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It is observed that to a problem like 'show that the sum of any two odd numbers in an even number', most of the students replied by quoting an example, say, 5 + 7 = 12.
Students answered this question inappropriately as
Students answered this question inappropriately as
- a)students firmly believe that if a statement is true for one set of numbers, it is always true and hence have developed strong strategy for making generalisation
- b)students have not learnt the logical proof for the statement in the class
- c)students have not understood that in Mathematics, 'any' is used to indicate generalisation and hence are not able to answer correctly
- d)students have attained the formal operational stage as proposed by Piaget
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
It is observed that to a problem like show that the sum of any two odd...
Explanation:
To understand why option A is the correct answer, let's analyze the given scenario and the options provided.
Scenario:
The problem states that students were asked to show that the sum of any two odd numbers is an even number. However, most of the students responded by quoting an example such as 5 + 7 = 12.
Options:
a) Students firmly believe that if a statement is true for one set of numbers, it is always true and hence have developed a strong strategy for making generalizations.
b) Students have not learned the logical proof for the statement in the class.
c) Students have not understood that in Mathematics, "any" is used to indicate generalization and hence are not able to answer correctly.
d) Students have attained the formal operational stage as proposed by Piaget.
Explanation of Option A:
Option A states that students firmly believe that if a statement is true for one set of numbers, it is always true, and hence they have developed a strong strategy for making generalizations.
In this case, students have provided an example (5 + 7 = 12) to support the statement that the sum of any two odd numbers is an even number. By doing so, they are assuming that if this example is true, then the statement must be true for all cases.
This type of reasoning is known as inductive reasoning, where individuals make general conclusions based on specific examples or observations. Inductive reasoning can be a useful strategy for problem-solving, but it is not a valid proof in mathematics.
In mathematics, to prove a statement for all cases, a logical proof is required. This involves using deductive reasoning, where general conclusions are reached based on logical reasoning and established mathematical principles.
Therefore, since students are relying on examples instead of providing a logical proof, option A is the correct answer. It highlights that students have not yet learned the importance of logical proof and are relying on inductive reasoning to make generalizations.
By promoting the understanding of logical proof and deductive reasoning, students will be able to provide a valid and accurate response to the problem, demonstrating a deeper understanding of mathematical concepts.
To understand why option A is the correct answer, let's analyze the given scenario and the options provided.
Scenario:
The problem states that students were asked to show that the sum of any two odd numbers is an even number. However, most of the students responded by quoting an example such as 5 + 7 = 12.
Options:
a) Students firmly believe that if a statement is true for one set of numbers, it is always true and hence have developed a strong strategy for making generalizations.
b) Students have not learned the logical proof for the statement in the class.
c) Students have not understood that in Mathematics, "any" is used to indicate generalization and hence are not able to answer correctly.
d) Students have attained the formal operational stage as proposed by Piaget.
Explanation of Option A:
Option A states that students firmly believe that if a statement is true for one set of numbers, it is always true, and hence they have developed a strong strategy for making generalizations.
In this case, students have provided an example (5 + 7 = 12) to support the statement that the sum of any two odd numbers is an even number. By doing so, they are assuming that if this example is true, then the statement must be true for all cases.
This type of reasoning is known as inductive reasoning, where individuals make general conclusions based on specific examples or observations. Inductive reasoning can be a useful strategy for problem-solving, but it is not a valid proof in mathematics.
In mathematics, to prove a statement for all cases, a logical proof is required. This involves using deductive reasoning, where general conclusions are reached based on logical reasoning and established mathematical principles.
Therefore, since students are relying on examples instead of providing a logical proof, option A is the correct answer. It highlights that students have not yet learned the importance of logical proof and are relying on inductive reasoning to make generalizations.
By promoting the understanding of logical proof and deductive reasoning, students will be able to provide a valid and accurate response to the problem, demonstrating a deeper understanding of mathematical concepts.
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Community Answer
It is observed that to a problem like show that the sum of any two odd...
The students have made generalisation by quoting one example. Therefore, they believe that if a statement is true for one set of numbers, it must be true for other numbers as well.
