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[Essay] Teaching Mathematics

This paper discusses the “Factors Affecting the Academic Performance of Children in Math particularly in counting”. Basically, the research will analyze and investigate the different variables that affect the learning capabilities of the students. This shall include a discussion on the positive and negative variables related to the academic performance of the students in mathematics; an analysis of performance of the Allfarthing Primary School students in relation to mathematics education stability was also conducted. Particularly, the research will focus on examining the impact of these variables to the progress of both the student and education system. 

In this changing world, those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their future (NCTM, 2000). On the other hand, Mevarech, Z. and Bracha Kramarski (1997) developed the instructional strategy that can be applied to heterogeneous classrooms in their study "IMPROVE-Multidimensional Method for Teaching Mathematics in Heterogeneous Classrooms". The strategy, IMPROVE, (Introducing new concepts, Metacognitive questioning, Practicing, Reviewing and reducing difficulties, Obtaining mastery, Verification, and Enrichment) has been proven to keep mathematics progress at a constant pace throughout the school year. The academic group as a whole continued to progress, and the progress of one academic group does not come at the expense of the other groups. It is important for teachers to have consistent strategy they could use in their teaching. The study of Alsup, J.K. and Sprigler, M.J. (2003), shows that the classroom teacher's perspective should consider the cost and time being spent by teachers and school district to implement reform math. Moreover, a reform mathematics curriculum is expensive to implement; teachers must be trained and supplementary kits must be purchased. Such expenses, in the author’s opinion, are questionable, since a reform mathematics curriculum did not promote an increase in the student achievement. In classroom, a traditional mathematics curriculum was superior with regard to teaching skills and procedural competency and, thus, would help students at the high school level, since success in high-school math courses in school district is "built upon the foundation of facts and procedures." Alsup, J.K. and Sprigler, M.J. (2003). Basically, Alsup, J.K. and Sprigler, M.J. (2003) statement should be considered since it depicts the future of mathematics education. In connection to cost and time being spent to receive quality education, the teachers and school administrators should give extra effort in designing teaching strategies that is applicable to London education. On the other hand, in relation to the variables of learning, the school environment is the broader context of the school that allows for classroom instruction and student learning (Tunney, 1996). A transformation to a community should take place throughout the school wide environment by maximizing the number of positive interactions with students and parents. Teachers are capable of producing profound and positive changes in student behaviours and learning by effectively modeling the positive processes, skills, and attitudes that parents teach (Hindle, 1996). 

School Size
Recent research on the effect of school size on student achievement indicates that a small school strategy may be a powerful school improvement model. While there is no single definition of “smallness,” some research indicates that an effective size for an elementary school is in the range of 300-400 students and that 400-800 students is appropriate for a secondary school (Cotton, 1996). Lee and Smith (1996) argue that slightly larger secondary schools, from 600-900 students, are necessary for good curricular diversity. On the other hand, small school advocates such as Deborah Meier and Ted Sizer of the Coalition of Essential Schools, believe that no secondary school should exceed 300 students (Cushman, 1997). For both elementary and secondary students of all ability levels and in all kinds of settings, research has repeatedly found small schools to be superior to large schools on most measures and equal to them on the rest. A recent review of 103 studies identifies the relationship of school size to various aspects of schooling (Cotton, 1996): Academic achievement in small schools is at least equal, and often superior, to that of large schools. The effects of small schools on the achievement of ethnic minority students and students of low socioeconomic status are the most positive of all. Student attitudes toward school in general and toward particular school subjects are more positive in small schools. Student social behavior, as measured by truancy, discipline problems, violence, theft, substance abuse, and gang participation, is more positive in small schools. Levels of extracurricular participation are much higher and more varied in small schools than large ones. Student attendance is better in small schools than in large ones, especially with minority or low SES students. A smaller percentage of students drop out of small schools than large ones. Students have a greater sense of belonging in small schools than in large ones. Interpersonal relations between and among students, teachers, and administrators are more positive in small schools than in large ones. Student academic and general self-regard is higher in small schools than in large schools. Students from small and large high schools perform comparably on college-related variables, such as grades, admissions, and graduation rates. Despite the common belief that larger schools have higher quality curricula than small schools, no reliable relationship exists between school size and curriculum quality. Larger schools are not necessarily less expensive to operate than small schools. Small high schools cost more money only if one tries to maintain the big-school infrastructure (e.g., a large bureaucracy). Apparenlty, in order to provide an optimal learning environment for students, one must first work to establish a classroom community (Au, 1993). A classroom community provides each child with space to develop specific capabilities and to experience a sense of inner balance and wholeness in a community with others. The school environment is the broader context of the school that allows for classroom instruction and student learning (Tunney, 1996). A transformation to a community should take place throughout the school wide environment by maximizing the number of positive interactions with students and parents. Teachers are capable of producing profound and positive changes in student behaviors and learning by effectively modeling the positive processes, skills, and attitudes that parents teach (Hindle, 1996). Bringing members of a class together for certain activities engenders the feeling of belonging to a group and in turn establishes class spirit (Bergin, 1999). With this, students who feel that they belong to a group have power in decision-making and have freedom of choices (Tunney, 1996). The classroom community can be developed by a number of means. Students should develop a process of understanding, sharing, compassion and empathy. The classroom should be referred to by the teacher as "our classroom" rather than "my classroom". The development of a community is moving from doing things TO students to doing things FOR students (Tunney, 1996). 

