Developing Teaching Practice as a Mathematics and Numeracy Teacher
Developing Teaching Practice as a Mathematics and Numeracy Teacher
1. Written Assessment
I have been teaching mathematics in the post-compulsory sector for diploma level in a polytechnic for one year back then. And it has been an wonderful experience. Not only did I teach mathematics and numeracy to the students but I also learned a lot about myself, mathematics and teaching mathematics itself. This experience has taught me how everyone student is unique and each one of them needs a different level of attention to grasp the topic and improve. I discuss this journey pointing out the mistakes I made, and how I tried to resolve them. I reflect back on my experience and share what I learned.
In this reflective article, I will discuss my personal experience as a teacher of mathematics and numeracy for both pre-primary and primary to university level courses. I will look over how I used to tackle both of them as a mentor and teacher, how did my attitude as a teacher changed over days for the subject, what theories I applied, What responsibility I behold for my students and what opinion I have about them now.
This essay is based on the development and practice undergone by me as a mathematics and numeracy teacher in the post-compulsory sector. Being a mathematics and numeracy teacher requires updating the portion, learning continuously and analyzing their own practice. They should continuously keep on updating and upgrading themselves. Being a math teacher is not limited to only teaching the subject, math. I must inspire the students to look beyond the pages of books and become a problem solver. I help the students to enhance their critical thinking skills. Many children have or develop fear towards mathematics. My role is not only the teach the syllabus and complete the portion, but also eradicate the fear of students and help them love the subject. Mathematics would not only help the students excel in tests and academics, but also in becoming productive citizens of the country. Teachers play a vital role in shaping the youth of a nation. We, teachers, are responsible for shaping and developing our students. We are supposed to provide the students with a positive, safe and enthusiastic environment. In the school, the teachers are the guardians to the children. My legal responsibilities are not limited to just teaching the subject, mathematics to the students. I must encourage and help them to think beyond the box. Mathematics is not only an academic subject but also have various applications in our day-to-day life. The mathematics skills help the students to enhance their problem-solving capability. I am also responsible for supervising and evaluating each student's progress and development in the mathematics. I must also ensure that there are some boundaries present. The teacher's conduct towards a student or students must always be professional. The environment or surroundings might change, but I must ensure that the student teacher relation is always maintained. As a teacher, it is my duty and responsibility to maintain the professional boundary.
Reflection on the Journey
Before I started on this journey, I had to understand the responsibilities I was taking on, and know the correct and legal way to oblige these responsibilities I was accepting. I was becoming a part of the education system, teaching the future generation, guiding them to help realize their potential and passion and also show them a way they can achieve what they want to. As a teacher I have certain legal responsibilities too,
- It’s my legal and moral duty that I have to provide a positive and encouraging environment for my pupils
- I must be fair and unbiased with my students and treat them all equally irrespective of their background, origin, performance.
- I should be fully aware of my students need, behavioral and medical problems that could occur. If any medical problems are to be addressed I should be aware of the same and know how to administer the same if needed
- I also have responsibilities towards the parents of the children
- If I find any suspicions of abuse it is my duty that I attend the same, intervene and help the involved student(s)
Along with these responsibilities, I realized I had certain rights that help me to satisfy the same
- I have the right to search a student without producing a warrant, this helps me to ensure that the students do not engage in unnecessary and morally and legally wrong activities.
- I am allowed to suspend a student in the form of punishment, to ensure that the student gets a chance for self-introspection, and also that the other students are kept from a bad environment
Basic principles for teaching Mathematics
Mathematics isn't a theoretical subject that even without understanding the concept you will get a thorough knowledge of the subject. Mathematics and numeracy are very logical subjects. They require a complete understanding of the topics so as to apply them perfectly wherever required.
