The mystery that is Math

Mahesh Sharma , whose ideas I was introduced to by Dsycalculia specialist Steve Chinn , talks about 6 levels of knowing mathematical ideas. Without going into too much detail, they are:

1. Intuitive: every new fact is introduced as an extension of something the child already knows.

2. Concrete: each new fact is presented through a concrete model

3. pictorial: the model of the new fact may be sketched or illustrated

and then 3 more! (Click on Mahesh Sharma’s name to read all) So before you show your child:

+ = 3

It may be useful to consider nos. 1 and 2. Experience builds on experience. Without concrete experiences, you fumble with ideas and will never truly understand. Montessori also proposes the idea of concrete experience as indirect preparation for later academic subjects like Mathematics. Some of the ways this is done, is through a Montessori Practical Life activity of Pouring Water.

In this activity, the adult demonstrates pouring water from a jug into maybe 2 cups. There is just enough water in the jug to fill 2 cups. An activity like this responds to the individual’s tendency for self-control, precision and estimation which are important mathematical skills. The child needs to estimate the tilt of the jug, control his movement to control the rate of flow of the water to ensure that the precise amount of water fills the jug so that there is just enough for the second cup. This is a straight forward thing to do but think of how often a 2 year old is allowed to pour a glass of water for himself. Pouring Water in a Montessori environment allows the child the opportunity to explore, experience and to do it many times without anyone thinking it a bit strange. What follows here are 3 tried-and-tested games to play with your child at home and which provide avenues for your child to have concrete experiences of exercising self-control (in other words, ‘being careful’), precision and estimation. This requires your child to almost be able to rote-count 1-10, if not, then it will certainly help.

1. Spot the chestnut

1. Stones in a Jar

The challenge here is to guess (estimate) how many stones will fit in the jar. Large stones are useful for younger children because, well, then there are fewer to count. Gather smaller stones with your child in the park for a bigger challenge. A useful tip is to demonstrate doing it once by yourself with a set of stones and thinking aloud for your child to observe : ‘hmm! I wonder how many stones I can fit in the jar? (Put a stone) *gasp* That’s one stone. I think I can fit another one in there. (Put another stone) *gasp* It fit! etc. etc,’ and I am not joking about *gasp*. Then, leave it to them to fill the same jar or another jar with a different set of stones.

*Note* It’s really not so important if little lucy counts 1,2,3, 5, 8,9,10. Instead of correcting this on the spot, show them again on a separate occasion and just work on rote-counting for fun.

2.Sorting pennies

2. Sorting Pennies

Got a spare- change box? Draw your child’s attention to it and say aloud something like, ‘I wish somebody could organise these coins.’ Have faith! If not today then one day, he will say, ‘Oh! I can!’ If he does not, leave it and on another day, take it out and do a little yourself in a place where he can see. A few things may happen, he will start to do a little along with you and you quietly slip away or he will just watch and you can suggest it for him again on another day. Older siblings are particularly helpful for this and can usually organise the whole activity. For the younger child, it will be a sorting and categorising exercise. To extend the challenge, suggest that he makes stacks of 5 or 10. Older siblings can of course be tallying these up. The older child will be very pleased at the challenge and because he will not be so interested in just counting and stacking whilst your 3 year-old will! Then, as a family, decide what to do with it!

3. The orange challenge

3. The Orange Challenge

This is the perfect challenge for 2.5-3 year olds. Ask your child how many sections he thinks the orange has and would he like to find out? The first challenge for your child is to peel his own orange. This can be a real challenge and can be scaffolded with you helping to take the first piece of peel off. To encourage your child to make a real effort and persevere, fiddle around with something else and say to little David that you are doing this and that and you will help him as soon as you can but you might take a REALLY long time, so he can keep trying to push his finger through the peel. Then separate the sections, count and eat them! Challenge 2: Do ALL oranges have that many sections?

Before long, your child will be inventing his own challenges and perhaps some for you!

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