Contributed by:
After going through this unit, you will be able to:
• explain the concept of professional development programs for mathematics teachers;
• illustrate the purpose of professional development programs for mathematics teachers;
• describe the importance of participation in seminars, conferences, online sharing, and membership of professional organizations in professional development;
• justify the concept of teachers as a community of learners;
• explain the role of reflective practices in the professional development of mathematics teachers;
• elucidate the concept of teacher as a researcher; and
• appreciate the importance of action research and innovation in mathematics teaching.
1.
Professional
Development of
UNIT 9 PROFESSIONAL DEVELOPMENT Mathematics Teacher
OF MATHEMATICS TEACHER
9.1 Introduction
9.2 Objectives
9.3 Need of Professional Development for Mathematics Teachers
9.4 Professional Development Programmes for Mathematics Teachers
9.4.1 Seminars
9.4.2 Conferences
9.4.3 Online Sharing Communities
9.4.4 Membership of Professional Organizations
9.5 Teacher as a Community of Learners
9.6 Reflective Practices for Professional Development
9.7 Teacher as a Researcher
9.7.1 Conducting Action Research in Mathematics
9.8 Let Us Sum Up
9.9 Unit End Exercises
9.10 Answers to Check Your Progress
9.11 References and Suggested Reading
9.1 INTRODUCTION
We cannot teach mathematics effectively without a thorough understanding of
content and knowledge of pedagogy, which includes acquiring knowledge and
skills for integrating technology into curriculum, instruction, and assessment.
In this unit, we will discuss the concept of professional development
programmes for mathematics teachers. The term professional development
refers to a comprehensive, sustained, and intensive approach to improving
teachers’ effectiveness in raising learners achievement. Such programmes help
teachers align their teaching techniques with the needs of their learners and
thereby ensuring better learner performance. We will discuss various ways of
promoting professional development among mathematics teachers such as
participation in seminars, conferences, online sharing; membership of
professional organizations etc. This unit will also shed light on the concept of
teachers as a community of learners, where they are actively and intentionally
involved in constructing knowledge together and disseminating it among their
collective group. Mathematics teachers act as researchers all the time in their
classrooms. Action research and innovation in teaching mathematics are part
and parcel of the job description of teachers. The importance of research and
evolving innovative practices in mathematics teaching will also be elaborated
upon in this unit.
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Mathematics 9.2 OBJECTIVES
After going through this unit, you will be able to:
• explain the concept of professional development programmes for
mathematics teachers;
• illustrate the purpose of professional development programmes for
mathematics teachers;
• describe the importance of participation in seminars, conferences, online
sharing and membership of professional organizations in professional
development;
• justify the concept of teachers as a community of learners;
• explain the role of reflective practices in professional development of
mathematics teachers;
• elucidate the concept of teacher as a researcher; and
• appreciate the importance of action research and innovation in
mathematics teaching.
9.3 NEED OF PROFESSIONAL DEVELOPMENT
FOR MATHEMATICS TEACHERS
Mathematics is often referred to as the science of numbers, quantities, and
shapes and the relations between them. Like every other branch of science,
mathematics is also constantly evolving. With technology growing by leaps
and bounds, the means available to teachers for improving the teaching-
learning process also grow. As teaching practitioners, mathematics teachers
need to keep abreast of all such developments pertinent to their learners.
Hence, the need for developing and promoting professional development
among mathematics teachers arises.
The term professional development refers to an in-service training to upgrade
the knowledge base and skills of the trainees. In the context of teachers,
professional development facilitates an in-service training wherein the teachers
get an opportunity to upgrade their content knowledge and pedagogical skills.
Usually, it is in a formal setting, though at times it can be provided informally.
It is essentially aimed at improving the overall efficacy of the teaching-
learning process by enhancing the potentials of the teachers, and ultimately, the
learners’ performance. Professional development is essentially a training
provided to teachers during the course of their service period to promote their
capacities in various aspects of content and pedagogy. To ensure learners’
bright future it is vital to support a cycle of continuous professional growth for
teachers.