The basic principles of teaching mathematics are to ensure that get a true knowledge of all the concepts studied. One of the most important principles is the clarity of concept for the teacher. The teacher must be himself up to date about the concept and should have appropriate knowledge so as to clear up the doubts of the students till the root and not just get away by saying that's it's just a rule (Beeli-Zimmermann, 1970). Secondly, the teacher must be fluent enough to convey his knowledge to his students. Communication is the key to understanding. All the knowledge of the mentor is a waste if he isn't able to express the instructions to the students. Next is what applies to every numerical subject whether its accountancy, physics, arithmetic or mathematics, practice is the key to success. It's often said if you don't practice, you don't deserve to win. So, whether you are a teacher or you are a student mathematics and numeracy will be on your tips if practice it all along. If as a mentor I have been a great teacher but as an applicant I am not able to solve up the real-life mathematics then all I have taught is nothing more than a waste. Last but one of the most important principles for both mathematics and life is no path is just the perfect one. Every person has its own pace of learning, own way to perceive a problem and own way to solve it (Boyd and Ash, 2018). There is no one particular method that can solve all the equations be it mathematics or life. The mentor should not be just sticking to his method of finding a solution rather he must give the ideas of his students a chance maybe one of them comes out to be a future mathematician.
As a human being, it is the sole responsibility of a mentor to inculcate interest and curiosity in his students for the subject. As per legal boundaries are concerned no teacher is legally answerable to the student rather they are answerable to the organization they are working for or their heads under whom they are pursuing their mentorship. Overall in my perspective, I find Mathematics is not something to be forced to be applied in the situations rather it is to be caught out of every single going on around.
My first experience at teaching numeracy
Going down back a year ago, was my first ever real-life experience of teaching mathematics to diploma level in a polytechnic for one year. Academically, I was in seventh standard myself, studying in a reputed school, good at studies and highly interested in teaching young kids. Since my very childhood, I had the ambition to pursue teaching as a career. For some financial causes, I and my mom started teaching kids at home. The chapters to be taught to them were quite simple for me as they were basic arithmetic oriented just addition subtraction oriented. To the pre-primary level students, we even had to teach them counting things and how the numerals were written. We adopted a practical method to teach children addition and subtraction. We formulated some real-life children relatable problems and worksheets. These included questions and pictorial representations of erasers, pencils, sharpeners and all the small things that children can understand and think of as a solution. Moreover, we played simple games of exchanging items so teach them the concept of borrowing in subtraction. This all not only helped them to understand the things well but also made my concepts clearer.
One of the most important theories that I feel I should have applied more was repetition. Our traditional method of teaching is completely based on it. Our schools have fitted all the multiplication tables and formulas in our head just by making us repeat the same things again and again. I feel once after understanding the whole derivation of any operation or formula if we repeat it again and again then it will surely stay in forever.
Another important practice that we missed in all our process of clarity was testing the students on what have they learned. We kept on adding more and more information and newer concepts but forgot to just check whether all our teachings were being interpreted in a right manner or not (Hudson, Henderson and Hudson, 2014). Testing plays not only as feedback for the teacher rather it adds more responsibility on the students’ side to focus more on the retaining of the concepts being taught. An age-old debate standstill over the testing methods and the frequency of the tests to be taken. In my opinion, a regular test should be taken once a month if the teaching process was continuous.
My Second Experience
I started teaching mathematics to the post-compulsory sector about a couple of months ago. I was young and inexperienced and frankly nervous on the first day. I had thought about many ways I could present myself to the students in the first day, I decided to keep a calm and friendly demeanor, and decided that I wanted to have an interactive class where students are encouraged to ask questions and participate in the class, answering and paying more attention to the class lectures.
I made sure that no student was intimidated by me and thus they trust me enough to share any doubts or other issues they need help with. Initially, I believed that I could treat and teach each student equally, following the same routine with each of them, and that is what I followed. It took me some time and after a couple of evaluations I was confused why there was so much difference in the performance between the students, I talked with my senior colleagues and they helped me realize that mathematics is not the same for everyone, certain students need more attention and hard work to grasp the same concept that others take up almost instantly.
