Wednesday, 10 April 2013

One-to-One Correspondence and Counting Skills

Children can find many opportunities in their daily life to experience one-to-one correspondence.

ü  Place one sock inside one shoe

ü  Place one lid on each of several containers

ü  Place a cup with a plate

Once children understand these relationships, they can link one number with one object and then count with understanding. “Rote memorization of a set of numbers is meaningless” (Moore, 1973, p. 67) and counting is a skill which should not be stressed until the child has shown understanding of basic classification, conservation, seriation and set comparison at both the quality level (attributes of objects) and the quantity level (general amounts in groups or sets).

When students are equipped with the counting skills, they can benefit from learning several other counting strategies to increase their accuracy and efficiency. Just like any other concepts or skills, it is vital to start working with real objects and manipulative as learning aids.


Basic Concepts

To work with formal mathematical concepts successfully, students must understand the concepts of classification, sorting and one-to-one correspondence, just to name a few. It is imperative to first work with and understand these concepts on the basis of quality that is the attributes such as shape, size or weight before moving on to their application to general quantity such as many, few or none.

In order for students to develop their distinctive number sense, and a working knowledge of the above concepts, they must be exposed and interact with their environment, exploring and manipulating, comparing, arranging and rearranging real objects and sets of objects.

Activities for teaching basic concepts

  • Involve children in daily living activities around the home or classroom. For example, helping to put manipulative in a divided tray with a sample in each section provides practice in matching, sorting and categorizing; helping to sort different items of utensils or cloths in the dramatic play centre provides additional practice with these concepts.
  • Give children various opportunities to use everyday items for matching and categorizing: eating utensils, work tools, food or fruit, and toys for function; shoes and shoelaces for matching by size or length.
  • Have children copy simple shapes on geoboards. After they are able to work independently, they can make their own shapes based on names or clues such as "four corners" “three sides”, etc.

4 Stages of teaching

In teaching Math, I have learnt the 4 stages of teaching.

1.      Modelling

2.      Scaffolding

3.      Providing

4.      Explaining

It is imperative for teachers to model first on how to find the solution to the problem sum. Give much support where necessary. After that stage, teachers can move on to scaffold and facilitate their teaching. Prompt the students too when need be and providing them with the possible solutions. The last stage would be the explaining stage. This is the high level process whereby the students are able to do most of the problem sums independently with no more of modelling, scaffolding and providing them but to explain what the problem is and they work the sums on their own. Vygotsky said that learning should happen in a group. It is beneficial that children learn in a social group. Bruner on the other hand believed in the CPA approach. That is through Concrete – Pictorial – Abstract.

“People are made clever, not born clever” ~ Jean Piaget

The difference between assimilation and accommodation in Math:

ü  A child will see numbers and add. For example:
1 apple + 2 apples = 3 apples
ü  A child will encounter something existing.
ü  A child is able to encounter a conflicting problem.
ü  A child will know that he/she has to solve the problem.
ü  Modify his/her thinking
ü  Create schema


*Implication: An adult shouldn’t be presenting things crystal clear for children. In simpler context: Do not spoon feed a child. Let him explore and try. It is alright to let the child know that it is fine to make mistakes. We learn and avoid it from reiterating.

Using nursery rhymes as a stimulus for teaching math

Humpty Dumpty sat on a wall.

Humpty Dumpty had a great fall.

All the king’s horses and all the king’s men.

Couldn’t put Humpty together again.

Question: Who is Humpty Dumpty?

Ø  Is he an egg? What evidence do you have to state that he is one?

Ø  How do you know he breaks?

In Math, we use Humpty Dumpty as a stimulus for perhaps young children.

We touched on:

ü  Measurement for the height of the wall.

ü  Counting for the number of horses and men.

ü  Perhaps even classifying first then counting the number of men and horses.

Another point that I learnt is that the word “similar” is not in mathematical terms. At times, people tend to ask a similar question between 2 different objects but of a similar property. That is wrong. For example, a teacher may show a picture of a lion and a tiger and ask the children, “What is similar about these 2 animals?” The answer the teacher may get is, “They are both big animals.” Is that right? Similar in this context means one enlargement of another. So therefore, it is not advisable to use the word similar unless you mean it.

Case Scenario and Estimation

Today, Dr Yeap gave a case scenario of a child named Tim who cannot count. As a teacher, what are some of the strategies can one work with him so that he is able to count?

1.      Get him to rote count together. If he can’t say it, perhaps teacher might want to say it out loud first then get him to repeat.

2.      Give Tim concrete materials to work with. Here, the teacher can do a 1 to 1 corresponding with him.

3.      Teacher might want to suggest aid or advice to parents to do the necessary follow up at home as well.

We did another problem sum that is to estimate the number of paper clips in the bottles.  Dr Yeap gave us a bottle that contained 3 paper clips as a benchmark to do a comparison with the other bottles that contained x number of paperclips. Benchmark is an important concept and is best used in fraction.

So, how did I guess the number of paperclips in the cans…

ü  I did so by moving the bottle back and forth and shaking it from left to right

ü  Listening attentively to the sounds of the paperclips.

ü  Estimate the number of paperclips in the other bottles by making comparison using the bottle that contained the 3 paperclips as the benchmark.

Cute numbers

In today's lesson (Monday, 1 April 2013), Dr Yeap covered the topic on the different uses of numbers. he introduced ordinal, cardinal, rational, rote, nominal numbers and conventions. That is quite a fair bit of information to internalize. Not that we need to teach the kids per say but it is definitely a good information for us teachers. Dr Yeap also did mention the properties of numbers like the odd, even, prime, perfect and cute numbers. Cute numbers? Really? Is there such a property? So I did my research.

Abstracted from this link:

For example of cute numbers are 4 and 10. The reason is if a square can be cut into n squares of at the most two different sizes, then n is called a cute number.