“Teaching specific terms in a specific way is probably the strongest action a teacher can take to ensure that students have the academic background knowledge they need to understand the content they will encounter in school.” Robert Marzano
For a long time, I thought about vocabulary in math much as I would think of language acquisition in early childhood. Children learn language skills as they hear people speak and see the objects about which they are speaking. I felt that using the correct vocabulary as I spoke and taught should be sufficient to build student vocabulary., but I was woefully wrong. I could see it as I read student writing, explaining their thinking. There were the obvious errors in which students reversed the verbal description of a division problem (12÷3 described as 3 divided by 12). There were the cases were the incorrect term is used to describe something (using the word mean when they mean median). There were the cases where they didn’t use math vocabulary at all. This left me struggling to understand why some students grasped the vocabulary but too many of them didn’t. Some of them were effectively communicating their thinking verbally and in writing while others were not.
Was this gap a gap in understanding or a gap in their communication? It turns out, it was probably both. Students who did not have a firm enough grasp of the vocabulary have significantly lower comprehension of academic content. As shown in the graphic (taken from Building Academic Vocabulary by Robert Marzano and Debra Pickering), a student with no direct vocabulary instruction is at the 50th percentile in terms of ability to comprehend subject matter taught in school. The same student has a comprehension level that has increased to the 83rd percentile after intentional, systematic instruction in the vocabulary. It’s pretty clear that my students didn’t have a firm grasp on the academic vocabulary and this was negatively impacting their ability to fully grasp the math. I needed to make a change.
Because Marzano’s results were fairly dramatic and were backed by research, I decided to follow the guidelines he set forth.
Step 1: Provide an explanation or example of the term.
You can do this a lot of different ways (a field trip, a video, a picture). I usually do this with a Frayer model in which I have provided some examples and some non-examples. You can download the Dilation shown.
I have students do a Think-Pair-Share on the things they “notice” and “wonder” about the examples and non-examples. This gives everyone some individual think time and a chance to talk about what they are seeing before we talk about it as a whole class. As we debrief the notice/wonder, students start to construct a definition. I refine that definition if I need to at the end of the discussion.
Step 2: Students restate the description in their own words
Next, students put the definition that the class generated in their own words and write in the “definition” box of the Frayer model. Their definition does not have to be perfect and complete but it should be error-free. I walk around and look over their shoulders as they do this to make sure they are doing OK. If they are really struggling, they can skip to step 3 and then come back to this step
Step 3: Students construct a picture or graphic representation of the word
Students create a visual representation of the word. I have students do this in the illustration box of the Frayer model. This makes them process the concept in a non-linguistic way. Sometimes, this is fairly straight forward and they can just draw the actual thing. Sometimes, it is less so and they might have to come up with a symbol to represent the word. They can also draw an example or a dramatization of the term
Step 4: Engage students periodically in activities that help them add to their knowledge of the term
This is really important. It was OK that the initial definition they wrote.was not “complete”initially because they are coming back to it and building additional knowledge. They can then add the new knowledge to their definition. Students might highlight a word part (eg., ob- in obtuse to make a mental link to the ob in obese). They might identify synonyms or antonyms. They might add another picture or graphic. The might add a note about a common confusion or misconception.
Step 5: Ask students to discuss the terms with each other every so often
A think-pair-share activity works really well for this
Step 6: Have students play games using the terms periodically
Marzano has an entire chapter of activities that you can use for this in Building Academic Vocabulary
My initial reluctance to “teach” vocabulary in math boiled down to a reluctance to give up “math” time for “vocabulary” time. I have come to realize that the vocabulary time is part of the math time. I have also discovered that it really does not take very much time. As I look back on where I have come on this issue, I can see that I have done pretty well incorporating the first five steps over the last few years but not as well with step 6. That is one of my goals moving forward.
I have some of the other vocabulary Frayer models that I will be using with my 7th grade students this year available for download below.