Improving Students Achievements in Mathematics - Research Paper Example

Improving Students’ Achievements in Mathematics by Developing Strong Teacher Student Relationships Project Proposal Improving Students’ Achievements in Mathematics by Developing Strong Teacher Student Relationships Methodology The auto-ethnography methodology has been envisaged for the study. The approach makes use of personal experiences, self narrative, and relationships. The examinations of these relationships occur in a cultural and social context. The association between autobiographic impulses and ethnographic moments are associated as ethnographic moments. The representation occurs as self narratives of the self, with the social contexts. The study has been planned in several stages. The stages of the study have been illustrated in the table A-1. Stage one includes the development of the proposal. Stage two includes review of relevant literature. Stage three includes design of the study. Stage four involves data collection for the study. Stage five includes development of conclusions and recommendations. Stage six involves development of the dissertation. Literature in the form of publications in journals and conference proceedings, white papers, reports, etc. would be reviewed. The methodology will include autobiographical narratives from a lived experience for engaging readers through pedagogical approach. The narrative form of discussion would be used to identify factors that cause underachievement among students. The approach will allow other teachers to critically reflect on their own experiences for the development of students learning. The findings have been described by the researcher (me) for integrating personal experience, involvements, and position while undertaking research. The process begins with the researcher’s own experience, and the researcher’s experience is studied by other participants. The focus is on change and improvement of the researcher’s praxis as a mathematics teacher or educator. It allows self-improvement, while giving the reader an opportunity to explore learning and teaching methods. An added advantage is that it will help understand the educational system in Saudi Arabia and experiences of other mathematics teachers. Justification for Methodology The methodology allows application of two types of approaches including narrative inquiry and personal reflections. Narrative inquiry is appropriate as it will allow me to reveal my lived experience as a learner, classroom teacher and tutor. The approach for unfolding and finding meaning for my lived experience will be based on stories, conversations and vignettes. Data collection will be focus on stories, reporting of personal experiences, and discussion of the meaning of experiences. Narration will help reveal metaphors and imagination of personal and social stories in a way that is more meaningful. This will be accomplished by the use of stories, poems, and dialogues. The meaning of past, present, and future experiences will be elucidated by encountering beliefs and suppositions in the direction of metaphor and imaginative thinking and learning practices. Each reflection will be re-imagined as metaphors and imaginative primary mathematics classroom that is desirable, which is a primary mathematics classroom reflecting change and growth in my teaching approach. Research Setting and Participants The setting includes a range of primary and secondary schools in Saudi Arabia. These are public schools with large student populations in Southern Saudi Arabia. Participants include mathematics teachers in a school setting. Data will be gathered from experiences and reflections presented through multiple genres of social sciences research including poems, stories and other styles of impressionistic literature. Perspectives for the research will include interpretivism, post modern paradigms, and criticalism. Resources required for the study include human resources and physical resources. Human resources include participants, faculty for guidance, library assistants for guidance on retrieving relevant literature, laboratory assistants for help with the use of computing resources, and respondents for the study. Physical resources include computing tools and accessories such as word processing tools, data analysis tools, and printing accessories; video and audio recording accessories; and literature in the form of publications. Research Methods a) Narrative Inquiry It has been a childhood dream to be in the teaching profession. My journey towards the teaching profession began in primary school. Being the eldest girl in a family of five, I do not recollect the number of hours I spent trying to help my sisters as I enjoyed the process so much that hours would simply pass by. My siblings trusted me as I did very well in school, although I started school younger. Throughout my education, I tried to help my sisters and friends understand concepts they were unable to grasp in class. Initially, they would not understand my approach as I did not follow a strategy. I explained things very quickly. I taught them the way I understood the concepts, and gave them the solutions for mathematical problems directly. Sometimes it was disappointing, but I did my best to help them by slowing down my words and giving them examples to connect the problem in front of us with the environment around us. However, my approach was not effective. There are several forms of qualitative research. Clandinin and Huber (2010) described a relatively new form of qualitative methodology as narrative enquiry, which is the study of experience understood from narrative. The approach allows thinking about, studying, and experience. Throughout the enquiry, narrative enquirers think narratively about experience. The approach includes a