Quick Images & Dot Cards: a Number Sense Routine

“… The best learning takes place when we love the activity so much we don’t even realize we are learning! . . .”

Can you imagine my delight, to hear my students enjoy our Quick Image routines as much as playing with their friends

Twice a week we begin our math lesson with a Quick Image warm-up.  This warm up routine allows me to spiral learning throughout the year, building number sense, encouraging mathematical conversations and increasing my students’ confidence in risk taking. The “Quick Images” routine is performed by presenting a picture of organized or random quantities to students for a short period of time (2-3 seconds).  Students are then asked to reflect upon what they saw either orally or by reimagining and re-representing the image. Quick Images provide students with the opportunity to subitize and/or use spatial sense for calculating quantities.

How many?  How do you see it?

How many?

This is how we participate in Quick Image and Dot Card warm ups.

There are two primary methods, both of which encourage the students to visually identify numeric patterns in response to these two key questions: 1) How many? 2) How do you see it?

In the first method, I project an image on the white board.  Students are invited to use a white board marker to circle and write a number sentence to respond: How many? How do you see it? Second, I flash the image for 3 seconds and ask the students to respond: How many? How do you see it?

How do you see it?

Sometimes the students sit on the carpet and I show a card to the entire class. Other times I project the image on the white board. And still other times, I ask the students to work as partners: one student shows the quick image card, and the other students answers our two key questions: How many? How do you see it?

Can you imagine my delight, to hear my students enjoy our Quick Image routines as much as playing with their friends!  The best learning takes place when we love the activity so much we don’t even realize we are learning! 

This is easy!

“… when we realized we just need to change our words (mindful speaking) to make our statements more accurate, we discovered it was magic . . .”

But what about your classmate . . . ?

This is easy‘ are three words that have the power to bring learning to a dead stop! I have always disliked this statement, but never really considered making this a lesson until I read Tracy Zager’s book, Becoming the Math Teacher you Wish You’d Had (2017). In her book she writes about how she had a discussion with her class about this statement, asking how it made people feel and what they really meant when they said, “This is easy”. 

So I decided to try this out for myself. I called a class meeting and we all sat around the outside of the carpet. I said, “When we start our math lesson I am often hearing students say, ‘This is easy,’ and I am curious to know how those words make you feel’. Just as in Zager’s class, my students started say:

  • ‘It makes me feel bad, like I am not smart’
  • ‘Sad’
  • ‘Like I am not good at math’
  • ‘I stop trying’

So I told my students that I had just read a book about this statement, ‘This is easy’ and the teacher said that what this really means is:

  • ‘I’ve seen this before’
  • ‘I feel confident about this math’
  • ‘I understand this math’

I wrote these statements up on chart paper and asked my students what they thought about these statements. Are these statements more accurate than, ‘This is easy’? How would it make our classmates feel to hear these statements instead of, ‘This is easy’?

My class began a process of awareness, reflecting on how our words impact our classmates. Everyone in our classroom takes great pride in being a ‘Mindful Classroom,’ so when we realized we just need to change our words (mindful speaking) to make our statements more accurate, we discovered it was magic! I never hear ‘This is easy’ anymore, yet I often hear, ‘I’ve seen this before’ or ‘I understand this math’.  This is a ‘magical’ lesson! Try it for yourself.

What is Mindfulness over Matter?

“Our daily classroom practices include daily mindful breathing, explicit teaching of what thoughtful listening is . . . community building exercises and deep conversations about holistic learning . . .”

Mindfulness over matter is my space to practice what I preach. A space that reflects that learning comes from passion, creativity, and play. Through mindful listening and thoughtful and responsive teaching I construct and reconstruct my professional practice to meet the needs of the students in front of me.  Our daily classroom practices include daily mindful breathing, explicit teaching of what thoughtful listening is (what it looks like and feels like), community building exercises and deep conversations about holistic learning (such as sleep habits, healthy eating and exercise).

 Building a learning community where it is safe to be vulnerable, take risks and believe that there is more than one way for us to get to where we want to go. There is not always one right answer, one path, or one way of being.  My recent focus on math lends itself so well to the mindful classroom. The standard used to be summarized in pragmatic terms: ‘Being good at math means you answer the teacher’s questions fast, right, and easily’ (Zager, 2017).  However, mindfulness over matter is the concept of providing access for all students to creatively engage in meaningful hands on learning experiences in a classroom that values risk taking, persistence, and courage. We believe there are many ‘right’ ways to get to an answer. Learning takes patience and time, and grappling with concepts. This is not ‘easy’ but it is a worthy challenge.

Why am I Starting a Blog; a learning journey . . .

“Building relationships is at the heart of teaching and learning and it is my desire to build my connection with the local and global community of teachers and learners . . .”

Over the years, I have discovered that teaching and learning are one in the same. I teach students to be curious, passionate, persistent, and take risks with their learning. This blog is a forum to collaborate, share ideas and build on the ideas of others. A space to intentionally and purposefully reflect on learning experiences in order to support responsive teaching that offers students meaningful learning experiences that are student-centered, inquiry-focused, and reflect real world experiences. Building relationships is at the heart of teaching and learning and it is my desire to build my connection with the local and global community of teachers and learners; to share stories, strategies, and ideologies. This is my forum to take risks, explore, wonder, be curious, and embrace challenges with the goal of creating powerful pedagogy and providing a window into the learning journey.