Inventive Strategies

In my problem solving interview at Houston Elementary, my student used direct modeling and traditional algorithms for most of the problems I asked her, but some of her strategies seemed particularly unique. For example, I gave her the following problem:

There are 30 kids in the cafeteria and 23 more kids come in for lunch. How many kids are in the cafeteria now?

She began using manipulatives at first, but then decided to use her paper instead. She first wrote out 30 - 23. Then she drew a line between the 3 and the 2 and wrote "50" underneath it, and a line between the 0 and the 3 and wrote "3" underneath it. Then she added the "50" and the "3" to get 53. This really showed how she was able to break the number apart into tens and ones and add them together separately.

When she wrote it out on her paper, it looked something like this:

In this way, she grouped her groups of tens together (3 + 2 to make 5, which she knew represented 50) and her ones together (0 + 3).

Another strategy she could have used would be to use manipulatives to demonstrate the addition by having one color (red) representing tens and another color (blue) representing ones. Then she could add the red manipulatives together and the blue manipulatives together to represent each place value of the answer : 53.

She could also use a counting technique of drawing out ten sticks on her paper and then adding them together. She could then draw out ones on her paper and add those together. Then she could add the two answers together.

Both of these methods are similar to the method she utilized, but are just slightly different ways of approaching it.

Talk Moves!

1. Although I didn't have an official written lesson plan to teach this week ,the teacher gave me a place value chart and a few worksheets to go over with the students. I have only been working with the students for about a week, and this was the first time we weren't testing . I wasn't very comfortable just going over a worksheet, since I'm used to doing more interactive activities to teach math, but I also wanted to be helpful to the teacher. I tried to use some of these talk moves, especially revoicing and asking the students to apply their own reasoning to someone else's reasoning. Wait time was more of a challenge because, although I felt the students did need time to think, the more wait time I gave them, the more off-task they seemed to get. I really had to find a balance between giving them "wait time" and giving them time to just goof around.

I feel that the talk moves I did use were effective, and had the students grasped the concept better, I would have applied some of the more "higher order" talk moves such as asking the student to apply their own reasoning to someone else's reasoning. But when working with students who have trouble explaining their own reasoning (especially ELL students) to begin with, this is often the last talk move I want to use.

2. If I could re-do this lesson, I would probably use the talk moves more deliberately and more effectively. I have to admit, I didn't consciously ask the students the questions with the "talk moves" in mind, but maybe if I had, the lesson would have gone more smoothly. Also, I think that after I practice the skill of identifying the place value of different digits in the numbers (which is the skill I was teaching) more with the students, I will be able to apply talk moves such as "asking students to apply their own reasoning to someone else's reasoning."

Once I was ready to apply this talk move to my teaching however, I feel that it would help my students better understand their own thinking as well as other students' ways of solving the same problem.

Blog Entry #2

1. The room I am in for most of the day is a portable. It's kind of...different being pushed off, away from the rest of the school, especially since I never went to a school with portables as a kid. The teachers in the portables have a slightly different culture than those in the main building. They don't usually eat lunch by themselves, they have to lock their rooms up with a key every time they go somewhere, and they have to have a special badge to get into the main building. Even when the kids have to go to the bathroom, the hall pass has to have a tag on it, so that the students can unlock the door to the school. Even though the teachers in portables don't seem to be all special education teacher (I think the subjects taught in the portables are pretty much equal), all of the students going to those classes can't help but feel a little isolated, as I do.

Apart from that, the school is what I would consider a typical middle school. The cute little posters and student artwork that used to line the walls of the elementary schools is replaced with blank walls and the occasional drug-free poster. But that's what the kids are used to--it's what they expect. And since the kids are more mature, I can understand why the halls are a little less fun, and a little more cold. It's just a big difference from elementary school.

The halls are crowed as soon as the bell rings, but that's to be expected. I feel like the kids are no worse behaved during the passing periods than when I was in middle school, so I feel like the students have a pretty good idea of what it expected of them.

2. I haven't been able to observe my teacher during math yet, or the students. But from what she has told me, her resource math students are very talkative during the period I will be teaching them. She told me it was a struggle to get to all of the students because there are so many in her class, to the extent that when I asked if I could help her, she was ecstatic. Many of the teachers in my school are overwhelmed with the increasing class sizes and (in the case of the special ed teachers) increased caseloads. They are learning fractions, decimals and percents in their classes right now, and are working at about a 5th grade level. I will be working with them on their computational and problem solving skills in these areas.

