You and Your MATH Teacher
Teachers are the backbone of an educational system. Children are like clay in a potter’s hands. Just as a potter gives a desired shape to clay in his hands, so do children become what their teachers want them to become. These days, more and more children live in a nuclear family where both parents are working and often, such children rely heavily on their teachers for help, advice and guidance. Teachers have the ability to create a strong like or dislike for the subject they teach their students. Mathematics is considered the most monotonous and insipid subject, but damn sure a true teacher can make it interesting and enjoyable. A good teacher can dispel the darkness from our lives. A good teacher in fact becomes a role model for students. Students tend to follow their teacher in almost every way like manners, style etc. Students tend to get affected by the teacher’s affection as well as love for them.
Dr A P J Abdul Kalam in his address to nation in 2003 on the occasion of Teacher Day said- A student during his school life up to 10+2 spends 25,000 hours in the school campus. His life is, more influenced by the teachers and the school environment. Therefore, the school must have the best of teachers with ability to, teach and love teaching and build moral qualities. Teachers should become role models. Similarly, the student must be alert to build himself with best of qualities and to get ignited with a vision for his or her future life.
Teachers work in close co-ordination with students to help them in building up their future. They mould the students to bring out their skills or improvise them, teaching good habits/attitudes and helping them to become good citizens of the nation.
Picture the scene: - You are in a cave. It is dark, damp, musty, and cold and you are surrounded by solid rock, with nothing but a dim bulb on your helmet and a pick-ax in your hand. But in the face of this bleakness, you keep chipping away and chipping away; because you know that somewhere deep inside that solid rock are some incredible uncut gems and some well disguised nuggets of high grade ores. That is why you become a teacher and you have a duty towards society to give an edge to the knowledge of students by means of your knowledge. There might be some unpleasant moment in your life when you fail to achieve the goal set for yourself but remember problems will crop in when you are doing some innovative work but you should not allow problems to be your masters but you should defeat the problem then only success will sparkle and the taste of this success will be immense. Now let us have a look on the points what a teacher can do to reduce maths anxiety among students.
1. Maths is not merely a test: - Most of teachers base students’ grades on more than just test scores. Many math teachers value neatness, interest in the subject, and punctuality in arriving in class. Let me put you few questions in this regard.
A) Do you hand in homework with your numbers and letters neatly formed?
B) Are your papers unwrinkled and free of stains?
C) Do you appear interested in class?
D) Are you punctual in class?
E) Do you ask questions in class?
Teachers think of these things when composing your grade. So next time you come to class, prepare well in advance the chapter/ topic that is running in class. If you have any doubt, don’t keep silence and raise your hand. If your math teacher asks a question in class, raise your hand and give the answer correctly if possible. Teachers generally make a pre-image of the students and base the grade accordingly. If you are active and paying attention to your teacher then you will certainly not getting an E grade.
2. The Knowledge of Teachers matter most: - Research suggests that greater content knowledge is a contributing factor to increased student learning. A successful mathematics teacher needs a deep understanding of mathematics content to create mathematically rich structures and to adapt to meet the needs of individual students. In addition to content knowledge, a teacher also needs pedagogical content knowledge, or specialized mathematics knowledge for teaching that includes representing the subject to make it understandable to others; knowing what topics will be easy or not; and insight about what pre-conceptions students of different ages and backgrounds have. Teacher can start a new chapter with an interesting story to instill the interest of students in that chapter, tell the story of great mathematicians , let student play some mathematical games etc and can make a class room live with his effort.
3. Involvement in Class activity:- During the class, the teacher should keep circulating , listening carefully to student’s thought and discussion; observing the dynamics of group work and questioning individuals or groups about the strategy they are using and their findings. Teacher should ask students appropriate questions to help them clarify the direction they are taking in solving problem and provide hints to students who need then to solve the problem in a different way. Moreover, it is important for teachers to encourage students to make extension or generalizations of the solutions. Teacher should also encourage students to reflect on their solutions and on the processes they used. Effective teachers engage the classes in productive discourse by letting students communicate their ideas. The classroom activities influence on students’ achievement is two or three times more than the school level. Classroom teaching is nearly a universal activity designed to help students to learn. It is the process that brings the curriculum into contact with students and through which educational goals are to be contacted with students and through which educational goals are to be achieved.
