Frustration

I'm just getting frustrated now. I feel as though my fourth block is just walking all over me. As though I have "WELCOME" stamped on my forehead. I'm getting tired of talking about it or thinking about it, but I can't stop.

So I talked with the professional development guru at my school. She's been very helpful, and I've got a couple ideas. Tomorrow I'll be starting a "Cool Down" in my class (to offset the "Warm Up" I do each day) where students self-evaluate. I'll let you know how it goes.

Moments That Make Me Smile

"Ms. Kimball, take a look at this," said one student, taking out his wallet. He showed me his license, just earned yesterday. I shook his hand and looked out the window with him at his truck that he drove to school for the first time today.

Constructions Project

Rather than give my students a test on geometric constructions, I chose to have them complete a poster project. They were required to think of a theme and find ways to incorporate the 10 - 12 constructions we've studied into the theme. The ideas is that students are looking for geometry in the world around them while they learn and perfect their constructions.

The projects were due today, and they spanned the entire range, from awful to amazing. (I'll show pictures when I get them.) So during class today I had my students grade each other's work. This is partly intended to give them practice following a rubric. But mostly it's to allow students time to appreciate each other's hard work.

Favorite student quote of the day: "I'm sick of grading." ~Honors Geometry Student after 90 minutes of peer assessment. ("Just imagine how I feel every day," was my response.)

A Safe Learning Environment

Yesterday was the type of day that makes you want to drown your sorrows at the local pub. In fact, the first thing I did when I got home was call a friend to meet out so I wouldn't be alone with my thoughts. Even today I can't stop thinking about everything from yesterday and worrying about Monday.

(Have I sufficiently built up my story yet?)

I don't understand how my students can sit in class and listen to me talk about the Pythagorean Theorem or squares and square roots of numbers when they have so much going on in the background. Yesterday I learned about the many troubles of several of my students. Without going into too many details, let me just say that the information I learned has made me re-evaluate what I want my classroom climate to be. I've always wanted a safe environment in which my students can learn, but prior to learning about the details of my students lives, I thought that meant that everyone should feel safe to ask questions and suggest answers without the possibility of being made fun of, etc. Now I'm thinking that a safe environment needs to begin with students understanding that they won't be physically or verbally attacked in my classroom.

One of the situations I "handled" yesterday was a screaming match between two of my female students. I didn't know the cause of the screaming, but my objective was to make the screaming stop, so I sent girl #1 out into the hall and kept girl #2 in the room. Talking with girl #1 we decided that she needed to go talk with guidance. Worried that girl #2 would run into girl #1 in the hall or the office, I decided to keep girl #2 in the room for the remainder of the class. I think this may have been the wrong choice. If I had it to do over again I would have sent for an administrator to come get girl #2 from class and escort her out.

I learned the cause of the fight later on, and it breaks my heart. How can students concentrate in class and see the point of learning anything in school when they're being attacked from all sides?

I'm worried about Monday. My goal is to use this incident to change my classroom for the better. Though I'm not entirely sure how. Maybe I'll begin class by having a discussion about what it means to be in a safe learning environment, and what actions I will take if I see or hear any thing that I perceive as creating an unsafe environment.

Investigations, Part II

Time for an update.

The Stacking Squares investigation I mentioned in a previous entry went very well while they were making the posters. Students got a good feel for the concept of a square root and where it comes from. The project really helped them understand how to simplify radical expressions.

As I predicted, my students definitely balked at trying a problem where they needed to be creative about their mathematics. I could see that my students were becoming less engaged the more frustrated they became. Because of this, I definitely gave them too much information while they were trying to solve the problem. I think I'll need to give less information when I do this activity with my honors students... Well, I hope I'll need to give less information.

I tried to create a worksheet for students to fill out as they looked at every one's poster today. The first couple questions that had to do with the posters were useful. But students became less engaged when they had to think through questions that had less to do with the posters they were looking at.

I also had a difficult time closing out the project. In general, I think this is something I'm bad at. I'm not good at concluding things. Maybe this should be one of my professional development goals for this year.

As a whole, I think I'll use this lesson again. I just need to make a couple adjustments to the questions I pose and help I give, and to the closing.

Mathematical Lens

How cool is this?

Imagine using an image like this to introduce mathematics in the classroom.

The NCTM journal Mathematics Teacher includes a monthly segment called Mathematical Lens. It gives interesting photos that can be used to investigate mathematics and link mathematics to the world around us.

The picture here is an image of stairs leading to a shrine for the Buddha in Angkor Wat, Cambodia. It was taken by Ron Lancaster (an editor of Mathematics Teacher), and it's a fabulous example of where extreme slope can be seen in the real world.