Mathematics teachers are all the time hard pressed to make the subject an
interesting and appealing one for their learners At the secondary and senior
secondary level, the intricacies of mathematics begins to get more and more
complex and the mathematics teachers find it increasingly difficult to retain the
interest of the learners in the subject. It is a crucial stage for learners as it
prepares them for higher education and also for their future profession. In order
to strengthen the educational delivery models practiced by the mathematics
teachers, especially at the secondary and senior secondary level, it is vital that
the teachers undergo professional development programmes from time to time
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so that they are better equipped to deal with the growing challenges of their
Development of
classrooms. Mathematics Teacher
Professional development programmes for mathematics teachers are designed
to be comprehensive and rigorous, equipping the teachers with a wide- ranging
set of pedagogical skills to become more effective in their classrooms.
Organizing and participating in such professional development programmes
help the teachers in the following ways:
• become more attune to the latest developments in the field of mathematics,
• develop greater commitment towards their learners,
• create a platform for sharing professional experiences,
• work towards continuous improvement of their teaching skills,
• keep abreast of skills required to adapt to ever- changing learners
curriculum,
• tailoring their teaching content according to the needs of their learners,
• acquiring knowledge and skills for integrating technology into everyday
teaching practices,
• to develop the knowledge and skills which they need to address learners’
learning challenges more effectively,
• integrate the latest research findings and teaching models to achieve better
learning outcomes,
• apply action research findings in diverse classrooms.
Check Your Progress
Note: a) Write your answers in the space given below.
b) Check your answers with the answers given at the end of the Unit.
1) What is professional development?
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2) What is the need for professional development of mathematics teachers?
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Mathematics 3) What are the benefits of professional development for teachers?
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9.4 PROFESSIONAL DEVELOPMENT
PROGRAMMES FOR MATHEMATICS
TEACHERS
Professional development involves adopting a variety of strategies to ensure
that teachers continue to strengthen their pedagogical skills throughout their
career. In formal settings, professional development programmes are often
disseminated through seminars, conferences, workshops etc. Sometimes,
professional development also occurs in informal conditions, through
interactions across online platforms, peer group discussions etc.
The common modes of professional development are:
• Individual reading and/or research,
• Peer group discussions focused on a common topic or area of interest,
• Observation-teachers observing other teachers so as to improve their own skills,
• Expert advice-an expert teacher advising colleagues,
• Group meetings to learn a new strategy or teaching skill,
• Adopting reflective and exploratory practices,
• Staff meetings,
• Online courses,
• Short term courses designed by experts at local / regional/ national level,
• Seminars/ Conferences/ Workshops to learn from a variety of expertise
from around the state or country,
• Membership of professional bodies to keep oneself updated with the latest
trends , practices and issues pertaining to the field of study.
9.4.1 Seminars
Seminars are formal presentations by one or more experts in which the
participants are encouraged to discuss a particular area of interest. In the
context of professional development, it may be described as an occasion when
a teacher or expert and a group of teachers meet to interact and discuss the
intricacies of a chosen topic or subject. Mathematics as a subject is very
interesting as well as challenging. Sharing experiences with other teachers and
listening to experts’ on the concerned topics help the teachers evolve into better
practitioners of teaching skills and improve learners achievement.
Seminars may be organized at the local, regional, state, national or
international levels depending upon the needs and requirements of the teachers
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Professional
as well as the resources available. These seminars help the teachers update their
Development of
knowledge base regarding latest developments in the field of mathematics and Mathematics Teacher
pedagogical skills being used. They also provide a platform for teachers to
interact with experts to discuss and evolve new, effective strategies to deal with
difficult classroom situations.
By attending seminars, not only do the teachers themselves benefit from the
discussions, but also their colleagues stand to gain from a summary of what
one has learned and obtain copies of relevant documents.
