Mathematics Pedagogy MCQ Quiz - Objective Question with Answer for Mathematics Pedagogy - Download Free PDF

Community mathematics involves connecting mathematical learning with students’ everyday experiences and local contexts. This approach helps students see the relevance of mathematics in their daily lives, making learning more meaningful and engaging. It also encourages students to apply mathematical concepts to solve practical problems they encounter.

Key Points

•  Using word problems that involve local market prices, familiar measurement units, and real-life situations from students’ surroundings creates a bridge between classroom learning and the community. It helps students understand concepts concretely and appreciate the usefulness of mathematics beyond textbooks.
• On the other hand, relying on international problems without adaptation, teaching only textbook problems unrelated to students’ context, or avoiding real-life problems limits students’ ability to relate to and apply mathematics in real-world situations.

Hence, the best approach for integrating community mathematics is to use word problems involving local market prices and measurement units familiar to students.

In effective mathematics teaching, presenting more than one method to solve a problem is a strategy used to deepen conceptual understanding rather than merely focus on procedural knowledge. It helps students recognize that problems can be approached in various valid ways, encouraging them to analyze and make sense of different strategies.

Key Points

• When a teacher asks students to compare two different methods for solving the same algebraic equation, the goal is to promote analytical thinking.
• Students reflect on the reasoning behind each method, examine their efficiency and accuracy, and understand that flexibility in thinking is valuable. This kind of activity fosters mathematical communication, critical thinking, and the ability to justify choices.
• Introducing multiple methods is not intended to confuse students or to make them memorize procedures without understanding. Nor is it about evaluating only speed or efficiency, as the emphasis is on mathematical reasoning and conceptual insight, not just getting the answer quickly.

Hence, the correct answer is Promote analytical thinking and understanding of mathematical flexibility.

In mathematics, properties or laws such as the associative, distributive, and commutative laws help students simplify and manipulate expressions efficiently. When learners apply these properties, they demonstrate a deeper understanding of number operations and flexibility in problem-solving.

Key Points

•  In the given example: 6 × 15 = (2 × 3) × 15 = 2 × (3 × 15) = 2 × 45 = 90, the student breaks 6 into 2 × 3, then groups the numbers differently as 2 × (3 × 15), and finally multiplies to get 90.
• This method clearly uses the associative law of multiplication, which allows the grouping of numbers in a multiplication problem to change without affecting the result: (2 × 3) × 15 = 2 × (3 × 15).
• The commutative law, which involves changing the order of numbers being multiplied (a × b = b × a), is not applied here, as the order remains consistent throughout.
• The distributive law, which involves distributing multiplication over addition or subtraction (like a × (b + c) = a × b + a × c), is also not used in this problem.

Therefore, the student has applied only the associative law.

Hence, the correct answer is Only (a).

Computational thinking is a fundamental problem-solving approach often used in mathematics and computer science. It involves breaking down complex problems into manageable parts, identifying patterns, abstracting general principles, and creating step-by-step algorithms. These skills are essential for analytical reasoning and logical thinking.

Key Points

•  Memorization is not a component of computational thinking. While remembering certain facts or formulas may aid in solving problems, computational thinking is more about process and strategy than rote recall.
• It focuses on understanding how to solve a problem by developing and applying logical steps, not simply remembering procedures without comprehension.

Hint

• Decomposition is a key element where a problem is broken into smaller, more manageable parts.
• Pattern recognition helps in identifying similarities and trends which can simplify solutions.
• Algorithmic thinking involves creating a sequence of logical steps to solve a problem effectively.

Hence, the correct answer is memorization.

Van Hiele’s theory of geometric thinking outlines how learners progress through different levels of understanding geometry. These levels are not based on age but on the quality and type of instruction provided. The theory emphasizes a sequential and developmental process in learning geometric concepts.

