Monday, November 22, 2010

Owl Pellet Dissection

Preparing experiments for science class can often be a time-consuming and stressful experience for me.

Time-consuming because I have to gather the materials (which sometimes requires going out and buying them), prepare the lab and report sheets, and sometimes do a practice run of the experiment to make sure it works. Stressful because I have 21 sixth graders, many of whom have short attention spans and issues with listening and following directions, and only one of me to watch over everything. I essentially have to design the lab so that only I handle the expensive/harmful materials, which means when I am working with one group of three students, 18 others are more or less unsupervised...

The upside to all of this, however, is that the students absolutely love working with their hands and doing actual experiments. Today, for instance, we dissected owl pellets and identified the bones that we discovered. Except for one or two students, everyone was engrossed in the oddity of the owl pellets and the meticulousness required to separate the tiny bones.

The nice thing about doing experiments like this one in class is that it fulfills two of the most difficult requirements of a successful lesson plan:

1. It engages a students curiosity and keeps them interested in the lesson.
2. It meets each individual student at their particular intellectual level.

In every class you will have students that are at different intellectual levels - particularly in the sixth grade at Chinquapin where students come from a wide range of educational backgrounds. One of the marks of a successful lesson is that each individual student can engage with the material at the appropriate level for him or her so that it is challenging enough to help them learn, but not so challenging that they are discouraged. Labs and experiments are so nuanced that they have many layers of intellectual rigor. For example, some of the students were simply intrigued by the sight of rodent bones, tried their best to identify them, and made basic connections between their findings and the food webs we have been discussing in class. Other students, however, were able to study the differences between the teeth patterns of mice and moles, consider the population dynamics of the meadow ecosystem, and even try to reconstruct complete skeletons.

I think these labs are really the embodiment of a question that all teachers ask themselves on a daily basis: Would I spend a few extra hours working on a lesson if I knew it could make a class even marginally better for the students? Those that can honestly answer in the affirmative are meant to be teachers, and I think too often we as educators lose sight of the direct correlation between our effort and our students' learning. It is days like this that remind me how much of my own time I would actually sacrifice so my students have an interesting, educational, successful class.

Wednesday, November 10, 2010


As a first year teacher and a relatively reserved person, one of my biggest fears this year was having to discipline the students if they misbehaved. What I've learned is that for the most part, misbehavior is not inherent to the students, but inherent to the teacher's ability to engage the students. It turns out that the classes with the fewest discipline issues are the ones that are the most interesting and thought-provoking. If the students are all paying attention to the lesson or working diligently on an assignment, they don't have the opportunity to be disruptive.

Last week I had a small problem with students talking during class while other students were still working on an assignment. When I confronted the group of students and asked them why they were talking, one of them replied, "well, we're done already..." At the time I chastised them and told them, "just because you are done, doesn't mean you have the right to disturb others." But the more I thought about it, the more I realized that students are inevitably going to chat or lose their concentration if they aren't kept active. To combat this, I decided to give them an ongoing extra credit assignment that they can work on whenever they have free time in class. It consists of 10 questions ranging from logic problems to riddles to Sudoku puzzles to difficult math concepts we have covered in class. The students responded quite favorably to the challenging questions, the opportunity to gain extra credit, and the possibility of figuring out the questions before their friends.

Here's one of the problems I posed to them, see if you can get it:

Monday, November 1, 2010

Goldbach's Conjecture and the Millennium Prize Problems

I just got out of my 8th grade Algebra I class, and we didn't get through any of the material I had planned on covering. Yet, it was one of the best classroom experiences I have had in my brief teaching career. The class was supposed to begin with some mental math warm-up exercises, then take a brief detour into number theory and Goldbach's Conjecture, and then seamlessly return to our lesson on functional notation so the students would understand their homework. Instead, what was meant to be a 5 minute nugget of number theory, turned into a 45 minute explanation of communication in the 1700s, a reading of one of the Millennium Prize Problems, and Google Image searches of Grigoriy Perelman and Terence Tao.

First, I baited the students with the questions: "Find two prime numbers that add up to 64" and "Find two prime numbers that add up to 90". They saw it as a challenge, and the fact that there are multiple correct answers to each question makes it such that multiple students can chime in with their answers. In essence, almost everyone was invested and involved in solving these math 'puzzles'. Then I presented Goldbach's Conjecture, that any even number greater than 2 can be written as the sum of two primes. I explained how Goldbach proposed it in a letter to his friend, Leonhard Euler, a fellow mathematician. The students loved the idea of two great math minds conversing through letters to present and prove conjectures and theorems. The Goldbach Conjecture is also one of the oldest open problems in math, which led me to talk about the Millennium Prize Problems and their $1,000,000 award. All of a sudden we were Googling, reading the open questions, and looking up Grigoriy Perelman (the mathematician credited for solving 1 of the 7 problems - the Poincare Conjecture) and Terence Tao (the preeminent number theorist in the world). One student asked, "What do they look like?", so we searched for images of them. It was a brief detour into history and current events and images, and while they will never have to know any of this for a math test or any other test for that matter, it piqued their interest to the extent that they left class saying, "I actually had fun!"

Building curiosity in students is far more important than building their knowledge base, so while I didn't get through my lesson plan, I think I achieved more in this class period than I originally could have hoped for. Here's what I learned from this experience:

1. Baiting students is important. If I had just presented the Goldbach Conjecture, which I find inherently interesting because I'm a math teacher, then the lesson could have flopped. Baiting students and getting them interested is critical to a successful class.

2. If a lesson is taking a detour, but you get the sense that the students are learning or sense that their interest is piqued, throw your original plans out the window and go with what is working. To be honest, I think this was the most fun the students had in class and the most fun I've had teaching.

3. Incorporating other disciplines into your class is a great way to build a lesson or a lecture. Too often students come into math class and all they think they will see are numbers and letters, when in reality our education system should focus on interdisciplinary approaches to learning. Even a 5 minute explanation of how Goldbach and Euler communicated brought the lesson to life, and took it out of the realm of pure mathematics and into the realm of real life.

My favorite professor at Williams, Michael Lewis, taught American Art and Architecture and the reason so many people loved his class was because his lectures weren't Art History lectures, they were just Interesting Lectures. He synthesized so much information into his class, from all sorts of disciplines, that it felt like you were just listening to him tell a story and you couldn't help but be engrossed.

One day I hope to be as eloquent, interesting, and knowledgeable as Professor Lewis, and today was the first time I really felt like I had the potential to get there.