4 Steps to Designing a Discovery Based Lesson

There are a few things to consider when designing a discovery based lesson to make it as successful as possible. There are four main points to focus your lesson and trailer it to your classroom and students. The ultimate goal of a discovery based lesson is for students to develop understanding of a concept or build a formula or theorem independently and through their own thinking. These steps will help you take your typical notes and change them into a lesson where students are taking ownership of their learning and forming connections to prior knowledge and new knowledge.

The first step is to know the target of the lesson. Your learning target should be derived from your state standards or common core standards but be careful to not use the whole standard. Rather you want to focus on specifically what the outcome of this discovery based lesson will be. For example, I recently co-taught a lesson on triangle similarity where the TEKS(Texas standards) stated prove theorems about similar triangles, including the Triangle Proportionality theorem, and apply these theorems to solve problems. However, the learning target we chose for this specific lesson was I can discover the triangle similarities. Since we knew the length of the class period would only allow for the discovery of the three similarities and that some background knowledge we needed to revisit would take time, we narrowed down the standard to that target. This helped keep the focus of designing the lesson and specific activity we chose to create.

Second is to break down the learning target into the steps to reach it, also known as the success criteria. These steps will help to guide your lesson and know the main focus of how to achieve the learning target. Since there are three triangle similarities, that helped to build our success criteria. We decided to focus on one at a time and essentially have three pieces to the activity. Your success criteria can be the steps you would take to solve a problem, guiding questions to help students think about necessary steps, or even a rubric. If you can lay out your success criteria or steps to reaching your target first, you will begin to narrow down the ideas you have for the discovery based lesson. I struggled with so many ideas for this triangle similarity and kept referring back to my target and success criteria to help focus my thoughts.

Third consideration is the constraints of your classroom including time and access to technology. The length of your class period can be a big factor into how long of a discovery based activity you can have. You may not want to interrupt classroom procedures already in place, such as a warm up and exit ticket, but you may want those to help activate prior knowledge needed for this lesson. Our warm up reminded students of how to measure angles with protractors since that skill was necessary for the lesson we designed. The rule of thumb is to measure how long it takes you to complete a task and multiply by three for students. You can also consider having a discovery based lesson be multi days or small components each day as well. The other piece to consider is whether you want this lesson to be technology based or hands on, or maybe offer both. I used to design these lessons in geogebra along with a hands on version so my students had choice as to which they preferred. I had a set of chrome books in my classroom so technology was readily accessible to my students. For the triangle similarity lesson I recently co-taught, technology was not as easy to acquire so we decided a hands on approach was best. Some technology sites that worked best for me were geogebra, geometer sketchpad, demos, google docs, and their graphing calculators. For hands on activities I found myself using patty paper, rulers, construction paper, graph paper etc. depending on the lesson and course.

The last step is knowing your students and the appropriate scaffolding to use throughout the lesson. I like to work through the lesson I have designed and write down all of my steps, including other ways to solve or ways to answer questions. This helps me to anticipate common misconceptions and build appropriate hint cards to give out. I use hint cards so students do not have to ask anything to me that their classmates can hear, and also others can not hear what i responded with. This helps build confidence with students while encouraging all to continue doing their own thinking. I also write down questions ahead of time to help guide students along without giving them any answers. Remember, the goal of discovery based lesson are for student to build the new knowledge and discover the math, so questioning is a huge piece that helps them reach the target.

These are the four main steps I take when designing a discovery based lesson for math classes. It makes my teacher heart so happy to hear and see students really taking ownership, explaining to others, getting excited about discovering the math, and fully engaged in a lesson. I have found through experience that students build this new knowledge and apply the concepts with more success that they need less rote practice of the concept after. It helps to build problem solving and critical thinking in the classroom and opens opportunities for interdisciplinary studies as well.