Techniques and Strategies Utilized in Teaching Mathematics - Essay Example

PGCE MATHEMATICS; MADE TO MEASURE due: PGCE Mathematics; Made to Measure Introduction Teaching is a profession that attracts comprehensive and specific view to the subjects, techniques, teachers, and students among other variables in the learning environment. The techniques and strategies utilized in teaching vary with age, subject, individual capability, and general comprehension of the content. There are insurmountable variables in teaching, since even society has contributed that is often in the form of misconceptions or predetermined prejudices (Anghileri 2006: 45). One of the popular prejudices in education is that mathematics and sciences are preferential to boys as opposed to girls. However, with time, research and unbiased techniques of teaching, girls perform just as well, if not better, than boys’ performance in the traditionally boy-oriented subjects. My focus in this report is avoiding the findings of the Ofsted report of 2012 of the increase in the number of underachievers with age, considering my current age group of students between 5-8 years. Following the concept of mathematics as a science, there has been a tendency of students avoiding the subject. However, recent trends have suggested an increase in the number of students studying the subject. The reasons behind the growing interest in mathematics are the topic of discussion in this study with a particular interest being in the GCE and A level mathematics. The roles played by the teacher, student, and government influencing the rapid mathematics students’ numbers are subject to observation (Hill, Rowan, & Ball 2005: 379). The participation of students does not automatically translate in the grades in school, but it has been noted that the younger students perform better compared to the elder students. Economic, social, political, environmental, as well as self-oriented variables, determine the popularity of mathematics in the UK, as with other regions of the world (Askew, Brown, Rhodes, Wiliam, & Johnson 1997: 2). Problem statement The uptake in the students taking mathematics has not had its challenges. Students who take up mathematics as a newfound interest do not necessary mean they excel in the study. Effective teaching of students has to account for the indifference between students, especially in the case of scholarly abilities. Types of students, categorically underachievers, average achievers, and overachievers need different teaching techniques with respect to effective lesson planning (Ofsted 2008: 8). Most practises where the teacher assumes the majority of students in the class determine a teaching strategy. Assuming that an average-achiever’s approach to teaching is effective may be less than optimal, as some students will show disinterest for lack of a challenge. Following the Ofsted report (May 22, 2012), three areas need improvement to ensure effective mathematics teaching in England: Inadequate efforts towards students who easily fall behind (underachievers). They are identified as students who are below the standard scores. At seven years old the number is 10%, doubles at age eleven to 20%, and doubles again at sixteen to 40% of the classroom. Weakest teaching is subjected to pupils who are categorized as having lesser ability and age. Individual schools implemented satisfactory teaching approaches, but a number of schools showed inadequate teaching approaches. Unsatisfactory potential realization for students in primary schools. The largest lot of students (37, 000) achieved a mere grade C in GCSE mathematics in 2011. The results were further supported by evidence, which suggested the introduction of young students to GCSE mathematics resulted in a higher number of students achieving lower grades, than higher grades. Justification Teaching mathematics demands a student specific technique, such as visual depiction of problems or peer-assisted structural training, among others. It is logical that not all students in any randomly chosen class possess the same skills and capabilities (Lobato, Clarke, & Ellis, 2005: 128). Therefore, it is unavoidable that some students excel better compared to the performance of their classmates. The objective of conducting the study on the effectiveness of teaching in the mathematics class is to encompass as much of the students in result and comprehension oriented training. The challenge that mathematics teachers face is keeping the number of students falling behind from increasing, especially exponentially as the students grows (Martin 2007: 78). As the students advance academically, there is a lack of realization in the importance of mathematics. Following the statistics by the Ofsted report, the number of students who can be considered overachievers in mathematics is well below half the class population in college (Ofsted 2010: 12). Teaching can be challenged from the argument that mathematical concepts increase in difficulty with every step up in the class grades. Exploration of radical ideas such as incorporation of technology in mathematical instructions present future opportunities that might be helpful in minimizing the disconnect that comes with aging of the students, consequently the falling grades. Literature Review The classroom, especially in teaching mathematics, is a complicated system that engages parties on interpersonal and intra-personal levels. It is by this assertion that the principles of pedagogy are recommended (Anthony & Walshaw 2009: 149). The principles encompass the following: • Teacher knowledge and learning • An ethic of care • Tools and representations • Arrangements for learning • Making connections • Building on students’ thoughts • Worthwhile mathematical tasks • Assessment for learning • Mathematical language, and • Mathematical communication The pedagogy approach as discussed by Anthony & Walshaw (2009: 148) makes claims on the variables to the classroom under investigation. The first claim is that all students are viable candidates as mathematics learners with no limitations to age, founded on the formation of mathematical identities. This claim contradicts the Ofsted report that shows a decrease in the number of students over average in the classroom. The second stipulation by Anthony & Walshaw (2009: 149) and is that the pedagogy principles are formulated with sensitivity and respect in interpersonal relations, incorporating multiple cultural heritages, thought processes and simulation of everyday classroom realities. The focus of the study is on the achievement of desirable academic outcomes, resulting from conceptual understanding, procedural eloquence, tactical