Introduction
The study of mathematics plays a backbone role in education, developing human cognitive abilities, including logical thinking abilities, affecting the teaching of other disciplines. High-quality mathematics education is necessary for everyone for his/her successful life in modern society. Modern educational concepts declare the creative development of the individual, but the practical implementation of this goal is not well worked out, at the same time school teacher is obliged to solve the problem. In practice, even strong students who have a good mathematical thinking and great store of knowledge, are not ready to work in the situations new for them, are not always able to apply existing knowledge and skills in solving non-standard tasks both in the classroom and in life. This is because mathematical competence in students is not formed, as the traditional study of mathematics, focused on knowledge and skills, does not involve qualitative development of intellectual and creative thinking, which is part of mathematical competence. The task of creation of such thinking in students is mainly the task of teacher. In this paper we will make an attempt to create the program of mathematics teachers’ professional development to maximize students’ achievement.
The traditional teaching of mathematics often causes in a number of children a sense of boredom that interferes the acquirement of program material. At the same time, at the level of basic and secondary education mathematics education should perform the following functions (Joubert et al, 2010):
- Provide each student with the opportunity to achieve the level of mathematical knowledge necessary for further successful life in society;
- Provide each student with developing intellectual activities at an affordable level, using the inherent beauty and fascination of mathematics;
- Provide to the country (society) the necessary number of graduates, mathematical preparation of which is sufficient to continue their education in a variety of directions and in practice, including the teaching of mathematics, mathematical research, work in the field of information technology and others.
In the basic general and secondary education it is necessary to:
- Provide training of students in accordance with their requests to the level of training in the field of mathematics education;
- Provide each student the opportunity to achieve compliance with any level of preparation, taking into account his individual needs and abilities (the ability to achieve the required level of mathematics education must be supported by an individualization of training, e-learning and distance learning technologies; development of a system of specialized educational organizations, specialized classes, system of additional mathematics education, etc.);
- Encourage individual approach and individual forms of work with remedial students;
- Remember that the achievement of any of the levels of training should not prevent the individualization of learning and close the opportunity to continue education at a higher level or change a profile.
Improvement of the content of mathematics education should be provided primarily through advanced training and additional professional education of teachers on the basis of leadership practices of mathematics education, formed in educational institutions. At this, it should be remembered that namely the competence of the teacher is one of the constitutive factors of efficiency of educational activity of the student (CCSSO, 2009).
Prevailing so far theoretical understanding of the system of continuous pedagogical education, which retain the traditional commitment to knowledge paradigm of learning, object-oriented professional activity of the teacher, localized in space and time method for training, appeared unable to create a conceptual basis for a breakthrough in a radical new practices of teachers training, focused in the strategic plan for the implementation of personal, subjective, activity, individual creative paradigm of education. Moreover, the existing theory of teacher education does not need, and even often opposed to really developing practice of creating new educational pedagogical structures (such as training, research and educational complexes of continuous pedagogical education system, etc.), that can more adequately respond to the needs of educational practice ever-changing in the above direction (Boyd et al., 2009).
The first level (after realizing own needs), providing opportunities for the teacher in continuous professional development, is the head of the educational institution. Strategic objectives of education, the transition to new educational results require updating of the teaching corps (Levine, 2006). For existing teachers the task of “renewal” is the task of continuing professional development, the expansion of professional competences and improving their level. For this purpose it is necessary to use all the features of a formal, non-formal and informal additional vocational training for professional and personal self-development. The task of the school leader is to create appropriate conditions: motivation and stimulation system, system of an internal organization of continuous professional training, support for professional career individual programs, professional development for all staff.
Professional education of teaching staff is kind of administrative activity aimed at training employees to meet new “production functions”, engage in new posts, meeting new challenges. Professional development can be carried out by external to the educational organization programs of professional development at the municipal, regional and federal training systems, as well as in corporate training can be used. Task of the manager is planning corporate and individual programs of additional professional training, organization of various both external and internal forms (Glickman et al., 2010).
