How does my subject specialism fit in with, and contribute to, the current context of formal education?
Mathematics is an interesting and highly useful subject. Yet it is a horror experience for many students of mathematics. There are a few who enjoy learning the subject. Why is math such an anathema? That is a question that seen from the side of the learner has a lot of experience and emotion based answers. I think that math offers the avenue to test the skills of persons in solving complex problems. However except for a few, the society has conditioned people to avoid problems and therefore a mathematical experience could be viewed as a challenge and a problem. Where the failure rate in solving problems could be high the individual learner avoids math as ‘a problem experience by itself'. That is the conclusion I come to when I observe the loathing that mathematical discussions bring to learners who have imbibed this social conditioning. Was my experience as a learner different and what could I gain from my experience as a learner that I can use in teaching? Analyzing my experiences would in the context of math be useful here.
(LO 1) Discussion of developing as a reflective learner:
One important aspect that has to be mentioned is the needs that vary between learners. For example in my case while I was a mature student at university, my course was at first a shock to me. As the gap between student and employment had been many years. In my previous employment I was a teacher rather than a learner, it was almost a culture shock to be back on the other side of the education system. Could the culture shock be a part of the learning experience that may have had some negative influence? All though in my case the effect was negligible, I wish to point out that cultural shocks must be considered in learners who are migrants, or who are attending classes on a global campus. My primary education was without any negative experiences.
My education was in Scotland where I attended primary and secondary education. As far as I am aware, during my years at primary school and enjoyed all aspects of this. At secondary school I enjoyed mathematics and art; these were favourite subjects mainly because of the way the teacher encouraged you to develop skills and to show your understanding of the subject, which has been reflected in my career choice as a mathematics teacher. The teaching style was very different then; you were taught one way of doing, you learnt it, and you only knew that one way, a teaching style closely related to classical conditioning. I personally remember learning my timetables in math by repeating them at the start of every lesson, but these methods are not used much now.
My experience in math thus shows that there was a fundamental love of the subject and a willing ness to go all the way to get the skills. The emotional and enthusiastic factors have had a large part to play in shaping the way I looked at math. There is also the constant practice. I believe that I was able to learn and retain the information from the repeated practise. My learning experience may have influence my learning skills and development. Now, to me this suggests that the end product was more important than the understanding of how and why.
The times have changed and the perceptions of the education paradigm at the time I was a student and now has changed. There have been many changes within the education system since I attended school and even before. The changes in the education system reflects in the society and government, new directions of social and economic policies and technology has opened up many avenues of development within the educational system. These changes are on a global scale, change is universal and the concept of lifelong learning has developed and progressed. The most obvious changes have been in science, mathematics and technology.
Historically, education systems have developed as a response to the changing conditions of the industrial society. Skills and knowledge was required to produce a skilled workforce to enable economics to develop.Changes occur at different rates but the effect on us is all over, it becomes global. It is not just that we should be educated at various times in your life but that you continue to educated and this is known as “lifelong learner”.Now as a mature student I am able to reflect on many learning styles within my own understanding. Keeping a journal for this module and other modules have helped me to gather my thoughts, using these thoughts has helped me to overcome some of my concerns that I may have had. Last year I completed an access course, this gave me the opportunity to further my career and fulfill my goal of becoming a teacher.
There are many things that I have learned by experience and by learning from experience as a teacher. For example during the access course I completed a quick assessment to discover your learning styles. These were kinesthetic, auditory and visual. I discovered that I used all of them in different situations and developments within my assignments and my continued development within my university course. I particularly find visual stimulus helpful for my own learning but both ways of teaching have their positive points - conditioning encourages repeat practise, while the new way enables teachers to tailor teaching to individual pupils.Because of the gap between my secondary education and my access course, I re-sat mathematics, English and science GSCE's in one year while I was still employed as an instructor. This was a challenge for me, as I had to revisit knowledge and skills that I had not for many years.
However, though it felt like an unnecessary nuisance at the time, it helped ease me back into the education system and the frame of mind I needed to get the best from my experiences on my access course and at university. This was further developed upon by my access course, which was a new and different learning experience that helped me understand a bit more what university would be like and set my expectations for the course, which I thought was going to be interesting and challenging. The course has lived up to my expectations, but it was still a bit of a shock for me, as I did not think I would find it as hard as I have. Being an instructor of mathematics at a secondary school prior to the course has given me the skills to co-ordinate my time and my pupils, as well as giving me real life experience of a school, all of which are invaluable in my chosen profession. It also helped to nurture my love of mathematics, and of teaching it, which will help me towards my end goal of teaching mathematics, even when I find it hard to cope, which I have.
