Tag Archives: group work

Let 'em Talk

We started the topic of Venn diagrams in Math 9 this week. In a class of international school students (and perhaps any group of students) the range of knowledge on a given topic is all over the place given their different backgrounds and school histories.

The teacher-me of ten years ago would have done an overview of the concept of a Venn diagram. I would have started by asking questions about different parts of what was there in a Socratic fashion. It would have been full of questions that I had written down in my lesson plan designed to get students to think deeply about the content. Based on asking questions of a sample individual students, I would have gotten an idea of what the class knew. The students who knew the material already would either raise their hands and try to answer every question, or stay silent and answer every question on the worksheet in a matter of minutes. The students that didn't know the concepts, but wanted to, would likely stay quiet until either I approached them or until they could ask a friend for help. The students that were used to being defeated by math class would pass the time by doodling, pretending to be involved, or by distracting their friends.

This isn't the teacher I am today. I've written about the power of social capital in the room before, so this is nothing new, but I don't tend to do the 'topic overview' style lesson anymore. The one or two students that nod while we go through material aren't representative of the class. The strength of my experience in the classroom is being able to observe students working and know what to do next. I can't do this while standing at the front of the room and speaking.

My approach now is, whenever possible, to make an item of the topic a conversation starter. I gave them this image of a Venn Diagram, which appears in a collection of questions from old New York State Regents exams at http://www.jmap.org:
Screen Shot 2015-09-11 at 8.34.49 AM

I gave them a series of questions that required them to figure out what they remembered, knew, or didn't know about the topic. Students made arguments for the definitions. Their disagreement drove the need for clearer definitions of what the intersections of the sets meant, for example. I was free to circulate and figure out who knew the concepts and who did not. Many of the issues that arose were resolved within the groups. Those that still had lasting confusion were my targets for conversations later on.

As I've added years to my experience, I've become more comfortable relying on this system to drive what happens in my classroom. Every time I get the urge to just go over a topic, I remind myself that there's a better way that involves students doing the heavy lifting first. There's a reason students are in a room together for the purpose of learning, and that reason is not (all) about efficiency. Humans are social creatures, and learning is one of those processes that is driven by that reality. There are moments when direct instruction is the way to go, but those moments are not as frequent or necessary as we might think at first.

Party games & geometry definitions

Today's geometry class started with a new random arrangement of student seats. It never fails to amaze me how the dynamics of the whole room change with a shuffle of student locations.

The lesson today was the first of our quadrilateral unit. Normally after tests, I don't tend to have homework assignments, but I decided to make an exception with a simple assignment:

Create a single Geogebra file in which you construct and label all of the quadrilaterals given in the textbook: parallelogram, rhombus, square, kite, rectangle, trapezoid, and isosceles trapezoid.

This appealed to me because I really dislike lessons in which we go through definitions slowly as a group. I also knew that giving the students some independence in reviewing or learning the definitions of these quadrilaterals was a good thing. Sometimes they are a bit to reliant on me to give them all the information they need. For this assignment, students would need to understand the definitions of quadrilaterals in order to construct them, and that was a good enough for walking into class today.

The warm-up activity involved looking at unlabeled diagrams of quadrilaterals, naming them, and writing any characteristics they noticed about them from the diagrams:

Some had trouble with the term 'characteristics', but a peek down at the chart just below on the paper helped them figure it out:

Based on what they knew from the definitions before class, I had them complete this chart while talking to their new partner. There was lots of good conversation and careful use of language for each listed characteristic.

This led to the next thing that often serves as an important (though often boring) exercise: new vocabulary. I used one of my favorite activities that gets students focused on little details - each student received one of the following four charts. The chart is originally from p. 380 of the AMSCO Geometry textbook, and was digitally ruined using GIMP.

The students had a good time filling in the missing information and conferring with each other to make sure they had it all. We then came up with some examples of consecutive vertices, angles, diagonals, and opposite sides.

 

From their work with the chart and using the new vocabulary whenever possible, we then did the following:

What information would you need in order to prove that a quadrilateral is... (use as much of the new vocabulary as possible!)

  • a square?

  • a rhombus?

  • a parallelogram?

  • a rectangle?

  • a trapezoid? (an isosceles trapezoid?)

  • a kite?

I was really pleased with how they did with this exercise - they really seemed to be interacting with the definitions and vocabulary well.

Finally, we arrived at the part that was the most fun. You know that annoying ice-breaker you sometimes are forced to do at professional development sessions where you wear something on your head and have to get the other attendees to tell you who you are?

I hate that activity. That usually means it's perfect for my students:

Here are the quadrilaterals:
Quadrilaterals - Who-Am-I activity

The students were all smiles during the ten minutes or so we spent going through it - yes, I had one too! They were using the vocabulary we had developed during the day and were pretty creative in getting each other to guess the dog names as well.

In the end, I feel pretty good about how today's set of activities went. The engagement level was pretty high and everyone did a good job of interacting with the definitions in a way that will hopefully lead to understanding as we start proving their properties in coming classes.