We know that Experience First, Formalize Later (EFFL) produces students who can think and reason with good long-term retention of knowledge. But using activities in a student-centered classroom is challenging. One of our biggest challenges is our own time. How can you take your more traditional notes and turn them into an activity that students can engage in without your direct instruction?

The best way we have found to turn our old notes into an EFFL lesson, is by taking each bit of information and figuring out how to ask students a question so that they will be able to tell me the information. Here is an example.

These are our old notes for introducing students to the graph of a quadratic for the first time.

Here are the two learning targets:

(1) To understand the vertex of a parabola as the point at which f(x) is a minimum.

(2) To understand that a parabola is symmetric around an axis of symmetry.

As we design the new EFFL lesson, we worked backwards from the intended learning targets. We identified the parts that had used direct instruction before and thought about how we could get students to discover these ideas on their own.

First, we needed students to identify the vertex. So we thought about what informal question we could ask students to get them to identify the point where the vertex was located. Then we could define it later. To do this, we asked students to identify where the lowest point of the graph was located. During the debrief later, we defined this point as the vertex and had students label it in the margin of their notes.

Next, we wanted students to notice the symmetry in the quadratic graph, and more specifically to notice that (x, y) and (-x, y) are both on the graph. To get at this, we asked students to find the value of x for which f(x)=16. Students noticed that there was more than one x-value that had a y-value of 16. This was true for all other values of y we looked at except for when y = 0. Notice how we formalized these ideas in the margins during the debrief.

Creating the **Experience** part of a math lesson may not always be as easy for us as it is in statistics, but that doesn't mean it can't be done! We've had to rethink what the experience part looks like. Start with the learning targets, and design scaffolded questions to lead students to the learning.

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