These days with technological advancements, many a times the teachers find
themselves attending webinars instead of seminars. Short for Web-based
seminar, a webinar is a seminar that is transmitted over the internet using video
conferencing software. A key feature of a webinar is its interactive elements-
the ability to give, receive and discuss information in real-time. Using webinar
software participants can share audio, documents and applications with
webinar participates. A webinar has all the advantages of a seminar without the
limitations of actually being physically present at the venue. This is a great
advantage for participates, especially in a profession like teaching which leaves
very little opportunity for the teachers to spare time for attending such
For example, a seminar on ‘New Developments in Mathematics Teaching’
inspires Mr. X to adopt constructive approach in his classroom. As per
constructive belief, knowledge is actively created or invented by the child, not
passively received from the environment. Learners create new mathematical
knowledge by reflecting on their physical and mental actions. Ideas are
constructed or made meaningful when learners integrate them into their
existing structures of knowledge. Applying this principle in the classroom, the
teacher Mr. X asks the learners to construct a triangle, where information about
all three distances and all three angles has been given. Next the teacher asks the
learners to construct the next triangle, with fewer specifications, with less than
six. Slowly, with each step the learners learn to construct triangles with
minimum information.
9.4.2 Conferences
Conferences may be described as formal meetings in which a number of people
gather to talk about their ideas or problems related to a particular topic, usually
for a few days. It is a large gathering of individuals or members of one or more
organizations, for discussing matters of shared interest. Organizing conferences
involving members of the teaching community is an effective way to render
professional development to the teachers. Here, peer group discussions, shared
experiences regarding classroom behaviors and results of action research,
adopting reflective practices are some fruitful techniques that ultimately lead to
the participates becoming better teachers.
For example, Mr. X attends a conference on ‘Methods for Improving
Mathematical Reasoning’ among Secondary Level Learners. Here, he comes
across many other secondary level mathematics teachers facing similar
predicament- how to improve learners’ reasoning abilities? In algebra,
encouraging learners to think how changing an input (x) in an equation would
affect the output (y). Discussing among themselves, the teachers realize that in
order to solve such problems, the learners need to clearly see the abstract linear
relationships. They all concur that explaining in simpler language, sometimes
in the local language, would be beneficial. Upon coming back, Mr. X tries to
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adopt this technique in his classroom by explaining the algebraic word
problems in Hindi and then asking the learners to solve the equations. He gets
much quicker and better responses from the learners.
9.4.3 Online Sharing Communities
With the advancement of technology, sharing of resources and experiences
among like-minded people through online platforms, has become a norm.
Teachers as a community have a lot of common interests- issues related to
learners, curriculum content and its implementation, new technologies
available to the teachers, etc. Online platforms such as blogs, Facebook
communities etc provide a good opportunity to the teachers to share their own
experiences among a peer group, hold discussions on pertinent topics,
participate in online seminars ( known as webinars), even avail of online
training courses aimed at enriching their knowledge and skill base. Nowadays,
online sharing has gained popularity among the members of teaching
community owing to its ease of use, versatility, global reach and cost
effectiveness. Teachers are now transitioning to the online medium as a means
for professional development. More and more teachers are looking to these
online resources for solutions to their teaching issues and/ or training needs.
For example, The Math Forum is a community of teachers, mathematicians,
researchers, learners, and parents using the internet to learn math and improve
math education. The forum offers a wealth of problems and puzzles; online
mentoring; research; team problem solving; collaborations; and professional
development. It helps educators share ideas and acquire new skills.
(Source: http://mathforum.org/)
7.
