“Tell me and I forget. Teach me and I remember. Involve me and I learn,” said Benjamin Franklin.
Learning is about involving both the teacher and the student in interactive ways, ways that provide a dance of questioning, activities, and doing. This amazing dance may occur at the seemingly most unprovoked moment, and leads to a bit of fun and a lot of learning. One such occasion occurred to me recently and it produced such an amazing bit of fun.
Setting the stage….
After a long day at work, I arrived home to the joyful glee of a precocious 7 year-old, bound with energy, and my wife making dinner. I was carrying a box of circuits from a fourth grade class, planning to return them the next day, but the physics nerd in me was tempted to play a little. When I began to play, the 7 year-old became curious, as I was thinking out loud, “What are these pieces for? How are they connected? I wonder if this will work?”
As she peered over the lip of the box, I asked her, “What do you notice?” With a tilted head she said, “I see blue color and a mess.” Side note, the box wasn’t a mess, but to a 7 year-old, with no words to describe what she was seeing, she went with what she knew.
We started pulling the materials out, when she saw that they were wires, the blue things we weren’t sure what they were for, and the light bulbs, she was both intrigued and confused. Again, I asked, “What do you notice?” She replied, “Light bulbs.” Then I asked, “What do you wonder?” She looked at me, thought a second, and said, “I think the same things you were saying earlier.” I know right?! So that happened, and we were off on our journey.
What we did….
Upon organizing the pieces, we started making connections (ha, cause it circuits...that’s funny) and we saw how the batteries connected, we placed the wires together on the board, screwed in the light bulbs, and observed what happened. Within a few minutes the light bulbs were glowing, and we were ecstatic. I didn’t expect anything to work, but it was brilliant.
So, I started asking questions and getting her to wonder about the connections, seeing if I could get her to make predictions, and then verify through the experiment. Now the nice thing about this experiment was she could immediately verify her predictions, and adjust accordingly.
She noticed that when the wire from the terminal of the battery touched certain wires one light, or both lights, would shut off. She noticed that only 1 or 2 configurations would allow for both light bulbs to be on simultaneously, and she noticed that based on how hard she pushed down on the wire, one of the bulbs was dimmer than the other at certain connectional values.
What was the outcome….
I prompted her thinking with guided questions, about why these observations are true. Her first responses hit on everything from the size, shape, direction, and straightness of the wires to the type of battery. Clearly this 7 year-old had no understanding of currents, Ohm’s and Kirchhoff's laws, and I was excitedly prompting for clarifications. Then an inspiration hit me….water.
So I painted a different picture, I said imagine if there was water flowing from this end of the battery, how might the water act as it flows around the circuit. Now, in case you’re wondering, this 7 year-old has limited exposure to electric circuits in a formal manner, but she has been to multiple rivers and we have had conversations on how silly water seems to act as it flows. So my inspiration was to try to tie this to things she has had a context from which to jump to this abstraction.
The next few moments were pure magic, she started experimenting with the which lights would turn off when she struck certain wires, and said that if the water flowed in a circle, then when the other light doesn’t come on, there’s a “rock” in the way. I knew she had the idea. So I asked, “So how might the correspond to when you touch this wire, and neither light turns on?”
She tilted her head, verified that when she touched the wire to that spot, both lights didn’t come on….”Oh I know!” she gasped. “It’s because there’s a rock stopping the water from reaching both lights.” Tracing out the circuit, she could see that the water wouldn’t reach the lights.
So, we traced out the circuit, played with a few more configurations, and then it was bedtime. May I tell you, we worked on the circuits for 2 hours, it felt like 15 minutes, and she was exhausted. My wife reported to me later, that she had complained her head was hurting, but she didn’t know why.
Two days later, the other 7 year-old exasperatedly proclaims, “I want to learn about the electricity thing.”
With some time to reflect on this experience I’m going to follow more of Benjamin Franklin’s advice: I am ready to provide a better stage, to involve them in their learning.
The beginning of my work with this idea came to light from an article I read from NCTM, this lesson was a handout. My lesson materials is found here, which includes the PPT and handouts I used for this 5th grade lesson.
What I liked….
The first thing that spoke to me about this lesson is the low barrier to entry, specifically, the task has students follow a pattern of crossing out numbers in a distinguishable pattern. With very little in depth thinking, once students see that pattern, the process of finding numbers is relatively easy. Connecting the students’ understanding of prime numbers to composite numbers, this process introduces “hidden” language, like factors in a natural setting as we explore this process. Specifically, the link of why content has developed a language as a necessary way to describe the things that we are interacting with. Finally, the cross curricular idea stands out as a natural progression of this lesson, from the history component of learning a little about Eratosthenes to the connection between mathematics and music.
What I wonder….
This section has less to do with the lesson, and more to do with my implementation of the lesson. Originally, I thought this lesson would take a few days, realistically though, this lesson is more like a unit, and probably would take a full week of instruction for students to really make connections. My implementation of the lesson required me to create a full sequence that spoke to “my style” of teaching, realizing that I would most likely leave behind the idea of the connection to music.
The teacher kind enough to let me use her classroom, also pointed out a really great point, that in showing videos, it would be beneficial to have questions next to video, so students would be able to refer to them, as they were not reading the questions on the handouts I created to accompany the lessons.
What the students got….
So all of the above to say, that the students got a very nice introduction to who Eratosthenes is, what he did, and some insight on how to say his name. Almost all students were able to get the process of how the sieve works, and the students were excited to go ahead with both examples. These pieces of the lesson went well, combined with the fun and many student interactions made for a success in those ways.
On the other hand, I felt I didn’t facilitate the flow of the lesson on the two days very well. The combinations of interacting with individual students, not explicitly detailing what interactions would look like, and being purposeful in the questioning, providing examples, or explicitly modeling left many students without the proper understanding.
My learning objective was to have students be able to recognize how composite and prime numbers are similar and how they are different. This was my target baseline, and I did not make that mark, though many students developed a deeper understanding, and a few were really trying to answer the questions.
My biggest learning is that when you set the stage property, the students will do amazing things, this was amazing thing to do; however, I did not set the stage properly for them to be able to reach out, explore, and do those amazing things. As I write this, I am realizing what it was that was missing, I failed to set the stage properly for the students to be successful. So now I am thinking, what that might look like in a week, or so, as I will be going into another 5th grade classroom. I will modify the lesson to provide a better stage.
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