Blog Entry 4 - Place Value

"Place-value understanding requires an integration of new and difficult-to-construct concepts of grouping by tens with procedural knowledge of how groups are recorded in our place-value scheme, how numbers are written, and how they are spoken" (Van De Walle, Karp & Bay-Williams, 2009, p. 188).

The main difficulty that children face when learning place-value concepts is the ability to conceptualize the idea of how numbers are formed. Teaching of place-value concept should move from simple to complex, which allows for children to assimilate their prior knowledge in attempts to accomodate with the new knowledge taught. The class was asked to brainstorm on what is our sequence of approach towards teaching place-value, and the following is my stance:

1. Number in Numerals

Children should be re-introduced to the numerals as an individual whole, not part-whole (e.g. 3+1 = 4), including the number "0". In reinforcing this concept, I would get the children to count the quantity of the abovementioned numerals with manipulatives, as those numerals denotes the "ones" value they would encounter when learning about place-value.

2. Place Value Chart

Introducing the place-value chart allows the children to assimilate their prior knowledge of numerals as a whole, numerals in words, number concepts; and put together to accomodate a new concept of how numbers are "broken up".

3. Tens and Ones

Using unifix cubes, I would introduce the numbers by "breaking" it up and get the children to count the "tens" using a colour, and the "ones" in another colour. This is to enable the children to conceptualize visually that for example, 38 is made up of 3 tens and 8 ones.

4. Number in Words

5. Expanded Notion

I perceive the Expanded Notion as the most difficult step to master as it involves assimilating, accomodating and then assimilate again. It requires that the child reognizes the numeral as a whole, "cut" it up mentally, and then conceptualize the numerals as a representation of a whole number again. For example the numeral 38, I would write the number 30 on a card, seperated into two different columns, and then on another card, write the number 8 and get the child to cover up the 0, which makes 38.