Professional
9.4.4 Membership of Professional Organizations Development of
Mathematics Teacher
A professional organization (also referred to as a professional body), is usually
a nonprofit organization which seeks to further a particular profession, the
interests of individuals engaged in that profession and the public interest. In the
field of education, there are numerous professional organizations that are
actively involved in facilitating better teaching- learning conditions and
learners achievement. With teachers juggling a multitude of roles, both in
professional as well as personal capacities, joining a professional organization
ought to be a high priority for them. These professional organizations offer a
plethora of benefits such as- exclusive online resources, networking
opportunities, free or discounted publications, chance to update their
knowledge of business and trade basics or acquire new skills through seminars,
workshops, conferences and online courses, develop mentoring relationships
with more experienced teachers etc. The Association of Mathematics Teachers
of India (AMTI) is one such organization in India that aims to assist teachers of
mathematics at all levels in improving their expertise and professional skills for
making mathematics interesting and enjoyable and disseminates new trends in
Mathematics Education.
For example, the Association of Mathematics Teachers of India (AMTI) has
been organizing seminars, conferences, workshops in various parts of the
country to meet and deliberate on important issues in Mathematics Education,
particularly at school level. Besides, the usual inauguration, valedictory
functions, there are endowment / memorial lectures on applied mathematics,
methodology and history of mathematics, group discussions, exhibitions,
recreations in mathematics, paper presentations, learners sessions, Quiz-written
and oral, Distinguished Mathematics teacher awards etc.
Check Your Progress
Note: a) Write your answers in the space given below.
b) Check your answers with the answers given at the end of the Unit.
4) Name various formal and informal modes of professional development.
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5) How do seminars and conferences promote professional development?
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Mathematics 6) How does online sharing help teachers in their professional development?
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9.5 TEACHER AS A COMMUNITY OF
LEARNERS
Any social unit irrespective of size, that shares common values, interests is
situated in a common location is referred as a community. It consists of an
interacting population of various kinds of individuals having common
characteristics or interests. The members of the teaching community share
common academic goals and attitudes, interests as well as problems. Today
teachers have realized the need for continuous improvement through learning
new developments, to succeed in their teaching endeavours. A community of
learners may be described as a group of people who believe in the concept of
continuous learning and actively engage themselves in learning from each
other. In a learning community, teaching professionals come together in a
group, forming an informal community committed to learn. The goal of such
communities is to advance the collective knowledge and in that way to support
the growth of individual knowledge.
Teachers are today actively involved in collaborative learning, wherein the
teachers as a group of people learn or attempt to learn something together. As a
community, teachers strive to create and sustain a learning-centered, mutually
respectful and cohesive environment where they are actively and intentionally
constructing knowledge together. Such groups of teachers often meet regularly,
share expertise, and work collaboratively to improve their teaching skills and
enhance the academic achievement of their learners. Nowadays, learning
communities are being used as an alternate strategy for professional
development. Teachers are encouraged to share their expertise and experiences
with their peer group, resulting in more effective dissemination of action
research results and incorporation of effective instructional techniques being
used by other colleagues.
The ultimate beneficiary of teachers forming learning communities are the
learners, as the teachers work towards improving their skills and knowledge
through collaborative study, expertise exchange, and professional dialogue,
thereby promoting improved learner performance.
For example, when a mathematics quiz competition was announced at the
national level for secondary school learners, Mrs. Y a mathematics teacher
decided to bring together all mathematics teachers of schools of her district so
that they may deliberate on better preparing their learners and also share their
previous experiences. These weekly meetings gave the teachers hands-on
experience using practical approaches to improve their learners’ skills and also
energize them. The meetings gave teachers a chance to be learners, and to
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experience a sequence of activities designed to be just as engaging and varied
Development of
as those they might devise for their own learner Teachers had time during Mathematics Teacher
meetings to consider what happened when they tried new things in the
classroom and discussed their experiences with their peer groups. As a result,
number of learners from the said district reached the state level quiz
Check Your Progress
Note: a) Write your answers in the space given below.
b) Check your answers with the answers given at the end of the Unit.
7) Describe the concept of teachers as a community of learners.
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8) How do teachers’ learning communities promote professional
development?
