Online Assignment

SMSG & SMP

School Mathematics Study Group      

                   The School Mathematics Study Group (SMSG) was an American academic think tank focused on the subject of reform in mathematics education. Directed by Edward G. Begleand financed by the National Science Foundation, the group was created in the wake of the Sputnik crisis in 1958 and tasked with creating and implementing mathematics curricula for primary and secondary education, which it did until its termination in 1977. The efforts of the SMSG yielded a reform in mathematics education known as New Math which was promulgated in a series of reports, which culminated in a series published by Random House called the New Mathematical Library. In the early years SMSG also rushed out a set of draft textbooks in typewritten paperback format for elementary, middle and high school students.

Perhaps the most authoritative collection of materials from the School Mathematics Study Group is now housed in the Archives of American Mathematics in the University of Texas at Austin's Center for American History.

   School Mathematics Study Group is a massive endeavour started in USA, in 1958 with a view to improve the existing system of mathematics curriculum. In addition to its improvement and compilation of study materials, SMSG prepared textbooks separately for both teachers and students. Yale university U. S. A. has published a set of 16 books prepared by SMSG. Eight of these books are textbooks for use in secondary school and eight companion volumes are teacher guides. Four books deal with arithmetic, two with algebra and two geometry.

                   Key ideas underlying these books are structure of arithmetic from algebraic view point, real number system as a progressive development; metric and non metric relations in geometry, experience with and appreciation of abstract concepts, the role of definition, development of precise vocabulary and thought, experimentation and proof.

                 In contrast to traditional beginning of textbooks in arithmetic the opening chapter of SMSG volume of arithmetic is ‘Mathematics as a Method of Reasoning’. Algebra is introduced through ‘Sets’. Similarly the stress in geometry is an explanation of concepts.

                 SMSG provided training programmes to teachers for handling novel methods and techniques of teaching mathematics. The curriculum and textbooks prepared by SMSG have got world wide recognition.

                   Working on this modern concept of mathematics curriculum as practiced in the U. S. A., the National Council of Educational Research and Training (NCERT) has prepared some model textbooks in mathematics for use in secondary schools in India. The textbook in Algebra prepared by the NCERT deals with the following topics: elementary number theory, fractions, rational numbers, linear equations, quadrilateral equations, radicals, complex numbers, integral exponents, polynomials, partial fractions, sequences and series, permutations and combinations, binomial theorem and logarithms. By 1970 Kerala also revised the Mathematics curriculum in tune with modern Mathematics sponsored by the SMSG.

 Scottish Mathematics Project

                   Scottish Mathematics Project was started in 1961 for making improvements in mathematics curriculum. The mathematics curriculum was reconstructed in Scotland with the intension of teaching mathematics heuristically in schools. They prepared with this intention 5 textbooks for pupils studying for GCE [General Certificate of Education] examination at 0 level. Later in 1967 they prepared a series of textbooks from A to H levels for the students studying for CSE examination. These textbooks were prepared by considering the problems and needs of teachers and students. It includes a number of experiments and problem solving activities. They also prepared handbooks for the teachers for effective teaching.

Powerpoint Presentation

Innovative Lessonplan

Reflective practice

Reflective practice is "the capacity to reflect on action so as to engage in a process of continuous learning".According to one definition it involves "paying critical attention to the practical values and theories which inform everyday actions, by examining practice reflectively and reflexively. This leads to developmental insight".

Reflective practice can be an important tool in practice-based professional learning settings where individuals learning from their own professional experiences, rather than from formal teaching or knowledge transfer, may be the most important source of personal professional development and improvement. Further, it is also an important way to be able to bring together theory and practice; through reflection you are able to see and label schools of thought and theory within the context of your work (2007, McBrien). What is important about reflection throughout your practice is that you are not just looking back on past actions and events, but rather you are taking a conscious look at the emotions, experiences, actions, and responses, and using that to add to your existing knowledge base to draw out new knowledge, meaning and have a higher level of understanding (2013, Paterson, Chapman). As such the notion has achieved wide take-up, particularly in professional development for practitioners in the areas of education and healthcare. The question of how best to learn from experience has wider relevance however, to any organizational learning environment. In particular, people in leadership positions have a tremendous development opportunity if they engage in reflective practice.