This invaluable experience in the classroom has given me the confidence to be the best teacher I can, and be comfortable in a classroom environment, skills that many people do not gain until after they have been to university. I think that this is one of my strongest points, one that gives me an edge over the others on my course. It also means that I find giving presentations more comfortable than some of the others. It also means that I am not afraid of giving my opinions and can deal well with pressure. The level of the work the course requires was higher than I thought it would be, and initially I struggled. I was pushed to do extra curricular reading to make sure I knew and fully understood the tasks that were set. This aided me in getting used to my new learning environment, and made university easier. Also, the workload itself was heavier than I expected, and though I adapted to this change, and am able to cope with the workload, these problems have taught me new skills, and have enabled me to deal with new learning experiences where I might have been overwhelmed before. This feeds back into my teaching experience, because now I have a fresh, different perspective on mathematics - being taught instead of being the teacher - and this will allow me to become a better teacher for when I pass my course.
As a mature student, I feel it has been even harder for me to adjust to life at university, where I have been so long out of education. Not only that, but I feel under more pressure, because I found that my understanding was not as high as I believed it to be, and my confidence took a blow. I still feel this way, but have taken extra time to make sure I do not fall behind, because I have always wanted to achieve the best results I possibly can. I can be too hard on myself when I do not think my work is good enough, and I can always see room for improvement, but that drive to be the best I can be is one of my attributes that will definitely help me through this course, and see that I get the grade I deserve. Another problem I have encountered as a mature student is that of the generation gap between me and my fellow students. At first I found it hard to connect to with them and get to know them, but this issue has been slowly resolved over time, as I have had the chance to get to know them better and feel more comfortable around them. I also personally feel my work ethic can be stronger than theirs at times, because they are younger than me.
Within my groups, I find that they can be immature and laid-back in their approach to tasks, and as a result I do not feel properly prepared for our tasks, such as giving a presentation. I like to be fully prepared for any task or lecture we have, so this makes me feel worried that I am not doing my best and could be doing better. Overall, I hope to develop a greater understanding of mathematics so I can make a difference to my pupil's learning experience and their future lives, and develop their understanding. Being a teacher is my major aim in life, and this course will be my way to achieve that. Reflective learning such as this is part of that path. It helps me to pinpoint any problem areas I have and identify what I can do to improve myself, but also to show the things that I am good at. These experiences stand as an individual perception of teaching and learning. It is well that these experiences are in conformity with some of the theories of learning. Learning is a complicated process as it can be seen by analysis of the concepts of learning.
(LO 2) Links with education theories and their learning experiences:
There is the question- what exactly constitutes the learning experience? There is a distinction in the mind of people between teaching and learning. There is lack of proper terminology.There is a need to therefore see the learning and teaching roles of the teacher both as inclusive and ongoing. According to Moon (2004) the actions where we help another learn is to be seen as an entirely different episode from the action taken by the learner in learning the subject. There appear to be some confusion, not only in the process of defining the concept of teaching but also of distinguishing between the learning and teaching processes, from very early child hood. (Moon, 2004)
It is therefore is a fundamental paradigm that a teacher can motivate learning. The teacher cannot do the learning for the student. Today both the teacher and student need not even share the same space for the process. Through remote education learning can occur across distances, and the distinction is that a learner can be well without a teacher, learn by himself or herself, but the teaching is entirely dependent on the learner. (Jarviset al, 2003)
The experience of the learner could be denoted as‘experiential learning'. The experience of the learner has been always taken for granted. (Jarviset al, 2003) The reason that we have to stress on experience is that for one experience is a lifelong affair not confined to any single episode of learning essays. There is more time and space involved than the actual time spent in learning in an academic environment. Once we acknowledge that then the experience could be seen as internal and external experiences. However one cannot draw a clear line in individual experience between internal and external experience. It is a continuous and amalgamated process that involves a lot of variables. The basic feature of experience is subjective and is just a sequence o0f thinking which is influenced by many conditions of the individual like social, cultural and background situation. Some writers call it a world of ideas and idea is also a form of learning. There are experiences that are based on our emotional response to typical situations. These occur based on the individual's level of experience. (Jarviset al, 2003)