I analyzed the students' performance and cross-referenced them with their interaction in the class, their friend-circle, and also asked other teachers about their performance in their subjects.
I realized that a certain group of students were lousy at studies and this was the same which didn’t interact much in the class but rather sit in a corner and gossip among themselves. I recalled my school days and realized it was the same then.
So then I took steps to change that, and understand why these students weren’t as attentive in class as others and what I could do to change that. As I was trying to understand this I realized that most of these students were not so strong on the basics of mathematics, their understanding of initial basic concepts was unclear and they also found it difficult to perform certain basic operations and calculations. I concluded that this made them feel shy and they masked this shyness with aloofness. This had to change and I made sure that everyone including and especially this group of people participates in the class. So I frequently put up questions on the board and called one of the students to solve it in front of everyone. If anyone was unable to do so, rather than criticizing and making fun of their inability to do so, I asked what they didn’t understand. If anyone else made fun of the same, he/she was definitely scolded and taught his/her place as I believe school to be a place to learn, nobody comes to school knowing everything, school is a place to learn. I helped the troubled student in help understanding the concept, even if that took extra time out of my class. To maintain a friendly environment, I allowed cracking jokes and sometimes cracked a few myself. I realized that these are teenagers and if someone comes and orders them that don’t do this and do that they are just going to rebel and do exactly opposite to as adviced. At this age, it is easy to lose confidence and indulge in bad habits. I made sure that each one of my students felt confident enough to speak their mind, and not be afraid to ask questions no matter how naive they thought them to be.
Sometimes I have spent an entire class talking about morals, sharing stories, where even the students participated with interest this created a bond between me and them and also strengthen the one among themselves. Sometimes we also discussed some major events coming up, like elections or if a festival is around the corner we discussed the reason behind the celebration and what values are to be extracted from them. One year an entire class, after one of this discussion, pledged to not burn crackers in the coming Diwali rather lit Diyas and truly celebrate the festival for what it is meant to be, about family and togetherness and great food of course. I give equal values to morals and education and thus consider these discussions an important and necessary part of the same.
Mathematics is a big subject and it requires both memory and logical power. It is easy to get lost in the various formulas and different methods of applications of the same. I also found that a student who was able to solve a particular question easily couldn’t solve similar ones after he/she lost touch of the concept for a long time (Jaworski, 2006). I believe that continuous and regular practice of the concept is a definite way to get strong in the subject. So I started giving regular homework and also assigning questions to solve in class on the topic just discussed so that any doubts on the topic can be discussed and cleared.
Mathematics also has certain exceptions and it is not always easy to detect them, rather than giving the solutions of such tricky questions I give them to the students and they try innocently to solve the questions on their own, this allows them to think creatively and maybe even discover the method themselves in an attempt to do so. This is to stimulate their creative part of the brain. I also encourage students to participate in various activities held in school which unlocks their creative potential rather than just having bookish knowledge.
I believe in class notes and made sure that each student maintained clean notes, with important formulas and exceptions highlighted for a quick revise. In the notes, I also encouraged students to write some solved questions along with a topic, for quick reference of the application of the concept.
The Difference I Felt
I look back on my first day and initial days of teaching and realize how much I have changed my teaching methods and grown along with my students. As I was teaching I realized that being a perfect teacher is a tough job and spend my time to continuously optimize my teaching methods for the betterment of all the students. Experience has helped me understand that sometimes I have to let some things slip and allow the student to solve some problems themselves. I also learned that in some situation being ignorant is one way to allow the growth of students. Now I have control over my level of interaction with the students, and also I realize that being friendly always could spoil the children. Thus I choose to be strict when there is a need but also keep the class light enough that students are not intimidated by me.