We will consider the possibilities of teachers’ professional development for maximization of student’ achievement on the example of one of the district schools. In this school, Algebra 1 State Testing Scores have been poor, students that are taking Algebra 1 in the High School are low-level learners that did not take Algebra 1 in middle school. This amounts to half the students. Those taking Algebra 1 in High school are low-level learners and many special education students. The situation is as follows:
Total Cohort Class of 2019 – 261 Students
Those Scoring Basic and Below Basic – 97
Of the 97 Basic and Below Basic – 12 have IEP’s
All 146 students completed the Algebra 1 course and passed.
Corporate training has the following theoretical grounds. In line with the andragogy concept of adult education, namely forms of collective and cooperative group activities are seen as the most effective for the development of personality (Levine, 2006). Theory and practice of psychology says that the development of personal qualities, the most effective changes in the human psyche does not occur in the individual activities but in group interaction. Consequently, the task of developing the personality of teachers and their professional development requires to organize group forms of study, to ensure cooperatively divided activity of the participants.
Corporate learning requires new skills of the teacher, who organizes and conducts classes. As a rule, such teacher becomes a moderator. In the processes of planning, preparing and conducting training activities leading in the moderator’ activity is the principle of orientation on the participants, i.e. teachers. Another important principle is focus on issues important for the school and for individual teachers. The main task of the moderators is such a work, in which teacher training process and the process of cooperation are simultaneously going on, as well as the establishment of contact between the teachers. At the same time the moderators are “adults among adults”: teachers among teachers, and equal partners for the course participants (Hammerness et al., 2005).
Corporate training is oriented on the strategic objectives of the educational institution that are specific to each school and are determined by the program of development of the school. This is achieved by such important advantages of corporate learning as the consistency, since any educational institution is a system, and solution to the problem of improving any function of this system is impossible without taking into account all the relevant features of the relationship of this function with others.
The second advantage of corporate training is that in its frames there is implementation of an adequate situation that has arisen in this school, the correlation of formalized and non-formalized knowledge. Real, non-formalized knowledge, which are theoretical generalizations, are in a variety of sources in the mediated condition. It is necessary to identify, isolate, process this knowledge, and then to provide it in a suitable form to specific category of teachers.
In the construction of the professional development programs for teachers of mathematics it is important to provide orientation of programs on the development of professional competence and the development of a reflexive professional experience. Under the terms of pedagogic innovation theory, preparation of the teaching staff to innovative activity on the acquiring and implementation of educational innovation in teaching practice should include three areas: information, psychological and methodological (Levine, 2006). The proposed model of internal corporate training involves all three areas, which determines its innovativeness. The implementation of a professional development model suggests participation of teachers motivated to learn, and teaching staff of support service (teachers-moderators and school administration).
Glickman, Gordon, and Ross-Gordon (2010) make emphasis on “school culture, teachers as adult learners, developmental leadership, democratic education, and collegial supervision has helped redefine the meaning of supervision and instructional leadership for both scholars and practitioners” (Glickman, Gordon & Ross-Gordon, 2010, P.3)
In general terms, the stages of the organization of process of improvement of professional competence look as follows:
1. Description of competencies which are critical to the educational institution.
2. The definition of a key specialist, or several experts, who are “carriers” of these competencies.
3. Drawing up of individual “dossier” for each key expert, including:
• Information about the employee;
• Description of his key (basic and special) competences;
• Individual motivation system;
• Assessment of the results;
• Development plan;
• Plan to participate in improvement of the professional competence.