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9.6 REFLECTIVE PRACTICES FOR
PROFESSIONAL DEVELOPMENT
Reflective practice is a way of studying one’s own experiences to improve the
way one works. The act of reflection is an effective method of self-
improvement. It is basically a method of assessing one’s own thoughts and
actions, to facilitate personal growth and enhance learning. Reflective practice
involves the use of self-analysis to understand, evaluate and interpret events
and experiences in which we are involved so that we may evolve and improve
our actions in future. It is an action-based skill which can be learnt and
improved, with time and sufficient practice. It is almost similar to action
research in terms of its cyclic and dynamic nature.
In a dynamic and challenging profession like teaching, the use of reflective
practices is vital to the success of the entire teaching-learning process. The
ability to reflect critically upon one’s teaching is infact crucial to become a
successful teacher. It helps the teachers become more proactive and better
skilled professionals. Reflective practices involve a process of self-observation
and self-evaluation.
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Reflective practice occurs when teachers consciously take on the role of
reflective practitioner, subject their own teaching skills to critical analysis,
reflect on their actions in the classroom, and work to improve their teaching
practices. Reflective practice can be a highly beneficial form of professional
development at the in-service levels of teaching. By adopting reflective
practices, teachers can gain a deeper understanding of their own individual
teaching styles and thus improve their effectiveness in the classroom.
Reflection in teaching may be considered to be working in two different ways -
reflection-in-action and reflection-on-action.
Reflection-in-action involves an immediate reaction. It refers to the quick
thinking and reactions that occur as one teaches in the classroom. For example-
the teacher while teaching in the classroom can observe that the pupils fail to
grasp the subject clearly. The reflection-in-action aspect allows the teacher to
realize this, contemplate why it is happening, and respond by doing it
differently. This might involve rewording one’s explanation or adopting a
different approach to teach the subject.
On the other hand, reflection-on-action involves a delayed reaction. It occurs
once the teacher exits the classroom and reconsiders the situation again. The
teacher gives deep thought as to why the pupils did not understand, what led to
the situation, what other options were available, what else could have been
done differently for a different and better result?
(Source: http://esthermyers.blogspot.in/2014_11_01_archive.html)
As a result of one’s reflection, the teacher may opt to do something in a
different way, or may just decide that the current method is the best way. Either
way, there is scope for self-analysis and/ or self improvement for the teacher,
that is what professional development, ultimately all about.
For example, Mrs. Y decided to record the proceedings of her mathematics
classroom. Later on she observed the video recording of each lesson and
discussed the observations with her peer group. She realized where her mistake
was while dealing with algebraic problems in her class. Based upon her
observations, and suggestions from peer group, she decided to opt for a
completely different approach to teach simple algebra to her learners, and
eventually, had better results. Observing a lesson enables teachers to shift their
thinking from a teaching focus to a learning focus whilst puzzling over their
learners’ mathematical thinking. As observers, they are free to focus on the
actual work the learners are doing, as well as the learners’ thought processes.
During the lesson observations the focus was on the teacher’s presentation as
110 well as on the learners’ content knowledge.
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Check Your Progress Development of
Mathematics Teacher
Note: a) Write your answers in the space given below.
b) Check your answers with the answers given at the end of the Unit.
9) What are reflective practices?
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10) How do reflection-in-action and reflection-on-action differ?
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11) What are the steps involved in reflective teaching?
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9.7 TEACHERS AS A RESEARCHER
Research is a voyage of discovery. It is a systematic quest for answers to
unsolved problems. Teachers are always on an unending quest for many things-
new knowledge, ways to improve learners achievement, techniques to enhance
their content delivery etc. As long as they are involved in the teaching-learning
process, all teachers act as researchers in some capacity or the other. Teaching
and research are, in fact, complementary to each other, one improving the
other’s performance.
Every day teachers actively involve themselves in research in their classrooms.
