A lot of students may find themselves struggling as they get into the higher levels of mathematics. One of the assumptions of mastering math is that you just need to memorize the formula and plug in the numbers. But to truly excel in any field, you must also understand the concept and the reasoning behind it so that you can play around with it. Well, this learning perspective can be applied to concepts in elementary school math as well.
Place value is the idea that each digit in a number represents a certain amount, depending on the position that it occupies (quick note: a “digit” is a particular number within a larger number; the “number” refers to the entire group of digits). Thus, a number like 465 has a 4 in the hundreds place, a 6 in the tens place, and a 5 in the ones place. The digit 4, in the hundreds place, does not represent 4 – it represents 400. This idea is generally introduced in the lower elementary grades in order to help students manipulate numbers and solve problems. If a child understands that 465 is actually 400+60+5, he or she can play around with this number more easily. Understanding this concept might make it easier to add or subtract numbers, as well as use multiplication in the future grades – 465 x 3 = (400 x 3) + (60 x 3) + (5 x 3). This method avoids carrying over in multiplication, which is where a lot of students make calculation errors.
The concept that numbers can be broken apart and put back together gives the student a more solid understanding of how different operations work. Not only that, but the student can also figure out how to solve problems independently by playing with the numbers. Once a child has a good understanding of place value, he or she will have an easier time with addition, subtraction, multiplication, division, expanded notation, etc. Place value is the “why” behind the basics of mathematics; it teaches beyond memorization and repetition.
Ruth Rumack has been a full-time teacher and educator since 1996. Visit her Google+ page to find out more about early childhood education.