A Master Teacher of Mathematics

By : Heather Bridges

Who is a mathematics teacher? Recently, I have been struggling with the answer to that question. During my student teaching experience, I learned that surviving all the trips to Boyd and the EMT papers was the easiest part of becoming a mathematics teacher. So now I am on the brink of my new career. People are already referring to me as a mathematics teacher and it has stirred up new thoughts in my head. It is very frightening to think that all someone has to do is pass the necessary courses and automatically they have qualified to be trusted to mold our future. I have decided that there is much more developing and preparation left for me to accomplish. I believe that the goal for all math teachers who get the degree should be to become a master teacher of mathematics. This surely has different meanings to different people but, I think it is important for every new teacher to focus on the definition of a master teacher of mathematics or in other words their ultimate goal. The next step is to design a path to take to fulfill that goal. So, I guess a mathematics teacher is more a person with only the qualifications but, a master teacher of mathematics is in short a developed and secure teacher in his or her mathematical knowledge, techniques of teaching, and further goals for further professional growth.

There are many elements that make up my definition of a master teacher of mathematics. One of the most necessary has to be experience. I recognize that it is very difficult for someone to jump into teaching and become great automatically. There is much more to it than that. It is kind of like learning to drive a car. People can give instructions or advice on the best way to do it and someone can memorize the driving manual forewards and backwards but, the actual learning is done behind the wheel. And just like driving, I believe it takes practice to become secure in one's ability and probably a few crashes can be expected along the way. Beyond experience, my definition becomes very detailed. There are several areas of which I wish to focus my development some of which deal with teaching in general and others specifically on teaching mathematics. These elements are as follows:

( 1. ) Instructional techniques
( 2. ) Assessment techniques
( 3. ) Teacher/student environment
( 4. ) Further professional development


Instructional Techniques

Throughout and since my student teaching experience, I have been constantly considering what kind of teacher I want to be. It has been much easier to define who I do not want to become with reference to educators I have witnessed. I have read so much information on how teachers mostly model their teaching after the way they were taught in high school and etc. but, I do not want to fall into that trap. This will be extremely difficult because I am returning to teach at my old high school with all the same teachers who still teacher the same way. Not that traditional teaching is terrible, I just believe there is more effective methods to teach. One thing that I do know is I do not want to sit behind an overhead desk day after day teaching students to solve problems by example.

My ideal vision for who I want to become is to be a teacher that greatly models his or her style of teaching after the NCTM Standards. I want to be the kind of teacher who coaches my students through there mathematical learning instead of just dispensing knowledge. This will require a great deal of preparation to keep the classes moving effectively. I think good planning is the key to this type of instruction. It would be very helpful to identify what possible questions might be expected from the students or necessary to achieve the goals of each lesson. With these ideas in mind, I see a master teacher as someone who uses several types of learning like small group work, individualized work, whole class explorations, and student lead presentation and instruction.

Another element that is very important in my mind to being a good teacher is how the students view mathematics. I want my students to enjoy math class to a realistic extent. This is directly related to what I discussed in the last paragraph. If students view math as just manipulation of numbers into whatever formula the teacher puts on the overhead that day then of course they are going to hate it because it is boring. One way to correct this is using the student lead learning as I previously discussed but, another immeasurable tool is technology. In my experiences, if you put a computer or "difficult looking" calculator (TI- 82, TI - 85, & etc.) in front of a student then you automatically have sparked some type of curiosity. Computer software should be used as much as is applicable to provide dynamic classroom demonstrations. When used for individualized explorations, it can give the students a feeling of superior intelligence just be being able to use it and the power and confidence to want to solve things independently. A master teacher realizes that these experiences are required to prepare students for their future in dealing with technology, needing the capability of exploration to solve problems, and to generally view mathematics as a useful, interesting, and interconnected body of knowledge.

There are so many things that form the idea of a mathematics teacher in reference to instruction. For instance, experimenting with a lot of the new ideas that accompany the views of the NCTM Standards. I like the idea of a teacher keeping track of how much the standards of problem solving, reasoning, communication, and connections are addressed in each week. This kind of self-assessment provides the teacher with a method to regulate her own teaching ensuring to stay out of the rut. One way to encourage problem solving is by using open-ended questions that provide the students with some flexibility in methods of solution. Thsi type of question also addresses the standard of communication. Student responses often promote written or oral explanations which alone can provide meaningful classroom discourse. I also believe it can be very useful to further these ideas by using journals in mathematics to cement the students understanding of concepts by forcing them to analyze their thoughts. A master teacher might also use the history of mathematics to humanize the classroom and promote the connections of math to other subjects.


