“I can count to 10!!” Tim shouted as he ran in the front door.
“Fantastic!” replied his dad. “Show me.”
“1, 2, 3, 4, 5, 6, 7, 8, 9, 10!” exclaimed Tim, excitedly.
“Wonderful!” cheered his dad. “Now,” he said, “can you show me how much one is?”
“Sure,” said Tim. And he proceeded to write the numeral 1. All smiles, he showed his dad, “There!”
“OK,” said his dad, “and can you show me how much four is?”
Tim took a moment to count in his head to four, scrunching up his face to concentrate, and began to draw some squiggly lines that looked a lot like the numeral 4. “That one is tricky,” said Tim.
“Good work Tim,” said his dad.
The problem is, Tim doesn’t actually know how much a number is worth at this point, he knows a sequence but does not have a value for each one, he also has a symbolic memory for a number word.
Sequences are fairly easy to remember but more difficult to learn, think of your phone number, a sequence of numbers that doesn’t change; your address, if more than one digit; your birthday; etc. These are sequences that we remember, but we do not attach value to them, nor do we need to.
Numerals are symbols that take the place of a word. Numbers are values that can be ordered as numerals or collections of objects. Learning numerals is an exercise in comprehension, memory and handwriting. Learning number is an exercise in value recognition and comparison.
Eventually, numerals can be used to great effect when the understanding of the value of the number is secure. Numerals get in the way of said understanding though and really should not be taught until after the value of a number is understood.