competence, and adaptive cognition (Anthony & Walshaw 2007:149) showed by the students (Steinberg, Empson, & Carpenter 2004: 250). Finally, the study commits to enhancement of holistic citizen productivity by engaging in social outcomes affiliated to mathematics. The student and teacher are the primarily elemental entities to the mathematical discourse. Considering the classroom, there are environmental variables that contribute to the outcome. It is vital to note that students learn as a group, and the teacher is responsible for instilling mathematical identities, (Anthony & Walshaw 2009: 159). It is the duty of society and authorities to facilitate the process. Computation of figures, as is the essence of mathematics, can be captioned other titles as it is with Askew et al.’s article. The reference numeracy, based on the definition provided in the article, revolves around the concept of processing, communicating, and interpretation of numerical information in various contexts (Askew et al. 1997: 6). The process of ensuring the aims of teaching numeral literacy achieved is founded on the capability of the teachers, with respect to their principles of operation in the classroom. As Askew et al. emphasize in their study, teachers are categorical to mathematics since they are tasked with the responsibility of identifying promotional factors influencing numeracy at the primary stage, and consequent strategies that would facilitate the application of such factors into practice (Askew et al. 1997: 6). By defining the role of the teachers, the efficiency at which numeracy lessons are conducted was defined. The characteristics of an effective teacher are covered the ability to acquire knowledge and facilitate the integration of understood concepts (Sullivan, Mousley, & Zevenbergen 2006: 136). This is achieved within a network by using techniques and strategies that allow the application of skills, and learning to apply the knowledge in different numerical contexts. The degree to which the teacher is effective is a measure based on the teacher and pupil behaviour and the pupil outcomes (Askew et al. 1997: 10). The study confers with other researchers who focus on the connection between the student and teacher as the key to mathematical progression. The teacher is expected to make adjustments and adapt to the classroom, as a professional, thereby involving strategies and techniques that would engage the students on a personal and interpersonal level (Thomas & Chinnappan 2008: 172). Structures based on both student and teacher is encouraged, as the capability of pupils is factored in this analysis. In a study done by Ofsted, it is argued that there are two traits that affect the assimilation of mathematical concepts. The report considers ability and age as the factors determining the student outcomes in mathematical studies (Ofsted 2011a: 17). Reference to the teaching strategies used in nursery schools is a pillar in Ofsted’s argument on age, ability and strategy. The younger children, who have shown a higher understanding of mathematics, with respect to their grade level, are engaged in interactive strategies that incorporate everyday activities aimed at establishing mathematical concepts. The involvement of adults in the activities establishes the foundation of mathematical language, thereby developing the vocabulary of children at the lower grades. The approach that is used by the teachers in the lower grades focus on the children left behind, to those that have understood the concept (Ofsted 2012: 4). This is founded on the concept that the overachievers do not advance their skills by engaging in activities whose concept they have understood (Ofsted 2012: 7). In the same report, it is reported that where the children are not able to interact with the ‘physical-mathematical’ objects (shapes, objects, blocks, and others). There is depreciation in the children’s ability to draw mathematical concepts from play. Therefore, mathematical depth is absent. In addition, children’s interaction in the absence of adults is noted to lack mathematical depth, and concentrates on the superficial features of the objects (Ofsted 2012: 63) are thereby decreasing the comprehension of mathematical concepts. The ability of a child develops with age, but importantly determined by the strategy and approach used in the teaching of mathematical principles. Ability is pegged to age but in stages of cognition. Once a student comprehends a mathematical principle, introducing a new principle stimulates the learning process, but in a classroom environment, this growth is standardized (Watson & De Geest, 2005: 224). Considering the curriculum of most education systems, the principles of mathematics get tougher with age, and more activities should be devised to inculcate mathematical language in the understanding of even more complex concepts, despite age. According to the Ofsted report, the authority in charge of introducing measurements in mathematics should be involved in programs that facilitate mathematical language and consider the variation across schools (Ofsted 2011b: 10). Anthony and Walshaw, in their definition for mathematics, include regional disparity by referring to the subject as a universal study. Mathematical practises transcend different subjects and hence are founded on a unique language. Unlike languages, mathematics is founded on comprehension of numeracy. The skills are instilled in young children, and schools are responsible for most of the mathematical education. The pedagogy of mathematics is founded on the assumption that all students can be taught mathematical identities, although due to personality, strategies and ability, there exists variations (DFES 2005: 6). The pedagogy of mathematics as discussed in the introduction, are successful where the entities are positive. An example based on this claim is that classes where an ethic of care exist, there is a higher chance of acquiring mathematical identities and proficiencies (Anthony & Walshaw 2007: 7). Under arrangements for learning, an environment that encourages individual and collective problem-solving is encouraged (Anthony & Walshaw 2007: 9). Teachers are expected to make use of what the students already know, and use this as a platform to catapult to more complex identities and proficiencies (Anthony & Walshaw 2007: 11). Incorporation of examples in the classroom environment is needed as worthwhile tasks influence how the students view, develop and comprehend mathematics (Anthony & Walshaw 2007: 13). In addition, connections in the relationship between the pupils and student are needed to solve problems and represent mathematical