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
10 Commandments for Teaching Maths
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
E.g. Tell me about # 5 and 8
- They both are one digit numbers
- 8 is the largest among the two numbers
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
- 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
only today morning.” Delhi
E.g. 5+3 = 8, also means
- 3+5 = 8
- 8-5 = 3
- 8-3 = 5
5. Multiple ways of getting to an answer
To achieve this, use the following steps:
Step 1: Pose an interesting problem before the students to solve
Step 2: Let the students employ their own ways to try solving it
Step 3: Allow them to explain how they got their answers
Step 4: 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 5: Give more interesting puzzles to solve using the currently discovered methods.
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.