In my last blog entry I talked about laying the foundation for fractions in K-2 by thinking about the standard for measurement 1.MD.2 as foundational for the conceptual understanding of fractions. In this entry, I am going to talk about what it means for a student to coordinate units.
The word coordinate, when used as a verb, is defined by Webster’s Dictionary as:
“To cause (two or more things) to be the same or to go together well: to cause (two or more things) to not conflict or contradict each other.”
This past fall at the AIMS Center for Math and Science Education, my research team looked into how students are able to coordinate units. In fact, we are designated the Coordinating Units team. The next question you probably have is what do I mean when I say unit? For our purposes, a unit refers to an amount. One example is our monetary system. We start with one penny. Then a nickel, which is made up of 5 pennies. A dime is made up of 10 pennies or 2 nickels. A quarter is made up of 25 pennies, or 5 nickels or 2 dimes and a nickel or 2 dimes and 5 pennies. A dollar is made up of 100 pennies or 20 nickels or 10 dimes or 4 quarters. This is a system with many levels of units. A student who is able to work within this system is able to see a penny, nickel, dime, etc. each as countable units and can coordinate all the levels of the units they are working with. This is not the only system with multiple levels of units that students encounter. Some others include: time (second, minute, hour, day, week, month, year, decade, century, etc.); place value (one, ten, hundred, thousand, million – tenths, hundredths, thousandths, etc.); standard measurement (inch, foot, yard, mile, etc.); and metric measurement (millimeter, centimeter, decimeter, meter, kilometer, etc.).
The last two examples are dealing with units of length measurement. There are also levels of units for measuring volume and mass. Our team is tasked with observing how students construct their understanding of coordinating different levels of units. This is critical for students to be able to develop a conceptual understanding of our number system. To do this they have to be able to construct a unit. A student cannot begin to coordinate levels of units unless they have constructed an understanding of number (a unit). This is the foundation for the work students do with mathematics. To learn more about coordinating units, I invite you to look at past blog entries from our Coordinating Units research team on the work we did on the “Tower Task” with students and keep on seeking out our blog entries this spring to see how coordinating levels of units connects to building a conceptual foundation to work with fractions.