In the case of experiential learning the learner is having a direct or at best a stimulated encounter with the real world. This has been subdivided into experiences of the primary level - where the senses of the learner is involved in the social context in which the experience is presented, and secondary where there is a mediation by the tutor and there is no social or background context of the learner involved. Video presentations are an example. (Jarviset al, 2003)
Other than these, other experience include experience that is recalled by the trigger event, and real experience which is nothing but first hand direct experience. There could be in the context of modern technology artificial experience which is a modeled system of the actual world and which can stimulate an experience. Can we include computer games, and stimulated studios and sets in this is a moot question. Some other authors have expressed conflicting opinions. There are numerous theories for each word that is used in the education theories. For example, Kolb cycle of experiential learning describes learning and is used for management training. However this is based on the learner and the action that the learner takes rather than the teacher's role. (Moon, 2004)
The concept ofreflective and experiential learning is different from the other theories in the sense thatthere exists no clear definition for the concept but at the same timethere is no clear cut understanding yet of these concepts and it may thus mean different things to different people. This makes the investigation into the interdependence between reflective and experiential learning worth pursuing. The forms are relatively free of mediation and learning goes beyond the syllabus. This helps in the growth of professional development. Then the question is if reflective and experiential learning are learner based and are independent of the teacher, the teacher plays the role of a mediator, and the teacher who provides material that could be beneficial in speeding up the understanding of the learner and provide the learner with a better method of learning itself. Thus mediation is a concept that will focus more on the way the mediation is done rather than theactivities and role of the teacher. According to Moon (2004) there is an impetus or will from the part of the learnerwhich can be decided as the purpose of learning and this will in turn cause the learner to adapt a paradigm regarding what is being learned.
(LO 3) Evidence of engagement in reflective learning using a variety of strategies such as journaling, critical incident, analysis and action learning sets:
There are more tools available today to the educator and the learner. Computers and technology have opened up many possibilities from electronic stimulations, presentations and visual learning techniques. Further electronic and manual notes, speed reference and other methods of access even to electronic libraries have brought changes to the learning experience. To day one can maintain online journals, blogs and inviteglobal view on issues. Informal and formal help and suggestions can be sought for from global teachers and peers. This was something unthinkable just 15 years ago. The learning experience I had could not be compared with others because each has unique experience based on their background.
However a learner's anecdote to which I could relate is that of Tim. On the comparison of Tim's experiences far back in 1960s, many instructors of this day will still find parallels. Tim contends that it was embarrassing to be a trainer of teachers, especially before having any experience in teaching first hand. The problems in teaching mathematics and the fact that at the time though he did teach mathematics, Rowland “knew little about primary schools” that they were not cared for. (Rowland, 2006)Thus innovations in introducing some new variety of teaching, like the introduction of games and puzzles and the ushering in of “New Mathematics” is noteworthy.
(LO 4) Exploration of the nature of their subject in the context of education:
The language of mathematics is to be understood in the context in which it is being used in text books and in class. Therefore there ought to be an insistence on clarity regarding the use of mathematical vocabulary in the class in the clear context the words or phrases are meant to be used. One of the methods that could be used for teaching is the use of analogy. Ian Thompson gives the example of ‘mathis like learning a foreign language'. As in learning the foreign language, Thompson (2003) emphasized the role of repetition of the class in understanding the concepts clearly. Mathematical phrases ought thus to be made standard and identical.
(LO 5) Evidence of the links between their understanding of learning and education theory in relation to their subject specialism
Those with a passion for mathematicsalso cultivate a passion for teaching it. Mathematics showers several eligibilities to the proficient in the society. For many learners mathematics is a set of hurdles and failure. Mathematics education is important because it marginalized a lot of children. It is the view of Gates (2001) children labeled ‘bottom sets' and fed with uninteresting math and these students all have “life experiences reflecting varying degrees of deprivation.” Thus math is important and the best method of importing is by creating a pleasant experience that could be related to by the learner. This is because the basis of all learning it is argued is experience. This is the stimulus that makes learning possible. Learning is a function of experience, holistic and social considerations and the socio economic situation of the learner. Thus student centered learning concepts that was based on the student response is based on the learners experiences of learning. There could be shifts in the direction of problem based learning but the insistence is always on experience. So it is relevant to say that the teachers must therefore view teaching in the light of experiential learning, bring their own experiences of learning the subject to bear with the art of teaching. Thus professionals ought to focus upon their own experience in learning.
