In the End

After reflecting on every one's blogs and comments, I realize that we are all in the same position. We all have the same concerns, hopes, and aspirations. We all have learned throughout our first phase of graduate education, and our views are being reshaped. I think we all are looking forward to being in the classroom, but still fear the unknown.
I feel confident because I have been in the classroom and I think my experience thus far will only make me a better instructor. I think my views have been improved not necessarily changed. I know I still have work to do, as it pertains to becoming an excellent teacher, but I can definitely say this semester was a great starting point. I think I can be successful in the classroom without the things I am learning at GSU but it will be a much more difficult task. "Education is important" and my experience as a student at GSU makes me realize the importance of this statement. It is a cliche used all the time, but I truly recognize the importance of what I am learning. I feel that my learning experience will help me to relate to my students and hopefully provide them with the same type of relevant learning experience.

I Love the Kids

The overall experience at the academy was great. I think there was no better way for us to transfer our learning from the classroom to a real world environment. I think the task of teaching was constructivism in practice, for us, as teachers. We had a hands on experience that taught us what we should and should not do in the classroom. These are the types of things you can only learn by doing. I learned by both teaching and observing. My classmates had both positives and negatives that I plan to learn from. My experience as the teacher was a positive experience that I could not have achieved through lecture.
I learned that my expectations of my students can play a major role in the effectiveness of my lesson. I also learned that an affective opening can serve as a springboard into a beautiful lesson. In addition I realized the importance of questioning. Questioning serves as the guide to instruction as oppose to direct instruction. If I am aware of where I want my students to go, it is up to me to make the connections needed to get them there without giving them step by step instruction. Effective questioning can accomplish this goal. One thing I noticed is that, in some instances the students prior knowledge will be all they need, but in other situations I have to help students build a bridge to access the appropriate prior knowledge.
This experience tells me that effective planning is a must. The vital parts to the lesson plan are the same things that Dr. Mathews has stressed to us this semester. The components include an a good hook, an appropriate task, the anticipation of student knowledge, and the questions needed to probe students. I have gained new perspectives in teaching and I think they were much needed.

We are on the right track

I really enjoyed my teaching experience today. I was excited and enthused about the opportunity to teach. My expectations were high and I think I met my expectations in some aspects but there are still some things that I need to improve. The positives in my experience were the level of student engagement and the fluency of the lesson. The students appeared to enjoy the challenges the task posed and related to the concepts very well. I think the part of the lesson that could have improved was the introduction of the task to the students. I think I could have been more affective in my introduction to help guide the students and help them make more connections to the concept. I also think my time management could have been more affective.
I feel that this is one of the best assessment methods for me as a student and a teacher. I think this was an excellent opportunity for me to test new strategies in the field as a student of the teaching profession. In addition, it made it possible to recognize the adjustments that I need to make as a teacher. I am learning the importance of planning and how improvization is also a must. I look forward to my next opportunity to expand my learning and become more efficient in the classroom.

Moment of Truth

I am excited about going to teach at Sandtown Middle. I think this will be an enlightening experience because it will allow me to put into action all of the new teaching strategies that I have been learning. I am anxious but I am also confident. I feel that my prior classroom experience coupled with what I have learned at Georgia State will mesh well and make me a more affective mathematics teacher. I think that the timing of me entering the TEEMS program and furthering my knowledge of education is perfect. I have dealt with the rough edges that comes with not having formal training in education. However, now that I am learning effective strategies I feel that I will be able to use them effectively.
Tomorrow at Sandtown I look forward to having a wonderful experience. I am familiar with the school because I have substituted for a teacher there once. The experience that I had there was pleasant I expect the same tomorrow. I envision the lesson going really well and the students enjoying learning. I hope to challenge them and facilitate an engaging environment. I feel confident in our group's lesson and I feel that we will reach our objective. The sixth grade students, in my opinion, will be able to grasp an eighth grade concept and truly be inspired. The experience will not only be inspiration for the students but for me as well.

Can I get a Little Help

When is it time to instruct? This is my concern right now as I prepare to enter the realm of the "new mathematics teacher". I know that I want to create a classroom were students are allowed to struggle, but when do I as a teacher intervene if the students appear not be moving in the right direction. If I do intervene how much intervention is appropriate. By this I mean, do I suggest strategies, or do I modify the task. If I present the task in a different way maybe the students will be able to develop a strategy. However, once class has started and a task has been introduced is it too late to change the task, if the task given does not connect to students prior knowledge.
If I opt to give instruction is this counterproductive. Can I provide a formula, and learning still occur. This is a concern of mine. How do I develop certain concepts without providing formulas and step by step instruction. The real world context of problems can draw certain desired outcomes, but I am uncertain if this will be the case for every lesson. I am willing to experiment, but there is still some skepticism about this approach. Of course, I want to implement a teaching style that produces efficient learning, and constructivism is the suggested method. I just want to know, in the constructivist approach, is there room for teacher guided instruction.