recursive, reflexive process of moving from the field such as telling or living of stories to data to interim and final research texts. A conceptual framework of commonplaces including temporality, sociality, and place allow different kinds of field texts and different analyses. The approach also highlights ethical matters including shaping new theoretical understanding of people’s experiences (Clandinin and Huber, 2010). Teacher’s knowledge in mathematics can be uncovered by indirect approaches. One of such approaches makes use of narrative enquiry. “Story constellations” are a form of narrative enquiry uncovering teachers’ knowledge. Stories are narratives, and constellations are collection of narratives, which are combined to give rise to the term “Story constellations.” Craig (2007) described a method for the use of story constellations. Story constellations could be used in a flexible matrix form, where narratives are paired. The matrix could be broadened, explored in detail, and restored in time unfolding in a three-dimensional inquiry space. The mapping of story constellations side-by-side provides visibility using the he narrative approach. By using conjoined analysis, particularities of place and human agency can be illuminated while applying “story constellations” as a form of inquiry. Kelchtermans (2010) found that the last two decades have witnessed human science researchers’ increasing interest in the use of narrative and biographical approaches and methods. Teacher educators apply storytelling and autobiographical reflection of practices. Narratives and biographical stories are powerful tools that unravel and understand the complex process of making sense in an interactive manner that comprises teaching and learning how to teach. The dimensions of teaching include emotional, moral and political that require technical knowledge and pedagogical skills. Narrative reflections open avenues for discussing, analyzing and learning from the dimensions of teaching. Strengths Strengths include allowing the researcher develop themes convincingly; and well described finer details and nuances of important situations. Assumptions of stakeholders, including the researcher, can be highlighted. Limitations As the stories are individual, they are not representative of mathematics teachers in Saudi Arabia. Biases creep into the study as the narratives concern the researcher’s past experiences, and are elucidated by narratives. The use of stories is fundamentally subjective, which could result in low peer and professional acceptability. b) Personal Reflections In the University, our teaching methods lecturer demonstrated how we could teach mathematics in different ways. This motivated me to use such teaching methods. When I accepted a teaching position in a private school, the principal came to my class two weeks after the beginning of the term to review my work. It turned out to be a disappointing experience for me and my students as our relationship was not yet strong enough. The consequence was that I was unable to conduct my session very well, and the class ended before I could complete the lesson. My supervisor asked me to drop by her office, before she left the class. I was almost in tears, and I asked myself what had happened. I had received A+ grades during training. I wondered what as the matter with me. However, I went to her office. The transcript of the communication has been included below. She: Are you ok? Me: No, because I know my class was bad. She: That’s fine but I realize that there was not any life in your class. Me: Although, I use the right methods in teaching mathematics. She: In the beginning only, but when you started in the main point there wasn’t any action from your students only some of them. Me: I do not know why? She: Did your students like your class? Me: Some of them. I don’t know. I am new here. She: Try to create interaction between you and your students, and then you will be fine. Me: Thanks! She being very strict gave me a “Good” evaluation for my work. This destroyed my dreams of being a good teacher, but only for one day. The next day, I decided that I had to be more confident. I went back to my books to revise my methods of teaching. Moreover, I concentrated on the relationship between me and my students. According to Olson and Craig (2001), effective facilitation requires dynamic and coexisting relationship for enabling successful uptake of evidence into practice. Teacher professional development requires paying attention to personal, interpersonal, contextual and situational factors that influence teacher knowledge over time. Teachers develop narrative authority in knowledge communities, and knowledge communities are important for sustaining the development of narrative authority. Phillion and Connelly (2004) described a narrative approach to diversity in teacher education includes contrasting stories. Initially a story is presented without context and layers of context are added providing additional information. The second story is contrasted with the first using three dimensional space – temporal, interactional and in-place providing more context for the stories. A framework allows analysis and making distinction between “teacher knowledge” and “knowledge for teachers.” Gomez et al. (2000) found that storytelling could prepare candidates for teaching. Personal experiences, instead of multicultural program ideals, are guides for teaching practice. Teachers could clarify their individual paths to school success, and attempt to transport these understandings for instructing students. Personal experience stories allow creation of a community of expectations about stories to be told; locating the narrators at the center of each tale; focus on individuals and ignoring contexts; and considering storytellers