Developmental Skills and Abilities of Children
Basically, knowledge of child development traditionally has been viewed as a core component for designing activities and evaluating curriculum in early childhood education (Charlesworth, Hart, Burts, & DeWolf, 1993 and Hyson, 1996). In addition, a considerable body of research indicates that teacher beliefs influence decision-making in the classroom (Fang, 1996). In addition, the consideration of the learning skills of the students in mathematics particularly to counting should be understood. Due to the considerable speed and interrelated nature of development during early childhood, early childhood educators tend to approach their mission from a more holistic perspective than do educators of older children. This philosophy of educating the whole child has led early education theorists to emphasize the importance of addressing children's social and emotional needs as well as their cognitive and physical ones (Biber, 1984 and Hendrick, 1996). Echoing these sentiments, the current dominant approach to early education (i.e., developmentally appropriate practice) stresses that education practice should be tailored to fit the developmental level of the children being served (Bredekamp & Copple, 1997). This approach argues that the educational outcomes that teachers focus on should change with children's developmental level, and it cautions against introducing academic content so early in the educational process that children have not attained the requisite developmental skills and abilities to allow comprehension of that content (Bredekamp & Shepard, 1989; Elkind, 1987; Katz, 1994). This early introduction of academic content is not only believed to be ineffective in terms of longterm learning goals, but also leads to increased levels of stress in children (Burts et al., 1992), and likely has a negative impact on their dispositions towards learning and the development of their self-conceptions, Katz & Chard, 1989). On the other hand, early childhood teachers' beliefs about educational practice are shaped both by the training they receive (Brown & Rose, 1995) and by their personal experiences working with children in the classroom (Williams, 1996). Examining these beliefs is important because research indicates that teachers' beliefs influence classroom practice. Measures of teachers' beliefs related to developmentally appropriate practice have been found to be related to their use of instructional methods that are consistent with that approach (Charlesworth, Hart, Burts, Thommason, Mosley, & Fleege, 1993). Similar relations between teachers' expressed beliefs and classroom practices related to literacy instruction (Wing, 1989) and children's play (Spidell, 1989) also have been observed. Despite these findings linking teachers' beliefs to classroom practice, it should be noted that this relation is often less than isomorphic, and that some studies report considerable inconsistency between teachers' expressed beliefs and the teaching methods they use (Sharp & Green, 1975;). Part of this inconsistency can be attributed to the fact that teachers do not always feel free to put their beliefs into practice because of constraints that they feel are imposed on them by administrators, parents, and the demands of standardized testing (Brown & Rose, 1995; Hitz & Wright, 1988). Insufficient professional training also may contribute to the observed inconsistency between teachers' expressed values and classroom practice, because teachers may not always have the skills and abilities they need to bring their beliefs to fruition. Apparently, knowing more about how teachers rate the importance of various developmental skills and abilities is crucial for several reasons. First, it helps researchers and policymakers consider how other factors affecting the early childhood classroom, such as administrative directives and assessment issues, either support or conflict with teachers' beliefs. Second, in that teachers tend to emphasize those skills and abilities that they consider important, knowing what those items are can provide us with valuable insights into teacher decision making. Third, policymakers and educators can highlight particular areas of teacher education and training programs, based on teachers' beliefs concerning the importance of various developmental outcomes. Finally, considering teachers' extensive clinical experience interacting with children on a daily basis, knowing which skills and abilities they see as important can help bring about valuable insights about children and child development (Zimiles, 1993). 