Jarvis11 says that only conscious experiences must be accounted for. On the other hand Knowles says that situations found by the learner created by the learner, situation and the teacher are all part of the process and thus must be included in the analysis. The process oflearning is largely aninternal process having the attributes of cognition, physical experience and lots of emotions. This could trigger responses that could bring about a change or conformity with the learner. Do all people learn from experience? It is not the case and there are experiences that the response tends to be of non-learning, which could be rejecting the premises encountered. Like-wise, it pertains to the rejection of the information. The other forms that learning can be encountered are where learning becomes incidental to an experience that has high emotional content. Thus experience by itself does not guarantee learning. The important thing which has to be stressed with learning math is that math could be an enjoyable experience or it could be a negative experience based on individual backgrounds.
As Muro & Terry (2007) suggest the important dependence in mathematics courses is entirely dependent upon the learner's application which has to be achieved either as individual or in groups. Thus the instructor has to examine the learning styles of the students. The Kolb's Experiential Learning Model is the popular model that is used in the analysis of the paradigm. The theory has the variables as the individual student's method of processing information. The argument could be widened further if we examine the learner's use of feeling, thinking and other internalized modes of reacting.
One such mode is the concrete experience mode, the learner responds based on his or her previous experience, and with the context of the current interaction between the group of learners with whom she or he is and the interaction with the teacher. The classification of the types of learners that is an issue in mathematics can be still further seen as abstract conceptualization where problems are grouped and systematic solutions are arrived at, and those who have a tendency to try out the concepts as experiments. They prefer hands on activities. While all these types of learners are present in a class, the different and noteworthy is the pupil tending to Reflective observation. These learners are the users of watching and listeningand then using the assimilated fact in developing their own theories. These prefer lectures are simulated by what if questions and have the tendency to provide longer answers to questions.
The Four learning styles result in various learning modes, which according to Muro, Terry (2007) are the “diverger, assimilator, converger, and accommodator.”Divergers are defined as those using information with concrete experience discussed above. Assimilators are good at problem solving, and convergers are the ones who find practical uses for a theory. The Accommodators in a math class are the ones who enjoy solving difficult problems. Thus in a single class there could be all these types of students. The teacher thus is envisaged in a normal context to offerteaching styles that could create a model for each of these learning types. This is of course impossible, and therefore we can only assume that centering the math education on lecturing,along with slight other activities that can satisfy the other types along the progress of the class can be attempted. One of the activities that could simulate all the type would be “laboratory assignments, in individual and group format, will expose students to multiple learning experiences that can foster functioning in all learning modes.” (Muro; Terry, 2007)
(LO 6) Taking into consideration of Globalisation and education. Its impact on education
Mathematics and education in general have to use modern technology and teaching media. Thus the reach is very far. As mentioned in my own life experience, the culture shock has to be taken into account in a global setting. New technology brings vast changes in all spheres and it is true with education. This coupled with the views of the French thinking will have us accept that today's society is rationalistic and humanistic and progressive. But while this is true to some extent there are other forces that are also getting control and the concept of a risk society and globalization have brought in changes in the way the paradigm shifts are now observed. Thus we have to move in theory form the classical and established thinking to accommodate not only globalization but also progressive development of many needs and systems that were not even envisaged in the old systems. (Jarvis et al, 2003)
There is a need placed on schools to consider globalization and reinvent the method of education to create competence in citizens. In the global context, financial independence, and community life take precedence. Thus today the insistence is on the Schools recreating in the learner the required “attitudes, perspectives, skills and knowledge that will help them find and keep a job, interact with their co-workers and neighbors and understand as well as make informed decisions about issues affecting society.” (Zhao, 2008)
The different cultures have different subjects by importance. For example in China- Mathematics, English and Chinese are dominant. Globalization has also caused Americans entering foreign businesses and even relocating abroad. American schools are successful in producingdiverse talents. This is a result of the American system encouraging creativity while elsewhere schools suppress creativity to promote conformity and obedience. In comparison Asian education systems kill creativity. Today all learners are affected by global issues and education must be geared to make learners become global citizens.
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Thompson, Ian. (2003)“Enhancing Primary Mathematics Teaching.” Open University Press. Philadelphia.
Zhao, Yong. (2008) “What Knowledge Has the Most Worth: Reconsidering How to
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