Combinatorics and Probability Before Exponential Growth

May 17th, 12 / 0 Comments

I am in the middle of my final unit of the year on exponential growth and decay and logarithms. Right now, I’m wishing that I had taught combinatorics and probability before teaching this unit, because of the connections between the topics.

We worked with compound interest, and I had a student who used a table like this to calculate the total owed on a 10% APR loan 0f $100 after 5 years.

Principle: 100 100 100 100 100

Simple interest: 10    20    30   40

Interest on interest      1       3      6

.1     .4

.01

This is an inefficient method if you’re compounding many times, but it’s also a fascinating use of the binomial theorem for (1+r)^t. If we had already discussed the binomial theorem and combinatorics, I would have had an easier time helping the students see this.

The other place where probability and combinatorics comes up is in exponential growth and decay applications. Today we did a simulation of half-life with skittles. (No S showing means the skittle/atom decays). And again I wished that we had already talked about probability.

Still teaching

May 17th, 12 / 0 Comments

I’m sorry for disappearing off the face of the internet. Life got busy and writing is hard for me.

Just to update everyone, I did finish grad school and get my teaching license. Then I had challenging job search, which finally ended in October. Now I teach part-time at a private gifted-and-talented school. The school is currently K-8 but is planning to grow to K-12. So I get to teach high-school level math to mathematically gifted middle school students, and develop a school-wide computer science curriculum.  This is an awesome job.

After ten days of teaching class…

Mar 9th, 11 / 1 Comment

I’m still feeling mostly lost. At about day five, I got past the begin uncertain and nervous just being “in charge.” However, my ability to plan in the environment I’m in feels really shaky. During class I’m trying to remember about 50 things I’m suppose to be doing, covering, mentioning, handing back, and watching for. After every class I teach, I look back and realize that I’ve forgotten something. Basically, I can recognize a large number of elements of teaching that I’m doing “wrong” or at least not the way I’d like to do them. I’ve only had three days where I’ve gone home and cried, and I guess that’s a pretty good ratio…

I mentioned these feeling to the teachers I work with, and one of them said that I was focusing too much on what I was doing rather than on what the kids were experiencing. She says that no one can predict where kids are going to go with something and that I just need to relax. This is easier said than done.

I’m getting a lot of reassurance from my cooperating teacher and ed school faculty. “Your classroom management was about as good as mine,” and “They were really engaged with that task,” says my cooperating teacher.  I told one of my professors that I was feeling overwhelmed and got the response that if I wasn’t feeling overwhelmed right now she would be worried.

I know that student teaching is mostly a mad scramble of trying to figure out the basics of teaching. And I know that the confusion and frustration and exhaustion I’m feeling is normal. But the stress still isn’t fun.

I feel kind of isolated too. I haven’t been having the time/energy be involved in the blog-o-sphere conversation. I’m stealing time from grading to write this post. Nearly all of my grad school classmates are teaching high school, rather than middle school. So while they can empathize with the work load, and the confusion, the specific issues I’m having are very different from them.

For instance, I have an untracked class of 6th graders, and it seems like any problem I give that is approachable for the struggling students is done in a snap by the most advanced students. How do I keep all the students engaged with such diverse background skills? I think there are problems that have an easy approach and depth to them, and occasionally, I think of one. However, I don’t have the ability to come up with those types of problems every day, nor am I able to find such problems for all of the topics I’m supposed to cover.

One of the teachers I observe does this brilliantly. Seriously, I sit in her class doing the same problems as the seventh graders and feeling like I’m learning something. And so are the kids. The students are engaged, attempting and succeeding at the mathematical tasks. I’ve seen students in this class beg not to be given the answer to a mathematical problem because they want to figure it out on their own. Another student stays after school to write up a proof, even though there’s no grade for doing so. I want to teach like that, but I don’t know how.

I’m tired. I think I’m going to go to bed early.

Pacing failure

Feb 15th, 11 / 4 Comments

Yesterday I took over my first class for student teaching. It seemed to go decently, although we ran out of material about 5 minutes before the class ended. I left feeling that the students had learned something.

I spent all last night planning for today. Today’s class we ran out of time to do everything, and it seemed like students had forgotten what they had seemed to have learned yesterday. I feel like I’m lumbering back and forth trying to figure out what I’m doing.