and contexts of stories. “Stories do not simply contain knowledge, they are themselves the knowledge.” Lewis (2004) suggested that the answer to how we can teach well could be answered through stories in the classroom. It is possible to make sense of our experience through our stories. Stories allow the potential for shared meaning, and by sharing them with the community, it makes it possible to enrich and enlarge each others’ experiences and understand teaching. Stories are about knowledge, and reflective practitioners require a closer look at the stories for gaining a deeper understanding and making small discoveries about our practice. The process of narration is two-fold, one of story and reflection. A month after the visit, my supervisor came back to my class. This time my performance was significantly better, and the session was very good. She formed a good opinion of my ability, and she supported me by giving advice to help improve my students’ learning. I felt confident of being a good teacher, which was confirmed by results of my students’. Several years later, I took up a teaching position at a public school, and my supervisor there asked me and my colleagues, the other mathematics teachers, to have weekly meetings. At these meetings, we would discuss problems in our teaching involving students’ abilities, lessons, curriculum and different teaching methods. This type of meeting is mandatory for all teachers in Saudi Arabia. We focus on the strategies and student’s achievement. Unfortunately, some of the meetings have been unsuccessful as we were unaware as to how we could solve these dilemmas. Strengths The use of personal reflections allow mapping of critical incidents from respondents, encourage writers to be proactive while reading related materials, and presentation of personal reflections is a persuasive method for influencing the audience. Limitations The sample sizes being small, the findings are considered subjective and personal. Responses are associated with specific educational context, and readers from different backgrounds could struggle to understand concepts and issues. Quality Standards The standard for quality will be ensured by application of strong pedagogical perspective and transferability. This involves representation of involving values and teaching experiences, and description of phenomenon for the creation of rich text. The writing will be shaped to encourage readers to reflect on their pedagogical experiences. This will allow the audience to think about educational issues, especially teaching and learning. The narrative will allow researchers reflect on their own teaching practices, especially colleagues teaching in this unit and other teacher educators. The study has been planned in several stages (see table A-1). The study would be designed based on findings from the review of relevant literature. While conducting the study, the protocol would be strictly adhered to during each stage of the study. The findings would be analyzed using tools of critical reflection, verisimilitude, transferability, and pedagogical thoughtfulness. Caution would be exercised to ensure that adequate data is collected for the analysis. Quality standards include critical reflection, verisimilitude, pedagogical thoughtfulness, and transferability. Beliefs, values and actions, and suppositions will determine the research process. Self-reflection is required to understand the research, and empowering understanding interaction between beliefs and readers. There is the opportunity to critically reflect beliefs and practices for engaging pedagogical thoughtfulness with the belief that students and teachers will realize the significance of reflection, and benefit from it. The understanding of the relationship will play a vital role in encouraging readers think about educational issues. The approach will allow ask questions on classroom practices and beliefs as a learner, and practices promoted as an educator or teacher. Ideology critique allows challenge dominant and hidden ideologies, beliefs and assumptions, including issues of language and practices in the classroom embedded in the Saudi Arabian culture. Pragmatist constructivism will allow emphasize on my role as I construct and deconstruct experiences. Critical Reflection Ginsburg and Amit (2008) argued that there is widespread agreement that early mathematics education should be implemented on a wide scale, and especially amongst disadvantaged children. Teaching mathematics to children requires profound knowledge of the subject matter; pedagogical content knowledge; application of symbolism; lecturing abilities; and connection of daily knowledge to abstract ideas. The implications for professional development of teachers include pre-service and in-service education to train a new generation of effective teachers. According to Stylianides and Stylianides (2010), the focus should be on issues of design and implementation of special mathematics tasks, which could be used in mathematics teacher education, and support the development of mathematics knowledge. The implications can be classified into two. The first being teacher education, and the second being promotion of mathematics for teaching. It is critical that teachers have the appropriate knowledge base. This knowledge could be deployed effectively for the promotion of mathematics for teaching. Magidson (2005) indicated that in mathematics education, the goals of teachers in the classroom, educational researchers, and instructional designers is to understand and improve the teaching, and learning of mathematics. Teachers work together with students to help students learn; researchers have a focus on how people learn and can teach mathematics; and designers focus on the development of instructional materials for supporting