**Part 1**

*An Action Research Proposal*

**Using Game to Encourage Students’ HOT in Mathematics Classroom **

FATMAWATI & RAHMI

**Introduction of Problem**

Fatma is a mathematics teacher in a private international school in Banda Aceh, Indonesia. After participating in the training of problem solving for mathematics teacher as a part of professional activity, she develops a new teaching methodology which she presumed can encourage students’ high thinking skills as well as problem solving using mathematical games.

Integrating games in teaching mathematics classroom is definitely new and challenging in her school. Typically, she has to select the sort of games and connect them to a particular topic in mathematics, yet keep them on track with the curriculum. Another important issue is choosing and providing appropriate materials needed by students, besides students’ activities and collaboration in the classroom.

In order to review her teaching at the first time she run the plan, Fatma requests her critical friend, Rahmi to observe her teaching. Fatma is a teacher who has experience less than two years, Rahmi, on the other hand is an experienced teacher with more than five years experience in teaching.

Fatma and Rahmi, then conduct one small action research activity to evaluate the usefulness of games in mathematics classroom. Action research is defined by Macintyre (2000) to be: ‘an investigation, where, as a result of rigorous self-appraisal of current practice, the researcher focuses on a ‘problem’ (or a topic or an issue which needs to be explained), and on the basis of information … plans, implements, then evaluates an action then draws conclusions on the basis of the findings’ (cited in Mead & Maxwell 2010:10).

Action research has systematic procedures that practitioners must follow, to gain a conclusion. Such procedures, indeed, makes action research distinct from other empirical research (Brighton 2009).

**Action Research Cycle**

*Identifying a focus*

The focus of this action research is to measure the effectiveness of games in enhancing the cognitive level of students and observing how students work in the group (whether they are on task).

*Lesson Planning*** **

Fatma created a lesson plan to be implemented in the classroom.

Topic : A hundred Lockers

Grade Level : Upper Secondary School Grade 1

Subject : Mathematics

Time Duration : 45 Minutes

Teacher : Fatmawati

Observer : Rahmi

The lesson plan is attached at appendix A.

*Acting and Observing*

In the mathematics classroom, Fatma implemented the lesson plan in the time duration 45 minutes. Before the implementation, she already gave observation check lists to her peer, Rahmi, including pre-observation questions, post-observation questions, and focus area observations (learner engagement).

In the pre-observation questions, observers find out the objective and expectation of the classroom observation, time duration for observing, and how the discussion between teacher and observer will occur. Moreover, post-observation questions point out the actual implementation in the classroom, the powerful strategies used by the teacher to engage the students, the strengths and weakness of the teacher, and the area to be improved by the teachers. Lastly, learner engagement questions to identify the activities of students in the classroom both individually and within a group, as well as students on task, whether the lesson provided by the teacher encourages students’ high order thinking and whether the teacher gives opportunities for students to present their ideas (refer to handouts and articles from NCSALL n.d) (observation checklists are attached at appendix B).

*Discussion & Reflection*

From the actual teaching in Fatma’s classroom, Rahmi pointed out some strengths and weaknesses of the teachers. She also observed the effectiveness of the game for this lesson. In this section, there are two main focuses of the observer, namely, the teacher’s observation and students’ observation.

*Teacher Observation*

Fatma’s lesson plan was well-prepared and clearly written. Similarly the materials were readily provided such as markers, a white board and class arrangement. In her classroom, Fatma involved students in the game simulation. The lesson was not the traditional lesson that stressed on procedure or algorithm but visualisation, patterning and conclusion.

The lesson also gave chances for the teacher to assess students’ prior knowledge as well as bridging it to new knowledge. However, she considered these implicitly. Consequently, students experienced difficulties in connecting their previous knowledge to the game.

The instruction given by the teacher was very clear (oral communication was excellent, understandable and loud enough) and there were active interactions between the teacher and students. Moreover, the teacher was a good facilitator that could direct the student to the solution.

In her teaching, Fatma could create good social and academic environment. She was very active to invite student’s participation in discussing and questioning. The discussion was done among students in group. They discussed and analysed the strategies to solve the problem and find the answer.

In addition, the teacher also succeeded in encouraging the students to develop their thinking to rationale the problem. This lesson also encouraged and enhanced mathematical concept as well as mathematical thinking and high order thinking skills (HOTS).

*Students’ Observation*

The students in Fatma classroom worked together in cooperative groups. They were divided into five groups of five students. The value of this method was to make the students worked together in their group and also to solve the problems together by sharing and discussing the information. Nevertheless, since there were some difficulties for students in understanding the question and game instruction, causing in-effective time that makes some objectives miss out.

