Pedagogy of Mathematics Questions and Answers

Answer: A

The appropriate statements are A, B and C.

Mathematics is a creative subject: children invent strategies, spot patterns and pose problems (A), and it nurtures imagination, for example in visualising shapes, numbers and possibilities (B). As a discipline it is built on deductive reasoning: results are proved by logical steps from definitions and axioms (C).

Statement D is wrong. Mathematics is not always convergent: many problems allow several methods and some have several correct answers, and the NCF 2005 encourages such open-ended, divergent thinking. Every option that leaves out A, B or C is incomplete.

Answer: A

The activity that is not effective is always praising the student who achieves highest marks in the class in the term-end examination.

Appreciation for mathematics comes from enjoying and valuing the subject itself. Praising only the top scorer makes marks the point of mathematics, encourages competition, and can make other children feel that the subject is not for them, which works against appreciation.

Videos on Indian mathematicians show the human story and heritage of the subject, puzzles and magic squares make it enjoyable, and a mathematics corner invites children to explore. All three build appreciation.

Answer: D

The statement that is not correct is that errors of the students should be overlooked as pointing errors will demotivate them.

Errors are a window into children's thinking: they show the reasoning or misconception behind an answer (statement 1), they are a natural part of learning mathematics (statement 2), and they help teachers plan lessons that address misconceptions (statement 3).

Overlooking errors leaves misconceptions in place. The right response is not to ignore them but to discuss them constructively, without blame, so that children learn from them.

Answer: A

The incorrect statement is that norm-referenced assessment is useful in diagnostic testing and remedial teaching.

Norm-referenced assessment compares each student with others in a group and ranks them (statement 4 is correct). A rank tells you where a child stands, not which concepts or skills the child has missed, so it is of little use for diagnosis and remediation.

Criterion-referenced assessment judges each student against fixed learning objectives. It shows exactly what a child has and has not mastered, so it evaluates mastery learning (statement 2) and is the kind of assessment used for diagnostic testing and remedial teaching (statement 3).

Answer: C

The correct statements are B and D.

Mathematical learning materials, such as manipulatives, models, number cards and geometry kits, let children explore ideas by handling them, so they support self-learning (B), and they create a rich, activity-based learning environment in the classroom (D).

Statements A and C cast the materials as aids for the teacher's demonstrating formulae or giving instructions. That is a teacher-centred use; the main value of learning material lies in what children do with it.

Answer: B

Olympiads and competitions will be strengthened.

The National Education Policy 2020 states that Olympiads and competitions in various subjects will be strengthened across the country, with coordination from school to national level, so that students with interest and talent are encouraged and supported. It also calls for such competitions to be offered in regional languages.

The policy says nothing about making them easier, discouraging them or reducing them.

Answer: D

They are important pre-number concepts.

Before children can count meaningfully, they need ideas of comparison and relationship: more and less, long and short, big and small, near and far, along with classification, seriation and one-to-one correspondence. These pre-number concepts are the foundation on which number sense and measurement are built.

They are not vague terms or mere English adjectives or antonyms. Comparing quantities and sizes is mathematical thinking in its earliest form.

Answer: C

The most appropriate reason is that gendered constructs of society have led to the belief that boys use more innovative strategies for problem-solving and thus have better conceptual understanding.

The NCF 2005 position paper on gender notes that classroom research has found teachers attributing girls' success in mathematics to hard work and rote following of rules, while attributing boys' success to ability and innovative strategies. This is a social construct, a stereotype, not a fact about girls or boys.

The other options repeat the very stereotypes the NCF rejects: that girls fear mathematics, that the subject is male by nature, or that boys' ability is innate.

Answer: D

The aspect is the abstract nature of primary concepts in mathematics.

Even the basic ideas of mathematics, such as number, place value, zero and fraction, are abstractions: a child cannot see or touch 'three' itself, only three objects. When abstract ideas are presented without grounding in concrete experience, children find them hard and come to fear the subject. The NCF 2005 position paper on mathematics names this abstraction as a source of difficulty.

Multiple answers and multiple methods are strengths of mathematics that make it more open, not sources of fear, and the size of its knowledge base is not specific to mathematics.

Answer: D

The correct option is only C.

The vegetable seller priced 350 g at the rate of ₹ 60 per kg by breaking it into convenient parts: 100 g costs ₹ 6, so three 100 g parts cost ₹ 18 and the remaining 50 g costs ₹ 3, a total of ₹ 21.

\[ \begin{aligned} 350\ \text{g} &= 100 + 100 + 100 + 50 \\ &= 6 + 6 + 6 + 3 = 21 \end{aligned} \]

The method is correct and exact, so it is not ambiguous (A is false). Such everyday strategies of decomposing numbers are valuable in class, so B is false too. They show that problems can be solved in different ways, which is exactly statement C.