Building Community in Mathematics Class

The best way to build a math community is through doing mathematics together.

I'm sure we all remember the first day of school when we woke up excited and ripe with anticipation about how our year would play out, only to be hit with a day full of rules, syllabi, and boredom that didn't actually look like a typical school day at all.

So let's flip that switch and start the year with mathematics, modeling the classroom we want to have all year. Norms are not set and learned in a day; they are nurtured and develop through discussion throughout the entire course of the year. By starting the year with an accessible, engaging, mathematics task and reflecting on what went well and what could be improved, we set the tone for this conversation and mindfulness about how our classes function to continue throughout the year.

I like to use this form to help gather students' reflections on the day.

Lots of folks in Twitter-land have great activities to use that they have generously shared. Here are some of my favorites:

• Sara Van Der Werf's "100 Numbers to Get Students Talking" has been fun for me to use with both middle school students and adults in professional development sessions. Establishing what group work looks like is achieved through purposeful scaffolding and photographs that she describes in her blog post.
• Annie Forest uses "Me In Numbers" to share some information about herself while also giving students a chance to showcase their number sense by providing a bank of numbers for them to reasonably match to a statement. I love how she then gives the students a chance to make their own that she attempts that night. 
• Sarah Carter uses "Broken Circles" to help establish group norms and roles. I love that it is a little variation from the wordy, algebra-heavy problems I tend to use, giving another access point to engage more learners. (Sarah also shares her awesome posters for classroom set-up).
• I also love these two books, which have card sets with clues to help kids work together to solve a math riddle. Get It Together has lots of levels and categories of problems, and even has a sample on its site to whet your palette. United We Solve is similar, and has a sample in the preview at this link.
• Get started with your daily number sense routines right away! Number talks are my jam, and I love using WODB at the beginning of the year since they are so open-ended, but there are many, many more.

Regardless of the task, focus on access, engagement, and reflection built around mathematics!

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.