In part 1 of this blog post, we looked at how our classrooms and lessons present students with much more than just content. Instead, they focus on developing life skills that students will use in all aspects of their future. A primary focus is on the 4 C’s:
1. Critical thinking
2. Creativity
3. Collaboration
4. Communication
The Experience First, Formalize Later (EFFL) structure of the Math Medic lessons was intentionally designed to allow students many opportunities to develop these four skills. So what are some specific teacher moves we can make to best support the development of these 4 C's within an EFFL lesson?
Setting Up The Lesson
When students enter the classroom and begin the lesson, we quickly introduce them to a new context or new scenario. We know that for the next 10 - 20 minutes, they will rely on each other to make progress towards their goal for the day.
In this specific lesson, we know that the end goal is for students to discover how to find the area of a sector. While this is our content learning target for the day, we will formalize how to do this after the students engage in their group work. Now is the time we remind them they should work with their group on the first page of the activity. They should do all work in pencil - as we are just creating a rough draft of initial ideas.
Inspiring Collaboration and Communication
As the students dive into their tasks for the day, they will need to recall some prior knowledge. They aren’t alone in this. A team of fellow group collaborators is there to jog each other’s memories so these ideas can resurface. The first couple questions of an activity are typically designed to have the group recall previously learned information and make sure they have a shared understanding before progressing.
For this lesson, we need the students to remember how to calculate the area of a circle.
As students are discussing, our primary responsibility is to listen and ask questions. Whether questions are used to draw out their thinking, extend their thinking or to help them make connections and move forward, using questions keeps the thinking on them. When a student says something that adds value, consider having group members rephrase it to make sure that knowledge is reaching everyone.
Tying new learning to previous learning is essential for building deep understanding. For example, in this situation, we can redirect them back to yesterday’s lesson where they learned how to derive the formula for the area of a circle.
Let Groups Add in Critical Thinking and Creativity
As they move past question 2, it is not uncommon that we hear the conversation slow down. That’s a prominent sign we are extending the concept a bit more, and the solution is not as clear. Here, they are using all 4 C’s to extend their thinking into a new concept. As the teacher, let’s look at some of the big things we are looking for them to do.
Understand Multiple Representations
Notice that question 2 specifically uses the words “half of a pizza” - leading groups to make the connection that we also need to cut our area in half.
However, question 3 never uses the word “fourth”. Instead, using the word “right” is going to push the groups to think a little harder about what is going on. When we look at the idea of creativity, multiple representations are an excellent way for students to get a perspective on what is going on and visualize the situation. In this question, by asking them for this sketch, we are opening them up to see the value of how the picture can be useful.
When discussing solutions with groups, we can ask them some extensions such as “how many people could have a slice with a right angle?” to make sure we establish the idea of taking the pizza and dividing it up into fourths.
Extend Student Thinking
We want the students to extend their current knowledge by pulling in new ideas.
The students will be comfortable dividing up the total area by the number of slices, so we add a layer to the problem by asking them about the angle.
We are looking to hear groups make this jump and get to statements like:
“Well, in the past problems, we divided up the total area of the pizza, so here we should divide up the total angle of the pizza.”
“I remember a circle has 360 degrees!”
As we work with groups on this critical thinking, we never want to take over the thinking for them. Instead, we want to use guiding prompts and questions only when necessary. This requires us to think about what could we ask the group to keep them critically thinking and communicating with one another to get back on track:
“What did you have to know about the pizza to find the area of each of the 12 slices?”
“If I needed to know the total area to find the area of each of the 12 slices, what would I need to know to find the angle of each of the 12 slices?”
“I remember in question 3 you said that four people could have slices with right angles. How many degrees is a right angle and can I use that to remind myself what the total angle of a circle is?”
Making sure the groups have a deep understanding of each question already answered allows these types of prompts to exist throughout the entire activity. Once the conversation restarts again, it is time to venture to the next group so that the students continue to rely on each other - never the teacher.
Be Flexible in their Thinking
Up to now, the students have always been told about the number of slices. However, now groups need to be a little creative to make a connection to the type of problem they already knew how to solve. We would consider this teaching a critical thinking skill - where you take a current problem and turn it back into something you know:
Again, we don’t want to tell them how to do this but we want to be prepared with some questions that will ignite the four C’s. For example:
“What did you know in the last question that you don’t know now (referring to not knowing the number of slices)? I wonder if you could start by trying to find that piece of information first, then focus on finding the area.”
Use Their Ideas to Defend Their Solutions
When the students work out some questions in the activity, they will often need to defend their ideas of what the best answer would be. The answer won’t always be straightforward and the purpose of these questions is for students to be able to communicate their work to each other.
Students need to communicate their methods so that groups can find the best one. Without solid reasoning and the ability to justify, a student’s solution can get overlooked when it may have actually been the correct one.
Questions like this are one of our favorite ways to showcase creativity. As a teacher, look for differences in students’ methods between individuals and groups to highlight during the debrief. Often, groups arrive at the same answer, but through different reasoning.
Notice Patterns To Formalize Their Learning
While the students work in their own groups, it is important for them to understand that this is a “rough draft” and revisions may need to be made. Coming back together as an entire class offers perspectives outside of the group - and may allow some holes to be filled in in the students’ thinking. All of this is great - and it’s the job of the teacher to guide the debrief into formalizing the solutions that hold up the best answers.
Finally, after noticing some patterns, the students soon discover the most efficient methods that can solve these types of problems from here on out. Call to their attention that they accomplished this all on their own by just the knowledge they had before the lesson started.
Thinking about the 4 C’s during an EFFL Lesson, can greatly enhance the way that we are preparing for the lesson. The more prepared we are to showcase the 4 C’s in the lesson for the students, the easier it will be for them to see “when they are going to use this'' each day.
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