Unit 1 Mathematical Reasoning
1.1 Process of Generalisation: Pattern Recognition and Inductive Reasoning
- How the ability of pattern recognition and inductive reasoning are important aspects of mathematical learning? Give two activities that would help children to develop these abilities. (5+5=10) (2016)
- What do you mean by generalisation of pattern? How is it related to algebra? (2.5+2.5=5) (2017)
- How will you develop the skill of generalisation in students of class 7? Explain using examples. (5) (2018)
- How pattern recognition and inductive reasoning are helpful in the process of generalisation. Explain with suitable examples. (5+5=10) (2019)
1.2 Structure of Mathematics: Axioms, Definitions, Theorems
- Explain the terms Axioms and Theorems with the help of suitable examples. (2.5+2.5=5) (2019)
- How is the theorem different from Postulates and Axioms? Discuss the types of theorem you discuss in your class, with suitable examples. (3+2=5) (2022)
1.3 Validation Process of Mathematical Statements: Proofs, Counter Examples, Conjecture
- Discuss the importance of definition and counter examples in Mathematics. Explain with suitable examples. (5) (2018)
- What is ‘Conjecture’ in mathematics? Explain with suitable examples. How will you develop mathematical reasoning in students at elementary level? (1+3+6=10) (2018)
- What do you mean by the word ‘conjecture’? Validate your understanding with suitable examples.
1.4 Problem Solving in Mathematics: A Process
- Describe ‘Problem Solving Method’ of teaching Mathematics with the help of an example. How is this method useful in daily life? (5+5=10) (2016)
- Explain “Problem Solving Process” in Mathematics with the help of suitable examples. What is the importance of “Problem Solving Process” in Mathematics? (7+3=10) (2017)
- Problem solving in Mathematics is an art. Do you agree with the statement? Explain it. What are the benefits of the problem solving process for students? (3+7=10) (2022)
1.5 Creative Thinking in Mathematics
- How will you develop creative thinking in your students through Mathematics teaching? Give examples. (3+2=5) (2016)
- What steps may be taken to promote creativity among students in Mathematics class? Give examples. (2+3=5) (2017)
- How creative thinking is helpful in developing Mathematical reasoning in students? Explain using suitable examples. (5) (2018)
- How will you develop the Mathematical creative thinking among students at elementary level? Explain with activities. (5) (2019)
