By Kristin Gray
When I first started thinking about how I would complete this sentence, analogies such as a marathon or really hard workout came to mind—an activity that is exhausting, a ton of work, but ends with a sense of pride for having completed it. While these analogies were accurate representations of how difficult I think lesson planning truly is, I was continually unhappy with where students and their ideas fit into my analogy.
Planning is like putting together a puzzle.
When sharing my reasoning with others for the first time, I included a lot of beautiful words around mathematical connections but in the middle somewhere I used the phrase “making connections explicit” in relation to the puzzle pieces and saw an immediate negative reaction from those with whom I was sharing. Of course, I had to ask, “Was it the word explicit?”—answered by many nods.
For a long time, the word explicit in relation to teaching held a negative, cringe-worthy connotation for me as well. If ever asked to paint a picture of what explicit teaching looked like in the math classroom, I would describe scenarios in which a teacher is either at the board telling students how to solve a problem or showing a struggling student how to solve a problem because they are stuck or “taking the long way there.” To me, being explicit meant telling students a way to do something in math class—typically in the form of a procedure.
Through teaching a problem-based curriculum [Investigations], designing and implementing math routines, and reading Principles to Actions, 5 Practices, and Intentional Talk, I realized I was guilty of making mathematical ideas explicit every day in my classroom, but not in the way that made me cringe.
I was explicitly planning, not explicitly teaching.
To me, those two phrases indicate a big difference in how I think about structuring a lesson. I have found when teaching a problem-based curriculum, it is easy for ideas to get left unnoticed and important connections missed, forcing me to explicitly teach an idea to ensure students “get it” before they leave the class period without any understanding of the mathematical goal for the day. Many days, I would find myself frustrated because students would completely miss the point of the lesson. I realize, however, this was because I was expecting them to read my mind for what I wanted them to take away from the problem. On the flip side of that coin, not teaching a problem-based curriculum and explicitly teaching students how to do the math in each lesson is not an option and is a topic that could be its own blog post.
This is exactly why I find the 5 Practices framework invaluable in planning. The framework forces me to continuously think about the mathematical goal, choose an activity that supports that goal, plan questions for students toward the goal, and sequence student work in a way that creates a productive, purposeful discussion toward an explicit mathematical idea.
If you are not familiar with the 5 Practices, let me offer you a quick look at each, as described by the authors Mary Kay Stein and Peg Smith on NCTM’s website:
- Anticipating what students will do—what strategies they will use—in solving a problem
- Monitoring their work as they approach the problem in class
- Selecting students whose strategies are worth discussing in class
- Sequencing those students’ presentations to maximize their potential to increase students’ learning
- Connecting the strategies and ideas in a way that helps students understand the mathematics learned
The authors also describe a Practice 0 of Choosing a Mathematical Goal and Appropriate Task in their book.
While the 5 Practices framework can be applied to many tasks, at any grade level, in any curriculum, this explicit planning is exactly how I would describe the open education resource (OER) curriculum authored by Illustrative Mathematics. Each lesson and unit tells a mathematical story in which students arrive at a specific mathematical landing point. While they may not all arrive at that landing in the same way, the problems and discussions are structured to ensure students do not leave the work of the day without any idea of what they were working toward.
To revisit my earlier statement, planning is like putting together a puzzle. It is hard, it takes time, and it is sometimes difficult to figure out where to start. We know all of the pieces connect in the end, but making a plan for all of those pieces to connect takes an understanding of the final picture—the goal. There will be missteps along the way and some parts will take longer than others, but we know it is important to carefully connect each piece to another as one missing piece will leave unconnected ideas and the final picture unfinished. As you work alone, the way the pieces connect to form the final picture may not always be obvious, but as others help us see the pieces in different ways during the process, connections become explicitly clear and the final picture is something in which you can take a lot of pride.
Check out the video to see teachers learning about these 5 Practices in a recent IM professional development.*
- If you are looking for an example of a lesson plan written using the 5 Practices, check out Grade 6, Unit 3, Lesson 4, Activity 1: Road Trip in Illustrative Mathematics 6–8 Math Curriculum.
- If you are reading the 5 Practices book, I would love to hear your personal connections and reflections as you read.
- If you are using the 5 Practices to plan for activities in your classroom, I would love to hear about your experiences.
- Click here to learn more about professional development of the 5 Practices for your classroom or school.