Wednesday, September 10, 2014

Redefining Geometry Vocabulary

It's no secret that a high school Geometry course is riddled with wordy, complex definitions for terms that students inherently know something about based on life experiences.  The struggle for a teacher is how to access that prior knowledge and make connections to the Geometric concept?  In the past, I have been the one to define the terms for the students, simply using the definitions from the textbook, thinking that those would be the most accessible to students.  Surprisingly, this was largely unsuccessful.

A few weeks ago, I read a blog post by Lisa Bejarano (Check it out here) where she spoke about similar struggles to provide access to students in the realm of Geometry terms and definitions.  The element of her blogpost that was the most inspiring to me was her use of examples and non-examples for each term.  I was also inspired by a colleague from High Tech High in San Diego who had created an activity that included an element of revision that I found very interesting (see sample below).

Headings: Word, Student Generated Definitions (words & images), 
Exact Definitions (words & images)

Together, Lisa and Jade inspired me to develop an authentic way for students to acknowledge what they already knew about a term or concept, but then also have the perseverance to learn more and build understanding.

I began with the first section in my textbook, and I listed all of the key vocabulary terms.  The list included point, line, plane, collinear, coplanar, segment, endpoint, and ray.  (The old me just fell asleep thinking about having to teach these terms) :) I created a chart that was similar to Jade's, but also brought in elements of Lisa's activity by addressing examples and non-examples (see sample below).

Headings: Word, Student Generated Definition (words/images), 
More Precise Definition (words), Picture, Non-Example

I gave each student a copy of the vocabulary chart and asked them to read through the list of terms, checking in with themselves about what they already knew about the word or concept.  They had the choice to write down their thoughts or not, but if they wanted to, they would do so in the "Student Generated Definition" section.  Next, students turned to their peers (at their table groups) and shared what they already knew about each term, again they had the choice to write down what they wished.

This is what I had written on my whiteboard as a reference after they had time to think independently:

The next stage of the activity involved students getting up and moving between tables where I had distributed strips of paper with examples and non-examples for each term (see sample below -- THANK YOU LISA!!!).  Students were asked to study the pictures in the two categories and record what they needed in their vocabulary chart.  If they needed to draw all of the pictures, that was fine, if they saw some were redundant, I left it up to them to choose what to include.

Please note that these pictures are computer generated, but the ones I created for my students were drawn by hand, so they looked slightly different.  For example, for the line pictures, I had more about labeling and I included points on the lines, etc.

What I found during this piece was that there was not a lot of discussion happening.  Students were traveling around the room simply copying the pictures as if that was the most important part.  So, what I did was I actually asked them to move around quietly as they observed and copied pictures; no talking.  I don't know why I thought to do it this way, it just seemed like a battle that I was not going to win if I kept asking them to talk, talk, talk.  It just seemed so forced.

So, when they were done checking out the pictures, I asked them to return to their seats and told them that they were not allowed to have their pen or pencil in their hand, that drawing and writing time was over for a little while and that this was now time for discussion.  I think by defining the time more clearly, it allowed for students to focus on one element of the activity at a time.  Sure enough, students began brainstorming what they thought was an appropriate way to define these terms.  They were building on each other's ideas, they were referencing the pictures, and they were accessing their background knowledge.

Once discussions began to die down, I invited them to write their updated versions for each term, still in the "Student Generated Definition" section.  I was pleased to see that students who chose to write something right off the bat were not afraid to revise and make their definitions better.  Students were open to learning from each other and building on each other's ideas.  This, however, is an area where I believe they can still grow.

Often times when I ask my students to discuss an idea and I leave it open ended, it's not much of a two-way conversation, but more of a "I did this..." and "I did this..." from student A to student B and vice versa.  They are still learning to engage in a conversation, not just telling each other what they did.

At this point, I was out of time for the period, so had to make a decision about what to assign for homework.  Any Geometry teacher will tell you that the first section of the book is often times an exercise in learning, recalling, and using the Geometric vocabulary that we have discussed above, so I thought, Why not see how and what they do with it?  So, I assigned 12 problems from the first section that involved everything from drawing pictures that used these terms, using the terms in ways to describe a picture, identifying these terms from a picture, and so on.  I was hopeful that things would all sort of "come together" for them when they were given an opportunity to practice.  I knew that I was risking the possibility of students solidifying an incorrect definition of a term, but I was confident, based on my observations, the opportunities to work with their peers, and access to the formal definitions in the book, that there was sufficient support for them to be successful.

When students returned to class the next time, I was pleasantly surprised by how well they were able to use the vocabulary terms in an appropriate context and when checking the homework, there were very few questions that were raised.  After reviewing the assignment, I did take the time to provide students with a "More Precise Definition" that was a balance of the textbook definition, items involving notation, and an approachable way to think about the term.  But, before I provided them with the more precise definition, I asked for them to share with me (and the class) some of the things they wrote down.  It was fun to hear how they described certain things: "a ray is half a line", "collinear means together on the same line", because it was obvious that they had made sense of the term, but perhaps didn't have an "academic" way of defining it.  That's where I could help extend their learning, not stifle what they authentically know.

It's been about a week since I did this activity and we have since moved on to discussing things like the Segment Addition Postulate and the construction of copying a segment  For the first time in my 9 years of teaching, I have found that students are willing to and comfortable using the Geometry vocabulary from the activity.  We are looking at problems that involve the use of the vocabulary and students are using them accurately.

Here's a perfect example:

Holt Geometry

After posing this question to my students, some of them asked clarifying questions like "Are these points collinear?", "Can we think of this freeway as a segment?  Or is it more of a line?", "Which towns are the endpoints of the segment?"

The last thing that I will say about this set up for teaching and learning vocabulary is that I'm finding that if a term comes up in class that they are still not quite sure what the definition is, they are so comfortable with opening up their binder and taking out their chart.  In the past, when I have taught the definitions of these terms as a part of their notes, they never return to them again.  I think that this is another strength of the chart and activity as a whole.  Students have interacted with the words and they hold on to that experience in a way that I have not seen in the past

I can't wait to hear about your ideas for how to make this activity even better!  And again, thank you to Lisa Bejarano and Jade White for the inspiration!


  1. Numerous efforts are made to learn the vocabulary words, but all the efforts goes in vain when they learnt words are not retained in the memory for ever. Retaining the words for a longer duration of time is easy only at

  2. I love this idea for a Gallery Walk with the vocabulary words! I head about this from another teacher and am looking for an electronic version of the example/nonexample cards. Are you willing to share them?