3. I haven't been able to work too closely with my math teacher yet, but I feel like her beliefs regarding mathematics is to help her students succeed in the real world. The class I will be working in uses calculators to help them with their work, with the focus more on how to get the answer than computing the numbers. I do agree that the students should focus on problem solving, but sometimes I feel that computation still has some part in the classroom. Calculators are not always available, and knowing some basic facts are still essential in everyday life, I feel. But the decision to set the class up that way was less my teacher's idea than the districts, so I'm not sure that I agree or disagree with *her* beliefs.

4. In terms of my own teacher identity, I am a little worried about being able to incorporate my own teaching style into such a rigid lesson plan (that we are required to implement in our internship). I am excited, however, to be able to work with a small group of students this semester

Response to Readings- Week 1

1. Taking a problem-solving approach to teaching math allows students to form their own ideas and methods for how to solve a given problem, which might not always be the easiest or the more effective way, but at least gets them thinking about the problem and how they see it in their head.

2. I think my experiences regarding math have made me a little more jaded about the way math is taught in schools (especially high school), but also more driven to change the way I teach it, as well as the way my generation of teachers approach teaching it, especially in the higher grades.

3. I think there is a place for both arguments, because even though I feel that the constructivist-oriented approach is probably the best for getting kids to generalize their math skills, there is often not enough time in public school classrooms, and some students do need to at least supplement their learning with a more rote kind of method.

4. Saying that something is easy would probably be more frustrating to the student, although I've found myself saying it automatically at times. It would be better to relate to the student and say, "I had trouble with this the first time too, let me see if I can explain it better," or something like that.

5. The tasks helped the students become able to generalize their math skills to real life situations and be able to explain them to their peers.

Math Life Story

When I was a kid, I liked math. I didn't love it, it wasn't on my list of favorite things to do with my time, but I was fairly good at it without having to try too hard. And it was rational, reasonable. Everything that life wasn't.

I.

In the 11th grade I took Pre-Cal with a teacher who I considered cool. She loved Harry Potter and Lord of the Rings and Star Wars and Star Trek. (I guess that's not most people's definition of "cool", but it certainly was mine.) She had life sized posters of Arwen and Frodo in her room, her clock looked like the unit circle, and she would occasionally show us Star Trek episodes to teach us about sequences and series. I made good grades in her class. Better than I had in the past, maybe because we got to sit on the couch if all our work was turned in, or because she put stickers on our tests if we got 90s or above. Even though I was 17, and thoroughly too old to be swayed by something so trivial, I wanted one of those stickers so bad. And I eventually earned quite a few. It was a good time.

II.

The next year, however, things began to change. Calculus wasn't as easy. The class was larger, the lectures were harder to follow, and I found myself caring less and less about earning that A on my test. By the end I was happy if I passed, and I had never been that person before. I found the classroom barren and impersonal, the teacher distant and unfeeling, and the work impossible. My friends didn't feel like helping me, and I was afraid to ask for help. It was probably the most alone and helpless I had ever felt in school.

III.

I dropped down from the BC calculus class to the AB class the next semester, feeling like a failure. I had always been able to do the very hardest classes offered at my high school, and I didn't like knowing that there were other people out there who could do the work that I couldn't. But I got over it. I was in the same class as my best friend, which helped, and joining me were several other people who didn't want to stay in BC Calculus. I finally began to understand the material, and math became fun again, and even easy at times.

IV.

After coming to realization that I still enjoyed math, I decided to pursue a math-intensive major at UT (Electrical Engineering). As much confidence as I had gained back at the end of high school, I lost a lot of it during that time. But I also began to realize slowly that math wasn't the answer to everything, and it definitely wasn't the answer to me. So after three semesters of struggling through I major I cared less about every day, I finally made the phone call to change my major to Special Education.

V.

The greatest challenge I have faced in math was probably just before I changed majors, when I realized that I was going to have to ask for help if I was going to succeed, and that I really really didn't want to ask anyone to help me. I'm not saying that I regret changing majors, but I do regret never going to anyone for help, because I was so determined to do everything on my own. If I learned anything from that challenge, it was that math is not something to try to do completely alone, no matter how smart you are.

VI.

I wanted to be a special education teacher because of my three cousins who have physical and mental disabilities. But I also have a very personal desire to change the way students think about math, to make it more collaborative even in the upper grades, and to make something so intimidating and isolating become fun again.