Constantly striving to attain balance between learners potentials and parental
expectations, optimizing the available resources for high learners achievement,
planning lesson delivery content and modes, evaluating learners’ performance,
and working cohesively with administrators are all part of teachers’ role as
Teachers as researchers follow the same steps of research as followed by a
researcher in any other field of study. Be it gathering information, planning,
analyzing data, reflecting, implementing results or generalizing beyond their
classrooms, all these are actually steps involved in systematic goal oriented
inquiry i.e. research. Most members of the teaching community involve
themselves in classroom based research, aimed at improving their classroom 111
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practices and outcomes. In other words, almost all teachers participate in action
research with classrooms as their field of study.
Adopting reflective teaching practices in classrooms helps teachers evolve as
better practitioners of the profession as well as discover new areas of research.
With today’s teachers forming close knit learning communities, sharing of
teaching experiences and findings of action research, teachers are better
equipped to be efficacious in their professional capacity. Ultimately, research
aims to enable teachers, administrators and policy makers to make sound
decisions and effective policies regarding educational aspects which will best
serve the learners with teachers acting as researchers, these decisions and
policies become more feasible.
9.7.1 Conducting Action Research in Mathematics
Action research is a form of applied research in which the researcher works in
localized settings with a view to solve an immediate problem. It is about trying
to understand professional action from inside; as a result, it is carried out by
practitioners on their own practice, not (as in other forms of research), by
someone on somebody else’s practice. In the field of education, action research
is employed regularly by the teachers to improve their classroom practices. The
purpose of action research is to solve classroom problems through the
application of scientific method. Action research is a cyclic process. It is a
continuous process, based upon constant feedback and improvement. It is a
four step process involving:
• Planning
• Acting
• Observing
• Reflecting
Action research helps the teachers in:
• improving their teaching performance
• enhancement of learners achievement and improvement of the situation in
which the practice takes place
• better understanding of classroom problems and deriving solutions
• developing new and improved classroom practices beneficial to the learners
as well as the teachers.
For example, Mr. X was facing some difficulty in teaching certain
mathematical concepts to class VI learner. He decided to opt for carrying out
an action research on his learners by adopting the cooperative learning
technique. He investigated the impact of cooperative learning on the
engagement, participation, and attitudes of his learners and also the impact of
cooperative learning upon his own teaching. He discovered that his learners,
not only preferred to learn in cooperative groups, but also that their levels of
engagement and participation, their attitudes toward math, and their quality of
work all improved greatly. Mr. X’s teaching also changed, and he found that he
began to enjoy teaching more. As a result of this research, he now plans to
continue and expand the amount of cooperative group work that happens in his
classroom.
Teaching of mathematics not only involves the knowledge of the subject, but
also the selection of appropriate content and skills of communication resulting
in improved understanding among the learners. While teaching mathematics,
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the mathematics teachers should adopt the most well suited teaching methods,
Development of
strategies and pedagogic resources that can facilitate their learners Mathematics Teacher
understanding of the content being taught. The teaching of mathematics is a
complex, multi layered, dynamic activity that depends upon various factors for
its success. The nature of the content, quality of the instructional material, the
mode of presentation, the extent of subject knowledge of the teacher, resources
available to the teacher, the skills of the teacher, the classroom environment,
the level of motivation among the learners etc.
Teaching of mathematics entails developing skills like critical thinking,
analytical thinking, logical reasoning, decision making, and problem-solving
among the learners. This cannot be achieved by teaching through tried and
tested methods adopted for teaching other conventional subjects. Mathematics
demands more in terms of input from the teachers. The teachers are expected to
be well versed in conducting action research and evolving new techniques to
teach the nuances of mathematics to their learners. While teaching
mathematics, the emphasis should be more on understanding of basic concepts
and principles rather than the mechanics of it.
