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## The First Steps in Developing Conceptual Understanding of Place Value

### § June 27th, 2011§ 2 Comments- Add yours§ Filed under Teaching Math§ Tagged conceptual understanding, counting, manipulatives, Maryscott Glasgow, place value

Photography by Kathy Cassidy

In an earlier blog I shared my concern about my eight year-old grandson knowing how to calculate the correct answer when adding two-digit numbers without knowing the value of the digits in the addends or sum.  But helping children understand place value is more than telling them which number is in the ones place and which number is in the tens place or even that the 5 in 54 equals 5 tens.    It takes their active involvement to develop conceptual understanding of this key concept.

Think about your own experience, your child’s or grandchild’s experience when learning to count.  I’m pretty sure  those experiences are similar to mine—that it seems intuitive to use one-to-one correspondence with real objects when learning to count.  One, two, three balls.  Four, five, six books.  However, when learning to count to ten and beyond, it seems that imitation and rote memorization are valued.  To illustrate my point, haven’t we all heard a parent claim that their child can count to 20?

My recommendation is to establish a more meaningful goal, such as helping the child learn how to explain what 32 actually is, for example, ‘three groups of ten and two ones.’   I realize rote memorization takes place before understanding when it comes to counting, so I am not here to discourage parents from teaching their children how to count to 20 and beyond from memory.  But by the time a child is four, teaching a child what to do when ten objects have been counted and relating it to the abstract base ten numbering system is not only desirable but recommended.   All it takes is patience, something to write on, and some objects to count.

Of course, there are many  types of objects that can be counted. There are proportional and non-proportional manipulatives (objects) that can be used.  An example of proportional objects are those that actually equal the number in terms of size or quantity.  Take base ten blocks, for example.  The ones are called units.  When you stack ten units together, that stack equals a ‘ten rod.”  Once the child reaches 10, those 10 units are exchanged for one ten rod.  The ten units can be stacked and compared to the ten rod.  Both are the same length.  Money, particularly coins, are considered non-proportional.  Ten pennies equal a dime, which is equal to 10 cents, but the coins themselves when stacked together do not equal the size of the dime.

My favorite way is to use drinking straws.  When the child counts out straws and reaches ten, have the child bundle them with a rubber band.  Call that bundle one group of ten, then write the number on paper.  Point out that the one in the number 10 stands for that one group of ten straws.  When you put one straw next to the bundle, then write the number 11 explaining what the new straw represents.  I think you catch my drift here.  Allow the child to count and work with the straws explaining what each addition to the group means.  Using the objects, or manipulatives, along with the abstract symbols, or numbers, provides a great bridge to understanding the true meaning of place value.

### 2 Responses to “The First Steps in Developing Conceptual Understanding of Place Value”

• It’s so important for them to understand the concept of place value and base ten. It helps eliminate some of the confusion when regrouping fractions later in their academic career:)

I like the examples and language used of non-proportional items and drinking straws– easy to relate to. The earlier they are introduced to the appropriate terminology the more likely they are to apply it succinctly and engage in meaningful discourse.

• LaToniya makes an excellent point when she states that the earlier children are introduced to the appropriate terminology the more likely they are to apply it and use it.