28th March 2015
We start off with a small group of 7 children (aged between 4 to 8 years) and their parents for an explorative approach to discover mathematics through activities and games. The session was meant for parents to observe and see how a child learns. Mathematics Explorers is what I would like to name the group as.
A certain number of tamarind seeds were given to every parent and they were asked to count them. Most counted one by one, a parent picked up random number of seeds like three or four at a time and kept adding; another parent made groups of three and multiplied the certain number of groups to get the result. The art of counting is very important and it is very difficult to get most children master counting after a certain age. The younger they start, the better they master it.
I generally ask parents and children why we need to learn multiplication tables. The most common answers are:
- It is useful (How? The question is unanswered but they have accepted blindly that it is useful)
- It is useful in higher classes (Again the same thing)
- We can use it to calculate area (But a child of 6 years doesn’t know area…so how do we explain it to them that it can be used in finding the area?)
- It is asked in the examination
- Because we have to learn (That’s it!)
The activity of counting is a good opportunity to show children how we can use multiplication and count faster (like the parent who made groups of three). It will also make them realize that multiplication is repeated addition.
While doing this, it is best suggested to take things that the child can touch, feel and take in its hands while counting instead of doing it use a pen and paper. Seeds, shells, coins, pebbles, marbles, the options are innumerable.
Video link: https://youtu.be/_NYWoAdWn8k
Odd & Even
While taking session for middle school students we ask them – What are even numbers? The most common answers are 2, 4, 6, 8 and so on. It takes a time to make them realize that they have answered to a different question (Which are the even numbers). Then we ask, what do you ‘mean’ by even numbers which is generally followed by a silence and a blank look on their faces which can be translated as ‘What is this guy asking?’
In most cases, the concept of even and odd numbers is not taught. It is directly told to children that 2, 4, 6, 8 and similar numbers are even and rest are odd. Reason is not emphasized. Instead, if we can show them what makes a number odd or even they would get a clearer picture of it.
Video link: https://youtu.be/gScdN7CQrOs
Mathematical games 10-10
10 seeds are placed on the floor in this two-player game. Each player can take away one or two seeds at a time from the pile. Players play by taking turns and the player who finishes last, wins the game. This can be played with kids of 6 years and onwards (even adults). It is a strategic game where one has to discover who has got the winning certainty before we start the game. Initially a child would randomly pick any number of seeds (even adults would), but later he starts analyzing the game. The real advantage of the game is that they start analyzing and foreseeing moves by the other player. As we see children after they have played 8-10 games, they slow down in playing because they take the time to think and play (a very important skill that we can impart to children – Taking a pause to think before acting). Usually, after having played around 20-25 rounds of the game, a child realizes the winning strategy. Some might realize much after 25 rounds but that’s ok…we as parents/teachers need not rush into it or get worried. Patience is the key!
There’s some mathematics to this game. Depending on the number of seeds and who plays first, the fate of the game can be decided. The parents in the session discussed and worked on it till they finally discovered the secret behind the game. Once the kids know the secret behind the game with 10 seeds, we can extend it to 11 seeds or 12 seeds and keep increasing the number. The one who can guarantee winning if given a choice whether he needs to play first or next, has got the essence of the game.
While this game is played with parents, it is generally noticed that some of them tend to get mentally tired of thinking to crack the question. The reason is simple…as a child they might never have gotten the opportunity to persevere something patiently because of which that attitude and capacity of holding only a chain of thoughts that leads to logical reasoning has reduced.
Video link: https://youtu.be/YLbihbNEfKM
Tips for parents
A true teacher is one who makes the student discover the knowledge on his own without actually teaching them much. Most of us are ‘taught’ and for the same reason we too teach children because we do not know any other way to make them learn. Taking the example of 10-10 to explain the kind of questions we can frame:
- Where do you think you went wrong (instead of showing them directly where they went wrong)?
- I’m happy that you got this correct, but had you not taking the number of seeds you took now; do you think you would have won? So, what was the number of seeds that if you would have taken would have made you lose in the game? (This will help the child realize the wrong move he could have made)
- The above types of questions are called ‘Incisive questions’ which when asked to someone would make them think and get the solution on their own instead of we supplying our solution to their problem. (Source: The Teacher who Taught us to Think)
- Patience is the key. Education is probably the slowest of all processes. Nothing is achieved fast. More than children, parents and teachers need to be patient and go by the pace of the child. A way a teaching and make or take way the interest of the subject in a child. So next time, do not blame the child.
- Each one teach one. Learning becomes more effective and strong by teaching.
- Play with your child as much as you can. It creates a strong bond between both of them and it also gives the parent an opportunity to see how the child is learning.
This was the first session I had done for such young children (apart from teaching my own son) and I should admit that it didn’t go exactly the same way I had planned. The task to keep the children engaged in an activity was important so that I could have discussions with their parents. The presence of the children was also very important for the parents to learn. Having helping hands to assist the session and a small group made it possible to engage in a two-hour session.
The person who benefitted the most was me. Thanks to all the children.