teachers and students. Each group of teachers, researchers, or designers develop its own perspectives, methods, and expertise. However, practitioners rarely have the opportunity to share their knowledge with other communities. Interactions between groups are helpful resulting in new insights, development of strategies to strengthen the products, and inform the practitioner. This could lead to tensions especially between teaching and research indicating that there are fundamental differences between teaching and research indicating fundamental differences between the approaches. This has implications for collaborations between teachers, researchers, and designers. It is desirable to gradually integrate teaching, research, and design in multiple settings. Changing the practitioner has rewards including improved methods for teaching, and evolution in the research design. There are several challenges in the integration of teaching, research, and design. These can be overcome by envisioning collaborations. Verschaffel et al. (2010) described a model for designing a powerful environment for learning and teaching mathematics is desirable, which should be structured according to interrelated components of competence, learning, intervention, and assessment. The knowledge of these interconnected components has advanced during the past few decades resulting in a better understanding of the components constituting mathematical disposition. It also enables the nature of learning and development process among students in the acquisition of competence, and structuring characteristics of learning environments. The environments are powerful in initiating and evoking processes and development of assessment instruments for monitoring and supporting learning and teaching. Chamoso and Cáceres (2009) argued that reflection should be fostered for preparation of capable professionals in mathematical educational practice. Teaching mathematics using a teaching-learning process incorporating an assessment system requires maintaining a learning portfolio. This allows assessment of each student’s learning as a reflection of his/her vision of the learning process in school classrooms, knowledge of methodological contexts and creativity. Rubrics could be built for each case with common criteria that will allow study the relationship between outcomes obtained, and comparison with a final written exam. The results will indicate the difference between assessments of student-teachers as a reflection, and determine the need for using specific assessment instruments for different capabilities for the training process. So et al. (2009) found that student teachers acquired knowledge of good teaching practices by the interactive use of video database and online discussion forum. Student teachers shared teaching videos, and received comments from members of a learning community. The use of content analysis and sharing in discussion forums, and individual reflections provide insight into the use of collaborative learning communities for creation of knowledge base for teaching. Use of videos allow interaction from teaching models to reflection; mental model to conceptual understanding of teaching; and creation of knowledge base. The nature of feedback from video providers includes explaining the classroom situation; planning for changes; and reporting the follow-up work. Learning through the learning community involves recognition of effective teaching; identification of ineffective teaching; and adoption of suggestions for future teaching. The approach allows creation of knowledge base for teaching by means of a learning community; extended use of online video database within larger communities; integration of technology in teacher education; and other applications of videos in teacher education. Warfield et al. (2005) suggested that teachers have the opportunity to learn through private and public enquiry about teaching and children’s learning. Adoption of reform-based strategies and allowing children report problem-solving strategies allow complex practice. Reflection and communication play important roles in learning, and beliefs while learning to teach play a critical role. Pauli et al. (2007) suggested that teachers in mathematics instruction can implement surface features of instruction for fostering self-regulated learning, and achieve quality at a deeper level of instruction. The approach allows a focus on higher-order thinking, problem-solving, and mathematical modeling. Educational reforms have been based on constructivist and socio-cultural theories of mathematics learning. The dimensions of self-regulated learning and conceptual understanding are targeted by these approaches. Data in the form of videotapes of mathematics lessons, student and teacher questionnaires, and achievement tests could be used. Surface level of instruction could be measured in terms of the number of opportunities for self-regulated learning. Deeper level of instruction could be assessed in terms of independent problem solving opportunities. The extent to which teachers’ pedagogical beliefs reflect constructivist orientation could also be assessed. Generally teachers implement the two dimensions independently of one another. Constructivist-oriented beliefs tend to influence opportunities for independent problem solving, but do not affect opportunities for self-regulated learning. However, opportunities for self-regulated learning have a positive impact on students’ learning experience. Teachers should be encouraged to take greater account of surface-level, and deeper level features of instruction. A video club could be designed to help teachers to learn to notice and interpret students’ mathematical thinking. Participation in the video club influences teachers approach. van Es and Sherin (2008) suggested that students’ mathematical thinking could be noticed by teachers in terms of direct, cyclical, and incremental learning. This form of teacher learning provides insight on teacher cognition, and help design video-based instruction material. According to Nilssen (2010), mentoring is an approach that could guide student teachers’ learning process towards constructive forms of teaching. One of the underlying assumptions is the need to understand what students know and say. Student teachers should start their teaching by developing a mindset by a focus on the kids. This could be achieved by the design and care of natural learning situations, and assisting them develop traits by seeing through their own teaching. Although some of teachers were relatively inexperienced, there were students who achieved good results in mathematics in my school. This could be attributed to the students liking them, and benefitting from the relationship. This has motivated me to investigate the link between students’ achievement and the good relationships between teacher and students in my class. Verisimilitude Verisimilitude involves narration of research that actually occurred, and other stories that have risen from the imagination of the teacher in a real-life setting. This will allow readers judge the honesty and knowledge. The version of truth will be mediated in subtle evocative characteristic resonating feeling of lifelike, plausible, and possible experiences. The process will help researchers communicate with others that are different from themselves and offer approaches to develop lives of the audience. Transferability Transferability will ensure that the results are appropriate to others in an educational setting. It refers to the generalization of findings for application in a different context. Generalization allows audience relate the results in their setting, or a setting that they are familiar with, and draw conclusions for their specific context. Pedagogical Thoughtfulness Pedagogical thoughtfulness allows critical reflection mirroring own practices and beliefs for engaging in the act of teaching with the belief that learners and teachers will approach understanding of the significance of being reflective in one’s own belief and consequent practices. The comprehension of the relationship between teacher’s imagination and metaphors, student’s belief and classroom practices is important for participation in a didactic imperative role encouraging readers reflect on educational issues foundational to their practices. Conclusion It is expected that technical mathematics knowledge in teachers could be better utilized for imparting mathematics instruction in a classroom setting by deploying effective student-teacher interaction strategies in classrooms in Saudi Arabia. Good practices for teacher-student relationships will help improve the state of the art in mathematics education. References Clandinin, D. & Huber, J. (2010). Narrative Inquiry. International Encyclopaedia of Education, 436-441. Craig, C. (2007). Story constellations: A narrative approach to contextualizing teachers’ knowledge of school reform. Teaching and Teacher Education, 23, 2, 173-188 Ginsburg, H. & Amit, M. (2008). What is teaching mathematics to young children? A theoretical perspective and case study. Journal of Applied Developmental Psychology, 29, 4, 274-285 Gomez, M., Walker, A. & Page, M. (2000). Personal experience as a guide to teaching. Teaching and Teacher Education, 16, 7, 731-747. Kelchtermans, G. (2010). Narratives and Biography in Teacher Education. International Encyclopaedia of Education, 610-614. Lewis, P. (2004). Trying to teach well: a story of small discoveries. Teaching and Teacher Education, 20, 3, 231-242. Magidson, S. (2005). Building bridges within mathematics education: Teaching, research, and instructional design. The Journal of Mathematical Behavior, 24, 2, 135-169 Nilssen, V. (2010). Encouraging the habit of seeing in student teaching. Teaching and Teacher Education, 26, 3, April Olson, M. & Craig, C. (2001). knowledge: the development of narrative authority through knowledge communities. Teaching and Teacher Education, 17, 6, 667-684. Pauli, P., Reusser, K. & Grob, U. (2007). Teaching for understanding and/or self-regulated learning A video-based analysis of reform-oriented mathematics instruction in Switzerland. International Journal of Educational Research, 46, 5, 294-305 Phillion, J. & Connelly, M. (2004). Narrative, diversity, and teacher education. Teaching and Teacher Education, 20, 5, 457-471. Verschaffel, L., Greer, B. & De Corte, E. (2010). Mathematics Learning. International Encyclopaedia of Education, 401-406 So, W., Pow, J. & Hung, V. (2009). Creating a knowledge base for teaching through a learning community. Computers & Education, 53, 3, 775-786 Stylianides, G. & Stylianides, A. (2010). Mathematics for teaching: A form of applied mathematics. Teaching and Teacher Education, 26, 2, 161-172 van Es, E. & Sherin, M. (2008). Mathematics teachers’ “learning to notice” in the context of a video club. Teaching and Teacher Education, 24, 2, 244-276 Warfield, J., Wood, T. & Lehman, J. (2005). Autonomy, beliefs and the learning of elementary mathematics teachers. Teaching and Teacher Education, 21, 4, 439-456 Appendix A: Tables Table A-1. Project Management Stage Activity Dates Deliverable One Development of proposal 01-06-2010 to 15-06-2010 Proposal Two Review of literature 15-06-2010 to 15-07-2010 Literature Review Three Design of study 15-07-2010 to 30-07-2010 Study design Four Data collection 01-08-2010 to 30-09-2010 Narratives Five Analysis of results; Development of conclusions and recommendations 01-10-2010 to 30-10-2010 Conclusions and Recommendations Six Development of dissertation 01-11-2010 to 15-11-2010 Dissertation Read More