On the basis of the data obtained differentiation of activity is carried out (groups of teachers are formed: clear leaders, creative groups working in a particular direction in the advance mode, a group of teachers the self-educational activity of which is carried out with the support of teachers - leaders, moderators and tutors, are defined). These variations may be different and depend on the input diagnostic results. A very important point is that the teacher easily builds up his own individual educational path; independent work with information cases and consultations in the virtual methodical “cabinet”, reflection are organized. At the third stage the self-esteem, self-determination of the teacher are carried out; the transition from subject activity to creative activity is going on, and as a result of personal action a new professional experience comes. The fourth stage is the practical; at this stage, the self-realization of the teacher is ongoing, the author (i.e. unique) professional activity is carried out, a new professional experience is created.
4. Determination of the tasks which selected specialists can solve in the process of professional development in cooperation with the administration:
• Conferences, seminars and trainings for young specialists with the results of assessment of the capacity and motivation to develop professionally in a particular direction;
• Supervision and training in the workplace by means mentoring young professionals;
• Overseeing the work of other teachers and professional counseling;
• Creation, together with specialists, of teaching materials and teaching aids on the specifics of the application of professional knowledge and teaching technologies;
• Documenting and placing in the knowledge base of the results of the work of Pedagogical team;
• Description of approaches and decisions which were applied - both own and of other professionals.
5. As a result of the above-described steps the educational institution obtains opportunity to smooth “bottlenecks” in the required competencies through the transfer of the knowledge and skills of key personnel to other employees. At the same time the problem of complex competencies is largely solved, as training alternates with work under the direction (or with consulting support) of key specialist. Accordingly, the complex knowledge and skills that cannot be taught by conventional methods (for example, at the seminar), are transmitted in the course of joint work. This is author’s development
The functioning of the corporate training model as a special multi-stage process provides a mechanism for the study of problematic issues that would later make up the program (plan) of corporate training. This mechanism is based on the diagnosis, it includes several basic steps.
1. In the first phase a comprehensive diagnosis of the needs of teachers in training and character of training requirements is organized. During the diagnostic information taking into account the three relevant positions is obtained: the customer - the leader, the future participants of training themselves and future teachers - tutors and innovators responsible for the learning process.
2. The second step is the formation of a training program, which reveals specific ratio of formalized and non-formalized knowledge. In the process of developing the program, the task of identification the problem, storage and transfer of methodological knowledge which are available at the best school teachers, is solved.
3. At the third stage the draft program (plan) of corporate education and training is formed, problematic cases, practical problems and questions are made. The collected theoretical and practical material makes it possible to differentiate the learning process itself.
4. The fourth step is preparing an analysis of the program (plan) of corporate training, relevant results, achieved objectives of the program, self-reflection of teachers, recommendations to individual students-teachers (trainees). This is author’s development
The effectiveness of the program of measures to address problematic issues is proved by effectiveness of teachers’ work, and the analysis of gaps and emerging needs in increasing the professional level of competence of teachers will serve as the basis for the development of new programs.
Shortly after the training a meeting of the resource specialist with participants of training can be organized. It may be a small training, some consulting activities or verification of the effectiveness of the work of some teachers. Results of the analysis can serve as a basis for the development of new training programs.
As a result of the professional development program, the mathematics teachers should:
- Conduct lessons, building on the achievements in the field of pedagogy and psychology, modern information technologies and teaching methods; promote the formation in students of positive emotions from mathematical activity, including the finding of errors in their constructions as a source of improvements and new understanding; to form a positive attitude on the part of all students to the intellectual achievements of classmates, regardless of the absolute level of achievement; promote the preparation of students to participate in the Mathematical Olympiads, competitions, etc., to provide the student suitable additional tasks, to lead clubs, electives courses, extracurricular activities.
- Develop and implement problem-based learning, carrying out connection of the practice with the subject; recognize and support the high motivation and develop the student's ability to study of mathematics; implement the principles meta-thingness in teaching mathematics.
Well-formedness of three required units (knowledge, skills, skills, motivation, communicative competence) would speak of the existence of mathematical competence. This will allow talking about improving the quality of teaching the subject.
It is expected that as a result of successful completion of a professional development program, the formation of the methodological complex by teachers should include the following: the development of teaching materials, tests; development and implementation of open lessons on their own, innovative technologies; creation of a set of pedagogical developments.