expressions and relate the experience to everyday experiences (Anthony & Walshaw 2007: 15). Assessing the students, with the aim of establishing the standard at which the students are thereby developing a plan to support them is an important element in the pedagogy principles. It virtualizes the students’ thought process and enables the establishment of support plans (Anthony & Walshaw 2007: 18). Dialogue that facilitates mathematics argumentation is another principle to the teacher-student interaction, helping students explains and justifies claims Anthony & Walshaw 2007: 19). This is only possible if the teacher can formulate a common syntax in language with which to communicate ideas and facilitate student understanding (Anthony and Walshaw 21). Teachers are also expected to select tools by which to influence the thinking of students, as well as support the student ideas (Anthony & Walshaw 2007: 22), and this is only achievable if the teacher has gathered adequate knowledge to serve the needs of the student (Anthony & Walshaw 2007: 25). A report conducted by The National Centre for Excellence in the Teaching of Mathematics (NCETM) and Swan expounds on the identified practises towards effective mathematics. As reported by NCETM and Swan (2012: 2) a teacher should engage in the following practises for the mathematical teachings to be effective: • Engage informative techniques that accommodate students’ learning needs allowing building on what the students know (Smith 2004: 19) • Get involved in discussions and exposes of mathematical misconceptions by society, students, as well as the environment, while incorporating other phenomena that suppress mathematical identities and proficiencies • Promote mathematical thinking by using higher-order questioning techniques that emphasize on explanation and application, as opposed to recall • Ensure that students are engaged in individual reflection, prior to participating in collective and whole-class activities • Using collaborative tasks and encourage reasoning founded answering techniques • Establishing a connection between mathematical concepts and the real world as this is the foundation of mathematical language • Facilitate the mathematical learning by encouraging productive incorporation of technologies in class work. • Engage in mathematical challenges as opposed to being involved in pre-empting the challenges, inculcating the idea of possible obstacles (Swan 2006: 8) • Engage in communicative activities that encourage mathematical language formulation • Identify what’s learnt, how it was learnt and therefore formulated a plan of how it should be learnt From the recommended practices, NCETM and Swan (2012: 4) have suggested acts to follow in improving mathematical teachings. The first suggestion is increasing the provision and quality of mathematically oriented development opportunities. Sharing of experiences and resources is another recommendation to the participants of the learning process (Zevenbergen & Lerman, 2008: 115). Assessment in the external assessment testing should also consider revision of the quality stages by which tests are set, and encourage the incorporation of standards in expounding on methods and strategies of teaching mathematics. Methodology I conducted the research of this paper by making use of previous work by other scholars. The hypotheses that are generated from the analysis focus on the students, teachers and government, and their role in the mathematical proficiencies. The first argument that is derived from the research is the break between the government and educational authorities in charge of standardizing mathematics and setting external examinations. Secondly, the teacher-student relationship is influenced by society, its misconceptions on mathematics and the attitude of the teens and young adults to the subject. Finally, the curricula must encompass a means of assessing student ability and development that does not solely rely on the grade outcome. Research was conducted on the interest and scores in mathematics, in an effort to promote mathematics as a study. The rate at which the uptake of mathematics in lower classes has been on the rise presents a quest for a study. The research conducted targeted establishing the reasons behind the failure in mathematics in the higher grades as opposed to the lower grades. Research conducted studied the social and educational trends where the key investigation concentrated on the failing grades of the students in the upper grades. The research was influenced by factors such as peer pressure, environment, resource availability, teaching strategies, techniques, and policies. The subject of the research was based on how the students relate to their mathematical scores and the expectations of the teachers and the resulting failure in meeting the government and ministry standards. Discussion Teachers are bound by professional obligations to deliver education to the students, and the curriculum is the guide offered to regulate the process. Since teachers are expected to deliver quality education, irrespective of the classroom environment, creativity must be encouraged in adapting strategies to facilitate a collective improvement in mathematical communication and problem-solving. Collaboration between the involved stakeholders is needed to standardize mathematics according to the ability and capability of students while accounting for more than the grades scored from external examinations. Progress in mathematical proficiency should not be founded in the curriculum, but rather the strategies and techniques used to interact with different student groups. Conclusion In conclusion, the strategy assumed by the teachers reflects upon the relationship between the students and teacher. Practice needs variation and adaptation, since the classroom is not specific to a single profile of students. A classroom may sometimes have an average of overachievers or underachievers, depending on race, parenting approach, exposure, and home environment. Variables affecting students influence individual performance, in different subjects, but the methods used in the classroom are important towards establishing the most productive approach. Bibliography ANGHILERI, J. (2006). Scaffolding practices that enhance mathematics learning. Journal of Mathematics Teacher Education, 9, 33–52. ANTHONY, G., & WALSHAW, M. (2007). Effective pedagogy in mathematics/p‚ngarau: Best evidence synthesis iteration [BES]. Wellington: Ministry of Education. ANTHONY, G., & WALSHAW, M. (2009). Characteristics of Effective Teaching of Mathematics: A View from the West. 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