4. Expectation from students: - Expectation from students also affects the learning outcomes of students. Teachers with low expectations of their students will most likely to teach only remedial skills and not move on to teach more advanced concepts or stress conceptual understanding. In common practice, teacher judge the students on the basis of marks/ grade obtained in previous class and make a pre- decision about the students ability in mind. This pre- concept in the mind of students divide the whole class into three sections—students with high IQ, students with medium IQ and students with low IQ and teacher handle the class accordingly. In order to achieve the 100% pass result in mathematics, teacher generally give some suggestion like--- List of Important Questions, list of chapters that require less effort, list of important theorems etc so that even a mediocre student or student with low IQ get at least the minimum passing marks. Teacher too often believe that attempting to teach High Order Thinking is inappropriate when students are struggling. If teachers consistently set high expectations by engaging all students in challenging mathematics, I am sure all students will deliver a positive response. Good teachers set an example and motivate students to take the challenge. Have you heard the story of Isaac Barrow, the teacher of Isaac Newton who resigned from the chair of professor and recommended the University to appoint Isaac Newton instead? Ramanujan, Gauss were the great mathematician and their success was due to their respective teachers.
5. Involvement of Parents: - Teacher should be polite with parents who show up for Parent Teacher meeting held once in a month in every school to know the progress of their children. Teacher should discuss the ways to help the grades of poor performer in a particular test. A unit test or class test can’t decide that students are backward in learning mathematics. The collective efforts of teacher and active involvement of parents can work like a magic for the students. It is common in our society that we assume in advance that mathematics is not meant for this particular student. Mathematics is for all. Euclid whom we regard as FATHER OF GEOMETRY used to draw lines and shapes in his copy and hardly used to care what his teacher was teaching in class. The teacher got annoyed with his behaviour and finally wrote to his father that your son had got mad and you should better consult the doctor for his treatment. Euclid’s father took him to doctor but his madness of drawing lines, geometrical shapes didn’t stop. But in the whole episode Euclid’s mother was highly affirmative and was sure that his son was not mad and he would himself prove this. One day Euclid began to jump with and came yelling to his mother that he had discovered an interesting branch in mathematics. The main aim to write this story was that a parent should have confidence in ability of a student. If parents start losing hope in their children then the frustration of students would certainly increase resulting to dislike of the subject.
6. Never discourage the students: - If you are teaching too fast during a lesson and a student raise his hand and politely ask you to speak more slowly then never scold the students. It is not so that rest of class are following you, there might be many students who aren’t understanding whatever you are teaching but still keeping mum. Listen to his request and teach slowly. Disheartening a student for a mistake that he /she has not committed will take him/her away from the subject. Give your students chance to interact with you. Encourage them to put up question if they are having problem in understanding. Let them be inquisitive, give them space to explore their knowledge. It is easy to learn a subject from a person you respect and students have great respect for his teachers. Your little effort might bring a change in your student’s life. So come forward and listen to the individual problem, though this practice will hamper the class functioning for sometime but imagine the amount of love and affection you will get at the end when 100% of your students will say sir, learning mathematics is fun.
Let me put one example from the life of our former president Dr A P J Abdul Kalam in his own words.
“When I think of my second teacher, I am reminded of my childhood days when I was studying in 8th class at the age of 13. I had a teacher, Shri Siva Subramania Iyer. He was one of the very good teachers in our school. All of us loved to attend his class and hear him. One day he was teaching about a bird's flight. He drew a diagram of a bird on the blackboard depicting the wings, tail and the body structure with the head. He explained how birds create the lift and fly. He also explained to us how they change direction while flying. For nearly 25 minutes he gave the lecture with various information such as lift, drag, how the birds fly in a formation of 10, 20 or 30. At the end of the class, he wanted to know whether we understood how birds fly. I said, I did not understand. When I said this, the teacher asked the other students whether they understood or not. Many students said that they also did not understand. He did not get upset by our response since he was a committed teacher.
Our teacher said that he would take all of us to the sea shore. That evening the whole class was at the sea shore of Rameswaram. We enjoyed the roaring sea waves knocking at the sandy hills in the pleasant evening. Birds were flying with sweet chirping voice. He showed the sea birds in formations of 10 to 20 numbers. We saw the marvelous formations of birds with a purpose and we were all amazed. He showed us the birds and asked us to see that when the birds fly, what they looked like. We saw the wings flapping. He asked us to look at the tail portion with the combination of flapping wings and twisting tail. We noticed closely and found that the birds in that condition flew in the direction they desired. Then he asked us a question, "Where the engine is and how it is powered"?
The bird is powered by its own life and the motivation of what it wants. All these things were explained to us within fifteen minutes. We all understood the dynamics from this practical example. How nice it was. Our teacher was a great teacher; he could give us a theoretical lesson coupled with a live practical example available in nature. This is real teaching. ”
7. Discuss the problem of students: - Furner and Berman (2002) write about the ways to prevent and reduce math anxiety. A great point they made is that teachers need to get an understanding of what their students are going through in maths by journaling and talking with their students. If there are some students in your class who have special needs, such as hearing problem or poor eyesight let them sit in the front row so that they can catch every word and see the chalkboard more clearly. Let your students have a good attitude and perception towards learning mathematics. If a student feels good about learning as a person then learning maths will be less challenging for them. If the student understands the math concepts then he or she is more likely to truly understand the concepts and develop confidence when learning math. It is truly said- A teacher’s purpose is not to create students in his own image but to develop students who can create their own image.