Key Points

•  Progression through Van Hiele levels depends on instruction, not biological age. That is, well-structured teaching and experiences are essential for a learner to move from one level to the next.
• Additionally, learners must pass through the levels sequentially, they cannot skip a level, as each stage builds the foundation for the next. These characteristics are central to Van Hiele’s framework and help teachers structure geometry instruction appropriately.

Hint

•  Visualization is not the highest level; it is actually the first level of geometric thinking in the Van Hiele model.
• The highest level is rigor, which involves formal deduction and proof. Therefore, statement (c) is incorrect.

Hence, the correct answer is (a) and (b).

Basic mathematics was created to meet the basic demands of individuals who want to learn the fundamentals of mathematics and how to use them in their daily lives. Basic mathematical concepts such as addition, subtraction, division multiplication, percentage, profit, and loss among others are essential for everyone in daily life.

Key Points

Hence, we conclude that the correct statement is only D.

 BALA  is termed as  Building as Learning Aid.It is about developing school spaces — the classrooms, the floors, walls, doors, windows, pillars, corridors, the outdoor spaces, and the natural environment — as learning resources.

Key PointsThe idea of BALA  was developed after comprehensive research in the following areas-

• For facilitation of all-around growth and development.
•  Need for a literacy environment.
• Socio-cultural-educational background at home.
• Spatial aspirations from school.
• Natural behavioral patterns in school space.

Thus, the ‘BALA’ concept which is an initiative supported by UNICEF is Built as Learning Aid.

Additional Information What can BALA do?
For children, it can help in developing

1. Language and Communication skills
2. Numeracy skills
3. Abstract notions through concrete examples
4. Respect for nature and the environment
5. Capability to realize the potential of available resources
6. Power of observation

Van Hiele Model of Geometric Thought in math education: the van Hiele model is a theory that describes how students learn geometry. 

Important Points

At Level 0 Visualization (Basic visualization or Recognition):

• At this level, pupils use visual perception and nonverbal thinking.
• They recognize geometric figures by their shape as “a whole” and compare the figures with their prototypes or everyday things (“it looks like a door”), categorize them (“it is / it is not a…”).
• They use simple language. 
• They do not identify the properties of geometric figures.
• Example: A child is not able to differentiate squares from rectangles and assigns both of them to the same category. According to Van Hiele's theory of geometric reasoning, the student is at Level 0 Visualization.

Additional Information

The van Hiele theory describes how young people learn geometry.
It postulates five levels of geometric thinking which are labeled visualization, analysis, abstraction, formal deduction, and rigor. Each level uses its own language and symbols. Students or pupils pass through the levels “step by step”

• Level 0 Visualization (Basic visualization or Recognition): At this level, pupils use visual perception and nonverbal thinking. They recognize geometric figures by their shape as “a whole” and compare the figures with their prototypes or everyday things (“it looks like a door”), categorize them (“it is / it is not a…”). They use simple language. They do not identify the properties of geometric figures. 
• Level 1 Analysis (Description): At this level pupils (students) start analyzing and naming properties of geometric figures. They do not see relationships between properties, they think all properties are important (= there is no difference between necessary and sufficient properties). They do not see a need for proof of facts discovered empirically. They can measure, fold and cut paper, use geometric software, etc.
• Level 2 Abstraction (Informal deduction or Ordering or Relational): At this level, pupils or students perceive relationships between properties and figures. They create meaningful definitions. They are able to give simple arguments to justify their reasoning. They can draw logical maps and diagrams. They use sketches, grid paper, geometric SW. 
• Level 3 Deduction (Formal deduction): At this level, students can give deductive geometric proofs. They are able to differentiate between necessary and sufficient conditions. They identify which properties are implied by others. They understand the role of definitions, theorems, axioms, and proofs. 
• Level 4 Rigor: At this level, students understand the way how mathematical systems are established. They are able to use all types of proofs. They comprehend Euclidean and non-Euclidean geometry. They are able to describe the effect of adding or removing an axiom on a given geometric system.

.Hence, we can conclude that the right answer to this question is the Visualisation level.  

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.