Theories of Learning and Models of Reflection to Analyze My Practice
The main theories of learning include behaviorism, cognitivism, constructivist, experientialism, social learning, humanism along with personal learning. These theories are used by many professionals, teachers, educators, and professional designers to attract people and meet the requirements of the target audience. Learning theories are the conceptual framework that provides us with data on how the information is absorbed, processed and retained during the learning process (Leon, Medina-Garrido and Núñez, 2017). The main three learning theories that I follow and utilize while teaching my students include behaviorism, cognitivism, and constructivism. These learning theories would help me in understanding my students and analyzing my subject and way of teaching. It would help me develop more student-friendly and easy mathematics sessions. This would help the learners to gain knowledge and explore various topics of and beyond the syllabus. Models of reflection is also a type of framework. This is a structured process.
A bag filled with different chocolates, is the same as a class full of students. Just like in the bag, the only common thing is that they are all chocolates, the same way a class is full of students of different backgrounds, ambition etc., with one thing in common that they all are students. As, every child or every student is different, attitude towards mathematics or numeracy among them is also different.
After studying all the theories of learning, the learning cycle by Kolb seemed most useful to me. It had four key elements; concrete experience, reflective observation, abstract conceptualisation and active experimentation. The most interesting part about this model is that there is no start or end to this model. To Kolb’s model, New South Wales Department of education and training curriculum gave an example model that didn’t have any start or end just like Kolb’s model. But I like to put it in my way where there is a start but no end, once it starts at the start of the session and moves like a cycle.
It will start by an assessment to diagnose where the students are, and then their positions are reported, then the most difficult task of deciding what my students are to learn to reach a higher position and then the planning and programming of the sessions and lessons takes place, followed by the question of deciding how to get my students or learners to that position as in accounting how to make learning easier for them, practical classes etc. Then, classroom practices take place. And once I know, teaching part is over, assessment and tests are taken to if they have actually reached or not. If they have, then the same process for a new and higher position. If they have not, then new ways for improving for both my students and me have to be found, by analysing and tallying everything, both right and wrong, and then worked upon in the same process.
Planning sessions didn’t just involve setting class timings and topics accordingly to the classes but more than that. It turned out to be much more difficult than I had ever thought. As a mathematics teacher, I had to gather all my study material, and find or make more practice numerical questions for my students to gain confidence in their lessons. The biggest task was to relate the lessons in a creative manner so that they could not just relate to it, but also feel interested in the topic. While, making their notes, I generally questioned myself about my student’s potential. But, I believe this is a sector I still need to improve.
Planning sessions and lessons helped me understand my student’s desire to grasp new skills and knowledge on my subject and also judging my content. I slowly, understood their need and figured out a way to fulfil their needs too. The most important aspect of planning lessons was that they enabled me to form the aims and objectives and also check with them.
The thing that is a big factor is the background of my learner, which includes their language, religion, experience, etc. that impacts my planning structure. For example, if someone is poor, the learner is going to do everything possible to flourish in his life, for those hard working learners my work for planning lessons is going to strengthening their basics and making them practice while helping them grasp new skills. There could also be students from scholar family; he would be carrying a different load on his shoulders, my planning would move around making his studies easier and his load less heavy. In a class full of all such kinds, the biggest challenge is to plan a schedule that suits and is in favour of all.
After experimenting and analyzing various methods of teaching, I have realized that the teaching method must be friendly and the session must be interactive. Students must be provided with a competitive environment and must be encouraged to ask doubts. The learning theories and models of reflection help me analyze my methods and way of teaching (Muir, 2008). From this, I can improve my way of teaching, if the current method is not giving satisfactory results.
Importance of Negotiating Individual Goals with Learners
Not all the students are the same. They vary socially, physically and mentally. Hence, in the classroom not all the children would benefit equally. The goals and ambition of each student would be different. Some students would like to pursue their career in the arts or sports field. Not all the children into academics would opt for a mathematical career. Hence, a classroom is only a common platform where children learn only the syllabus (Muir, 2008). Students who are math prodigies and want to pursue a career in statistics, engineering, or any mathematical field would be more interested in the subject and would be faster than others in solving the problems.
