[Essay] Teaching Mathematics

Introduction

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.

Discussions

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.

Synthesis

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 (www.encylopedia.com).

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.

References:

Alsup, J.K. and Sprigler, M.J. (2003) A Comparison of Traditional and Reform Mathematics Curricula in an Eighth-Grade Classroom, Education. Volume: 123. Issue: 4. Publication Year: 2003. Page Number: 689

Au, K. H. (1993). Literacy instruction in multicultural settings. Austin, TX: Harcourt Brace College Publishers.

Biber, B. (1984). Early education and psychological development. New Haven, CT: Yale University Press.

Bredekamp, S. (Ed.). (1987). Developmentally appropriate practice in early childhood programs. Washington, DC: National Association for the Education of Young Children.

Brown, D., & Rose, T. (1995). Self-reported classroom impact of teachers' theories about learning and obstacles to implementation. Action in Teacher Education, 17(1), 20-29.

Burts, D. C., Hart, C. H., Charlesworth, R., Fleege, P. 0., Mosely, J., & Thommason, R. (1992). Observed activities and stress behaviors of children from developmentally appropriate and inappropriate kindergarten classrooms. Early Childhood Research Quarterly, 7,297-318.

Charlesworth, R., Hart, C. H., Burts, D. C., & DeWolf., M. (1993). The LSU studies: Building a research base for developmentally appropriate practice. In S. Reifel (Ed.),Advances in early education and day care: Perspectives on developmentally appropriate practice (Vol. 5, pp. 3-28). Greenwich, CT: JAI.

Charlesworth, R., Hart, C. H., Burts, D. C., Thommason, R. H., Mosely, J., & Fleege, P. O. (1993). Measuring the developmental appropriateness of kindergarten teachers' beliefs and practices. Early Childhood Research Quarterly, 8, 255-276.

Cotton, K. (1996). School Size, School Climate, and Student Performance. Portland, Oregon: Northwest Regional Educational Laboratory.

Cushman, K. (1997). “Why Small Schools are Essential.” Horace (January 1997).

Fang, Z. (1996). A review of research on teacher beliefs and practices. Educational Research, 38(1), 47-65.

Gardner, H. (1995). Reflections on multiple intelligences: Myths and messages. Phi Delta Kappan 77:200-209.

Graue, M. E. (1993). Ready for what? Constructing meanings of readiness for kindergarten. New York: State University of New York Press.

Hendrick, J. (1996). The whole child: Developmental education for the early years (6th ed.). Englewood Cliffs, NJ: Merrill.

Hindle, D. (1996). Planning together: Positive classroom environments. Diversity in the Classroom series, number four. Paper developed by the Saskatchewan Professional Development Unit, Saskatchewan, Saskatchewan Instructional Development and Research Unit, Regina. (ERIC Document Reproduction Service No. ED 434 889)

Hyson, M. C. (1996). Theory: An analysis (part 2). In J. Chafel & S. Reifel (Eds.), Advances in early education and day care: Theory and practice in early childhood teaching (Vol. 8, pp. 41-89). Greenwich, CT: JAI

Ilg, F. L. & Ames, L.B. (1965). School readiness. Behaviour tests used at the Gesell Institute.

Katz, L. G. (1994). Knowledge of child development and the competence of developing teachers. In D. Day & S. G. Goffin (Eds.) ,New perspectives in early childhood education: Bringing practitioners into the debate (pp. 124- 1310). New York: Teachers College Press.

Lee, Valerie E. and Smith, Julia B. (1996) “High School Size: Which Works Best, and for Whom?” Paper presented at the 1996 annual meeting of the American Educational Research Association in New York.

Lewitt, E. M. & Baker, L. S. (1995). School readiness. The Future of Children, 5, 128-139.

May, D. C., & Kundert, D. (1997). School readiness practices and children at risk: Examining the issues. Psychology in the School 34(2), 73-84.

Mevarech, Z. R., & Kramarski, B. (1997). IMPROVE: Multidimensional method for teaching mathematics in heterogeneous classrooms. American Educational Research Journal, 34(2), 365-394.

Peterson, R. W. (1994). School readiness considered from a neuro-cognitive perspective. Early Education and Development, 5, 120-139.

Sharp, R., & Green, A. (1975). Education and social control. London: Routledge & Kegan Paul.

Spidell, R. A. (1989). Play in the classroom: A descriptive study of preschool teachers' beliefs. Early Child Development and Care, 41, 153-172.

