An Ode to Card Sorts

Why are card sorts so dang magical?

Any chance we get to shift students' thinking is great, but resources like Formative Assessment Lessons (Classroom Challenges) from the Shell Center take it to a new level. I have implemented many of these as a classroom teacher and now as an instructional coach, and each and every time kids make new connections, experience "a-ha" moments, have meaningful mathematical discussions, and are highly engaged.

I have used card sorts to review and reinforce concepts, to make connections among representations, and establish group work norms. Some of them have even helped me allow students to discover new ideas, including vertex form of quadratic equations through this gem!

Today I was in a classroom where the teacher was helping students make connections among linear tables, graphs, and equations. She used Mrs. Math's sort to give her class time to explore. Her launch was to ask them what they noticed and wondered about the three representations in purple. Students' thinking is in green.

Next, students explored only the graph and equation cards to try to make matches. They were overwhelmed at first, but then started to create subcategories like "positive slopes" and "goes through the origin."

And thus began the magic. Some of their observations and strategies were noted on the board as they discovered them. The scribing doesn't do the conversations justice, but you get the idea of some of the connections they were making.

The Shell Center was my first introduction to these powerful tools, but since then I have discovered several other sources.

• Desmos has some labs, complete with Pro Tips for implementation
• States like Georgia and Kentucky have expanded to K-5 resources
• Lots of teachers are creating their own, too, like Beth at Algebra's Friend, and this one at Better Lesson

I'm sure many of you have come across some great resources, too. Please share in the comments so that we can all build our arsenals of these amazing tools! 

Begin again.

I started a blog a while back, and had every intention of writing faithfully. Then my world was shaken when my dad, who was also my closest friend and most enthusiastic soundboard for all things life and education, lost his battle with acute myeloid leukemia. That was three months ago today. Suddenly, all of my efforts were needed simply to function and the blog ended as quickly as it had begun.

But this space will not be used for wallowing in that enormous loss. I can't call my dad to share my excitement, challenges, revelations, or random thoughts anymore, but I hope that writing them here will honor those conversations and make navigating the tumultuous world of education a bit more mindful, for myself and for others. 

Losing my father made me come to a full emotional stop. Slowly, I am shifting toward a new normal. My dad’s favorite number was 53, and I felt it was an apt number to describe the turn I have made in the grieving process; significant, but not impressive, not a clear mathematical benchmark. It also seemed relevant to what I am starting to shift in my practice leading professional development.

It is common practice to throw things away in education quickly and with reckless abandon in our pursuit of the latest trend. Often, the replacements for those original things are not fundamentally different, but they are presented as if a whole new philosophy has emerged. This presentation often demotivates those doing the work, and leads to poor buy-in, or worse, viewing all PD or all new initiatives as useless.

So what is a gal to do when she is responsible for leading PD and knows that we humans do not learn something deeply the first time we work with it?

Rather than dwelling on the frustration I feel when sharing information that people think they have heard before, I try to focus on the shift that has been made to get to the “new” tool or idea.

Take, for example, number talks. This year with my quarterly PD groups I have tried to illustrate how my own practice with number talks evolved over time to help them reflect on best practices. Here are my stages:

1.    Just do them.

·       When I learned about number talks, I just tried a bunch of them.

·       The CCSS-M Standards for Mathematical Practice (SMPs) 1, 3, and 6 were my goals.

·       I learned that the power was in the routine; the more I led them, the better my students got at them.

2.    Try to illuminate structure.

·       The discovery of number strings helped me think about how I could foster SMPs 2, 7, and 8.

·       I learned about them here and worked to build effective strings to help my students recognize and use structure to compute mentally.

3.    Purposefully plan toward a big idea.

·       I was sold. I wanted to incorporate them into my daily instruction to address needs my students had.

·       I started to plan a set of 3-5 related prompts that built toward a big idea.

·       This helped me be faithful to implementation because I was prepared, and it also helped me dissect the standards to understand how big ideas developed conceptually.

So yes, we have all heard number talks and many of us are using them with our students. But if we make just a 53-degree shift in our thinking about them, we might just find something new to enhance an already solid practice.