I was educated in Scotland at a primary and secondary school. Whilst at primary, my education was an enjoyable experience as was my secondary education. At secondary school I was an active student and a keen participant in many of the sporting activities. This gave me a feeling of belonging and a sense of security. In Education today this is an aspect of the SEAL initiative - Social Emotional Aspect of Learning.
"The SEAL programme is based on curriculum materials which aim to develop the underpinning qualities and skills that help promote positive behaviour and effective learning focusing on five social and emotional aspects of learning: self-awareness, managing feelings, motivation, empathy and social skills." Hallam (2009)PUT IN APPENDIX SEAL
Although, SEAL may not be what it was called during my education but personal, social and health education was taught and this helped many students to understand how important social and emotional learning can be. A learning experience is not just evidence of your abilities at school it is also between your peers and teachers. What can be described as the school's 'hidden curriculum', my experience in school relates to the social relationships that are developed whilst in the school environment. (Jarvis et al, pg.42). This is referred to as 'social context of learning', how we develop and learn through our peers and our relationships with teachers. (Pollard, p.452).
Rote learning, or classical conditioning as it sometimes referred to, this is a method of teaching that I recall from my mathematics lessons. Specifically recalling the facts of multiplication tables, an example of my experience of this was that all around the classroom were large posters and individual cards of the multiplication tables and we repeated these daily, once learnt and you were competent you knew it then you could move on onto the next set. This approach to my learning experience was one of behaviorism. Based on studies by Borger and Seaborne on classic behaviorist definition
"any more or less permanent change in behaviour which is the result of experience" (Jarvis, P et al p.24). Behaviorist theory has been used in education and in my experience it was applied to the whole class with a didactic approach. Positive results may have occurred by this method of learning of memorizing tables but there may still be a place for this type of learning to be used in schools, as there are aspects of Mathematics that still require you to learning this manner, for instance specific formulas, such as in algebra and geometry, you need to be able to apply them within Mathematics. Today these methods are not always the preferred method of teaching; the emphasis is on the child's individual needs and their preferred learning methods. The view proposed by Skinner (1954)
"Modern children simply do not learn arithmetic quickly or well". (Skinner, p.107)
Is this due to the method being taught or that there are many ways a problem can be executed to gain the correct answer. Is one way the correct way or can many approaches benefit each individual student.
Today, to be an effective teacher, we have a responsibility to interact with children to enable a learning process to develop using varied teaching methods which does not necessary mean that rote learning does not have its place. Research by the General Teaching Council for England suggested that
"those teachers with a strongly connectionist orientation were more likely to have classes that made greater gains over the two terms than those classes of teachers with strongly discovery or transmission orientations. Another finding was that the connectionist teachers who were highly effective had engaged in extended continuing development (CPD). The researchers acknowledge that there is no unique description of the effective numeracy teacher. However, they do highlight approaches from their study which, for these 90 teachers and their pupils, appear to contribute to effective numeracy teaching" (GTC- Effective Teacher of Numeracy (2003)
Structured, ordered and disciplined with a didactic practice was the teaching method for most of my primary and secondary education. The teaching styles were based on a formal framework and the control was very much in the hands of the teacher. What are being tested are the students' abilities to recognize patterns and methods, this can be an excellent teaching method but was I being provided a way of processing and developing my abilities and not my individual needs and preferred learning style. Stapleton's conclusion (2001, p.84) supported the views of Bennett on formal and informal teaching styles, that formal teaching styles appear to achieve a more academic result and suggested that the formal style out performed informal style. An informal approach to education is very much communication and negotiation between students and teachers with a learner-centered approach. This requires students to discover for themselves relationships that may exist with the given information. The teacher role is not to impact learning and knowledge but to offer guidance and support which means a more student-centered approach. Learning styles are concerned with how learners learn and how teachers teach and Kolb suggests that
"individual's learning is an interaction of heredity, past experience and present environment" (stated in Stapleton p. 79)
Although, the learner centered approach has many benefits, the 'rote learning approach can work also. Whilst, employed as an instructor of mathematics, many of the students I taught were unable to develop their understanding of mathematics without having to be shown a method of how to solve the questions that arise. They required to be shown the basic principles and methods. This didactic method of traditional formal education may have worked for some but not for others. Did I use this approach to teaching because this is what and how I was taught or was it because this teaching approach worked in my education?
Now as a mature student returning to full time education I now feel that my approach to my individual learning is of an informal approach. I am far more active in my learning and this can be seen in my approach to many of my units of study. For example the P U F M's unit is one where there are many questions that can arise and answers are not given by the lecturer, building on your own understanding, to begin to develop and learn. It can be associated with a humanistic approach, based on studies by Carl Rogers. Stapleton's conclusion (2001, p.73) supported the views of Carl Rogers. Rogers argues that
"for a humanistic approach that is centered around problem solving and builds on the natural potentials of the student. He argues that students are eager to develop and learn, and that the desire if for knowledge" (Rogers, p.73).
