Numerical fluency can be defined as the ability to perform mathematical operations with accuracy, flexibility, and efficiency. Fluency also involves having a solid understanding of mathematical concepts and being able to recall them without much thought. Accuracy is so much more than memorizing the correct answer. Students must understand and connect ideas – to make a visual in their minds so that when they encounter quadratics and other polynomials, they have a solid understanding of factors, products, quotients, etc.

Let’s say you are a student struggling to learn your multiplication facts. There are 33 facts in the 7s, 8s, and 9s assessment. When interviewed, our 4th, 5th, and 6th graders tell us that 7s, 8s, and 9s are tough. Oh, and sometimes 6s are tough too. What if we help our students focus on what they know and what they need to work on?

Let’s look at data from August and September for one student.

The data above says how many of the 33 facts were correct. What if we empower students to see what they know and need to know? Another view of the same data reveals known facts and facts that are yet to be understood.

What if we focus on sense-making? What if we see the strength in what this student knows? How can we help them work on what they need to know? Will understanding, accuracy, and sense-making improve given a narrowed focus and more time? Look at the data in October and November.

Okay, true confession. I am not always confident about 7×8, either. But I can quickly reason with 7x4x2. We see growth in this student’s accuracy and understanding. I wonder if this student is rushing through the accuracy checkpoint. Maybe we need to help this student slow down, check their work, and pay attention to the commutative property.

If you know 6×7, how might you use this knowledge to find 7×7? Since accuracy is more than memorizing facts, what sense-making tips might this student respond to?

Every student has different strengths and different needs. How might we empower students to take action based on their data, their strengths, and their needs?