In the past two years, I’ve been convinced to introduce definitions always using the Frayer Model. If you don’t know of it, there’s a video I just found online here. This is what a blank one looks like:
Now, let me say that I avoided it for many years because it felt to me to be a bit too contrived or too geared towards younger students. However, I’ve come around on my thinking, and I use it in all my classes, 7th grade through Calculus, and I LOVE it.
Part of the reason I love it is that it forces me to thoroughly flesh out the new vocab word, for the benefit of my students.
Another reason I like it is that I’ve found two ways of structuring how we fill in the boxes (see below).
Let me just add that I hand out to students a page where this box covers half a page (pictured to the right). I usually have two boxes on the front and one or two on the back, depending on how many important definitions I plan to go over in the span of a class or two.
I then also display one box on the board when we are filling it out in class.
Now, on to the two ways I work through the boxes:
A nice, straightforward way to use the model is to follow it in a U-shape. It flows like this:
- Start in the top left corner: I give a formal definition.
- Move to the bottom left corner: as a class, let’s come up with some examples.
- Move to the bottom right corner: with a partner, come up with some non-examples (which I may have some students put on the board).
- End in the top right corner: As a class, we add any notes that came up during our examples of things we want to remember. I may also come back to this box in the following day or two to add more notes if necessary.
Here’s an example we did in my Integrated Math 3 (Algebra 2) class.
We filled in the examples with tables and sequences that had a quadratic pattern. The “Essential Characteristics” popped up as an animation after we filled in the bottom boxes. We later went back to fill in “Essential Characteristics” with notes like forms a parabola when graphed.
My newer use of the box (inspired by one of my awesome colleagues at TMC17) forces students to create good definitions based on examples. I fill out the bottom boxes and they come up with a definition that is “unbreakable.” It flows like this:
- Start in the bottom left and bottom right: Prepared examples or on the spot examples. Have students look at those, consider.
- Move to the top left box: have students pair share a good definition (that is unbreakable) and then discuss as a class. The teacher tries to “break” the definitions students come up with using examples and non-examples (possibly the ones already there), until the class comes to a solid definition.
- End in the top right box: fill in notes about anything important that came up in the “trying to make a definition” process. I may also come back to this box in the following day or two to add more notes if necessary.
This time, the thing I start with looks like this:
Here, students started to say things like “it goes through the vertex.” However, my horizontal and diagonal lines go through the vertex, too. So I was able to “break” that definition. Students love playing this “game” of making a solid definition, and in this class they eventually honed in on the point that it had to vertical and cut the parabola “in half.” The fact that it went through the vertex was a “cool side effect” as one student said, and that went in our Essential Characteristics box.