The Vocabulary Gap

I have been thinking about formal language quite a bit this summer. My summer started with professional development from Dr. Kenneth Wesson and his work on learning and the brain. His statement that the “vocabulary gap drives the achievement gap” has left me thinking about how we help close the vocabulary gap. He would suggest that positive relational experiences are essential for learning and that knowledge is co-constructive. “We do our best learning with one other person”.

How can we best help close the vocabulary gap in our classrooms? At my site, our Algebra students (about 80% of our 8th grade population) bring to the classroom a wide range of background knowledge and experiences. We need to be intentional about developing a shared common set of experiences and vocabulary for all students. Below are some of the activities we planned into our unit on quadratic functions this year.

We begin with Polygraph Parabolas from Desmos. Here is a screenshot typical of a first round game. Partners were chosen by the computer with one selecting among 16 graphs of a parabola and the other asking questions trying to determine the chosen parabola.

Screenshot 2017-07-09 15.16.12

Students are using their language to describe what they see in the graphs. In this shared informal experience, every voice is heard and honored. Every student found success. We still have some work to do. Our language isn’t very efficient but we start and build together.

We followed that up the next day where students are paired sitting back to back. One student can see the screen and the other has a individual whiteboard for graphing. We display a parabola on the screen and ask the “describers” to describe the graph to their “drawer”. We start with a single parabola and eventually describe more complex graphs.

desmos-graph (10)

Here is a link to a google slides and a desmos version. These have more graphs than we would use in a day. You may want to select 4 or 5 on a single day.

There are a few teacher moves we have found helpful with this activity.

  • Ask the drawers “What did you hear from your describer that was helpful?” It is affirming when someone else honors your ideas. Collect ideas and begin labeling vocabulary on the screen as you hear it from students.
  • With multiple graphs ask “What is the fewest number of directions you can use to describe this set of graphs?” … “Can you name that graph in 5 statements? Fewer?” Think – Pair – Share. They will work together to find strategies to become more efficient with their language to meet the need of describing the picture with the fewest directions.
  • Rotate after each round. We switch places and then rotate the new describer (boards and pens will stay put this way) clockwise and next round switch and counter clockwise around the room.

On the next day, after sharing a few informal experiences we distribute a vocabulary list as part of our unit preview that also includes learning targets and homework options. We ask them to take a moment and find a term that they can share something about and a term that they can’t describe well. Everyone in the class will be able to find a term they can’t describe and a term where they can share some knowledge. In groups they share and then they work together to select a term that no one in the group can describe. These are shared to the class and we use the offered terms to help tell the story of the upcoming unit. We then ask them to circle the terms that they need to learn more about. We return to their circled list at the end of the unit and students give us a grade in how well we helped them learn the vocabulary in the unit.

If we are going to develop vocabulary through experiences, we need to build in those activities into our lessons. We try to utilize our “fire up” time to open the class. We find constructs like WODB or “Which one doesn’t belong?” helpful. We put up this graph and asked students which one doesn’t belong.

Screenshot 2017-07-09 16.27.39

Give students time to think and share in groups. As they share to the class, the students will find the more formal vocabulary as useful in arguing that their parabola is the one that doesn’t belong. We used this activity later in the unit and a visitor said they were “blown away” by how well students described parabola features and their equations.

Card sorts are another tool that can be used to fire up the class upon opening. In your purpose is vocabulary development, it is essential to pair students to do these sort activities. This parabolas card sort is part of Desmos’ quadratics bundle. Here is a one screen card sort that might fit the opening of the class. We have also used a physical set of cards for groups to sort. This one matches three quadratic forms and their graphs.

How can we close the vocabulary gap? I think it starts with shared informal experiences in the classroom. It can’t stop with those shared informal experiences and notes on a vocabulary list though. We need to offer opportunities that generate the need for being efficient and refined with mathematical vocabulary. We need to pause and offer the formal language when it is needed. I don’t think the rich discussion that resulted in the WODB can happen without the informal experiences early in the unit. Nor should we expect students to develop formal language from a few informal activities. We need to be intentional about vocabulary development and plan shared experiences throughout a unit. We need to close the vocabulary gap.

What do you think? What activities have helped you develop formal language with your students?

More links to activities or thoughts about developing language in math class

Follow up to the polygraph: Polygraph Part 2

Jon Orr’s blog entry: Better Questions: Two Truths and One Lie

Suzanne Von Oy’s blog entry: What’s In A Name?

MARS Lesson: Representing Quadratic Functions Graphically





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