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

It should be noted that teaching methods and the ability to use math tools come under the vast category called classroom operations. So instead of choosing three different opinions, one single opinion is selected which covers all three aspects.

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

This is what exactly is done in mathematics class -

• In the beginning, the teacher introduces the concept of drawing the attention of the learners toward the topic;
• Then, try to explain that concept by demonstrating different materials, performing activities, or doing other activities to clarify the concepts making the students participate;
• Lastly, ask some questions for assessing whether the learners have learned the concepts as you desired.

Hence, 'Class Room operations' are the major problem of teaching Mathematics.

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.

In the above question, there is comparison addition is performed.

Given that:-

I have 6 pencils but Manish has more than 2 me

It means Manish have total pencil :- 6 + 2 = 8 pencil

Now we can easily understand their addition is performed and also compared with Manish pencils and my pencil.

Comparison Addition: In this method, we find the relation between two amounts by asking or telling how much more (or less) is one compared to the other.

Additional Information

• Comparison Subtraction: The difference between the two groups of numbers, namely, how much one is greater than the other, how much more is in one group than in the other. e.g., if Munna has 15 erasers and Munni 5, how many less does Munni have than Munna? 
• Takeaway: It is used for subtraction which means 'Remove', or  'Reduce' the group of words or numbers. E.g. How much is left if you take away 3 marbles from 5 marbles. In this way, the children learn to understand 'take away', and relate it to 'add'. 

Hence, it becomes clear that the given problem is comparison addition.

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. 

• Mathematics relies on logic and connects learning with children's day to day life. It acts as the basis and structure of other subjects. 
• It visualized as the vehicle to train a child to think, reason, analyze, and articulate logically.

Key Points

The Nature of Mathematics is Logical as it relies on: 

• evaluation of truth or likelihood of statements.
• development of skills like speed, accuracy, estimation.
• improvement of reasoning power, analytical and, critical thinking.

• enhancement of scientific attitude like estimating, finding and verifying results.

Hence, it becomes clear that the nature of Mathematics is logical.

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

• Teaching methods of mathematics include problem-solving, lecture, inductive, deductive, analytic, synthetic, heuristic and discovery methods. Teacher adopts any method according to the needs and interests of students.

Key Points

Analytic method: 

• In this method, we proceed from unknown to known.
• We break up the unknown problem into simpler parts and then see how it can be recombined to find the solution. Therefore it is the process of unfolding the problem or conducting its operation to know its hidden aspects.
• In this process, we start with what is to be found out and then think of further steps or possibilities that may connect the unknown with the known and find out the desired result.

Hence, it could be concluded that "Unknown to known" is used for the Analytical method.​​

Additional Information 

• Synthetic Method: In this method, we combine several facts, perform cer­tain mathematical operations, and arrive at the solution.
• Demonstration method: It is a strategy in which a teacher demonstrates concepts and students learn by observing and improving understanding through visual analysis.
• Experimental method: It refers to a method that is designed to study the interrelationship between an independent and a dependent variable under controlled conditions.

Pre-number concept: These are defined as math skills that are learned by pre-nursery or kindergarten kids to make them understand the different variations in shapes, sizes, colors, etc. These concepts can be developed in children during the preschool years. i.e. before attaining 7 years of age(before the concrete operation stage).

Important PointsStages of Pre-number concepts include:

• Classification: Children need to look at the characteristics of different items and find characteristics that are the same and classify them accordingly.
• One to one correspondence:- The ability to count one object while saying one number is known as one-to-one correspondence. If you are counting items, for example, you can point to the first one and say '1' then, ;to the second and say '2', and so on.
• Patterns:- It refers to the understanding of the repeated arrangement of numbers, shapes, and designs and making a generalisation based on some rules and structure.
• Matching:  Matching forms the basis for our number system.
• Comparing: Children look at items and compare by understanding differences like big/little, hot/cold, smooth/rough, tall/short, and heavy/light. 

Thus, it is concluded that Classification, patterning and one-to-one correspondence are part of pre-number concepts in young children.