasizes a holistic and inclusive approach to education. It recognizes that students have diverse learning styles and that effective teaching should cater to these differences. These learning styles typically include auditory (learning through listening), visual (learning through seeing), and kinesthetic (learning through hands-on activities). 

Key Points

•  The best example of this approach is using a combination of auditory, visual, and kinesthetic methods to cater to different learning styles.
• This method ensures that all students, regardless of their preferred learning style, have opportunities to engage with the material in a meaningful way. For example, a lesson might involve explaining a concept (auditory), showing a diagram (visual), and allowing students to engage in a hands-on activity (kinesthetic).
• This approach supports a broader range of learners and fosters a deeper understanding of the subject.

 Hint

• Providing only written assignments and tests or focusing solely on visual learning strategies would limit the diversity of engagement with the material and fail to meet the needs of all students.
• Giving priority to one learning style over others could exclude students who may not resonate with that style, hindering their learning process.

Hence, the correct approach is using a combination of auditory, visual, and kinesthetic methods to cater to different learning styles.

Mathematics plays a significant role in the curriculum as it encourages students to develop problem-solving and logical thinking skills. By engaging with mathematical concepts, students learn how to approach and solve problems in a structured and rational manner, which is essential for their intellectual growth.

Key Points

• The assertion is valid, as the objective of mathematics in the curriculum is indeed to foster problem-solving and logical thinking. 
• Reason (R) highlights that mathematics nurtures critical thinking and the ability to analyze complex problems. This is true because mathematics requires students to break down complex problems into simpler components, analyze patterns, and apply logical reasoning to find solutions.
• Reason (R) supports this by emphasizing that mathematics develops critical thinking and analytical skills, but it does not directly explain why mathematics fosters problem-solving and logical thinking. Instead, it elaborates on the cognitive benefits of learning mathematics.

Hence, both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

Teaching Aids: These are sensory devices, they provide a sensory experience to the learner, and i.e. the learners can see and hear simultaneously using their senses. These are instructional devices that are used to communicate messages more effectively through sound and visuals.

Important Points

Cuisenaire rods are the teaching aids for teaching and learning mathematics. A Cuisenaire rod is made up of squares equal to the number the rod represents, and the rods help us visualize math operations.

This aid is providing hands-on experience to students which helps to explore mathematics and learn mathematical concepts:

• Arithmetical operations
• Working with fractions
• Finding divisors

Additional Information

Other Teaching aids for teaching mathematics

• Number Charts are a really useful tool when teaching a young child counting of numbers in learning mathematics.
• Abacus is the best teaching aid that makes math make sense. The kids who use the abacus concretely understand numbers, they can see what they are doing in math and why they got the answer they did. It is hard for young kids to understand abstract concepts.
• Geoboard is an electronic teaching aid for teaching geometry basics, including shapes, perimeter, area, and much more.

Hence, we can conclude that Cuisenaire rods are most suitable for teaching children the concept of fractions.

Multiplication represents the repeated addition of a number with itself. For example: 3 + 3 is represented as 3 × 2. 

Important Points

Addition: When two collections of similar objects are put together, the total of them is called addition.

Properties of addition in natural and whole numbers:

• Closure property: The sum of two natural/whole numbers is also a natural/ whole number.
• Commutative Property: p + q = q + p where p and q are any two natural/ whole numbers.
• Associative property: (p + q) + r = p + (q + r) = p + q + r . This property provides the process for adding 3 (or more) natural/whole numbers.
• Additive Identity in Whole Numbers: In the set of whole numbers, 4 + 0 = 0 + 4 = 4. Similarly, p + 0 = 0 + p = p (where p is any whole number). Hence, 0 is called the additive identity of the whole numbers.

Key Points

Properties of Multiplication:

• Commutative Property: a × b = b × a. Example, 9 × 4 = 4 × 9 = 36
• Closure property: If p and q are natural or whole numbers then p × q is also a natural or whole number. Like in the above example, 4 and 9 are natural numbers, so is their multiple (36).
• Associative property: (p × q) × r = p × (q × r) (where p, q, and r are any three natural/whole numbers)
• Identity of multiplication: The number ‘1’ has the following special property in respect of multiplication. p × 1= 1 × p = p (where p is a natural number)
• Distributive property of multiplication over addition: p × (q + r) = (p × q) + (p × r).

