"Only when the child has a secure cognitive grasp of the physical model can they successfully transition to the symbolic language of mathematics."
~Jerome Bruner (Psychologist who developed the CPA—Concrete, Pictorial, Abstract—approach)
Traditionally, place value has been taught using place value blocks.
Will students learn the concept using the blocks? Almost all do eventually grasp it.
But they have limitations.
Cost, which limits quantity, in turn limiting manipulative practice.
Don't bring real-world experience and understanding to undergird learning.
Noisy as well as comparatively time-consuming to use.
Hard with sharp edges, potentially hurting someone.
While students frequently encounter math problems that have pictures of place value blocks, they are not the most effective tool for initial learning about place value. It's important for students to know about place value blocks — eventually.
What is a better way to learn about place value and regrouping that was easier to use in classroom or other settings and more effective for helping students understand the concepts?
Actually there is!
Place Value Money manipulatives and models have some built-iin advantages over Place Value Blocks.
They are:
Inexpensive, allowing each student access to the manipulatives and more practice than can occur with limited supplies.
Bring with them some basic prior understanding since students observe parents and others use money, make change, and exchange bills – in other words, regroup.
Have their place value written on them.
Quiet as well as relatively quick to use; less distracting.
Include decimal place value manipulatives with dimes (tenths) and pennies (hundredths).
Last but not least, no hard surfaces or corners that could hurt or trip anyone.
"Kids don't learn math because they use manipulatives; they learn because they think about the manipulatives."
~ Kate Snow (Math Author)
"Concrete materials provide a vehicle for students to clarify their thinking, discover relationships, and verify their insights."
~ Marilyn Burns (Prominent Mathematics Educator)
What's a manipulative?*
"Manipulatives are physical objects that students are explicitly intended to use to discover mathematical ideas."
~ John Van de Walle (Late Mathematics Educator and Author)