Creating Strong Teacher-Student Relationships - Research Paper Example

Review of Relevant Literature - Creating Strong Teacher Relationships to Improve Achievement in Mathematics Introduction Mathematics is a form of expression. Vinner (2010) reasoned that mathematics education requires meaningful learning for developing mathematical contexts such as procedures and argumentation. Strogatz, the author of the Calculus of Friendship, described how he took calculus lessons from Joffray when he was 15, and went on to become an Ivy League university professor. Strogatz considered Joffray the best teacher a student could have. Joffray would tell stories about his former students making them sound like the gods of mathematics, marvelling about the problems they could invent and solve. Joffrey, with preparation and a sense of delight and gratitude, gave students a chance to explain mathematics inculcating a love for the subject (Strogatz and Joffray, 2009). The Calculus of Friendship is not only a delightful read for aspiring mathematics teachers, but also emphasized the importance of teacher-student relationship for mathematics learning. Curricular History Mathematics education has evolved over the last hundred years (Jankvist, 2010). Recent perspectives on mathematics teaching and learning have stressed on the importance of mathematical reasoning, problem-solving skills, and their application of real life situations. Depaepe et al. (2007) argued that aspects of classroom culture assumed to enhance beliefs and problem-solving competencies include establishment of classroom norms; instructional techniques and classroom organizational forms; and set of tasks. Strong focus on heuristic skills and embedding tasks in real life are aspects that are easier to implement. The use of technology has been brought about by professional thinking about pedagogy (Katz and Solomon, 2008). Systems include the use of computer-based tools and resources (Smith, 1998; Pear and Crone-Todd, 2002). Ruthven et al. (2004) described the contribution of technology in seven themes including improving working processes and production; supporting processes such as trialling, checking, and refinement; enhancing the variety and appeal of classroom activity; fostering independence among pupils and peer support; overcoming difficulties among pupils and building reassurance; broadening reference and increasing activity currency; and focussing on overarching issues and accentuating important features. Professional thinking and use of technology is anchored in student motivation and classroom learning. Mathematics Learning Philosophical Basis Kilpatrick et al. (2001) argued that students need to think mathematically for learning mathematics. In order to be mathematically proficient, students must understand mathematical ideas, be able to solve problems, and be able to engage in logical reasoning. School mathematics is unable to develop the basis for mathematical proficiency. Changes are required in curriculum, instructional tools, classroom methods, preparation of teachers, and professional development. There is a need for coordinated action from policy makers, teachers, and parents for effecting the necessary changes. Kilpatrick et al. (2001) recommended that teaching of mathematics in schools should be based on the five strands of mathematical proficiency. Learning should be a balance between internalizing lessons and inventing mathematics. Professional development of teachers should be of high quality, systematically designed, and sustained for developing mathematical proficiency. Schools must focus on improvement by coordination of curriculum, instructional material, instruction, assessment, professional development, and organization of the school’s resources. Students’ learning should be based on scientific evidence, and effectiveness evaluated systematically. The development and assessment of mathematical proficiency is a continuous process, and research continued. Critical Constructivism – the Epistemological Basis The philosophical perspective on knowledge and learning is known as constructivism (Cobb, 2006; & Sjøberg, 2010). Constructivism has been influenced by the thinking and writings of Vico, Kant, Piaget, and Bruner. Mathematics curriculum has been grounded on constructivism (Elby, 2000; & Davis and Sumara, 2010). The focus shifted from “objective reality” to “experiential reality.” Cognition and learning are adaptive. Steffe and Thompson (2000) described strategies for mathematics education as increasing comprehensibility, and retainability of mathematical concepts. Constructivism provides a viable model for the construction of the experiential self. Learning as a constructive activity requires the understanding that ”interpretation implies more than one possibility, deliberation, and rationally controlled choice .. to do the right thing is not enough; to be competent one must also know what one is doing and why it is right.” English (2002) argued that a frustrating phenomenon is that students with the knowledge for solving a problem are unable to employ the knowledge to solve unfamiliar problems. This requires a special form of knowing and is known as “Knowing to act in the moment.” Epistemological distinctions include knowing that something is true; knowing how to carry out the procedure; and knowing why. Education is driven by these three types of knowledge. Knowledge can be passed from one generation to another in the form of facts; techniques; skills; and theories. Social Constructionism – the Pedagogical Basis Mathematical truth is social consensus, and consonant of the trend of ultrarelativism. Social constructivist theory involves mathematical development among students in a social and cultural context (Detel, 2004). This involves accounting for the process of mathematical learning among students in the classroom. Steffe and Thompson (2000) described students’ development of mathematical understandings can be classified into four paradigms. These are the single-frame paradigm; multiple-frame paradigm; motion-picture paradigm; and the participation in communities’ paradigm. In the single-frame paradigm, a comprehensive picture of conceptions is developed at a point in time. The students’ mathematical activity is compared with the normative model of mature activity. In the multiple-frame paradigm, sequences of developmental