Teaching Methods MCQ Quiz - Objective Question with Answer for Teaching Methods - Download Free PDF

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.

Van Hiele’s theory explains how students develop geometric understanding through distinct levels of thinking. According to this theory, learning geometry is a stepwise process where students move from recognizing shapes based on appearance to understanding their properties and relationships at deeper levels. 

Key Points

• Statement (a) reflects the core idea of the theory that thinking in geometry occurs in stages or levels.
• Statement (c)  highlights the importance of aligning teaching methods with students’ thinking levels to improve their learning outcomes.
• Both these points are supported by Van Hiele’s work.
• Statement (b) contradicts the theory, as it ignores the need to consider students’ thinking levels for effective learning, which Van Hiele emphasizes as crucial.

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

In mathematics education, introducing concepts through familiar language before introducing symbols helps students build a strong conceptual foundation.

 Key Points

• Symbols like greater than (>) and less than (<) are abstract representations that can be confusing if introduced too early without context.
• Using everyday language first ensures students understand the meaning behind these symbols, making the learning process more natural and effective.
• The strategy of using symbols only after students grasp the idea in daily language is a deliberate approach to delay the introduction of abstract symbols.
• It helps bridge concrete experiences and abstract representations, allowing students to connect their intuitive understanding with formal mathematical notation. 

Hint

• Introducing symbols too early without language support can lead to rote learning without real understanding.
• Ignoring language or focusing solely on memorizing symbols can cause misconceptions and hinder meaningful learning.

Hence, the correct answer is delayed introduction of abstract symbols.

In geometry, quadrilaterals are four-sided polygons, and there are various types of quadrilaterals with specific properties. For students like Ravi, understanding these properties is crucial for identifying and distinguishing between different types of quadrilaterals. Each quadrilateral has unique features that set it apart from the others.

Key Points

• Square: A square has four equal sides and all angles 90°. This means that all sides are of equal length, and each interior angle is a right angle.
• Rectangle: A rectangle has opposite sides equal and all angles 90°. This means the opposite sides are equal in length, and all angles are right angles.
• Parallelogram: A parallelogram has equal opposite sides and equal opposite angles. This means the opposite sides are of equal length, and opposite angles are congruent.
• Rhombus: A rhombus has four equal sides and opposite sides parallel. The key feature of a rhombus is that all its sides are equal in length, but the angles are not necessarily 90°.

Hence, the correct sequence of meanings is Four equal sides, Opposite sides equal, Equal opposite sides, Opposite sides parallel.

When a student like Riya struggles with understanding fractions and becomes confused with operations involving them, it's important to adopt teaching strategies that not only address her confusion but also help her build a strong conceptual foundation. Fractions are abstract concepts, so it’s essential to approach them in a way that makes them more relatable and understandable.

 Key Points

• Course of action (I), which suggests using visual aids and real-life examples, is an effective approach for Riya.
• Visual aids like fraction bars, pie charts, or number lines make fractions more tangible and can help her visualize how fractions work in different situations.
• Real-life examples, such as sharing a pizza or dividing a set of objects, allow her to see the practical applications of fractions, making the concept more concrete.
• This approach addresses the root of her confusion by connecting abstract concepts to her experiences, making learning more meaningful.

 Hint

• Course of action (II), which focuses on assigning a lot of repetitive practice worksheets, may not be the most helpful for Riya initially. While practice is essential for reinforcing understanding, without a solid grasp of the concept, repetitive worksheets might lead to frustration rather than improvement. 

Hence, the most suitable course of action is Only course of action (I).

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.

Mathematics is not just the study of numbers and statistical data but also studies the different types of shapes, figures, and patterns.

• In early schooling, the learners began to learn about shapes and try to differentiate various shapes from each other.
• The students learn according to their level of experience and their individual differences, the age can be different in each stage as they learn at their own pace. 
• Van Heile's theory provides an insight to the teacher about how the students learn geometry at different levels. It was originated in 1957 given by Pierre Van Hiele and his wife from the Utrecht University in the Netherlands.
• It helps in describing how the students learn at each level and pass to another level and shapes their learning of geometry at each level of learning.

Key Points  

Van Hiele levels: The Van Hiele levels are described below:

Hence, it is concluded that at Level 2 (Relationship) level of Van Heile's spatial/geometrical understanding, a child is likely to accept that a square is also a rectangle.

Inductive method:- The inductive approach is based on the process of induction. In this, we first take few examples and greater than generalize. It is the method of constructing a formula with the help of a sufficient number of concrete examples.

• Induction means to provide a universal truth by showing, that if it is true for a particular case, it is true for all such cases.
• The children follow the subject matter with great interest and understanding. This method is more useful in arithmetic teaching and learning.

Important Points

• To teach prime numbers at the primary level, the inductive method is used. Each prime number has two factors. This statement is proved by the inductive method. In the Inductive method of mathematical reasoning, the validity of the statement is checked by a certain set of rules, and then it is generalized. 
• The principle of mathematical induction uses the concept of inductive reasoning. 
• The concept should be introduced by reviewing fundamental operations on natural numbers in such a manner that a pattern strikes the imagination of pupils and they can formulate a new generalization which can be named as a new definition or property.
• A teacher should ensure that induction is planned and encouraged. 

Key Points

1. Particular cases to general rules of formulae
2. Concrete instance to abstract rules
3. Known to unknown
4. Simple to complex

Following steps are used by teaching this method:-

• Presentation of examples
• Observation
• Generalization
• Testing and verification

Hence, we can conclude that Each prime number has two factors", for teaching this concept at the primary level, the inductive method of teaching should be followed.

