Back in the mid-2010's when my position in math education expanded outside my own classroom as an instructional coach, presenter and trainer, I realized I didn't have a succinct and portable definition of number sense. This was a problem because I had numerous conversations with teachers and we agreed that many students struggle with number sense, but we couldn't necessarily put it into words. We described actions with examples, but I was hungry for a concise definition of number sense.

Steve Leinwand and Marilyn Burns (Two of 5 Math Giants who have inspired me) have given us buckets full of guidance on this topic. Steve Leinwand's book Accessible Mathematics is a great motivator for prioritizing students developing their number sense. Marilyn Burns has a strong resumé full of student interviews and articles where she showcases student thinking and the importance of number sense. She has also gifted us with many attributes of number sense and what it can look and sound like with students. I am eternally in debt to these two giants in math education. In this video, I share a few of their contributions and three questions I frequently ask my students that have all come together as my definition of Number Sense.

I frequently ask three questions that sound like this: 

1. How did you come up with ______?
2. Why did you decide to _______?
3. How do you know you were correct? [without me telling you]

The result is my definition of number sense. 

Number Sense is "thinking flexibly about numbers with purpose and accuracy."

Having this definition really captures how I can assess a student's number sense. There's a gem of an article written by Marilyn Burns titled How I Boost My Students' Number Sense and one of the exercises she endorses for developing students number sense is for students to "Estimate. Estimate. Estimate!"

I AGREE!!!  However, this begs the question... what is an estimate? Stay tuned for future blog posts (and videos) on why estimation is so important and how I define an estimate.  

Click here to get the FREE Definition of Number Sense poster to print and hang in your classroom. I hope you find it helpful when encouraging students.