I think that’s sort of how all new teachers feel. I would be more reflective right now, but I’ve also managed to get sick. I’ve been feeling worse and worse all day. I think maybe being around lots of kids while being somewhat stressed about beginning to actually teach was a one-two punch to my immune system. Right now, my thought process is moving at the pace of snail, so my plan is rest until I feel better, and then figure out what to do next.

My mantra for right now is “teaching is a marathon, not a spirit.” I need to stay healthy to keep doing this work.

, ,

Productive Snow Day

Feb 2nd, 11 / 2 Comments

We’re having yet another snow day here in Massachusetts, but it’s been a productive one.

When I woke up this morning trying to think of how to make practicing multiplying and dividing decimals fun. This is what the 6th graders I’m working with are currently studying, and it’s the kind of topic where developing fluency as well as understanding is important. I had an idea for a review game/lesson, so I wrote it up in formal lesson plan format.  So here’s a Decimal Operations Review Game (with Game Cards for printing)

One thing I like about this lesson game interactive experience is that the game goal (“get the largest number”) inherently encourages students to use multiplication, division, and scientific notation, and to think about the structure of decimal operations to make good strategy decisions. I deliberately made the game whole class cooperative, since these classes have a fair number of students who worry about seeming “stupid” and I thought a competitive game would intensify that worry.

I don’t have a clear idea of how students would react to this activity. I hope someday I’ll have some ability to predict students, but right now I have to rely on other teacher’s opinions and experimental testing. I’m a little concerned about what with happen in terms of organization as the player groups get large and the numbers get more digits.

This lesson plan took me about about  two and half hours to write up, which is a lot less time than I spent on lesson plans for classes last semester. I still don’t like finding state and NCTM standards that lessons are relevant too. I find that my lesson ideas tend to touch on about a half dozen standards, but only a part of each one. I think that’s probably good for the lesson, but bad for the lesson plan.

I also updated my online portfolio so that I’ll make a better impression on potential employers.  I miss just being able to send a resume and cover letter, but I’m hoping the effort I put into this job search will pay off.

I’m happy for feedback on both of these.

When a student says, “That’s so gay.”

Jan 27th, 11 / 11 Comments

When I was in middle school, every time someone used the word “gay” as an insult, it cut me to my core. See my mother had been gay, but none of my friends or classmates knew that. At the time, I was afraid that if I said anything I would lose my friends.

During student-teaching, I was circulating around a class I had only met a day or two earlier, when a student said, “That’s so gay.” Since I didn’t know what the teacher’s policy on this was, nor the student’s name to begin a conversation, I let it slide. It didn’t hurt the way it had in middle school (thank goodness!), but I was painfully aware that there might be a student in that class who was hurt and I would have no way of knowing.

I don’t want to allow “gay” to be an insult in any classroom I have any control over. But I don’t know how to address it. I understand that in general, I’m should address behavior I don’t like privately with the student, to minimize the risk of the student arguing to gain social status. However, in this case, I do want other students to know that, in my class, using “gay” as an insult isn’t ok. So that calls for a public statement of some kind, right? The need for going public in this case is emphasized by statistics like “82.9% of LGBT students report that faculty or staff never intervened or intervened only some of the time when present and homophobic remarks were made.” (GLSEN 2003)

Also, once I decide to enforces this rule, how do I explain why I have this rule? Do I even need to? I feel like I should offer an explanation, since I know I hate arbitrary rules, and I can only imagine that my students will feel the same way. So if I’m offering an explanation, I want to use a specific example of someone being hurt by this language. Do I use my own example, or will that lose me respect? I teach math, and possible computer science, so as a third party example, Alan Turing springs to mind. Maybe his story would be a good lesson? Or do I take a precision-of-language tactic, pointing out that they are claiming that having homework (or whatever) is homosexual and that doesn’t make any sense?

I’ll figure something out, since this is important to me, but advice is welcome.

, , , ,

Student-Teaching After 1 Day

Jan 25th, 11 / 0 Comments

Today is going to be my second day of student teaching, and I woke up before my alarm full of enthusiasm and ideas. I’m mentally running through the names I learned yesterday. I keep thinking about plans for a game design class I’m creating in the back of my mind.

I realized that in the 6th grade textbook, there is a chapter on fractals. Fractals are one my favorite topics, and I’ve mentally indexed a lot of resources, activities, and connecting discussions for them. I’m going to ask if that’s a topic I’ll get to teach later in the practicum.

I’m student-teaching at my old middle school, which means I know my way around the layout, although everything looks a little smaller. The biggest physical change I saw was in the the library: there is now a large circular table and some computers were the card catalog used to be. Apparently, there are also “temporary” classrooms in a corner of the school I haven’t been to yet.

