Certain fundamentals
[pg.no.16]

- To create an interest in a concept/ subject of discussion should be the main aim of a teacher.
- Use concrete and existing materials
- The students should be able to build upon their already existing prior knowledge and build upon their mental models
- If I cannot learn the way you teach, can you teach me the way I learn
- Learning to learn is education

**1. Ask open-ended questions**where there is no single answer for it.

E.g. Tell me about # 5

- It has only one digit
- It is an odd number
- It is between 4 and 6
- Etc..

- They both are one digit numbers
- 8 is the largest among the two numbers
- Etc..

**2. Ask continuous multiple questions:**

- This
helps to elicit curiosity
- Helps
navigate and introduce new concepts easily
- Can
give an interesting problem and/ or a situation for class work or home
work
- Children
have the joy of finding an answer for themselves
- Posing
a puzzle always hooks them.
- Asking
questions like
- Why?
- How?
- What
will happen if?

**3. Maths as Language**

- What is addition?
- What does 5+3 means?

We should treat and translate abstract and symbolic concepts
in Maths into Language. The above examples try to do that.

**4. Multiple meanings in one statement**

We should make the children derive multiple meanings in one
statement just like in a language statement.

E.g. “I came from Delhi
only today morning.”

E.g. 5+3 = 8, also means

- 3+5 = 8
- 8-5 = 3
- 8-3 = 5

**5. Multiple ways of getting to an answer**

E.g. 674+308

600+300+70+4+8

670+4+300+8

600+300+74+8

To achieve this, use the following steps:

**: Pose an interesting problem before the students to solve**

__Step 1__**: Let the students employ their own ways to try solving it**

__Step 2__**: Allow them to explain how they got their answers**

__Step 3__**: Discuss which method could be the best or introduce the most apt step saying that ‘This is how I would solve it. If you find it useful you can also use it.’**

__Step 4__**: Give more interesting puzzles to solve using the currently discovered methods.**

__Step 5__**6. Develop theorems/ axioms from solving problems**

Let the students ‘deduce’ the theorem or a rule instead of
giving it to them in the first place.

E.g. Introduce the following problem saying ‘There is a
magic in this. Can you find it?’

5+3 =
6+5 =

3+5 =
5+6 =

The concluding theorem is “Distributive property of
Addition”

Note: This method of teaching is more formally called
‘Inductive Teaching’. This works on the idea of ‘allowing students to construct
theories internally.’

**7. Reverse theorems**

E.g. ‘In a triangle, the sum of its angles is 180 degrees.’
A student should also be able to state ‘A shape with the sum of all its angles
180 degree is a triangle.’

**8. Find out the derivates as well**

If in a number statement 5+3 = 8, a student should be able
to answer

3+5 = ?

8-3 = ?

8-5 = ?

E.g. 20% of 50 is 10, then

What percentage of 50 makes 10?

20% of what gives 10?

**9. Make your own questions**

The best Mathematician is the one who is able to make his/
her own questions.

**10. The beauty of Maths**

Introduce various Math puzzles, Number games, Interesting
Mathematical patterns, Maths stories, Number songs to generate interest in the
subject

**Characteristics of a good Math Activity**

Based on the 10 Commandments, we could conclude that a good
Math Activity will have the following characteristics.

- There should be an unquenchable thirst to find the answer
- Will have the qualities of a sport/ game, the uncertainty factor in the activity.
- Will give the children a chance to think, estimate, hypothesise and test one’s own hypothesis
- A question that is open so that children could try multiple ways to do it [instead of asking one question – one answer kind of problems]
- Will have the possibility of asking continuous questions
- The students will be able to construct a theorem/ axiom at the end of the Math activity.

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