phases, levels or stages are identified. The motion-picture paradigm involves questioning of the passage of students’ mathematical concepts through a sequence of well-defined stages or phases. This involves developing a model of the process of the development of mathematical concepts instead of a fixed sequence of fixed points. Students’ mathematical interpretations, solutions, explanations and justifications are acts of participation in a collective and communal classroom process. Mathematics classroom is about participating in a culture of mathematizing. The skills, measured by the observer, form the procedural surface. The core of learning through participation is when to do what and how to do it. School mathematics enculturation is effected on the meta-level, and is “learned” indirectly. Groth and Bergner (2007) argued that the relationship between research and practice involved the conceptualization the positive influence of research on teaching. These include conceptual understanding of core knowledge; fluency in instructional material; strategic competence; adaptive reasoning; and productive disposition. Kilpatrick et al. (2001) were found to be influential among teachers with the strands of proficient mathematics teaching. However, teachers were also negative about the ability of research to influence mathematics teaching. Factors include authoritativeness or the persuasiveness of research; relevance of research to practice; accessibility; and the nature of schools. Exportation and Importation - the Curriculum Transfer Teaching and learning are central to what students learn. Mathematics curriculum in the USA, UK, Australia, and Singapore has a heavy dose of problem solving. Stacey (2005) argued that problem solving is more of a teaching method rather than a goal in itself. The idea is to promote the fundamental goal of making students good at solving problems. Boaler (2000) reasoned that social interactions, variety, and meaning are central for positive learning experiences. However, memorization, reproduction of procedures, and individualized work continue to be dominant practices. Bilingual Education The focus of behaviourism and constructivism is on the acquisition of knowledge. Knowledge acquisition is by transmission in behaviourism, and by construction in constructivism. Situationism is the initiation of a practice emphasizing on social engagement, while behaviourism is about units of behaviours (English, 2002). Bilingual education, prevalent in many non-English speaking regions around the world, has struck a balance between behaviourism and constructivism. The Impact of Imported Curriculum on South Pacific societies Mathematics, along with English and Science, are taught in South Pacific societies as a part of global citizenship education. A story includes Atlantis in ecological, social and cultural decay as a consequence of the blind pursuit of prosperity and modernisation by its rulers. Students are presented with different problems, and expected to research and suggest solutions to the problems faced. Lim (2008) found that such education has helped develop strong research culture in schools, and building the capacity of teachers. Teaching Mathematics The Diffusion of Authority English (2002) argued that teachers should be knowledgeable, and aware of students’ learning for contributing to various aspects of teaching. Aspects include student conceptions; different forms of knowledge; and classroom culture. Research has shown that learning mathematics is complex, time consuming, and not straightforward. An example is the van Hiele theory that claims that students progressing from one discrete level of geometrical thinking to another when learning geometry, in sequential and hierarchical levels and discontinuous process. Other approaches claim that learning occurs as a chain of transitions from operational to structural conceptions. Students’ errors have been considered flaws that interfere with learning and should be avoided for replacing misconceptions with correct knowledge. Mathematical activity requires the basic elements of mathematical knowledge namely algorithm; formal; and intuition. Algorithmic dimension consists of rules and procedures. The formal dimension includes axioms, definitions, theorems, and proofs. The intuitive dimension includes cognition of ideas and beliefs; and mental models. Teachers’ pre-service knowledge of teaching methods is critical in imparting mathematics education. Donmez and Basturk (2010) found that teacher training program is deficient in providing teachers tools for integrating teaching methods implying that the practical aspects are not as persuasive as the theoretical aspects. The metaphor theory has been influencing beliefs about mathematics and learning, and teaching among mathematics’ teachers. The theory allows engendering self-critique, and professional development among teachers. The Vitalisation of Relationship Researchers (Aultman et al., 2009; Newberry, 2010; & Wu et al., 2010) argued that teacher-student relationship is integral for successful teaching and learning. A balance between demonstration of care and maintaining a healthy, productive level of control in the classroom has been considered important in the relationship boundary. Boundaries in teacher-student relationships include communication boundaries; cultural boundaries; emotional boundaries; personal boundaries; relationship boundaries; temporal boundaries; institutional boundaries; financial boundaries; curricular boundaries; expertise boundaries; and power boundaries. The Generation of Meaning in Practice English (2002) and Corte et al. (2008) argued that classroom culture has received a lot of attention in recent years. This is a shift from examination of human mental functioning in isolation to a classroom based on cultural, institutional, and historical factors. Interaction includes questioning breaking up teacher monologue ensuring that students are listening, and ascribing whether the concept has been grasped. A characteristic of the revised culture is the alteration of traditional roles and responsibilities of teachers and students in classrooms. During mathematics instruction, interaction of knowledge occurs in several forms, and the contribution of the teachers’ knowledge and understanding of student mathematical learning cannot be underestimated. Classroom culture