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

In mathematics education, open-ended problems are those that allow for multiple possible answers or solution paths. These types of problems help develop higher-order thinking, reasoning, creativity, and real-world application skills among students.

Key Points

•  The given problem does not have a single correct answer. Students are asked to determine the possible number of pencils and pens sold that together total ₹100. 
• Multiple combinations of quantities and prices could satisfy this condition. By exploring different solutions, students practice critical thinking and problem-solving, aligning with an open-ended, constructivist approach to learning.
• This fosters flexibility in thought and encourages mathematical reasoning beyond procedural calculations.

Hint

• It is not a closed-ended problem, as it does not have just one fixed answer.
• The problem does not involve algebraic expressions explicitly.
• It is not about using the unitary method, which typically deals with cost per unit.

Hence, the correct answer is to use open-ended questions to encourage multiple solutions.

The constructivist approach to teaching is based on the idea that learners actively construct their own understanding and knowledge through experiences and reflection. In mathematics, this approach emphasizes exploration, hands-on learning, and connecting concepts to real-life situations.

Key Points

•  Using grid paper and real objects like books and tables allows students to explore and discover the concepts of perimeter and area through direct interaction.
• They can count squares, trace shapes, and observe how measurement works in tangible contexts.
• This practice promotes conceptual understanding by allowing learners to build knowledge from their own observations and experiences, which is the essence of constructivism.

Hint

• Giving formulas to memorize without context supports rote learning, not understanding.
• Copying board work is passive learning and limits student engagement.
• Completing a worksheet with 20 problems may reinforce procedures but doesn't encourage exploration or deep thinking.

Hence, the correct answer is using grid paper and real objects like books and tables to let students discover how perimeter and area are calculated.

Mathematics education has increasingly emphasized the importance of conceptual understanding, grasping the underlying principles behind mathematical ideas rather than mere procedural memorization, which focuses on performing steps without truly understanding why they work.

Key Points

• Focusing on conceptual understanding helps students internalize mathematical principles, making them more capable of solving new and unfamiliar problems.  When students truly understand the “why” behind operations, they can adapt that understanding across diverse contexts, not just routine exercises.
• The reason provided application of mathematical knowledge to unfamiliar problems is a direct outcome of deep conceptual understanding, which validates the assertion.

Hence, the correct answer is both A and R are true and R is the correct explanation of A.

 Key Points

• In the Analysis level, students begin to recognize shapes based on their properties (like sides, angles, and parallel lines), not just by their overall appearance.
• They might say a figure is a rectangle because it has four right angles and opposite sides equal, rather than simply because it "looks like one."
• This level marks a shift from visual to property-based reasoning.

Hint

• Visualization is the first level, where students identify shapes mainly by how they look (e.g., "this looks like a square").
• Informal Deduction involves logically ordering properties and understanding relationships between classes of shapes.
• Formal Deduction is where students begin constructing logical proofs using definitions, theorems, and axioms.

Hence, the correct answer is Analysis.

Assessing students holistically includes evaluating not just their written performance, but also their process skills such as observation, creativity, and engagement in activities. For this, qualitative assessment tools are more effective than standard tests.

Key Points

•  An anecdotal record is a tool where a teacher maintains brief, descriptive accounts of significant incidents related to a student’s learning behavior.
• It is especially useful for documenting students' observation skills, creative problem-solving, and participation in experiments or hands-on tasks. This tool allows the teacher to capture authentic learning behaviors and reflect on them to guide future teaching.

Hint

• Report Card summarizes performance, often in grades, but lacks detailed insights into specific skills.
• Teacher-made Test mainly evaluates content knowledge and is usually written.
• Teacher Diary records the teacher's reflections and classroom events but is not student-specific in detail like anecdotal records.

Hence, the correct answer is Anecdotal Record.

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.