The students who are weak in math and have math fear would find it difficult to cope up with the other students. Hence, before starting the session, I interact with the students to get to know their interests, goals, academic scores etc. This helps me to interact with each student and help him/ her accordingly. I conduct an assessment test before starting the session. The performance of each individual and the class as a whole is analyzed. This helps me set my syllabus and teaching method for the class. I also analyze the previous reports of the student and other formative assessment information of the student. Accordingly, I practice and deliver my lecture. This would help each student gain knowledge and get good marks in the exam without putting much effort and would give them ample time to pursue their hobbies and passion.
As we have talked about initial diagnostic assessment that is to be taken in the very start to understand the learner’s level of knowledge, I’ll throw light on what I did during my first practice session. After I took the diagnostic assessment of my students, I told them their position or level of knowledge, but with that I also warned them to maintain or increase the level because the level could have a drop too. I even discussed the weak areas of the learners which mainly included trigonometry and algebra. We decided to understand both the topics and clear all its tests with distinction by the next two months. The students agreed and signed for the classes. We worked on each problem and issue of every individual in details as we had the chart of all the troublesome with every individual by their diagnostic assessment. By the end of the two months, they were made to sit for another assessment followed by midterms in the next few weeks. The assessment they sat for before the midterms were consisting of all easy, medium and hard questions, so that tallying their level would become easy and also so that the question paper doesn’t feel unfair, as in below or above the learner’s level. There were many who rose above their levels, and also those who maintained their level, but there were none who degraded their level. And, this felt like a small victory with more miles to go and more things to learn.
Evaluation and Improvement of My Practice - Planning, Delivering and Assessment
My teaching method can be evaluated by viewing the student's academic performance. It can be improved further by making the class interactive and fun. For example, many students find algebra and word problems difficult and boring. The class can be made interactive by using the names of the students of the class in the word problems. Real life examples can be taken as algebraic sums. Geometry can be taught easily to the students. The geometry sessions can be made interesting by combining the math class with the craft class (Ng, Nicholas and Williams, 2010). Origami is one of the most effective and fun methods to learn geometry. Students while creating some craft, would also learn the shapes and geometry. Another topic the high schoolers find difficult is the calculus. But even this topic can be made easy by conducting group activities and by assigning projects based on the topic. For example, activities like group writing, involuntary discussion, reading quizzes, lecture outline etc can be carried out to get more familiar with the topic. Proper planning, execution, and delivery is required to carry out these classroom activities. I have observed that compared to the regular and monotonous sessions, these activity sessions yield more satisfactory results. This is because all the students participate in this activity with full concentration. They don't find it boring and do not doze to sleep. Moreover, it is an effective method as children would enjoy the learning process and learn quickly.
As a teacher, after my first practice with these students, I felt, not just my students are learners, I too am one. I also learn about my teaching skills and learners, just like they learn their studies and grasp them to implement them perfectly to gain both in life and assessments.
During these assessments I also realised, that some students are well aware of their studies and have a good knowledge on their topics but don’t implement the important keys and steps that gains maximum marks. I also realised in a room full of different thought processes, a unity in the planning is to be made that suits all of the learners with no issues.
I have also figured out many areas where improvement is necessary such as clarity of instructions, planning sessions, managing a varied class, accepting and understanding the mix composition of the class better and find new ways to keep my learner motivated to learn. These are a few that I discovered and there are many more strings left to untie for there is an ocean to learn and I am only working on the river.
Being a teacher is not hard, it’s challenging. It teaches one to read a thousand minds at work upon their problems by understanding their hardships, ambitions and lifestyle all at the same time.
After analyzing in depth all the factors needed for a successful mathematics and numeracy teacher, I realized understanding is the pinpoint. Every child is different and so is his capabilities. It is your responsibility as a mentor to engross the student to the fullest in the subject. After all, it's a good teacher that paints the bright future of the student because no one comes learned to this world.