Another example of this can be shown in my Math's Audit Unit; this unit is all about improving your understanding and knowledge of Mathematics, throughout this module I have developed my abilities within the subject. The Teachers Development Agency states that as a teacher you must be able to reflect, improve and take responsibility for all your professional requirements, have the knowledge and understanding in a range of teaching strategies. As the Q14 standard states:-
"Have a secure knowledge and understanding of their subjects/curriculum areas and related pedagogy to enable them to teach effectively across the age and ability range for which they are trained" (TDA, 2008)
Assessment has become a part of education, which was introduced as a way of measuring a student's understanding. The government used assessment in two forms, one of a summative and the other formative. Summative assessment is used to enable comparisons with other students and to produce national averages and statistics on the schools performance. Tracking progress using whole school targets, pupil and teacher performances to attain a level of knowledge and understanding throughout. In other words it tracks the schools progress. Formative assessment indicates how each student progress throughout their education, using continuous assessment within their education to highlight how they are developing and what progress they may or may not have made. These methods are called assessment for learning (AFL). For AFL to be used effectively teachers need to use this information effectively. A review by Black and William (1998) points out that
"for assessment to be formative the feedback must be used" (Black & William (1998b)
To become a successful student you need to be able to understand mathematics than just to achieve a better grade but we must still understand that even if progression is not made with every student they can become disheartened and may not feel that they are able to contribute within the classroom and their peers. Teachers need to take this into consideration and try not to contribute to this. A report by OFSTED reported that
"where pupils receive good constructive feedbackâ€¦ they respond well and their motivation improves" (Ofsted 2003)
Effective formative assessment plays a major role in an individual's motivation for learning and improving their understanding. Ofsted states that
Assessment for learning is most effective when it:
Is embedded in the teaching and learning process
Shares learning goals with pupils
Helps pupils to know and to recognise the standards to aim for
Provides feedback for pupils to identify what they should do to improve
Has a commitment that every pupil can improve
Involves teachers and pupils reviewing pupils' performance and progress
Involves pupils self-assessment (Ofsted 2003)
Is assessment a vital part of a student's education or is it a negative experience. Assessment allows schools to place a student in the correct set and ability, placement of the student in a particular set or group labels them as 'bright' or 'thick'. There are pressures on the student from their peers and can have a negative effect on their education and self esteem. (Pollard, 2008). During my secondary education, at times I felt under pressure to achieve my best and exams seemed to contribute to this. A different approach to assessment, without the emphasis on continued development, may have benefitted me as a student in secondary school. Although, today there is still the pressure of achieving your best but as an adult I look at it in a different perspective. I analysis the problem and consider how to approach it and what is the best way forward to enable me to complete my assignments.
What makes some teachers of mathematics better or more effective than others? Is it their ability to convey the subject in an interesting and innovating manner, to be able to encourage students to explore and develop further or is it the passion for the subject that is conveyed to the students. QUOTE HERE TO BACK UP
In my secondary school a particular teacher made me feel confident in my subject, this was my art teacher. He always seemed to be full of new and exciting ideas to develop further. To be an effective mathematics teacher you need to find ways to engage the students and to ensure that they feel competent in each area. The National Centre for Excellence in Teaching of Mathematics (NCETM) implies:-
Providing a caring and supportive classroom climate.
Enabling all students to feel equally valued.
Providing activities which students find challenging and enjoyable.
Enabling students to find a deeper understanding of mathematics.
Providing opportunities for students to collaborate (NCETM 2005)
The report also states that to be an excellent teacher a combination of knowledge and understanding within your choosen subject allows you to ensure that progress is a continuing spiral. The Venn diagram (see appendix) is an excellent visual of this.
Continued Professional Development is a highly important factor within teaching.. This enables you to access areas that need to be developed, to fill in the gaps in their knowledge and contributing to your individual needs. CPD is a reflective role of each individual to be able to take control of your own learning experience and to develop a greater understanding of what, you as an individual, can improve and use the new skills within your teaching career. Moon suggests that a journal in professional education and development is "the beginning stage of professional education, as well as in practicing professional stages, often in the form of a professional portfolio" (Moon, p.71)
I AM FORTUNATE that I have a good understanding of Mathematics and enjoy solving problems using my subject. I really want to share this experience of the subject with others and in my role as an unqualified teacher of Mathematics in a secondary school. I was able to do this by encouraging pupils and engaging them with Mathematics. The experience in school has benefitted me in being confident in the classroom environment and being with pupils. I am also able to present work to an audience and have an understanding of the role of the teacher as a professional.
[ my emotional experience at uni has it helped or hinder me learning have I felt that support a primary and secondary school not felt included outsider ] END WITH THIS