Note: There is no distributive property for addition. One should not be confused (p + q) + r = p + (q + r) as distributive, the given property is associative property for addition.

Mathematics plays a vital role in the education system as it has universal applicability. Mathematical knowledge is used in almost every aspect of our everyday life such as money exchange, etc.

• The mathematical understanding will develop best when the learners learn by doing only.
• The teacher should try to engage every child in the classroom activities, quizzes, and experiments.

Key Points

Teaching 'Numbers' at the primary level:

• At the primary level, the teacher expects the children to develop a positive attitude and a liking towards mathematics.
• The concept of "numbers" is taught in the primary classes in which they learn the sub-topics of counting, numerals, face value, place value, etc.
• It is not necessary that writing of numbers is taught in a sequence i.e., children might learn to write 9 first and then they learn to write 2.
• Also, writing numbers in numerals i.e., 9 as IX is not encouraged at the primary level.
• Numerals should be introduced only after the learners have experience with counting.
• Intuitive understanding of numbers should be encouraged at the primary level i.e., children will be able to identify the number of objects before counting them. 
• Order irrelevance of numbers should be encouraged at the primary level.
• For example, children should first practice writing numbers and then move to number names.

Hence, we can conclude that statements A and D are true regarding teaching 'Numbers' at the primary level.

According to NCF 2005, the main goal of mathematics education at the primary level is the development of children's ability in mathematization.

It means that children should learn to think about any situation using the language of mathematics. They can use the tools and techniques of mathematics in real life.

Important Points

• The National Curriculum Framework 2005 is among the four National Curriculum Frameworks approved by the National Council of Educational Research and Training NCERT in India.
• At the Primary level, children learn from concrete objects and visualization processes.
• In the primary school mathematics curriculum, the following topics have been included;
  • Tessellation
  • Symmetry
  • Patterns
• Mathematics takes place in a situation where mathematics is a part of children's life experience.
• Mathematics subject to be learned in order to perform daily life activities in a better way.
• Constructing the Mathematics curriculum we need to consider those topics Mathematics or themes, which would help children to succeed in their everyday life.

Hence, it could be concluded that NCF 2005 doesn't include the topic "ratio" at the primary level.

National Curriculum Framework (NCF), 2005 provides a guideline with which teachers and schools can choose and plan experiences that they think children should have.

• It seeks to reform the curriculum and to bring learning experiences in and outside the classroom.
• According to the NCF 2005, “Developing children’s abilities for mathematization is the main goal of mathematics education.”

Key Points

There are two kinds of aims in mathematics for school education such as broader and narrower aims.

Narrower aim-

• to develop numeracy related skills
• to develop ‘useful’ capabilities particularly those relating to numeracy- numbers, number operations, measurements, decimals and percentages

Broader aim-

• Problem- solving
• Use of heuristics
• Estimation and approximation
• Optimisation
• Use of patterns
• Visualization
• Representation
• Reasoning and proof
• Making connections
• Mathematical communication

Hence, we conclude that to make students proficient in handling numbers and number operations is one of the narrow aims of NCF.

Mapping is the creative process of organizing content and can be used in planning lessons, learning, and developing mathematical literacy and spatial thinking. With the help of mapping concepts at the primary level, we can also promote reasoning thinking and solving power in children. Key Points

• Map interpretation is an aspect of mapping because a map should be properly interpreted before it is used as a tool in the teaching-learning process.
• Unscaled drawing of maps is also a part of the primary curriculum because children first get familiarized with mapping without scale and gradually they learn about scale and axis in the further stages.
• Using symbols makes the method of problem-solving easy where the usage of sentences is minimized and symbols are used in place of them. Every symbol indicates a particular action, so symbols should be included in such a way that whenever they come across the action should be applied.

