Wednesday, April 13, 2011

Circumference: The Evolution of a Lesson

In this post, I'd like to share how I was able to transform the way I taught Circumference in order to make it more Memorable for students.  This transition took place over several years of my teaching career.  It is important to note that I made these transitions while teaching students in Title I schools.  

The ideas presented in this lesson transformation can and should be applied to other topics and concepts in order to make content more memorable for students.
Scenario 1:  Rote Learning (Not Memorable!)

When I first started teaching, I pretty much taught everything in a rote and abstract manner.  So to teach Circumference I would just tell my students the formula for Circumference, show them how to input the variables, and finally I’d show them how to solve the equation.  We would do several guided practice problems and they were let loose to practice about 20 problems on their own.  There was no meaning associated with the learning at all!  There was no Novelty involved in the way I taught the lesson.

Scenario 2:  A Discovery Lesson (Somewhat Memorable!)

After a few years of teaching, I learned how to teach math conceptually. This was HUGE for me since I had not learned math this way!  I immediately began to implement Conceptual Development of mathematical concepts into my teaching. 

Once I had this enlightenment, I began to teach Circumference differently.  Here’s how I taught Circumference:

  •           I would bring in different sized circular objects and string.
  •           Students would use the string to compare the diameter of the circle to the Circumference of the circle. 
  •           Students would measure the string used for the diameter of the circle and the string used for the Circumference of the circle.  They would record their findings in a table.

in inches
in inches


We would then repeat this process with the radius.

The point was to get students to see the relationship between the diameter and Circumference of the circle.  This would lead to the discovery of Pi and the Circumference formula. 

Teaching the lesson this way was much more memorable for several reasons.
  •           Students were engaged in the learning process by having to actually measure and compare the diameter to the circumference.
  •          By discovering the formula, Circumference had much more meaning to students.  
  •          We had incorporated some Novelty because it wasn’t just another worksheet.  It was also different to have to measure the various circular objects.
After teaching the lesson this way, I definitely noticed an improvement in understanding and retention rates.  If students did forget things about Circumference, I could jog their memories by just reminding them about when we measured the circular objects with string.

Scenario 3:  Adding in Some Novelty (Now it’s Memorable!)

Several years later after learning about Brain-Based Learning, I decided that I could make this lesson even more Memorable for my students by adding some Novelty.

We basically did the same lesson as described in Scenario 2 with these variations. 

  •            Instead of just bringing in basic circular objects like paper plates and container lids, I decided to use different sized hula hoops. 
  •          I made more of a production about introducing the lesson. 

Introducing the Lesson:

In order to build curiosity and anticipation, I would place hula hoops at the front of room.  I wanted to make sure that they were seen when students entered the room.  As you can imagine, they were!  The hula hoops definitely created a buzz, which was exactly what I wanted.

Just by the sight of the hula hoops, my students were being “hooked”.  They wanted to know what was going to happen.  In fact, they could hardly make it through the” Warm Up” because they were so curious about the hula hoops.

When it was time to start the lesson, I would choose a hula hoop and attempt to use it.  After the laughter subsided, I would ask the class these questions.

             Does it matter what size hula hoop you use?  Why?
             Is it easier to use a large hula hoop or a small hula hoop? 
We would spend a few minutes debating these questions.  Based on their prior experience, they tended to agree that the larger hula hoops were easier to use. 

Next, I would ask students what “Math” word could be used to describe the size of a Hula Hoop. These were 7th graders so they had prior exposure to the term Circumference.  It sometimes took a few prompts, but someone would eventually get the correct word.

After discussing the vocabulary related to circles, I would explain that we were going to compare the relationship between the diameter and the Circumference and the relationship between the radius and the Circumference.  I would have them make predictions about the following.

  •          How many diameters will it take to equal the Circumference of the hula hoop?
  •        How many radii will it take to equal the Circumference of the hula hoop?
  •      Will these relationships change based on the size of the hula hoop?
The Lesson:

I would give students the instructions for the activity and get them started.  While doing the activity, they would complete the recording sheet (see below) where they filled in the tables and graphs.  I changed the activity by not having them measure the string.  This time, they were just noticing that the Circumference was a little more than 3 times the diameter.

Circumference Introduction (Hula Hoop Lesson)

The Result:

After teaching the lesson this way, I noticed marked improvements in understanding and retention rates!  This time even my weakest students and my ELL seemed to be able to grasp the concepts of Circumference and Pi.  Overall, my students rarely had trouble remembering that the Circumference is a little more than 3 times the diameter and that it’s a little more than 6 times the radius.  (We did transition to Pi is approximately 3.14.)  Throughout the year if it had been a while since we had done anything with Circumference, it might seem like they had forgotten.  I would just remind students about the activity we did with hula hoops and it would come right back to them.

So, what made the difference?

There are actually several reasons this lesson became more memorable, but Novelty is definitely one of the big reasons students were able to better recall what they had learned.  By bringing in Novelty with the hula hoops, students were interested in and curious about what they were about to learn.  They were more attentive to the learning because it was something different and fun.  When students needed to remember things about Pi and Circumference later, it was easier to recall because it was the only time they’d ever seen hula hoops in a math class.

Relevance and emotions also played a part in making this lesson more memorable.  Students were interested in the hula hoops, they had prior experience with the hula hoops, and they enjoyed seeing me “try” to hula hoop.  Along with the Novelty of the lesson, these things really made a huge impact on student’s understanding and retention rates.
If you want to make learning more memorable, Novelty should be a regular part of your daily lessons.  As you begin to include more Novelty into your lessons, you’ll notice that retention rates are not the only benefit.  You’ll also notice that attention and motivation are positively affected!

Remember, something is only novel for a short time, so we have to continually find new ways to introduce novelty into our lessons. 

If you like this post, you may also like these:

Now that's a Novel Idea!


Anonymous said...

Thanks for sharing this evolution in your teaching. I think it is a great model for teachers as we try to offer more meaningful experiences for our students. Bravo!

Monica said...

This is fantastic! I'm currently doing my Masters of Education degree with a specialization in Inclusive Education and Neuroscience and am just trying to get something together for an action research project that I'm going to do this fall. I knew I wanted it to be related to math and including students with significant disabilities but I also wanted to tie in some neuroscience. I was looking at multiple modalities and exploratory learning but your post related to novelty may have given me exactly what I've been looking for :). Thanks!

Kristi Grande said...

Thanks for the comments. This was definitely a fun and fulfilling lesson transformation!

@Monica I'm glad you got some inspiration regarding your action research. It sounds like it will be a great project. I'd love to hear how it goes for you. Best wishes as you complete your degree.

Guillermo Bautista said...

How about making it more open? Investigate the circumference and diameter of a circle? I think our aim in teaching is to be able to ask questions like that, and students will just investigate on their own, the find patterns and generalize them. :-)

Kristi Grande said...

You're right, Guillermo! We really should aim to have students formulate their own questions, search for patterns, and make generalizations about the patterns they find. Those are the skills students need to be successful in life beyond school.

This is not how we've traditionally approached math instruction in the U.S., so it will take some time and guidance in order to get students to understand the expectation. It's important to have class discussions about the types of questions that should be asked and what an investigation of diameter, radius, and circumference might look like. Teachers should ask questions like: What types of things are you investigating? What relationships may be important to compare? etc. After having these types of discussions and following up with the investigations for a while, students will learn what it means to formulate their own questions and then carry out an investigation to discover patterns and formulate answers to their questions. Teachers just need be patient and stick with the process knowing that it will take time to get students out of the habit of having the questions and information given to them all the time.