Tracking the current and intermediate outcomes of professional development program includes:
1. High rating indicators of students in passing the final certification.
2. Creation of a bank of creative intellectual products.
3. Increasing the number of prizes in math tournaments, competitions of various levels.
4. Increase the number of students who are ready to make a conscious choice of individual trajectories of development.
Presentation of the results is expected in the following form: discussions, meetings, exchange of experience with colleagues, conducting of open lessons for the analysis of peer.
Dissemination of experience is expected in the following forms:
1. Creation of teaching aids.
2. Preparation and conduct of urban activities for students.
3. Presentation of experiences on urban workshops of methodical association of teachers of mathematics.
4. Thematic meetings and individual consultations with parents.
We believe it appropriate to consider the effectiveness (effects) in terms of the development of professional competence of the teacher, and the possible impact of the effects produced on the obtaining of new learning outcomes. In addition, the teachers gain an opportunity to express their opinion, develop the ability to analyze their performance and decision-making (in the assessment of the activities in the classroom at the forefront of students’ self-esteem). The effects achieved by the project are relevant, multi-faceted and are reflected not only on the teacher, but also on the students' works with the teacher. This will allow implementing the concept of “dynamic school” (Glickman, Gordon & Ross-Gordon, 2010).
Implementation of the project would provide a solution to a number of urgent problems of the educational institution (school): development of professional competencies of teaching staff; the establishment of a creative environment for self-development of teachers and students; improvement of students’ performance; creating a competitive educational institution.
Results-products are as follows: the Bank of project works for students; the layout of the student portfolio; guidelines for the organization of internal monitoring of the quality of education in educational institutions, the Regulations on the assessment system; collection of diagnostic operations to monitor the formation of knowledge and skills of students; a master class on creating worksheets; a series of webinars on the use of ICT in educational activities.
The strategy of modern education confronts each education employee tasks of considerable restructuring of professional activity, the development of new psychological and pedagogical competences. Pushing the boundaries of freedom of the teacher, the professional standard at the same time increases his responsibility for the results of his labor.
In the context of the introduction of new standards, teacher becomes a key figure, because he is charged with the mission of the transition from the “knowledge”-oriented activity to education-oriented one. The standard dictates not only a new quality of education, but also a new quality of teachers. Professional and psychological readiness of the teacher to the introduction of new standards is one of the guarantors of the implementation of standards’ ideas.
Under the psychological readiness, psychology scientists realize stable mental state of the individual or the collective, forming as a consequence of understanding the content and importance of the new standards, and expressed in a positive active attitude towards innovation. Readiness is not based only on the attitude. It is based on the realization of content of innovation, its personal and collective significance, on the purposes and methods of participation of the individual or collective in the innovation.
References
Boyd D., Grossman P., Lankford H., Loeb S. & Wyckoff J. (2009). Teacher preparation and student achievement. Educational Evaluation and Policy Analysis, 31(4):416–440.
Ernest, P. (1991). The philosophy of mathematics education. London: The Falmer Press.
Glickman C.D., Gordon S.P. & Ross-Gordon, J.M. (2010). SuperVision and Instructional Leadership: A Developmental Approach (9th Edition) (Allyn & Bacon Educational Leadership). Pearson.
Hammerness, K. et al. (2005). How teachers learn and develop. In: Darling-Hammond, L. ed. Preparing teachers for a changing world: What teachers should learn and be able to do (pp. 358–389). San Francisco: John Wiley & Sons.
Joubert M., Back J., De Geest E., Hirst C. & Sutherland, R. (2010). Professional Development For Teachers of Mathematics: Opportunities and Change. Lyon France, INRP.
Levine, A. (2006). Educating School Teachers. Washington, D.C.: The Education Schools Project.
The Council of Chief State School Officers (CCSSO) (2009). Effects Of teacher Professional Development on Gains in Student Achievement. Working Paper, June.