Different pedagogical methods are effective for different teaching contexts. In
a complex and diverse subject like mathematics, there is a plethora of methods
that can be applied. The onus is upon the teacher to choose the most
appropriate method for a given content. In certain situations, the teachers find
themselves at a loss regarding the most suitable method to employ since most
do not fit their classroom requirements. In such cases, it is imperative that the
teachers work towards innovating new methods to make their classroom
teaching more effective. Some such teaching methods that have been
developed and nowadays being employed very effectively across classrooms
for teaching mathematics are:
• Inquiry based learning
• Problem solving
• Active learning
• Cooperative learning
• Team based learning
• Participatory learning
Some activities which the mathematics teachers can adopt in their classrooms
to make certain topics more appealing to their learners:
(Source: waymadedu.org/pdf/Rachnamadam.pdf) 113
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Mathematics Check Your Progress
Note: a) Write your answers in the space given below.
b) Check your answers with the answers given at the end of the Unit.
12) How do teachers act as researchers?
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13) Discuss the importance of teachers acting as researchers.
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14) Why is action research important in education?
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15) Name some innovative practices employed in teaching mathematics.
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9.8 LET US SUM UP
The following issues/concepts are dealt in the unit:
Professional development is essentially a training provided to teachers
during the course of their service period to promote their enrichment in
various aspects of content and pedagogy. To ensure learners’ bright future
it is vital to support a cycle of continuous professional growth for teachers.
15.
Professional
Professional development programmes are often disseminated through
Development of
seminars, conferences, workshops, interactions across online platforms, Mathematics Teacher
peer group discussions etc.
In a learning community, teaching professionals come together in a group,
forming an informal community committed to learn. The goal of such
communities is to advance the collective knowledge and in that way to
support the growth of individual knowledge. Learning communities are
useful as an alternate strategy for professional development of teachers.
Reflective practice is a way of studying one’s own experiences to improve
the way one works. Reflective practice can be a highly beneficial form of
professional development at the in-service levels of teaching. By adopting
reflective practices, teachers can gain a deeper understanding of their own
individual teaching styles, teachers thus improve their effectiveness in the
classroom. Reflection in teaching may be considered to be working in two
different ways - reflection-in-action and reflection-on-action.
Research is a systematic quest for answers to unsolved problems. All
teachers act as researchers in some capacity or the other. Teaching and
research are in fact complementary to each other, one improving the other’s
performance. Research aims to enable teachers, administrators and policy
makers to make sound decisions and effective policies regarding
educational aspects, which will best serve the learners.
Action research is a form of applied research in which the researcher works
in localized settings with a view to solve an immediate problem. The
purpose of action research in education is to solve classroom problems
through the application of scientific method. The mathematics teachers are
expected to be well versed in conducting action research and evolving new
techniques to teach the nuances of mathematics to their learners.
9.9 UNIT END EXERCISES
1) Explain the term professional development and its benefits for teachers.
2) Discuss the concept of teachers as a community of learners.
3) Describe reflective practices and the steps involved in reflective teaching.
4) List some innovative practices which may be employed in teaching
mathematics.
9.10 ANSWERS TO CHECK YOUR PROGRESS
1) Professional development refers to an in-service training wherein the
teachers get an opportunity to upgrade their content knowledge and
pedagogical skills. Usually, it is in a formal setting, at times it can be
provided informally.
2) Mathematics teachers need to undergo professional development to
strengthen their educational delivery models, especially at the secondary
and senior secondary level and improve themselves in various aspects of
content and pedagogy.
3) It equips the teachers with a wide- ranging set of pedagogical skills which
helps them to become more effective in their classrooms. It keeps the 115
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teachers abreast of skills required to adapt to ever- changing learners
curriculum and also integrate the latest research findings and teaching
models to achieve better learning outcomes.
4) Formal modes of professional development programmes are seminars,
conferences, workshops, etc whereas informal modes of professional
development include learning through observation, interactions across
online platforms, peer group discussions, expert advice etc.
