Pendulum part 2

Near the end of last quarter, I wrote about my constant struggle to decide between teaching middle school math or an upper elementary classroom in Pendulum. At the time that I wrote that post, my heart pendulum had begun to swing more toward being a classroom teacher; however, I am once again beginning to swing back the other way.

In one of my classes, we are reading A Sustainable Start: A Realistic Look at the First Year of Teaching by John Spencer, and I am also reading with a group Teach Like Your Hair's on Fire by Rafe Esquith. Reading these two books side-by-side has been helping me decide what kind of teacher I want to be. Spencer has been talking about teaching sustainably in the sense of not getting burnt out as a teacher. One should teach not like a firework, flaming in brilliance for a moment, but like a campfire, burning steadily for a long time. Esquith has been giving me aspirations to be a great teacher, but he has also been giving me things that would transform my career into a firework rather than a campfire.

In the way the Spencer and Esquith books are in conversation about teaching, so too are my thoughts about who and how I want to teach. I have become worried that my wanting to be a classroom teacher is more for the firework reason than the campfire sustainability. If I were a classroom teacher, I would aspire to be Rafe Esquith doing incredible things and changing kids for the rest of their lives. I would want greatness and aspire to teach 5th graders everything they need to know about life. While aspiring to be this amazing of a teacher is just fine for some, I think I would burn out within the first couple years as suggested by Spencer.

If I were to go the route of being a middle school teacher, I think I would be more likely to create a sustainable career for myself yet still aspire to great things later. I can still be a great teacher without changing the world in my first year. I will be able to teach the subject I love, math, without trying to force myself to teach subjects I am not as comfortable with. Don't get me wrong, I am not swinging back toward teaching middle school math simply because it would be easier. I am swinging back toward teaching a subject I love, toward a sustainable start to my career, and the ability to be a great teacher without forcing myself to be what I'm not.

Read Aloud on Negative Numbers

When I was given the assignment to read a book aloud to my middle school math class, I was lost as to what I should read. After getting the suggestion from my cooperating teach to find a book about negative numbers to read to the 7th graders, I searched around the internet and found this book, Less Than Zero, by Stuart J. Murphy.

Less Than Zero is a book in a series of books by Murphy relating mathematical concepts in story form. This particular book has the following succinct summary on the back cover:

Perry the Penguin needs 9 clams to buy an ice scooter—but he’s not very good at saving. As Perry earns, spends, finds, loses, and borrows clams, a simple line graph demonstrates the concept of negative numbers.

To add to the summary, Perry has ‘less than zero’ clams for a part of the story because he borrows clams to buy things besides his ice scooter. In the end, Perry gets enough clams to buy his ice scooter by getting a loan of 4 clams from a neighbor that he will pay off by working shoveling snow, so he ends the story with a debt of negative 4 clams/hours of work.
 
This book has two possible messages to talk about with students. One message is about negative numbers and what negative numbers mean when applied to amounts of money. The other message is telling students that if they borrow more money than they have, then they will be negative in how much money they have. Furthermore, the second message also puts being negative money as something unfavorable and should be avoided.

Although I read it with middle school students, it could be used with almost any age to introduce negative number concepts, graphing practice, or just as a story about saving money. My students thoroughly enjoyed it, and I hope you find a use for it with your students. 

Comfortable classrooms

When I had my class on the middle school learner last spring, we talked a great deal about how classroom environments could be made more comfortable for the students and match their physical needs better. Most of what we talked about we're great ideas, but I feel that ideas like tables students could stand at and squishy balls to play with are rarely implemented. It probably doesn't come to fruition due mainly money and partly simple follow through. However, I observed a class today that through the generously of a PTA grant had exercise balls available for students to sit on instead of chairs. Although it wasn't necessarily apparent whether they aided in attention over the 40 minutes I was observing, I was so thrilled to see the students getting their wiggles out during class in a generally non disruptive way. Great use of grant money in my opinion.

Math Manipulatives in Algebra

I just started observing a junior high class and was pleasantly surprised when the teacher pulled out Manipulatives to help the students visualize balancing algebraic expressions. I had never seen or experienced their use in learning algebra, and it gave me wonderful new ideas of how to use them in my future teaching.

The Manipulatives are used to represent the x terms and the integers and differentiate positive and negative terms. In this way students need to follow logical rules of keeping the equation balanced by literally taking away or adding the same thing to both sides. The long bars represent 1x and each small square represents 1. Furthermore, both bars and squares are positive when green/yellow, and negative when red. I think it's a quite brilliant way of physically representing a potentially abstract concept for learners. I definitely plans on utilizing this type of manipulative strategy in my future classrooms.

Below is an example of an equation being represented by the manipulatives. 3x-5 is represented by 3 green bars and 5 red squares while x-3 is represented by 1 green bar and 3 yellow squares. To solve for x, students would first remove a green bar from both sides and rewrite the equation to be 2x-5=3 with the visual matching. They would next add five yellow tiles to each side which would cancel out the red squares on the one side while adding with 3 to be 8 on the other side. The equation would then be written as 2x=8. The final move of the Manipulatives would be to divide the positive eight squares evenly with the two remaining green bars(x's). This would mean there would be 4 squares per bar, meaning x=4. I wish I had pictures for each step, but I don't at the moment. I'll try to update when I get a chance to take pictures of other examples.