We are making great strides in mathematics teaching and learning. We are supporting our teachers to understand the content and employ strategies that make the math accessible and rigorous, all while using problems worth solving in class.
Following much conversation, feedback, and contemplation, I am working to design what I am currently referring to as a lesson structures for both my elementary and secondary mathematics teachers. This comes in response to a request and will be communicated in that way, as opposed to a top down mandate. Great things are happening in our schools, but our teachers need direction when they are overwhelmed, a nod of support when they are on the right track, and tools for on-boarding when they are new. That is what this work is about.
Even though we are moving forward in math education, we have an opportunity to collectively do math differently – for the better. We have the chance to empower our students with skills to retain and retrieve what they have learned so that they may connect, compare, extend, transfer, and create with this knowledge. The problem is that we do not do this well, if at all. Why do we not teach our kids how to use metacognitive skills to own their learning? I cannot grasp why we are not transparent with students, providing them with clarity about what they will learn, what they are learning, and what they have learned so that they can be in control.
So, consider a team of teachers gathered around a planning table, looking at the next unit of study, making decisions about the learning experiences they will provide for their students. What steps do they take? Do they use a calendar to plan 8 consecutive lessons followed by a day of review then a unit test? I so very much hope they do not. But, since hope is not a strategy, this is where the lesson structures comes in.
Back to the planning scenario. Based on that given topic, using the lesson structures, the teachers may choose a few inquiry-based tasks, some whole group mini-lessons with small group next steps, and even some days structured solely as small group days. Each of these experiences should be purposefully chosen, equitably designed, carefully sequenced, all with learning as the goal. What I strive to see is learning design that pulls from the best-in-the-world content and resources so that all students have the opportunity to learn and be successful. I also look toward design that is centered around what the students will do, not what the teacher will do.
In my design there are three lesson structures, each including a few portions that are consistent across the various means:
- Number Sense Routine;
- Reflection; and
- Retrieval Practice.
The Number Sense Routine may look like a Number Talk or various other formats such as Which One Doesn’t Belong?, Notice & Wonder, Numberless Word Problems, Would You Rather, Same & Different, Estimation 180, Count Around the Circle, or Clothesline Math. The point is that there is an opportunity EVERY DAY for students to make sense of mathematics, develop efficient computation strategies, communicate mathematically, and reason and justify solutions. The emphasis here is on the students doing the math.
Also, EVERY DAY students are provided an opportunity to intentionally reflect on their learning. This may include posting content to their portfolio, writing in a journal, or responding to a well written prompt with a classmate. As adults, we reflect on our day in the car during our commute, at the gym while we work out, or at home as we cook dinner. We think about what worked, what didn’t work, and what we would do differently if given the opportunity. Let’s move toward providing this reflective time for our students as well.
The final commonality amongst the lesson structures is Retrieval Practice. My first experience with this tool was when I read Make it Stick. Since then, I have listened to the 15 podcasts on the subject by the Learning Scientists, explored the content on the Retrieval Practice website and began reading Small Teaching by James M. Lang. I have only begun in my learning of this under-utilized opportunity to support our students. It is exciting to think that a few intentional, purposeful moments in our classrooms can empower our students to become owners of their learning – teaching them how to learn, how to study, and how to use this knowledge to be successful. Why not?
In addition to the work to incorporate Number Sense Routines, Reflection, and Retrieval Practice into the lesson structures, I am working to communicate the role each of these (along with Inquiry-Based Tasks, Whole Group Mini-Lessons, and Small Group Mathematics) fit into our structure of Understanding by Design. The clarity on this connection came to me recently and I am comforted in the alignment – when connections are this apparent, I am assured it is the right thing to do for teachers and students. Within Understanding by Design, we design learning for one of three purposes: acquisition, meaning making, or transfer. For many years, we have struggled to articulate the distinction among these three outcomes. Until now.
- Retrieval Practice is for Acquisition.
- Number Sense Routines are for Meaning Making, as are Whole Group Mini-Lessons.
- Inquiry-Based Tasks, Small Group Mathematics, and Reflection are all for Transfer.
The images above depict Elementary Mathematics lesson structures; however, those for Secondary Mathematics appear very, very similar.
I will continue to work to design supports for clarity around each portion of these documents. In the mean time, I know the intersection of UBD and Retrieval Practice makes sense.