On the other hand, pretty much all the people are new. Only one of the teachers I saw yesterday was mutually familiar from my time as a student. The students, unsurprisingly, seem very young compared to when I was a student.

Overall, I’m hopeful and excited about this. My cooperating teacher is awesome! We have to be careful not to spend too much time getting distracted by interesting mathematical problems, which all-in-all is a good problem to have. Everyone else I’ve met has been very friendly.

, , ,

[Video] Math is Everywhere

Jan 21st, 11 / 0 Comments

This is my first video. I’m trying to give viewers a sense of what it’s like in my head when I start looking for math in the world.

, ,

Art Styles and Teaching

Jan 18th, 11 / 0 Comments

I have just returned from a weekend convention where I was deeply involved in music. I’m going to be starting student teaching (at my old middle school) later this week. This convergence got me thinking about teaching and art, and my style of both.

My artistic background is in game design, improv theater, and folk-style music. In all of these, the mode is less “performer and audience” and more “leader and followers” or “designer and team”.

A video game designer almost always works with a team: different people create the visuals, compose the music, program the interactions, and write the dialog. Moreover, a game designer is always depends on the actions of the players to make the game happen. If the audience for your game, is only looking at it and not playing, then you, as a game designer, have failed. Sometimes the appeal of a game is largely dependent on the community of players, who share in-game creations or create game mods, which change the game play.

In the musical tradition I play in, music is done in circle with minimal distinction between audience and performer. We sing along if we know the words, and improvise harmonies and percussion. We build on each others songs, writing parodies and performing covers.

So when I think of teaching as art, I don’t think “I am the performer, and my students are my audience.” Instead, I think “We will create learning and mathematical pieces together, with me taking lead.” Some teachers have told me that creating a student-centered classroom is very difficult. To me though, a classroom where I am only the first of a team of students seems the most natural way to do the art of teaching.

, , , , ,

Knowledge, Experience, Humility, and Values

Dec 21st, 10 / 1 Comment

I have minimal classroom teaching experience: three days of substitute teaching, a little bit of helping out during observations, seven weeks of leading a college math section nearly ten years ago.  What I do have is a lot of second-hand knowledge from reading from blogs and books this past year or so, watching my boyfriend Paul doing the work that teachers bring home, and taking classes. All this second-hand knowledge has allowed me to form a fairly consistent framework of idea about teaching and how I want to do it. However, these ideas are untested. As much as I believe them, I need to remember that until I’m actually trying to put them into practice I really can’t know if the ideas I have are any good. What I have now are theories, potentially useful approximations of reality, and I need direct experience to see how closely they match with reality. Humility in acknowledging how little I know is called for, as is a willingness to adapt to new experience.

On the other hand, a few of the ideas in my network of beliefs about good teaching didn’t come from the bodies of knowledge about teaching I have been trying to absorb and integrate. These ideas came more broadly from all of my life’s experience and a larger moral framework. These ideas are better termed values, and while they may someday change, I am much more inclined to hold to them. When I think about significantly altering my values, it feels like a betrayal. These values are my foundation as a teacher.

If I have power over someone else, I have a deep responsibility to make sure that I use that power for the good of the other person, especially if that power was given to me by a third party. We, as a nation, compel children and teenagers to attend school through laws and threats of future financial ruin. Because of this, most of my students will not have a real choice in whether to attend my classes. Hence, I have a deep responsibility to assure that my classes, which are the part of school I have control over, are truly benefiting my students.

People, including students, are individuals. Treating them according to classifications, when you have the option to know them as individuals, is wrong. Additionally, acknowledging that students are whole people in addition to be students is important.

Mathematics is valuable, both practically and aesthetically, and accessible to everyone.  I have an obligation to bring real mathematics, not just calculations and algorithms, into my classroom to give students a chance to see it first hand.

People can disagree with me and still be good people, worthy of being treated with respect. I really fell down on this one in my classroom observations last semester. I felt like my values were under attack, and without thinking I acted disrespectfully.  I regret that, and will endeavor to do better in the future.

I want always to seek personal improvement, to move towards ideals I know I’ll never reach, but to know that the movement is the important part.

In some way, all except the last of these of values are specific examples of the golden rule, but I call them out separately because they are more clear that way.  This is not a comprehensive list, but these values are core to me.  If I can be faithful to these values, I will be satisfied.

, , ,