Making it Count

As I reflect on my experiences as a student, I can definitely say that I am learning how to become a"new mathematics teacher". The reason I say this is because I don't remember ever having a mathematics teacher that took my interest or strentghs outside of their classroom into consideration in designnig their lesson. I have had mathematics classes that were engaging and I did have concepts that I could apply to my life outside of school, but the difference is I don't think my teacher had my particular likes and dislikes in mind when they designned the lesson. The engagement came because I enjoyed being able to meet the challenge. The confidence that it gave me to be successful in mathematics was motivation for me as a student.
As a teacher I feel that it is very important to make connections to students personally because it makes the learning tangible. In my classroom I try to provide these types of connections by creating my own real world examples and even re wording word problems from text books to cator to my students cultural backround. This approach I feel is affective because it can give students information that can carry with them outside of my classroom. I have had lessons where I have heard students say that there are going to shock their parents by showing them what they have learned. One student in particular mentioned that he would show his mother how to calculate the total cost of a sale item the next time they were out shopping. This is the type of genuine learning that is essential for true progress, because the application outside the classroom is what really counts. I feel that the purpose of education is provide students with the skills to survive and be productive citizens in society outside of the classroom. This can not happen if students feel that information learned in the classroom is totally detached from their lives outside of school.

My Philosophy

When I sat down and completed my first lesson plan I felt it had plenty of, what I thought to be, good ideas and strategies. I was confident that my ideas and thoughts were clear, and there would be only a few corrections to make. However, as I now think about how my lesson was laid out, there were definitely some critiques that I should have expected from Dr. Mathews. If this plan was being evaluated by a traditional mathematics teacher, he or she may have seen it as exemplary. In contrast Dr. Mathews is trying to develop a "new mathematics teacher" and knowing this now, I am not surprised by his comments. Though I do admit, I was initially shocked, but as I read and made sense of them, I could see the reasoning behind the critiques. One of the comments he made I could see coming before hand. That comment was in regards to my opening activity. I was not shocked because it was not very engaging. Dr. Mathews felt that I had an engaging opening in a classroom presentation but in my lesson plan the activity was really "old school".
As I worked on refining my lesson plan, using the comments as a guide, I noticed more and more that the plan did have traditional methods and could be improved. The constructivist approach was not really evident in my initial plan. I noticed how in my classroom presentation the initial conversation got the class engaged and this is what I needed to construct a more powerful lesson. I also noticed that I had some algorithm problems as one of my task, which I know is not the best way to promote a constructivist plan. As I progressed through my refinements I also noticed that there was no point in my original plan where I thought to "let go", but in hindsight "letting go" is a must. I can definitely say that I can see the change in my thought process through the lessons in Dr. Mathew's course, and I hope I am able to apply this approach in the classroom and have positive results.

The Big Comprimise

"Letting Go" is the hardest concept to get acclimated to as a new teacher. The concept of teaching has always appeared to be a teacher centered task until I entered Principles of Instruction. Now I can not wait to get back into the classroom to try this new approach because I know that I need to improve as a teacher. I don't feel this way because I think that I have been doing a poor job but because I know that I can do better. In the classroom I can definitely say that I have experienced the type of learning where students don't fully grasp concepts but they follow the steps to get an answer. With all of the pressure of standardized testing getting an answer sometimes becomes the main concern as oppose to students being able to think mathematically and understand the logic of problem solving.
I think that the time to "let go" is after the teacher has encouraged the students to think about a particular familiar concept that will allow them to build onto a new concept. In addition the teacher should also engage the students interest in learning by connecting the concept to something relevant to the student's life. After these things are done I think the students will be motivated to accept challenge and solve problems.
There will be sometimes I think that the teacher will have to intervene. For instance if there is no learning taking place, and the students appear to be lost or confused as the instructor I feel the need to provide guidance. I don't think that giving students one defined method is the answer but providing possible strategies may help. If the students get side tracked away from the main idea of the lesson and spend to much time on something of little importance I would also step in to redirect the students' attention. Overall, I think that letting go will be a much needed challenge for both me and the students. This is the type of challenge that will make us more efficient learners and teachers.