History and background

Professor Emeritus Donald Schön

Reflective Practice was introduced by Donald Schön in his book The Reflective Practitioner in 1983, however, the concepts underlying reflective practice are much older. John Dewey was among the first to write about Reflective Practice with his exploration of experience, interaction and reflection. Other researchers such as Kurt Lewin, Jean Piaget, William James and Carl Jung were developing theories of human learning and development. Marcus Aurelius' Meditations has also been described as an example of reflective practice.

Dewey’s works inspired writers such as Donald Schön and David Boud to explore the boundaries of reflective practice. Central to the development of reflective theory was interest in the integration of theory and practice, the cyclic pattern of experience and the conscious application of that learning experience. For the last 30 years, there has been a growing literature and focus around experiential learning and the development and application of Reflective Practice. Reflective practice also contributes to learning and expressing our own and others' stories (Ivan, 2012).

Application

Reflective Practice has been described as an unstructured approach directing understanding and learning, a self regulated process, commonly used in health and teaching professions, though applicable to all professions. Reflective practice is a learning process taught to professionals from a variety of disciplines by practitioners, with the aim of enhancing abilities to communicate and making informed/balanced decisions. The practice has historically been applied most in the educational and medical field. When reflection in action and reflection on action described by Donald Schon are utilized in practice and when practitioners are able to identify these actions they become better at reflective practice. Professional Colleges such as the College of Nurses and College of Dental Hygienists are recognizing the importance of reflective practice and require practitioners to prepare reflective portfolios as a requirement to be licensed, and for yearly quality assurance purposes.

Education

In education, reflective practice refers to the process of the educator studying his or her own teaching methods and determining what works best for the students. It involves the consideration of the ethical consequences of classroom procedures on students.

The appeal of the use of reflective practice for teachers is that as teaching and learning are complex, and there is not one right approach, reflecting on different versions of teaching, and reshaping past and current experiences will lead to improvement in teaching practices. Schön’s reflection-in-action assists teachers in making the professional knowledge that they will gain from their experience in the classroom an explicit part of their decision-making.

According to Paterson and Chapman (2013), reflection and learning from experience is key to staying accountable, and maintaining and developing aptitude throughout your practice. Without reflection you as a practitioner are not able to look objectively at your actions or take into account the emotions, experience, or responses from your actions to improve your practice. Through the process of reflection teachers are then held accountable to their teaching practice to students, parents, administration, and all interested state holders; to the standards of practice for teaching (in Ontario)- commitment to students and student learning, professional knowledge, professional practice, leadership in learning communities, and ongoing professional learning. Reflection is a vital process of learning from experience that allow you to evolve as a practitioner; through learning from past experiences, it allows you to develop a more through schema for practice (2013, Chapman and Paterson). Through reflective practice, you as a teacher are committing yourself to students and student learning; you are looking back on your practice and reflecting on how you have supported students through treating them “…equitably and with respect and are sensitive to factors that influence individual student learning” (2013, Ontario College of Teachers). By this, you are asking yourself, have I to the best of my abilities supported student learning, and provided all of my students with an entry point into learning. Through reflective practice you are reflecting on your professional knowledge and professional practice; you are looking at how you teach and the information and forms of learning you are bring to your students, and taking a critical look at whether or not you are current and if your ways of teaching are having an impact on student learning that they will be able to translate into future endeavors. If this is not the case you are then addressing the standard of ongoing professional learning. Here you are looking at and trying to recognize where you need to enhance your own learning so that it had a bigger benefit to student learning. In addition, teachers are the leaders in their learning communities; it is from their cues and attitudes that their learners develop from. Through reflection, and sharing this with your learner, you are showing strong leadership because it shows that you are willing to learn from your mistakes and improve your practice for all of those affected by it (2013, Ontario College of Teachers).

As Larrivee argues, Reflective Practice moves teachers from their knowledge base of distinct skills to a stage in their careers where they are able to modify their skills to suit specific contexts and situations, and eventually to invent new strategies. In implementing a process of Reflective Practice teachers will be able to move themselves, and their schools, beyond existing theories in practice. Larrivee concludes that teachers should “resist establishing a classroom culture of control and become a reflective practitioner, continuously engaging in a critical reflection, consequently remaining fluid in the dynamic environment of the classroom”.