requires consciously encouraging the intellectual autonomy among students, and the development of specific social and sociomathematical norms. It is not only important to pay attention to students’ individual learning and cognitive development; but also the development of the classroom culture. According to English (2002) situationism involves questioning the kinds of cognitive processes and conceptual structures, and determining social engagements for providing a proper context for learning. Knowledge is viewed as practices of a community, and the abilities of individuals to participate. The central characteristic of situated learning is “legitimate peripheral participation,” allowing the learner become a full participant of the sociocultural practices within the community. Mathematical learning environments foster participation in inquiry and reasoning supporting the development of personal identities of students. The Breaking of Boundaries Karaduman (2010) argued that mathematics is perceived as an abstract course, causing anxiety among students. A strategy for eliminating this problem is the application of teachers optimally to the level of students. This allows understanding of cause-effect relationships in nature. The history of mathematics enables taking advantage of this strategy allowing students think about the cause of operations. English (2002) reasoned that teachers must be knowledgeable of the three main aspects of student mathematical learning including student conceptions; different forms of knowledge; and classroom culture. Constructivism suggests that teachers should aim to understand students’ thinking, allowing them to design appropriate ways for fostering knowledge construction. The situative theory prescribes participation in shared mathematical activities. Knowledge must be developed in different forms including conceptual knowledge; strategies for problem solving; and metacognitive abilities. Teachers must be knowledgeable about different forms of knowledge, and their understanding of the interrelations between classroom norms and learning of mathematics is important for designing appropriate learning environments. Participation in complex activities involves the use of different forms of knowledge. The Center for Science, Mathematics, and Engineering Education, National Research Council, USA (2000) recommended that the quality and depth of mathematics learning in schools should be enhanced, and the needs of young adolescents should be addressed sensitively. Gholami and Husu (2010) argued that teachers practical knowledge is based on two epistemic statuses including "practicable" knowledge and "praxial" knowledge. Şahan (2009) found that many teachers know the properties that teachers should have, but also know that it is not possible to enact these behaviours in class. A clear and compelling need has been felt for higher expectations for all students for achievement in mathematics, and realizing these expectations would require renewed effort from teachers, schools, and parents. Mathematics content should be delivered in ways respecting students requires prepared and motivated teachers. Teacher preparation programs have not been adequate, and programs for certification do not support adequate content or pedagogical preparation. Instruction, for maximizing learning among students, requires participation in professional development activities for improving their practice and becoming a part of a community with shared goals. Possani et al. (2010) demonstrated that the use of models and modelling to be effective in teaching mathematics. Teachers must take the time to reflect on their skills in relation to learning among students, and work together to improve classroom culture. Classroom talk involves responding to and interacting with learner contributions are a shift in practices accounting for towards learners thinking. The organisation structure is important, and it must support and display commitment for mathematical excellence. The NRC (2000) also recommended that in addition to good curriculum and pedagogy, policy and political issues should be taken in consideration. Success in implementing innovative programs requires resolution of conflict between perception of quality mathematics program and the goals of mathematics educators. Heterogenous grouping is difficult to implement, but grouping students be perceived ability is in conflict with the goal of mathematics learning. Students should be capable of seeing connections between mathematical topics; their lives; and their learning. A balance must be struck between the needs of students and content, but integration should not be at the expense of mathematics as overemphasis could result in loss of focus on content. Learning mathematics requires careful construction, and making links and blending content from different disciplines in an attempt to develop a common language. Conclusion A central theme of what students learn is teaching and learning. Teacher-student relationships play a vital role in mathematics education. Mathematical proficiency requires understanding of mathematical ideas; solving problems; and engaging in logical reasoning. Students must be able to think mathematically for learning mathematics. Learning mathematics should be a balance between internalizing mathematics and inventing mathematics. Teachers should be knowledgeable, and be aware of students’ learning for contributing to various aspects of teaching. Teachers’ pre-service knowledge of teaching methods is critical in imparting mathematics education. Teacher-student relationship is integral for successful teaching and learning. Teachers must be knowledgeable of the three main aspects of student mathematical learning including student conceptions; different forms of knowledge; and classroom culture. The situational perspective advocates learning in a classroom culture. References Aultman, L., Williams-Johnson, M. & Schutz, P. (2009). Boundary dilemmas in teacher–student relationships: Struggling with “the line.” Teaching and Teacher Education. 25(5). 636-646. Brodie, K. (2010). Working with learners’ mathematical thinking: Towards a language of description for changing pedagogy . Teaching and Teacher Education. Available: http://sciencedirect.com. Last Accessed October 29 2010. Boaler, J. (2000). 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