Student’s Readiness
In connection to the factors that lead to errors in counting of children, student’s readiness should be considered. Apparently, there are many factors that directly affect the learning capabilities of the students particularly in counting i.e. external factors (students background), individual differences, teaching methods, learning setting, and behaviour. Thus, the teacher should facilitate an appropriate teaching method that suits to the learning capabilities of the students. In providing a quality teaching method, the teacher should construct a very capable and appropriate lesson plan (see appendix for sample mathematics lesson plan). The term 'readiness in school' is used to describe a number of different understandings of what constitutes the ingredients necessary for a child to make a successful transition from preschool or other prior-to-school setting to the formal school environment. Initially it was regarded as a child characteristic (e.g. Ilg & Ames, 1969). Later, the role of environment in children's early learning became a focus of interest (Graue, 1993) with contemporary conceptions incorporating both views. Currently, the predominant view is that school readiness is an interaction of child characteristics and school capacity to be flexible in meeting the individual needs of children in their initial year(s) of formal schooling (May & Kundert, 1997; Peterson, 1994). Basically, preschool teachers are influential in determining the day-to-day experiences of children in the year(s) before formal schooling as well as in decision-making about whether a child should progress to school (Tanner & Galis, 1997). It is clear that many teachers believe maturation is crucial to the development of skills necessary for a successful transition to school, with many supporting delayed-entry for some and boys being more likely to be retained in preschool than girls (May & Kundert, 1997). Investigations of teacher views of skills considered to be important for successful transition to school have found an emphasis on language abilities, including listening skills, self-confidence and social skills, with academic skills having a relatively lower priority (Lewitt & Baker, 1995). Moreover, for preschooler, adults can nurture preschooler's positive self-esteem by helping them discover what they are good at doing. Part of a child's self esteem comes from feeling competent and skilled at something she or he enjoys. You can play a big role in helping children to be successful and feel good about themselves. A place to start is by creating opportunities for children to explore different objects, activities, and people. Early in life, children show personality traits and preferences for what they like and dislike. By planning learning opportunities with children's unique personality styles in mind, you nuture their positive feelings about themselves. In addition, children learn about the world in many different ways. One educator, Howard Gardner (1995), believes that children's ways of learning can be grouped into different categories. To help children discover their personal abilities and learning preferences, you can provide opportunities that cover the eight different types of learning. Some children have many interests and want to learn about a variety of things; other children are satisfied with one or two kinds of learning and want to focus mostly on them. All children are unique; what is important is that you help them to learn what they are good at, what they enjoy and what makes them feel good about themselves. Recognizing children's unique personality styles can help adults to better understand children and to plan activities that children can learn from and enjoy. Research shows that a child's emotional style, activity level and social nature are present during the first few months of life and are unlikely to change much over time. 

This world is a tremendously huge place. It is a fact that in your existence you will never identify all there is to recognize. But learning is the greatest gift you can give to yourself. Basically, by learning about the world around you, you’re giving yourself the chance to understand just how far we have come since the beginning of man. If it weren’t for learning, you wouldn’t speak or write, you wouldn’t be able to communicate through the use of language, you wouldn’t have the use of things like telephones, televisions, bicycles, cars, and any man-made invention that exists today. In connection to learning development, researches reveal that preschooling is one of the most important stages of brain development which is the considered factors in learning. There is more happening in colorful, wonderfully busy preschools than meets the eye. Fun, role playing, block building, finger painting, laughter, negotiating, singing and dancing are just a few of the types of activities you will see in good preschool programs. Basically, this simple program has a great impact to the learning process of the children. Children are developing the critical but important skills, which are the foundation for life. For the children, families and community it is very important to consider the quality childhood programs. A growing body of research indicates that children who attend high quality early childhood programs benefit socially, emotionally and cognitively. Research shows that children enrolled in good preschool programs tend to have a positive transition into kindergarten, are more successful in later school years and show higher verbal and intellectual development than children who do not attend high quality programs ( Moreover, these children (preschool learners) demonstrate high levels of social competence - self-esteem, social behavior, and motivation - a critical predicator of adult adaptation. Under the guidance of responsive and consistent teachers in a nurturing environment and communication with parents, children learn important social skills such as initiating and developing satisfying relationships with adults and peers; developing the ability to regulate emotions; communicating needs, desires and difficulties; and engaging in age appropriate problem solving; are all acquired. Socially competent preschool children are not only more likely to have success throughout their school years, but are also more likely to make positive contributions to our community. Social competence, along with intellectual and physical development is facilitated in high quality preschool programs by providing children with lots of opportunities to engage in play. Responsive teachers follow children's lead and provide them with developmentally appropriate opportunities to use their imagination, listen to stories, make choices, explore and understand materials and the environment, and exercise their bodies. Preschool programs experience maximum success when they support children and their families. High quality preschool programs make important contributions to our community by nurturing the unique strengths of each child thereby allowing children to reach their full potential. After successfully completing preschool we hope children will have an increased love for self and for learning, and be prepared for a promising future. Ultimately it’s up to the parent to decide what they believe is best for their child, but research shows that starting school at an early age will positively effect their learning process. 

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[Essay] Teaching Mathematics


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