How I write lesson plans
I strive to use the Effective Mathematics Teaching Practices outlined by the National Council of Teachers of Mathematics. What this means is that lesson planning begins with choosing a specific goal to focus the day's learning. A good goal is not to just "do" a task or activity or section of the book but an articulation of what skills or knowledge the students will gain from the day's lesson.
After a goal has been chosen, then tasks are chosen that will best support that goal. Here it becomes critical to use our knowledge of our students (their prior knowledge, their interests, their competencies) to structure the order of tasks to best support learning. We want to start with rich tasks that help students construct a strong conceptual understanding first, and then we develop procedural fluency through appropriate follow-up activities.
While lesson planning, I try to anticipate roadblocks to the learning process. For example, after choosing a task, I imagine multiple ways that students could attempt to complete that task. What mistakes might they make? Which parts might be frustrating and cause them to stall? Are there other solution strategies they might use other than ones we're focusing on in class? If there are parts of the task that could be unnecessarily frustrating or confusing, I adapt the task to remove the obstacles.
However, some parts of math need to be challenging, so then my task is to prepare purposeful questions that I can ask when the students hit the (necessarily) frustrating or confusing parts. My questions are designed to help move the students forward without reducing the cognitive load. If I make the work too easy, then the students will never gain confidence in being able to work through the challenging parts of math. They'll believe that they just aren't "good at math" and give up. Instead, we have to help them realize that persistence and asking questions are as much a part of being a mathematician as is any type of computation.
Finally, good lessons elicit examples of student thinking, and teachers can then use that knowledge to drive future instruction. The type of assessment can take a variety of forms, but it's essential to know what the students 'got' from the lesson before I know where to go with the next day's lesson.
Examples of Lesson Plans
- Linear Transformations of Data -- In 2017, as part of a math methods class, I was asked to teach a lesson on linear transformations of data and then deliver the lesson as a guest teacher at Paw Paw High School. While I was given the goal and required to use the TI-Nspire, I had the freedom to create my own task and structure the sequence of the lesson. This link will take you to the lesson and materials. While there are aspects of this lesson that I would revise if I were to teach it again, this plan is a good example of the sorts of considerations that go through my head while planning.
- Linear Inequalities & Systems -- In 2009, I taught this lesson as part of my Advanced Algebra (Algebra II) class. This plan is presented as an artifact of my teaching from that time period -- it has not been edited or revised in any way to make it look 'fancier' or 'more complete.' I have added some annotations in the margin to explain some elements, but it would be an example of what I would consider to be the bare minimum when planning.
- Horizonal / Phase Shifts of Sine and Cosine -- This plan was written as part of a group project designed to create tasks that would lead students into deep conceptual understandings of sine, cosine, and their transformations. I volunteered to cover this particular transformation because students often struggle with understanding why f(x+k) will shift a graph to the left instead of to the right. The plan uses worksheets to lead students through exploring phase shifts in tables, then on the TI-Nspire, and finally using Desmos. You can download the .tns file I created for this lesson here. I'm very please with the result and hope to be able to use all or part of it in my future classroom.