In this first of action research, Fatma was not able to promote HOTS because students were not involved intensively on how to find the pattern because students had different abilities in understanding the question. Moreover, students needed more time to adjust to the new teacher’s teaching style. During the class, Fatma as a leader in the class lead the students to solve the problems. She went around the class during the lesson. Some students sometimes could not understand about the problems, therefore she observed to the groups and asked to the students which was the questions or the problems that they could not understand. It helps students deeply understand the problems and they will think how to solve the problems. She succeeded in making students to give summary and conclusion about what they had learnt.

The students in Fatma’ class enjoyed solving mathematics problems through games. In her teaching, she encouraged students to excavate what they had learned about factors and multiples to solve an interesting problem about 100 lockers’ game. In the end, students would connect this game to the concept of perfect squares.

On the other hand, the teacher failed to control and to monitor the activity of each student in the groups because they focussed in his/her individual work rather than engaged in the group discussion.

*Re-plan *

From observation of Fatma’s teaching, there are some recommendations about teaching and learning that Fatma can implement for the next class. The re-plan are discussed below:

1. When the teacher gives a question to the students, she should give adequate time for the students to think for the answer.

2. The teacher should create creative ideas to make competition more excitement to the students.

3. For those students who have low performances (weak) this task could be very difficult for them and they can easily bore. In this case, teacher should find other alternatives to attract their enthusiasm and encourage their thinking.

4. In the next class, the teacher can integrate the technology such as using Microsoft Excel to make the game more interesting.

5. The teacher should increase the ability in managing class, students, and time more efficient. To ensure all students engage in the discussion and the task, perhaps in the next class teacher can employ one student to be a checker to ensure all students in the group are participating in the group discussion.

**Part 2**

**Professional Development in the School Setting**

FATMAWATI

Deakin University, Victoria – Australia

January, 2011

**Overview of Professional Development**

The intension of teachers change nowadays has grown dramatically. Professional development activity for teachers is expected not only to enhance knowledge and understanding about teachers’ profession, but also to change their role. As the world change, teachers’ roles also change. Groundwater-Smith et al describes that ‘today teachers are expected to provide students with basic skills, but at the same time to nurture and encourage the students as whole people, and to allow their creativity and problem-solving activities to blossom’ (2003:187).

Professional development emerges within a conceptual framework which enables teachers to develop their knowledge and understanding about their professions as well as to contribute for their improvement. The conceptual frameworks provided in the professional development are essential to assist teachers become self-directed professional development (Clark 1992), enhance ability for self and collaborative reflection (Hoyrup & Elkjaer 2006), as well as adjustment to the context and culture where teachers live and work (Foley 2004).

Teacher’s commitment to personal development stresses on the teacher as a self-directed professional development that required them to become agent of change and lifelong learners. Collaborative reflection, in addition, will improve teachers performances in teaching that involving peers to work together as a group. Lastly, recognizing the context and culture, in which professional development is run according to the social, cultural, and political context in the workplaces (e.g. schools).

In this section, I would like to elaborate the important of professional development activities in my school and my context as a mathematics teacher and a future teacher educator.

**School Overview**

I teach in a private international school in the city of Banda Aceh, Indonesia. The school was officially opened by vice governor of Aceh province and mayor of Banda Aceh city in 2009, which is pioneer to non-coeducational program that have only girl students. The school has qualified and professional teachers especially in mathematics and science. The teachers are from Turkey, Java, and Aceh, who have different cultures and backgrounds. The aim of the school is to breed new generation who are appreciative of the values of high moral, and willing to struggle and serve throughout their life as the devoted offspring of the nation. The curriculum applied in the school is the combination of the national curriculum and the International curriculum.

**The Benefit of Professional Development in My School**

It is necessary to note that the purpose of professional development activities is to initiate teachers’ change in attitude, beliefs, and perceptions about teaching for improving students learning outcomes (Guskey 2002). In order to improve teacher performance in my school, the *inside-in* model of professional development (Hoban 1997) would be appropriate to be implemented in which teachers are required to explore knowledge and improve teaching strategy and reflecting in collaborative with their peers in the school-based practices.

Moreover, reflection as “the heart of educational practice” (Black 2002:14) contributes to professional development in my school that teachers are required to analyse, discuss, and evaluate their practices (Calderhead 1993 cited in Pedro 2006). Such reflection, in addition, can help the teachers to strengthen their ability in teaching.

Creating communities of practice in the school is also important in the aim to initiate particular group of teachers who are willing to work together and share their repertoire (Wenger 1999). In addition, Wenger notes that mutual engagement that exists in the community of practice engage to collaborative action (1999). The teachers in this community will learn together focusing on the problem related to their work as well as generating new understanding and renew themselves (Wenger & Snyder 2000).

