Teaching Day 2

I was able to see some really great teaching today. On individual stuggled a little with his lesson because the students where not advanced enough to do the presented task. He was able to modify the task to draw the students in and begin to push them up. Unfortunately, the task was a little long and he did not have enough time to really draw out the concept that he was wanting the students to learn. He did a very good job at trying to probe the students and get them thinking critically. The second teacher was able to get right in with the students and relate with them. He talked a lot in their terms (slang) and had a laid back demeanor. He was not a push over, though. He was able to challenge the students and forced them to think critically about their answer. The students were required to prove/justify their responses.

The students even commented that they liked the way they were being taught. The liked working in groups and being challenged. So, I hope I can get my students to buy into it this fall.

The Big Day...

So I had a chance to try out my new teaching style...and it went very well. I had five students, 3 boys and 2 girls. The students were quiet and did not work together initially. This is the one thing that I really did not anticipate and prepare for. I assumed that the students knew how to work in groups and would just jump right in. I had to continually encourage them to talk to each other and look to each other, not me, for help. My lesson related to finding the cost of a cell phone bill if the company charged by the minute. The students were interested and immediately began working on the problem. It took a little too much time to do all the computations, in hindsight calculators would have been beneficial. This put more of the focus on the computations instead of the concepts. We where able to put the equation in words and then with variables. In addition, I felt rushed in the after stage. I was not able to really probe the students and draw out big ideas. Knowing your students is definitely beneficial. It allows you to make modifications that will help to draw out the big ideas and not cause the task to become blogged down with mole hill issues.

Time to Put it to the Test...

Tomorrow I am going to walk before 10 sixth graders and a group of my peers and put this constructivist teaching to the test. Am I nervous? Yes and no. Yes, more because my peers are going to be there analyzing everything I do or don't do. And no, because I generally feel at home in the classroom. I really want to put this into practice in the classroom and this is a good opportunity for me to practice. It will give me an opportunity to see what I am going to be good at and what components I am going to have to work on. I really think that I am going to have to work on questioning and not taking charge and doing the math. It is going to be hard for me to let the students struggle and develop this on their own. I feel really confident that the lesson is relevant and one that my students will be able to grasp without having to do a lot of prompting, but not so easy that it is not cognitively demanding. We'll see.

The Future...

I really buy into the whole student-centered concept, but there is one thing that is troubling me. What happens to students the next year? What I mean is, when they spend a whole year in my classroom constructing their knowledge through student-centered task, and then the next year they are placed in a room where the teacher doesn’t use this, what happens? This is not going to stop me from accepting the challenge, but I have wondered that. What if the teacher doesn’t allow the students to use their methods to solve problems and counts off on tests because they don’t solve the problems the teacher’s way? Also, if I push beyond the curriculum, is that teacher going to refuse to push further and only do what the standard says, causing students to repeat the same curriculum and become bored? Does this really work when only a handful of teachers are on board?

Relevance

My response to relevance of middle school mathematics task is a yes and no. In middle school it is good to use task that relate the students’ interest, as it will help to engage them. It also needs to be relevant to things that know about, or background knowledge needs to be given. For example, students in Atlanta probably have no concept of what a yacht is and a problem using a yacht would not make sense to them (particularly without a diagram). At the same time students should not be catered to, or they will only be willing to be involved in tasks that are relevant to them. Talking about a yacht would not be relevant, but it would expand their knowledge base. When these students take a job, the task they are assigned will probably not always be relevant to their interest, but they will be relevant to the job they were hired to do.

Creating Lesson Plans

Creating the first lesson plan was a challenge for me. I wanted to do a lesson plan on integers. My students struggled to remember the "rules" for adding, subtracting, multiplying and dividing integers. It is so critical to all future math courses, because from the time we talk about them until forever, they will encounter positives and negatives. I wanted it to be tight (not as in cool) and very focused. I was constantly refining and refining the task. In fact I totally changed the task for the refined lesson plan. I struggled to know when to introduce terms and explanations and when to let the students discover. In the end, I feel like I developed a plan that would be student centered and relevant to the students.

Letting Go...

As teachers, we like control and order. Constructivist ideas contradict everything we love about control and order. But I am so ready to implement these ideas, that I almost wish school started next week (again I say almost - I'm not ready to go back to work just yet) . I can envision this going on in a classroom and I am excited by what I see. I think the thing to remember with letting go is that the students don't just walk in the classroom and have a task on the board and start working with no instruction. The purpose of the pre-task is to get the students prepared for the task. This includes getting them thinking mathematically, thinking about the current topic, assessing what they already know, making sure they have the tools/knowledge base to begin the task. But letting go also means that the teacher uses questions and student response to make it happen - not doing a problem and the students mimicking the teacher on the independent problem. The teacher should not release the students to begin the task if the students are not ready. This will cause more confusion and chaos and lead to unnecessary frustration.