Additional Information

• Deductive method:- It is based on deduction. In this approach, we proceed from general to particular and from abstract to concrete. At first, the rules are given and then students are asked to apply these rules to solve more problems. This approach is mainly used in Algebra, Geometry, and Trignometry.
• Analysis method:- In this method, we break up the unknown problem into simpler parts and then see how these can be recombined to find the solution. So we start with what is to found out and then link further steps or possibilities that may connect the unknown built the known and find out the desired result.
• Synthesis method:- In this method, the child proceeds from known to unknown. Facts that are already known are applied to new situations so that the combination of known facts helps us to find new facts.

Spatial relationships refer to children's understanding of how objects and people move concerning each other, comparison of two objects like big-small, fast-slow, long-short, colour comparison, near-far, etc.

Important Points

The Spatial Ability is the capacity to understand, reason, and remember the spatial relations among objects or space.

• For understanding spatial thinking, students should enable them to understand visualization.
• It is the ability to mentally manipulate 2-dimensional and 3-dimensional figures.
• Hence, drawing the top view of the bottle is an example of a spatial thinking concept.
• It is typically measured with simple cognitive tests and is predictive of user performance with some kinds of user interfaces.

Key Points

• Representing number on a line show concept of rational, irrational and whole number concepts.

Hence, drawing the top view of a bottle is a best-suited activity for the development of spatial understanding among children.

Associative Law:

• It means the numbers are associated in any desired way or sequence. The grouping of numbers doesn’t affect the result.
• Changing the grouping of multiples does not change the product.

For example:-

a × b × c = b × c × a = c × a × b

16 × 25 = 400 = 40 × 10.

Hint

• Repeated Addition: It means a number is added the number of times by which it is multiplied.
• Eg: 25 × 5 = 25 + 25 + 25 + 25 + 25.
• Inverse Multiplication Law: It states that the product of any number and it's reciprocal is always 1     
• Eg: a × 1/a = 1.
• Distributive Law: It means the monomial factor is distributed or separately applied to each term of the polynomial doesn’t affect the result.
• Eg: a(b + c) = ab + ac.

Hence, from the above points, we can clearly infer that the student used Associative Law in the Question.

Learning strategy is 'the sum of an individual's preferences for physical, social, emotional, and environmental elements in the course of learning'. Each learner develops his/her strategy to learning which is rooted in his/her interests and habits. Note that:

• While teaching decimals to students, students should be taught using visual method or aids so that they can understand the concept in a better way.
• 'Multiplication as repeated addition' can be emphasised when teaching multiplication of non-decimal numbers because repeated addition of decimals can be complicated for students.
• Algorithm shows how to solve the problem but it does not connect with the real-life meaning of multiplication.
• Teaching multiplication as 'inverse of division' will not concretely explaining the concept of multiplication.

Hence, the most appropriate strategy is to teach visually.

Proportional materials are base 10 materials where a ten is physically the same size as 10 ones, and a hundred is physically the same size as 10 tens. This helps children understand the place value relationships. Groupable materials are proportional, and so are many pre grouped materials. Key Points

• Dienes blocks are proportional materials as the material for 10 is 10 times the size of the material for 1 where 100 is 10 times the size of 10. Place values can be taught using this proportion where the students get the idea of ones and tens without increasing materials just by increasing proportion.
• Bundles of match sticks are also proportional as one match stick can be taken as ten and ten match sticks as a hundred and make students understand the place values of numbers.

​Hence Dienes blocks and Bundles of match sticks are proportional materials. Additional Information

​Mathematics improves the children's thinking by providing clarity of thoughts, which helps them in converting the assumptions to logical conclusions.

• Mathematics education aims to make mathematics an important part of children's life experiences.

Key Points

• The children attain expertise in mathematics when their basic concepts are well-cleared and it also helps them to learn the higher-level concepts of mathematics effectively.
• To make the children attain expertise in basic mathematical concepts, it is necessary to make them proficient in using numbers and numerical literacy.
• The most common use of numbers is counting. The process of counting involves two steps - the ordinal and cardinal aspects of numbers.

Hence, it is concluded that in the given statement "Four teams participated in the show", the number 'four' is used in a cardinal sense.

The commutative property deals with the arithmetic operations of addition and multiplication. It means that changing the order or position of two numbers while adding or multiplying them does not change the end result. Key PointsThis law simply states that with the addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer.

• a+b = b+a = c
• axb = bxa = c

Hence the property that states 'the product of two numbers remains the same on reversing their order' is called Commutativity Property. Additional Information

Spatial reasoning- Understanding the location and dimensions of objects, as well as how different objects are related, requires spatial reasoning. You can also use it to visualize and manipulate things and shapes in your thoughts. 

Key Points

Spatial reasoning is the ability to mentally manipulate and orient shapes. It is the ability to recognize items by understanding how diverse shapes fit together.

• Activities to develop spatial reasoning-
  • Tangrams- They are seven pieces of ancient Chinese puzzles. Animal, people, and objects can all be created by arranging the pieces in various ways. It is a teaching tool that can help a child develop his or her spatial abilities.
  • Identifying the Nets of solid shapes- Nets are simply a 2D picture of what the 3D shape look like if all its sides were folded out flat. Identifying the net of the solid shapes will provide the children with the opportunity to practice their spatial skills.
  • Identifying the line of symmetry of different shapes- A line of symmetry is a line that cuts a shape exactly in half. The students should make regular use of concrete materials in hands-on activities designed to develop their understanding of objects in space. Students can begin an exploration of symmetry, congruence, and similarity.

Hence, it is clear from the above points that the activity that is least likely to develop spatial reasoning among students is drawing pictographs to represent data, as it develops creative skills.