Professional development that emerges the cooperation work in the professional environment, also noted by Clark (1992) in the following principles: “ask for support and help” which stress on the need for collaborative work rather than individual coach and “blow your own trumpet”, which underlines the need to learn how to teach about what you are learning by demonstrating how you are teaching, let your peers to observe your teaching and give feedback about your strengths and limitations for the improvement. These two principles basically are the foundations of the action research activity.

*Overview of Action Research*

According to Foulger (2009), action research is defined as the collaborative work among teachers in groups doing research and investigation about problematic issues in the classroom and school settings, and solving them.

Vogrinc and Zuljan (2009), in addition, state that action research activity is one of the important factors in the professional development that engages cooperative works and reflection among teacher for improving teaching in the school-based activity. Such activity is typically undertaken in a school setting. Therefore, action research is suitable to be implemented in my school.

There are four steps of action research cycle: Firstly, *planning* is the essential step where teachers discuss the problems and decide how to deal with them. Secondly, *acting* where the teacher conducts the plan in the actual classroom while the others teachers are observing her/his teaching. Thirdly, *observing* where the observers are paying attention and recording what happens in the classroom. Lastly, *reflecting* where teachers spending some time and sitting together to discuss and analyse the outcomes and re-plan (Foulger 2009).

Figure 1 The common action research cycle, which consists of four processes

(Cited in Foulger 2009: 137)

Action research has a wide range of teachers’ collaborative activities such as identifying solution to the real problem in the classroom, and investigating new methodology to improve instruction and increase student’s achievement (Ferrance 2000). Collaborative action as one of the types of action research includes few or more teachers who work together as group of practitioner in addressing classroom or school issues regarding teaching and learning. These teachers may be supported by individual outside of the school, such as a university lecturer or a community practice (Ferrance 200).

*Benefit of Action Research*

Action research has widely recognised by teachers to bring positive aspects for education field. According to Ferrance (2000), there are several advantages of action research for teachers. Firstly, action research focuses on school issues, problem, or area of collective interest which means that research is conducted in the school setting where teachers work and familiar. Secondly, action research is the form of teacher professional development that allows teachers to grow and gain confidence in their work. Such activity, influences cognitive skills, self efficacy, “willingness to share and communicate, and attitude toward process of change” (2000:14). Thirdly, action research in pairs or a group is a “collegial interaction” that provides opportunities for teachers to talk with the others about how to improve teaching and teaching strategies (2000:15), how to enhance communication among them, and how to reflect their own teaching. As a team, they determine a variety of instructional strategy, learning activities, and material used in the class.

Lastly, action research is a potential to impact school change where the teachers as an agent of change plays an important role to improve education in the school setting. This process creates a new pattern of collegiality, communication, and sharing.

In my school context, where teachers come from different background and culture, it is importance for them to recognise the context and the culture in Aceh, before they actually involve in the education activities. Another important issue arises is the existence of gap between local and foreign teachers which may cause in-balancing treatments. As regard, the teachers tend to work individually rather than mix in a group. I personally think if it continuous, it will create ‘un-healthy’ situation for good learning environment and workplace.

Therefore, as a mathematics teacher, I would like to create collaborative work that joints all mathematics teachers from different culture and backgrounds. Recently, we have three mathematics teachers who are active in teaching. Some small activities in school-based project such as classroom action research and peers observation are appropriate to be applied in order to share knowledge and improve teaching styles among mathematics teachers. Perhaps, this small group will create another community of practices in other science and social subjects, and in the end, the idea of creating community of practice among teachers will be facilitated and materialized in my school.

**Conclusion**

Action research as a sort of professional development that encourages collaborative work among teachers is a suitable model to be applied in my school. Such collaborative work, in addition, will eliminate the gap between local and foreign teachers. Furthermore, action research is apparent to be an effective school-based model for teachers for improving teaching, diagnosing problems and dilemmas in classroom, as well as providing solution.

Creating community of practice, however, is extremely challenging, typically for pioneer school that have teachers from different background and culture. Therefore, as a future teacher educator, I would like to pay more attention on how to bridge and cross the culture and context of the teachers so they are willing to cooperate and share their repertoires. “Unless educators expose themselves to the popular culture across the board, their discourse will hardly be heard by anyone but themselves.” (Freire 1996 cited in Weil 1997).

**Further Reading**

Several readings below are strongly recommended for teachers not only for in my school context, but also for teachers in general.