5) Seminars help the teachers update their knowledge base regarding latest
developments in the field of mathematics and pedagogical skills being
used. They also provide a platform for teachers to interact with experts to
discuss and evolve new, effective strategies to deal with difficult
classroom situations. Organizing conferences facilitates teacher peer group
discussions, shared experiences regarding classroom behaviours and
results of action research, adopting reflective practices are some fruitful
techniques that ultimately lead to the attendees becoming better teachers.
6) Online platforms such as blogs, Facebook communities etc provide a good
opportunity to the teachers to share their own experiences among a peer
group, hold discussions on pertinent topics, participate in online seminars,
even avail of online training courses aimed at enriching their knowledge
and skill base.
7) A community of learners may be described as a group of people who
believe in the concept of continuous learning and actively engage
themselves in learning from one another. Teachers as a learning
community, come together in a group, forming an informal community
committed to learn with the goal of advancing their collective knowledge
as well as support the growth of individual knowledge.
8) As a community of learners, teachers promote their own professional
development by creating and sustaining a learning-centered, mutually
respectful and cohesive environment where they are actively and
intentionally constructing knowledge together. These groups of teachers
often meet regularly, share expertise, and work collaboratively to improve
their teaching skills and enhance the academic achievement of their
learners.
9) Reflective practice is a way of studying one’s own experiences to improve
the way one works. It involves the use of self-analysis to understand,
evaluate and interpret events and experiences in which we are involved so
that we may evolve and improve our actions in future. It is an action-based
skill which can be learned and honed, with time and sufficient practice. It
is almost similar to action research in terms of its cyclic and dynamic
nature.
10) Reflection-in-action involves an immediate reaction. It refers to the quick
thinking and reactions that occur as one teaches in the classroom. The
reflection-in-action aspect allows the teacher to realize this, contemplate
why it is happening, and respond by doing it differently. On the other
hand, reflection-on-action involves a delayed reaction. It occurs once the
teacher exits the classroom and reconsiders the situation again. The
teacher gives deep thought as to why the pupils did not understand, what
led to the situation, what other options were available, what else could
have been done differently for a different and better result?
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Professional
11) Reflective teaching is a cyclic process which involves the following steps:
Development of
1) Experience Mathematics Teacher
2) Observation
3) Reflection
4) Planning
12) Every day teachers actively involve themselves in research in their
classrooms. Teachers as researchers follow the same steps of research as
followed by a researcher in any other field of study- gathering
information, planning, analyzing data, reflecting, implementing results or
generalizing beyond their classrooms.
13) Research aims to enable teachers, administrators and policy makers to
make sound decisions and effective policies regarding educational aspects
which will best serve the learners. With teachers acting as researchers,
these decisions and policies become more feasible.
14) Action research helps the teachers in improving their teaching
performance, enhancement of learners achievement, gain better
understanding of classroom problems and deriving solutions and develop
new and improved classroom practices beneficial to the learners as well as
the teachers themselves.
15) Some innovative practices employed in teaching mathematics are- Inquiry
based learning, Problem solving, Active learning, Cooperative learning,
Team based learning, Participatory learning etc.
9.11 REFERENCES AND SUGGESTED READING
• Diaz-Maggioli, G. (2004). Teacher-Centered Professional
Development.Alexandria, Virginia, USA: Association for Supervision &
Curriculum Development.
• National Research Council. (2001). Adding it up: Helping learners learn
mathematics. J. Kilpatrick, J.Swafford, and B. Findell (Eds.). Mathematics
Learning Study Committee, Center for Education, Division of Behavioral
and Social Sciences and Education. Washington, DC: National Academy
Press.
• Schon, D. A. (1996). Educating the reflective practitioner: Toward a new
design for teaching and learning in the professions. San Francisco: Jossey-
Bass, Inc.
• Sharma, N.( 2015). Professional Development of Teacher. New Delhi
Publishers.
• www.htttp://waymadedu.org/pdf/Rachnamadam.pdf
• www. http://esthermyers.blogspot.in/2014_11_01_archive.html
• www. http://mathforum.org/
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