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?".