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It is observed that to a problem like show that the sum of any two odd numbers in an even number, most of the students replied by quoting an example, say, 5 + 7 = 12.Students answered this question inappropriately asa)students firmly believe that if a statement is true for one set of numbers, it is always true and hence have developed strong strategy for making generalisationb)students have not learnt the logical proof for the statement in the classc)students have not understood that in Mathematics, any is used to indicate generalisation and hence are not able to answer correctlyd)students have attained the formal operational stage as proposed by PiagetCorrect answer is option 'A'. Can you explain this answer?
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It is observed that to a problem like show that the sum of any two odd numbers in an even number, most of the students replied by quoting an example, say, 5 + 7 = 12.Students answered this question inappropriately asa)students firmly believe that if a statement is true for one set of numbers, it is always true and hence have developed strong strategy for making generalisationb)students have not learnt the logical proof for the statement in the classc)students have not understood that in Mathematics, any is used to indicate generalisation and hence are not able to answer correctlyd)students have attained the formal operational stage as proposed by PiagetCorrect answer is option 'A'. Can you explain this answer? for CTET & State TET 2024 is part of CTET & State TET preparation. The Question and answers have been prepared according to the CTET & State TET exam syllabus. Information about It is observed that to a problem like show that the sum of any two odd numbers in an even number, most of the students replied by quoting an example, say, 5 + 7 = 12.Students answered this question inappropriately asa)students firmly believe that if a statement is true for one set of numbers, it is always true and hence have developed strong strategy for making generalisationb)students have not learnt the logical proof for the statement in the classc)students have not understood that in Mathematics, any is used to indicate generalisation and hence are not able to answer correctlyd)students have attained the formal operational stage as proposed by PiagetCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CTET & State TET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It is observed that to a problem like show that the sum of any two odd numbers in an even number, most of the students replied by quoting an example, say, 5 + 7 = 12.Students answered this question inappropriately asa)students firmly believe that if a statement is true for one set of numbers, it is always true and hence have developed strong strategy for making generalisationb)students have not learnt the logical proof for the statement in the classc)students have not understood that in Mathematics, any is used to indicate generalisation and hence are not able to answer correctlyd)students have attained the formal operational stage as proposed by PiagetCorrect answer is option 'A'. Can you explain this answer?.
It is observed that to a problem like show that the sum of any two odd numbers in an even number, most of the students replied by quoting an example, say, 5 + 7 = 12.Students answered this question inappropriately asa)students firmly believe that if a statement is true for one set of numbers, it is always true and hence have developed strong strategy for making generalisationb)students have not learnt the logical proof for the statement in the classc)students have not understood that in Mathematics, any is used to indicate generalisation and hence are not able to answer correctlyd)students have attained the formal operational stage as proposed by PiagetCorrect answer is option 'A'. Can you explain this answer? for CTET & State TET 2024 is part of CTET & State TET preparation. The Question and answers have been prepared according to the CTET & State TET exam syllabus. Information about It is observed that to a problem like show that the sum of any two odd numbers in an even number, most of the students replied by quoting an example, say, 5 + 7 = 12.Students answered this question inappropriately asa)students firmly believe that if a statement is true for one set of numbers, it is always true and hence have developed strong strategy for making generalisationb)students have not learnt the logical proof for the statement in the classc)students have not understood that in Mathematics, any is used to indicate generalisation and hence are not able to answer correctlyd)students have attained the formal operational stage as proposed by PiagetCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CTET & State TET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It is observed that to a problem like show that the sum of any two odd numbers in an even number, most of the students replied by quoting an example, say, 5 + 7 = 12.Students answered this question inappropriately asa)students firmly believe that if a statement is true for one set of numbers, it is always true and hence have developed strong strategy for making generalisationb)students have not learnt the logical proof for the statement in the classc)students have not understood that in Mathematics, any is used to indicate generalisation and hence are not able to answer correctlyd)students have attained the formal operational stage as proposed by PiagetCorrect answer is option 'A'. Can you explain this answer?.
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