8. Change your teaching style occasionally: If despite your more than 100% effort, your students are not coming up to your expectation, your teaching style is sure to blame. Research suggested that teaching style exerted effects on student achievement that were independent of students’ characteristics. The promise that – one teaching style fits all is attributed to a teacher centered teaching style and it is not fit for a growing number of diverse student populations. Problems occur when teaching styles conflicts with students learning styles resulting to limited or no learning. Leaner centered approach will meet the diverse need. In teacher centered approach the control is in hand of teacher and students have a minimum say in this approach. The general approach of teaching is – I teach, you listen. This is the wrong way of communication. This style of teaching will do no good to students so teacher should adopt another teaching style i.e. I learn, you learn and together we learn. An open ended discussion and change in teaching style with a focus on student learning will give greater opportunity to students to interact with teachers and inquire their doubts with ease. Cooper (1998) found that student learn more in classes where they spend most of their time being taught or supervised by teachers, rather than working on their own. The extent of students’ opportunity to learn in a free and fearless environment directly and decisively on students’ achievement. Jacques Barzun said: - Teaching is not a lost art, but the regard for it is a lost tradition.
9. Provide students opportunity to learn: - The opportunity to learn refers to the amount of time students are given to learn the curriculum in and outside the class. Since the class time is limited say a maths class of 30-40 minutes runs every day so the teacher is bound to give some additional work to students to be completed at home known as Homework. Homework is seen as a contribution towards students’ learning, extending the curriculum beyond the classroom and it can be conceived as one facet of opportunity to learn in the sense that home assignments offer students the opportunity to continue school work after regular school hours. The homework provides students chance to solve the problem independently and if mistakes occur during this process then that will be clearly examined and instructed by the teacher in the very next class. This gives the students chance to explore the knowledge and improve the mistake if any.
10. Brush up your knowledge regularly: - Teaching is a lifelong learning process. Even if you are completely knowledgeable about teaching standards based mathematics, using current technology and understanding new fields of mathematics, within six months or a year there would be a new need for professional development. You can’t be static when the world is in a state of dynamic flux and we daily witness changes in technology, mathematics, schools, students and society. You have to be innovative and adapt the technology in the changing world. You must know that the Fermat Last Theorem proposed in year 1670 was solved in 1995 after a span of more than 350 years. It means you have to be patient and more vigilant towards your goal and keep updating your knowledge so that you can make aware about the changing mathematical scenario to your students. For long pi (π) was considered as the standard notation to refer the ratio of circumference to diameter but in 2012 mathematicians have proposed to change pi with new symbol tau as the circle represent the 360 degree that is equal to 2π , hence the value of pi should be changed from 3.14 to 6.28. Such information should be passed to students and that require that you update your knowledge with recent development in mathematics. In the year 2012 itself Prof Ken Ono has solved the 110 years old Ramanujan Puzzle.
I hope if teacher become friend to students and the fear of learning mathematics disappears from the mind of students, the gap of learning and teaching will be minimum and mathematics learning will be an enjoyable activity. The idea of doing something new will come in the front path and the idea of rote learning that too in mathematics will take a back seat. Once teacher ignite the candle of why and how in mathematics, the learning approach will be a smooth drive.
In order to make teaching learning process more effective I am putting here one table with a hope that it will lighten the stress of teacher and make classroom teaching enjoyable.
Teaching Action Purpose
BEFORE
1. Read the problem... Discuss words or Illustrate the importance of reading
phrases students may not understand carefully; focus on special vocabulary
2. Use whole-class discussion to focus on Focus on important data, clarification
importance of understanding the problem process
3. (Optional) Whole-class discussion of Elicit ideas for possible ways to solve
possible strategies to solve a problem the problem
DURING
4. Observe and question students to Diagnose strengths and weaknesses
determine where they are
5. Provide hints as needed Help students past blockages
6. Provide problem extensions as needed Challenge early finishers to generalize
7. Require students who obtain a solution Require students to look over their work
to "answer the question" and make sure it makes sense
AFTER
8. Show and discuss solutions Show and name different strategies
9. Relate to previously solved problems Demonstrate general applicability of
or have students solve extensions problem solving strategies
10. Discuss special features, e.g. pictures Show how features may influence approach
__________________________________________________________
Table 1 (Adapted from Lester, Garofalo, & Kroll, 1989, P. 26)
The above table will help the teacher to decide which action plan should be implemented for better result in class.
DR RAJESH KUMAR THAKUR
(THIS ARTICLE IS TAKEN FROM MY BOOK ENRICH YOUR MATHS SKILL -- PUBLISHED BY PRABHAT PRAKASHAN)
rkthakur1974@gmail.com