Hence, A, B, and C  are the correct options. Additional Information

Scaled drawing is not considered an aspect of mapping in the mathematics curriculum because the scale is something the children need time to understand. Children first get familiarized with the mapping without scale and they get to know about the scale in the upper primary stages.

NCF-2005 is the National Curriculum Framework published in 2005, by the National Council of Education, Research, and Training (NCERT). 

• It is the official document which states that the curriculum must be student-centric and beyond the textbooks.
• It also emphasized making classroom activities more flexible and related to daily life.  

Key Points

According to NCF-2005

• Developing the basic abilities of a child to do mathematics is the main goal of mathematics education.
• The narrow aim of school mathematics is to develop 'useful' capabilities, particularly those relating to numeracy–numbers, number operations, measurements, decimals, and percentages.
• The higher aim is to develop the child's resources to think and reason mathematically, to pursue assumptions to their logical conclusion, and to handle abstraction.
• It states that mathematics should be taught in a way that children learn to enjoy mathematics rather than fear it.
• The teaching of mathematics should be done in the way, in which a student learns the best i.e., following the child-centred approaches by engaging students actively in the learning process.
• The teacher should provide the students more opportunities to experience typical processes of mathematical activity like looking for patterns, making quizzes, puzzles, and proving arguments, etc.

Hence, it is concluded that the narrow aim of teaching mathematics according to the NCF-2005, is the development of useful capabilities related to numeracy.

A decimal number is one in which the whole number and fractional parts are separated by a decimal point. For example- 5.69 is a decimal number.

Key PointsApproximation in mathematics is finding a number that is nearest or closest but not exactly equal to a number. it assesses the students' ability to compare two decimal numbers.

• In the above question, the possible decimal numbers that can be formed by using digits 6,3,2, and 9 are- 62.39, 63.29, 69.23, 69.32, 62.93, 63.92, etc.  
• But, the decimal number that is closest to 64 will be only 63.92 
• Hence, there can be only one possible answer to this question i.e. 63.92.
• The response of student B was correct that by rearranging the digits again, we can get a number closer to 64.  

Hence, we conclude that the correct options are (a) and (d).

Curriculum:-It includes the complete school environment, involving all the courses, activities, reading, and associations furnished to the pupils in school.

Key Points Principles of curriculum construction:

• Principle of Child Centredness
• Principle of Flexibility and Variety
• Principle of Correlation
• Principle of Creativity
• Principle of Integration
• Principle of Utility
• Principle of Community Service
• Principle of activity
• Principle of Values
• Principle of Totality

Thus by all these references, we can conclude that the Spiral approach does not belong to the “principles of curriculum construction.

Hint

• Spiral approach to learning:- As children progress, they will revisit certain concepts/themes which are repeated consciously as an entry-level behavior to build new learning.
  • For example:- Planning lessons taking into account prior knowledge and experiences of the children. Thus, the new learning would be built on the previous experiences of the child.

The aim of teaching Mathematics at school is to develop useful capabilities, particularly those relating to numeracy- numbers, number operations, measurements, decimals, and percentages. 
The broader aim is to develop the child to think and reason mathematically, to pursue assumptions to their logical conclusions, and to handle abstractions.

Key Points 

A good mathematics curriculum should present suitable learning experiences to foster common needs as citizens and special needs as an individual. The main consideration should be given to desirable pupil growth within the overall purposes of all levels of education.

• In the primary school mathematics curriculum, the following topics have been included;
  • Tessellation
  • Symmetry
  • Patterns
  • Fractions
• The negative numbers concept should be introduced at the upper primary level for better understanding.
• The concept of area measurement should be introduced at both levels as per the conceptual understanding and difficulty level.
• The foundation of algebraic thinking can be laid at the primary level.
• The concept of fractions should be introduced only at the primary level.
• Natural numbers, whole numbers, properties of numbers (commutative, associative, distributive, additive identity, multiplicative identity), number line.
• Seeing patterns, identifying and formulating rules to be done by children. (As familiarity with algebra grows, the child can express the generic pattern.)

Hence, we can conclude that option 4 is correct concerning the mathematics curriculum. 

Hint

• The concept of negative numbers should be introduced at the upper primary level for better understanding, not at the primary level.