Mathematics Is Everywhere

When I was preparing to approach the topic of "How is mathematics used by the public domain?", I thought about some of the more obvious uses first. Some of these include money transactions, and in reporting of statistics. However as I paid more specific attention to the news and everything around me I noticed that there is evidence of mathematics used everywhere in almost everything. I thought about how mathematics is used to make sense of some 0f the everyday concepts we encounter. On small example, is the fact that when you use certain items one can expect there to be a line of symmetry. Examples of this range from a sheet of notebook paper, the car you drive, the bed you sleep on, to the computer screen that you are looking at all have at least one line of symmetry which makes them appear as normal to us.
All of the news articles and print media that I have recently observed had at least one reference to mathematics. One of the articles was titled "Cost Conscious" which referred to the state of the economy, stock market, and inflation which all revolve around the mathematical interpretation of data. Another article was about the closing of food factories in China which was also explained using mathematical percentages. A very interesting article was about how half of humanity will be living in cities, as oppose to rural areas, by the year 2030 which again required mathematical reasoning to predict. One last article that I found also to be very interesting was about riots in Iran because of laws that will ration out fuel. The law will only allow private car owners to purchase 100 liters of fuel per month which led to rioting. The math connection is shown in the fact that someone had to mathematically figure out that 100 liters per month would be an amount that would allow their economy to function.
In the overall scope of things I see mathematics being used everyday by everyone both consciously and unconsciously. In fact it is a tool that allows us to function and make sense of the world around us. The concept of mathematics can be learned and recognized by anyone, and its use is critical to our future.

There's No Limit

I can say with confidence that we (me and my colleagues) all have seen some sort of "limitation" with the constructivist method of teaching. One of these "limitations" is the ability to "let go" as the teacher. I think that our instincts as the teacher is to want to guide the students to the right answer, and the required "letting go", allowing the student to struggle is a challenge. Another "limitation" is the thought of how to assess student work when the assignments will not look like traditional mathematics with computations and answers. Also, just the idea of constructivism which is foreign to most of us is intimidating because we don't know with certainty that we will be able to effectively implement the strategy.
Currently I am thinking of myself in the student's position under a constructivist instructor, which leaves me with the task of finding my own understanding. What I have come up with thus far is that I will be able to complete this task and the only way for me to learn and become confident is through the hands on experience. Once I am in the classroom and begin to truly use constructivism I think everything will come more natural and I will solve my problems ("limitations") as they occur. The key is I will also be a problem solver overcoming challenge just like my students. I can now make the connection that what might be called "limitations" are really just constraints.
Engineering (planning) is a big influence on the level of confidence a teacher can enter the classroom with. A well planned (engineered) lesson can eliminate much of the doubt about constructivism because all of the possible issues or concerns should be addressed before entering the classroom. If a plan is well engineered the likelihood of the teacher encountering something unexpected is very small and the chance of the students gaining understanding is increased. I look forward to implementing constructivism into my classroom and don't see constraints as an overwhelming challenge but a challenge that can increase my potential if correctly addressed.

Constructivism and Understanding

The constructivist approach to teaching is a model which I have learned a lot about thus far in my graduate studies. It is actually a strategy that I have heard of previously but had not known the term "constructivism". A friend of mine that is in education questioned my method of teaching and informed me of some of the constructivist strategies but did not associate it with the term. As I implemented some of their suggested techniques I found it to be effective. Through my classroom experiences I became aware that true understanding can not be taught be the teacher but developed by the student. These experiences make me very receptive to the constructivist approach and interested in developing effective strategies of implementing constructivism.
Some of the things that imply constructivism is taking place is more of a learning community in the classroom. An environment where the students are interacting. The teacher is more of a facilitator and sets the tone of the classroom. The teacher would lead the lesson through effective questioning and the students would be able to make connections to build on their prior knowledge to draw accurate conclusions relevant to the lesson. The effectiveness of the constructivist model still lies in the hands of the teacher, and as a new educator I feel that it is vital for me to learn and become an excellent constructivist.

Teaching and Learning

In my past I have experienced math as an early source of motivation for all of my academic accomplishments. When I was in 3rd grade I can remember my teacher telling me that my math scores (standardized score) was one of the highest scores in our school which was a huge inspiration for me not just in mathematics but in all aspects of education. I have also experienced what some might perceive as failures in mathematics courses. In my entire academic career there have only been two courses that I have had to repeat and both where math related. The reason I would not view these experiences as failures is because in both situations the second time around I was among the top performers in the class. These experiences in mathematics have raised my confidence tremendously in terms of facing challenges.
The types of challenges that I have faced as a teacher coupled with my experiences as a student have made me very much open to change, and learning new ideas. I have had experiences where students have come up with problem solving methods that I did not initially recognize, but as a result had to acknowledge. These types of experiences made me feel very much connected to our classroom discussion of "The New Mathematics Teacher". I have also experienced in teaching that when I tie in real world examples that relate directly to the students, they tend to become more engaged and willing to work. As a student the same applied to my learning. I really enjoy learning when it has a direct correlation to my life. These factors influenced my input in our discussion of, "what is teaching and learning?".