Assessment Techniques

The views about instruction that I have explained place a great deal of focus on the type of assessment a teacher should use to promote learning that parallels the instructional techniques. It is important for a teacher to remain aware of the effectiveness of lessons, achievement of the students, and the long term progress they are making. If group explorations are used for instruction then it is a good idea for groups to be used in the assessment. The use of open-ended quesions broadens the correct answer from one solution to various solutions that may not be anticipated. To account for this a teacher must be prepared to develop rubrics to assess the student's responses. To promote good performance, the teacher needs to enform the students of the criteria they will be judged on in the rubric. I believe when rating a student's performance that it is important to focus on the good points as well as the bad. The students are sharing their ideas which may be difficult in some situations. Positive comments will do more to keep interaction going. There are some other important factors to me of how a master teacher assesses students giving them more opportunity to prove what they know that tests and homework. Projects and discussion could be very helpful. The teacher could alternate focusing her attention on a small group of students at a time to rate their participation in class discussions. A teacher should also be very swift to give all students feedback on their performances. By this I mean grading any assessment promptly. It would not hurt to take a few minutes to jot down some thoughts on each student's group participation throughout the semester to make them aware if changes need to be made. Assessing homework is also an element that needs to be addressed in a mathematics class. A master teacher is also one who develops a good plan individually or through research and practice to evaluate the students' performance on homework. I know several techniques but, I have not decided on what method is the most effective.


Teacher / Student Environment

One of the necessary qualifications of a master teacher of mathematics in my opinion is having a good repore with the students. Recently, I have learned that everyone will not always be happy but, they must feel respected. In most cases if a teacher treats the students as a important individual then they will respond accordingly. This eill create an open environment in the classroom making it easier for students to share their ideas. The relationship between teacher and student is a great deal more complex that I originally thought it was. With the new ideas of mainstreaming children with disabilities, the teacher must be sensitive to the individual needs of each student and make adjustments to meet those needs. Mathematics is a very difficult subject for a lot of kids. A master teacher of mathematics in my ideal scenario puts a lot of focus on softening the accepted view of math and breaks it down to where all students are interested and can understand. This again supports the ideas of using technology and real world situations to increase the favorability of math classes and mathematics in general.


Further Professional Growth

The final element of what it means to be a master teacher in my opinion is teacher having a continued strive to improve. A good method to ensure this is constant self-evaluation. A teacher can discover a lot of things about his or her teaching through reflection. After reflection comes discovering areas for possible modification to be more effective. A teacher must also stay up with the latest technological advances to keep the students up to date. Several conferences and teacher workshops are available for these types of advancements that can be very valuable. I also think that after a teacher becomes secure in their position that having others sit in on their lessons and evaluating them is a good idea. I value the opinion of the students as well. It would not hurt if evaluation sheets are given to the students. There are several approaches to rate one's teaching. It does not matter which ones are used just as long as a teacher remembers that there is always room for improvement.


Basically, I have summed up what it means to be a master tacher of mathematics in my opinion. Do not misunderstand me. All of the methods I discussed earlier are not necessary to be a master teacher of mathematics but, the major ideas are. By this I am referring to modeling instruction and assessment after the NCTM Standards, maintaining good relations with the students, and seeing room for future development. It is very hard to define what the ideal mathematics teacher should be. Teaching is such a complex job. From this preservice teacher's point of view, the scary thing is I probably do not even realize how challenging it really is.


How to become a master teacher of mathematics?

Honestly, the answer to this question still eludes me after months of trying to find the solution. I have studied the NCTM Standards, several journals and various articles to discover no set method. One thing that I do know is that I am closer to it now that I was last winter when I embarked on my first classroom teaching experience. I also know that I am still very far away from being the type of teacher I have been discussing. I believe and I hope that experience will take a pre-service teacher a long way. After removing that factor, what is the next step in becoming my view of the ideal teacher.

My First Year

My plan is to take things a little bit at a time. When I start my new job, I expect to be overwhelmed at first by the newness of teaching without taking into account anything discussed in this paper. Because of this I will try to not put any undo pressure on myself during the first week. I have made preparations to discuss planning proceedures for the classes I will be teaching, Algebra and Pre-Algebra, in regards to pacing with the new block scheduling format. I hope from that I will get sort of a tentative guide to monitor myself. I plan to make very detailed lesson plans that provide all material to be introduced, possible assignments, and good questions to promote discussion and anticipated thoughts and ideas of the students. I have designed a chart to regulate my methods of instruction. This will help me keep track of when I use group or individual work, technology, and writing. I hope this will help to promote a shift away from falling back into the more comfortable traditional methods of teaching. To begin with, I will start off slowly and then gradually increase the amount of cooperative learning, writing, and technology. I want to be careful not to overwhelm my students. I also believe that it will be very helpful if I keep a notebook full of all the lessons, assignments, and worksheets with some of my personal comments as to how I judged the success of each task. This will provide a solid foundation for improvement.

Future Growth

Hopefully, improvement will continue with each year of experience. To ensure this, I plan to always try to attend some type of workshop each summer. I also hope to return to UGA to work on my Master's degree very soon. One very important factor in this journey to become a master teacher of mathematics is my attitude. I think it would be a good idea to reread this paper at least once every school year to keep the "change the world" dreams alive in my mind as well as my ultimate goal of teaching as defined by this paper. The world is constantly changing. A mathematics teacher should always recognize that and try to change with it to better prepare all his or her students. If I keep these ideas in mind then it doesn't seem that "master" statis is unreachable. The teachers I have witnessed who in my opinion are master teachers all have common characteristics. They love and respect kids, have a passion for learning and teaching, and recognize that there is always room for improvement. If it is possible to maintain these same characteristics combined with the methods suggested earlier for professional development then becoming a master teacher of mathematics maybe somewhere in my future.

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