My philosophy of education is simple, but very critical. Too often we find that our educational system involves the process of presenting information to our students and then have them automatically reproduce that information back to us. This can be justified by looking at our standardized tests. We present learning in a way where students can memorize information for the sole purpose of reproducing it for a test. Education has become a one-way street where the student is a passive entity. IS THIS REALLY LEARNING? What have we taught our students?

I believe that purpose of education is to create independent learners where students can learn on their own. In the past, all we have taught them is how to retrieve a piece of information and spit it out when needed. But, do the students understand this information? Do they know why it is the way that it is? And, can they apply it? To me, these three questions are the foundation for the underlying process of critical thinking. I feel that it is the purpose of critical thinking that causes students to consider alternative points of view, to analyze those points of view, and to come up with their own conclusions, and not the conclusions of the teacher. This way education becomes a two-way street, where teachers facilitate learning, but learning becomes student directed, rather than teacher directed. I strongly believe that this is what education is all about, making learning student directed! The students analyze information and determine what it means to them. Critical thinking requires that students become independent learners, and take learning into their own hands.

I believe that critical thinking is not only important to education, but extremely necessary. It is a process that requires the student to become an active entity in the learning process, rather than a passive one. By making education a two-way street we encourage student interaction. The students take learning into their own hands by analyzing, questioning, and coming to their own conclusions. I feel this is extremely important. I believe that through the process of critical thinking students can develop skills in the following areas: problem solving, reasoning, communication, connections and representation. According to the New York State Math Education Standards these are the key areas that students should master, and therefore I believe critical thinking is imperative to those standards. Students also learn how to investigate, discover, conjecture, reason, argument, justify, proof, and apply what they have learned. To me, this is how learning becomes more personal, and meaningful to the student. By incorporating critical thinking, I feel we are better preparing our students to become more active and critical members in society.

Why should we integrate critical thinking into the mathematics classroom and how can we do this? I feel this is the major question that we as mathematics teachers should be asking ourselves as we enter the classroom. We want to make math fun and exciting for all of our students and we want them to be able to apply it to their own lives. We want them to be able to explore mathematics in a way which will excite them and challenge them. We want to instill upon them the passion that we have for mathematics.

Why should we integrate critical thinking into the mathematics classroom? I believe that as it is now, many students go through high school wondering why math is important, and what can I do with it? Many students dislike math and want to avoid it at all costs. What can we as teachers do to help students realize the importance of mathematics in the real world? I feel that this is the big question we as math teachers will face when we get into the classroom. How can we begin to embark upon this task? Critical thinking is the answer! Not only is critical thinking important to all disciplines, but it is especially important in mathematics. Sure we can give students definitions, postulates and theorems and we can teach them how to use them, but the big question is do they understand where they came from, and how they are developed? Anyone can use a formula to find an angle, or a distance, but do they know why the formula works, and could they develop the formula for themselves if it wasn’t given to them? I feel that we need to get students to question the information we are presenting to them, we need to encourage them to ask how this works and why it works! These are some of the big questions in critical thinking. I believe that only when the students examine these questions with guidance from the teacher, they will begin to understand the underlying concepts of mathematics and begin to apply them. This is the biggest problem with mathematics today. We teach students how to use a formula, but what we don’t teach them is how to mold mathematics to fit their life. When students can understand why we use a specific model to solve a problem, and why that model works, then and only then they will begin to apply mathematics to their life. If we can do this, we can get students to begin to understand the fascinations about mathematics, and we can make math fun and interesting for them. I believe this is one of the main goals of education and it is major component of the NCTM (National Council of Teachers of Mathematics) standards.

How can we integrate critical thinking into the mathematics classroom? I believe that the most important thing is to avoid reverting to a teaching style that is one-directional that is, feeding information to the students, and telling them how to use it. This is the biggest obstacle, especially in mathematics. I feel that most traditional mathematics classes are those where the students are passive, and sit and take notes. There is little interaction, and it becomes especially difficult for students to retain information and apply it. To me, the structure of the lesson is extremely important! Instead of starting out with fancy definitions and theorems, I feel that it is better to start a lesson with an applied problem that is personal to the students in your classroom. Then talk about all the definitions and theorems as they come up in context and not as abstract concepts. This way it is easier for the student to see the real connections. I feel strongly that as mathematics teachers it is imperative that we introduce the idea of questioning in our classrooms and to facilitate a discussion that will encourage them to ask questions to get them involved. I believe it is also important to introduce a little history into the lesson. I feel that when our students can see how mathematical ideas are discovered it will be easier for them to put those ideas in context. Student’s will be able to start making their own conclusions about mathematics, and start thinking in a logically way. At this point they will be able to start seeing applications for themselves, and not relying on the teacher to apply the material for them. Their active involvement reinforces the concepts of critical thinking, and contributes to their never-ending quest to be independent learners.

Critical thinking requires that we question what we know, and question knowledge in general. It allows us to develop our own concept of knowledge that makes us who we are. By creating well educated and critical thinkers, we are creating a society in which education is a common ground for the evolution of a new era.

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