Health professionals

Reflective Practice is associated with learning from experience, and is viewed as an important strategy for health professionals who embrace lifelong learning. Due to the ever changing context of healthcare and the continual growth of medical knowledge, there is a high level of demand on healthcare professionals' expertise. Due to this complex and continually changing environment, healthcare professionals could benefit from a program of reflective practice.

Price (2004 ) recognizes that there are several reasons why a healthcare practitioner would engage in reflective practice: To further understand yourself, motives, perceptions, attitudes, values and feelings associated with client care; To provide a fresh outlook to practice situations and challenge existing thoughts, feelings as well as actions; To explore how the practice situation may be approached differently.

In the field of nursing there is concern that actions may run the risk of habitualisation, thus dehumanising patients and their needs. In utilising Reflective Practice, nurses are able to plan their actions and consciously monitor the action to ensure it is beneficial to their patient.

The act of reflection is seen as a way of promoting the development of autonomous, qualified and self-directed professionals. Engaging in Reflective Practice is associated with the improvement of the quality of care, stimulating personal and professional growth and closing the gap between theory and practice. Activities to promote reflection are now being incorporated into undergraduate, postgrduate and continuing medical education across a variety of health professions Mann (2009) found through her research that in practising professionals the process of reflection appears to be multifactorial and to include different aspects. In addition to reflection both on and during experiences that the anticipation of a challenging situation also stimulated reflection. Practicing professionals vary in their tendency and ability to reflect.

Davies (2012) identifies that there are both benefits as well as limitations to reflective practice:

Benefits to Reflective Practice

·         Increased learning from an experience for situation

·         Promotion of deep learning

·         Identification of personal and professional strengths and areas for improvement

·         Identification of educational needs

·         Acquisition of new knowledge and skills

·         Further understanding of own beliefs, attitudes and values

·         Encouragement of self-motivation and self-directed learning

·         Could act as a source of feedback

·         Possible improvements of personal and clinical confidence

Limitations of Reflective Practice

·         Not all practitioners may understand the reflective process

·         May feel uncomfortable challenging and evaluating own practice

·         Could be time consuming

·         May have confusion as to which situations/experiences to reflect upon

·         May not be adequate to resolve clinical problems

Environmental management and sustainability

There is some criticism that traditional environmental management which simply focuses on the problem at hand, fails to integrate the wider context in which the environment sits into the decision making. While research and science must inform the process of environmental management, it is up to the practitioner to integrate those results within this wider context. In order to deal with this and to reaffirm the utility of environmental management Bryant and Wilson propose that a “more reflective approach is required that seeks to rethink the basic premises of environmental management as a process”. This style of approach has been found to be successful in sustainable development projects where participants appreciated and enjoyed the educational aspect of utilising reflective practice throughout, however the authors noted the challenges with melding the “circularity” of reflective practice theory with the “doing” of sustainability.

Leadership Positions]

Reflective Practice provides a tremendous development opportunity for those in leadership positions. Managing a team of people requires a delicate balance between people skills and technical expertise, and success in this type of role does not come easily. Reflective Practice provides leaders with an opportunity to critically review what has been successful in the past and where improvement can be made. To support reflective learning organizations have invested in coaching programs for their emerging and established leaders. Coaching is defined by the International Coaching Federation as partnering with clients in a thought provoking and creative process that inspires them to maximize their personal and professional potential. Leaders frequently engage in self-limiting behaviours because of their over reliance on their preferred ways of reacting and responding. To help support the establishment of new behaviours, coaching is extremely useful as it encourages reflection, critical thinking and transformative learning. Adults have acquired a body of experience throughout their life or frames of reference that define their world. Coaching programs support the process of questioning and potentially rebuilding these pre-determined frames of reference. The goal is for a leader to maximize their professional potential and in order to do this, there must be a process of critical reflection on current assumptions.

Other professions

Reflective Practice can help an individual to develop personally, and is useful for professions other than those discussed above. It allows professionals to continually update their skills and knowledge and consider ways to interact with their colleagues.

Suggested ways for professionals to practice reflective management include:

·         Coaching;

·         Keeping a journal;

·         Seeking feedback;

·         View experiences objectively; and

·         Taking time at the end of each day, meeting, experience etc. to reflect-on-actions.

·         Anecdotal Notes

·         Group discussion