Investigations

If I had my way I would run every class as an investigation for the students. Students would be given a task or a topic to explore, and would need to complete this in the time given. In fact, I often use this teaching method, and it works very well with my honors students.

Too often, however, I've found that when I give my middle-level students an investigation, they don't understand either what the task is, or how it relates to the practice problems we work through afterward. I'm beginning to wonder if that's because I give too much structure to my investigations, leading my students through a series of steps in order to "discover" the solution.

Tomorrow I'm planning to try a very unstructured activity with my middle-level students. By unstructured, of course, I simply mean that they will be given little instruction as to the manner in which they should/can complete the task. I found the lesson (Stacking Squares) through the NCTM website, which has been a valuable resource for me throughout this and previous years.

I expect I'll hear a lot of whining about not understanding what to do or how to do it. But with a little luck I think they'll get through it. I'll report back on how it went.

Symbols and Vocab

I don't think my middle-level students really understand what the geometry markings mean. Last week I marked the legs of an isosceles triangle with tic marks to show that they were equal, and my students didn't understand what the tic marks meant. (Actually, they thought they meant the lines were parallel... "How can sides of a triangle be parallel??" I asked... At least they've learned not to trust their eyes with the figures we use.) In the future I'll need to spend more time being very explicit about what the different markings mean. If I stop writing the words out on handouts or on the board and just use the symbols, that should force them to create meaning for the symbols as well.

I think another part of the problem is that I haven't been going through the book in order. I've been organizing sections into my own units. My reasoning for this has been that chapters 1 and 2 have so much vocabulary. Students learn all the basic vocabulary for points, lines, planes, triangles, quadrilaterals, other polygons, circles, and angles. (And I'm sure there's more that I'm missing.) What's nice about spreading out the first two chapters, then, is that students don't have to learn so much vocabulary all at once. Additionally, I'm not forced to teach them about the parts of shapes twice. What a time saver, right?

The problem with spreading out this information is that the vocabulary and markings from future units are sometimes used within the current unit. For example, there are interesting questions about isosceles triangles that use the radii of circles. But since we haven't gotten to circles yet, I can't expect my students to understand how to solve these problems.

Maybe next semester I'll try going in order in the book and see which way works out better. I just need to come up with a way to introduce all that vocabulary without lecturing all class...

Good Choices

A couple years ago I found myself in a dilemma. Having recently realized that I could no longer continue in my Ph.D. program I was forced to decide between several different paths. After a lot of discussion with a councilor, my very supportive ex-boyfriend, and my mother, I decided to work toward my teaching certification rather than continue in another doctorate program.

Two years later, here I am; part-way into my first teaching job. And after this (admittedly short) period of time, I've concluded that I made the right decision. Maybe it was just a really good day. Or maybe it was the breakthroughs I made this week with my block 4 class. But I truly feel that teaching high school mathematics is the right choice for me right now.

So I want to say thank you to everyone that helped me get to this point (even when I didn't realize this was where I wanted to be).

Thank you, Mom & Dad, Evan, Melissa, Jon, Megan, Sue, William, Liza, Heidi, Karen, and everyone else I'm missing right now.

Fortunate Discovery

I got angry at my block 4 class on Monday. Very, very angry. I was so angry, in fact, that I decided I wasn't going to teach them on Tuesday. They were going to have to teach themselves. So I created investigations and worksheets, and (surprise surprise) the class was fabulous. The students had a great time working through the problems.

I think part of the success of the class was the threat (or was it a promise) I made that if they didn't finish either of the worksheets, they would get a zero for the day. The other promise was the three-strikes rule (three times asking them to get back on track, and they would be spending their Thursday afternoon in detention with me).

The students worked hard. I was excited to see that. The investigations almost worked. The students didn't seem to understand how to relate the investigations to the worksheet problems. Even so, by the end, everyone had some idea how to do most of the problems.

Wednesday we went over the basics of the concepts for Tuesday, and the details of some of the trickier problems, before I set them loose on another investigation. This whole investigation-short discussion-example problems routine seems to work well with them. They love working together, and they actually work. (My fear prior to today was that they wouldn't work, but only socialize during group-work time.) Before class on Wednesday I had students coming up to me to tell me how much they liked Tuesday's class, and how every day should be like that.

So I suppose this is my new plan: to have some sort of investigation in order to teach the concepts they need, then to quickly discuss the concept and a couple example problems before letting them loose to work on their own problems. As I write this, I'm remembering that this was my style of teaching all last year during my internship. I wonder why I ever stopped. Why did I think lecture was a better way to get the material across? Maybe it's because these students look so much older than my freshmen last year. I need to remember that I'm teaching children, not adults.