What we really need to let go of is the idea that students can't come up with a solution without first being told how to do the problem. If we will let go of this idea, I believe the rest will come a lot easier. We will be willing to let students take control of their learning.

Mathematics and Media

Math, math everywhere…It’s in the beat to the music on the radio, the speed my car travels as I zoom home, the statistics of the presidential poll on the nightly news, the calories and carbs we count for each meal…the list goes on and on. One thing that I think is important to note is the distinction between numbers and math. Room 319 designates the room a class meets in, as opposed to Room 320, but is there really any math involved? Of course this goes back to our discussion on what is mathematics.

As far as the use of math in the public domain, let me preface my comments by saying that I am an ostrich and very much disconnected from the media so my comments may be a little elementary. In the media we hear of math largely in the form or statistics and probability (for those that distinguish between the two). We hear about the probability of rain and sunshine in the nightly weather report. Commercials are filled with statistics on the likelihood of pregnancy, cancer, heart disease, adverse reaction to a medication, etc. We here about the popularity of individuals based on “polls” (I put it in quotes, because no one has ever called me and asked my opinion, have they called you?) Often though the math is done for you and the message is explicated stated or implied to you. Often the observer does not do the math, but simply accepts the reporter’s remarks as fact. I think that is one of the beautiful things about constructivism. If we will really get a hold of this concept, we can produce future generations that will critically think about what the media portrays as fact.

Limitations on Student-Centered Learned

One of the biggest problems I have encountered in trying to implement student-centered learning is students’ unwillingness to think for themselves. Students have been programmed not to think. Often I have made the statement that I didn’t learn to think until I got to college. Students were told how to do a problem and expected to follow the procedure. (Again that’s what I liked math, right?) Those that could grasp the procedure were fine, the ones that couldn’t were left behind. By the time they get to middle grades they don’t even try. Our textbook has been so empowering though. Even for me, I’m learning things. I want to go back to my school and teach these basis operations again – the student centered way. We spend so much time in our curriculum re-teaching the same old way, and students still don’t understand it. When I see the strategies in the book, I am totally buying into it. The way I plan to engineer the shift from limitation to constraint is to first recognize that this is prevalent. Secondly, I plan to begin with something simple, like an addition problem where they can’t use traditional methods. By giving them something early that allows them to be successful, I believe this will empower them to continue to try.

The effects of constructivism on my thinking

The idea the math is not simply a set of standard rules and formulas is one of the most radical, maybe even revolutionary, ideas that I have heard. I liked math because I thought it was so structured, so black and white, so clear cut. I thought the objective of math was to get the right answer. I liked it because it did not appear to be subjective. This class has caused me to rethink my ideology. In ways it has pulled my foundation right out from under me. But the interesting thing is that I don’t feel like my world is falling down. Just as quickly as the old ideas are crumbling – or at least let’s say the fallacies and inconsistencies are become apparent – new ideas are forming to replace them.

As I have previously stated, I tried to implement the new constructivist ways (although I didn’t know that’s what it was called at the time), but I also tried to keep the traditional way as well. I wanted to live in both worlds, but that will not work.

A constructivist classroom looks like ordered chaos. Students are engaged in mathematical discussions and activities. Each group may be doing something completely different in their efforts to hash out their ideas. It is such a contract to traditional classroom where at any given moment you should be able to hear a pin down. It is also different because it eliminates the plug-and-chug approach. The importance is not solely on obtaining the correct answer, but obtaining and retaining the key concepts needed to derive the correct answer. Oh, how I long for this in my classroom.

June 14 - My Student and Teaching Experiences in Mathematics

My experience in my mathematics has been very much along the traditional lines. While I was a student in middle school and high school, my math classes followed much of the same routine. The teacher went lesson by lesson from the textbook, we copied notes and were assigned nightly homework problems. The next day, we would discuss the homework from the previous night, then proceed to learn the next lesson. This was not very hard for me because generally it was memorization of a formula and plug-and-chug from there. When I did question the why (in geometry), I had a teacher that could not answer the “why” in terms that I could understand.
When I started teaching last year, I went into the classroom with the preconceived idea that teaching mathematics was just like I had learned it. I do not recall ever hearing the word manipulative before I started teaching and I certainly didn’t have a clear understanding of how to implement them in my lessons. When I was introduced to GPS, I loved it, but had a very hard time implementing it in my classroom. I felt like I still needed to teach the students the procedures/material first, then give the problem-solving task. In addition, I had late afternoon math classes and a lot of discipline problems. When I would try to do problem solving task they generally flopped.