I have briefly made reference to the concept of operational fluency in the past. It is the idea that students need to know more than just basic facts and standard algorithms in order to truly understand any given operation in mathematics. For example, students need to know addition facts from zero through twenty, the inverse relationships in subtraction, the multiplication facts from zero through twelve, and their inverse relationships through division. They need to know the standard algorithms for operations so that they can add, subtract, multiply, and divide with ease.
But they also need to know what is actually going on when performing an operation. That means understanding different change situations, such as an unknown starting quantity, unknown addition or subtraction, and unknown final quantity. Operational fluency means that students can recognise multiplicative or additive comparisons, equal-shares, and what a remainder represents.
We only have two items on our progress reports that relate to operational fluency. One is that students will use the four operations with whole numbers to solve problems and assess the reasonableness of answers. The other is to use place value and properties of operations to perform multi-digit arithmetic. However, these concepts are fundamental to everything else we will do in math this year, which is why we spend so much time working with the four operations and developing fluency. Our first arithmetic unit focused on the properties of multiplication. We have just started our second unit, which will explore addition and subtraction properties. My goal is for students to understand that these basic operations are foundational to mathematics in general. I fully expect this unit to move quickly and I hope that students will use what we are learning throughout this unit as we move on to concepts beyond basic operations, especially adding and subtractions fractions and mixed numbers later in the year.