**‘Teacher as designer in self-directed professional development’. Clark, C 1992, in a Hargreaves & M Fullan (eds), Understanding teacher development, Teacher College press, New York, pp. 75-84.**

In this article, Clark stressed on teachers who are responsible for their own professional development. Clark introduced seven principles to help teachers designing their own professional development.

**“Professional development and teacher change”. Guskey, T.R 2002, ***Teachers and Teaching: theory and practice, ***8( 3/4): 381-391.**** **

In this article, Guskey explained the model of professional development for teachers to enduring change in teachers’ attitudes and perceptions.

**“Uncovering the inner power of teachers’ lives: Towards a learning profession.” **

*Kwo,*

*Ora W.Y 2006, International Journal of Educational Research. 41 (2004):281–291.*This article is very useful for both teachers and teacher educators. The former, to built passion of teachers in learning and changing, and the latter, to focus their attention on how to excavate the inner power of teachers as a foundation of their action in the context of professional development. Indeed, inner power of teachers will lead them to self-understanding and self-improvement that will encourage them to engage with peers school’s principals, community, and policy maker (eliminate hierarchy).

**Reference**

Black, S 2002, ‘Thinking about teaching: How teachers can put reflection at the heart of their teaching’. *Inform *5(2): 14-17. Retrieved in December 4^{th}, 2010 from Springer Database.

Brighton, Catherine 2009. ‘Embarking on action research’. *Educational Leadership. *Retrieved on December 14, 2010 from Springer Database.

Clark, C 1992, ‘Teacher as designer in self-directed professional development’, in a Hargreaves & M Fullan (eds), *Understanding teacher development*, Teacher College press, New York, pp. 75-84.

Ferrance, Eileen 2000, *Themes in Education:* *Action Research *[e-book]*, *Brown University, US. Retrieved on January 7^{th} 2011 from

Foley, G 2004, ‘Introduction: the state of adult education and learning’, in G Foley (ed.), *Dimensions of adult learning: adult education and training in a global era*, allen & Unwin, Crows Nest, NSW, pp. 3-18).

Foulger, Theresa S 2009, ‘External conversations: An unexpected discovery about the critical friend in action research inquiries’. *Action Research, *8(135). Retrieved from arj.sagepub.com at Deakin University library on December 19,2010.

Groundwater-Smith, S,. Ewing, R., Le Cornu, R 2003, *Teaching challenges and dilemmas (eds). *Nelson Australia Pty Limited, Sydney. * *

Guskey, T.R 2002, ‘Professional development and teacher change’. *Teachers and Teaching: theory and practice, *8( 3/4): 381-391.

Hoban, G 1997,’Opportunities for knowledge building in professional development models’, in R King, D Hill & J retallick 9eds), *Exploring professional development in education*, Social Science Press, Wentworth Falls, NSW, pp. 1-20.

Hoyrup, S & Elkjaer, B 2006, ‘Reflection : taking it beyond individual’, in D Bound, P Cressey & P Docherty (eds.), *Productive reflection at work: learning for changing organizations*, Routledge, London, pp. 29-42.

http://www.alliance.brown.edu/pubs/themes_ed/act_research.pdf

Mead, K., & Maxwell, T, W 2010. ‘Using the counting on mathematics strategies: An action research case study’. *Australian Primary Mathematics Classroom*, 15 (3). Retrieved on December 14, 2010 from Springer Database.

NCSALL n.d, ‘Handouts and Articles on Classroom Observation, Peer Coaching, and Mentoring’. Retrieved on December 14, 2010 from http://www.ncsall.net/fileadmin/resources/teach/mentor_b.pdf.

Pedro, J 2006, ‘Taking reflection into the real world of teaching’. *Kappa delta pi record. *42(3):129-132. Retrieved in December 4^{th}, 2010 from Springer Database.

Vogrinc, J., Zuljan, M. V, ‘Action research in school – an important factor in teachers’ professional development’. *Educational Studies, *35(1): 53-63. Retrieved on December 11, 2010 from Informa World Database. http://www.informaworld.com/smpp/title~content=t713415834.

Weil, S 1997, ‘Postgraduate education and lifelong learning as collaborative inquiry in action: an emergent model,’ in RG Burgess (ed.), *Beyond the first degree: graduate education, lifelong learning, and careers, *Society for Research into Higher Education, Buckingham, pp. 119-39.

Wenger, E & Snyder, W 2000, ‘Communities of practice: organizational frontier’. *Harvard Business Review, *78(1): 139-45.

Wenger, E 1999, *Communities of practice: learning, meaning and identity, *Cambridge University Press, pp. 72-85, 287-9, 306-7.

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