Tanner, C. K., & Galis, S. A. (1997). Student retention: Why is there a gap between the majority of research findings and school practice? Psychology the Schools, 34(2), 107-114.

Tunney, K. (1996). Growing stronger: Teaching and learning responsibility. Diversity in the Classroom Series, number three. Paper developed by the Saskatchewan Professional Development Unit, Saskatchewan, Saskatchewan Instructional Development and Research Unit, Regina. (ERIC Document Reproduction Service No. ED 434 888)

Wing, L. (1989). The influence of preschool teachers' beliefs on young children's conceptions of reading and writing. Early Childhood Research Quarterly, 4, 61-74.

Zimiles, H. (1993). The adoration of "hard data": A case study of data fetishism in the evaluation of infant day care. Early Childhood Research Quarterly, 8, 369-385.

Appendix

Lesson Plan - Mathematics

School - Allfarthing Primary school, London

Class - Reception class

Date - 24/11/04

Subject - Mathematical development

Resources - Text - One mouse, twenty mice. Worksheets

Learning Objectives

* To be able to recognise, count, order and use numbers up to 20

Key vocabulary- Count, Numbers 1 to 20

Key questions - Can the children recognise numbers 1 to 5, 1 to10 or 1 to20

Can they count reliably on a 1.1 basis to 5, 10 or 20

Content (activity - organisation - differentiation)

* Gave children individual cards with a number between 1 to 20. Calls out a number and the child with the number card raises it to show the class.

* Introduce tittle authour and illustrator of book - one mouse, twenty mice.

* Read text to whole class. Counting the mice together on each page.

* Where is the cat hiding on each page?

* Teacher reads book again and children describes where the cat is hiding.

*Home corner *Book corner - Children to learn about numbers in number books

Possibilities for assessment-

* Can the children recognise numbers 1 to 10?

* Can they rote count to 20?

* Can they count on a 1.1 basis to 5, 10 or 20

I.C.T opportunities

Harry To work with number train programme on computer.

Poppy

Class information

AA - Above average

Av - Average

BA - Below Average

Activities

AA - To write over numbers1 -10 and write some of their own.

Av - To write over numbers 1 - 5 and write some of their own.

BA - To work with me, counting dinosaurs and recognising numbers 1 to 10 ( evidence attached )

2 children - to practice writing on the board.

Evaluation

As the children settled on the carpet, they were given a number card each. They discussed their number with the child next to them until they were all seated and focused. Then I call out a number and the child with the number shows it to the class before handing the card over to me. Where a child is not sure of the number with him I call out the child with the number and discuss the number with the class. For example, child A has number 17 and when I called number 7 he raised it up to show the class. I took both numbers and explained to class that number 7 has one number in it whilst number 17 has two numbers, a 1 and a 7 in it. The 1 is always before the 7 to make 17. My explanation was brief because numbers 1 to 10 is the target for the class and only children above average could be stretched to 20.

The colourful text was introduced to the class. It attracted the children and made them want to count the mice and find the cat. We counted the mice and was able to tell where the cat was hiding on each page. After this I worked with a group of children reccognising numbers and counting dinosaurs.

CHILD A -

Teacher - Can you tell me what these numbers are?

1 4 2 3 5 6 8 10 9 7

1st attempt - correct correct correct correct correct # # # correct #

2nd attempt - correct correct correct correct correct correct correct correct correct correct

*6 - "I think this is 9". He looked at it again and counted 7, 8, 9 in his head then he looked at the numbers on the window counted 1 to 6 and shouted 6

*8 -" this sounds like 7"

*7 - he pointed first to 5 before saying 6. After asking again he said "I think it's 7

Next we counted dinosaurs on 1 to 1 basis - 1, 2, 3, 4, 5, 6, 7,- - - 11, 12, 13, 14- - - 16- - - 20. After 2 minutes he counted another set of dinosaurs one after the other - 1, 2,3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14 - - -16

Child B -

Teacher - What are these numbers?

1 4 2 3 5 6 8 10 9 7

1st attempt correct correct # # #

*3 - I asked him to look at this number and tell me what it is called. at first he said 5, then I don't know and he started rote counting 1, 2, 3, 4. 5, 6. He shouted 6 before I told him the answer.

*5 - I asked him what this number is. He looked up the window and said" That is em- - - - 2, oh this is 2 ( pointing to 2 ). What do you think the number is? I asked. ( after thinking again, he said 5 )

*8 - what's this number I asked? He looked up to the window, pointed to it and I asked him what it is called. He started counting from 5 in his head and asked if it is 20? He then admitted he doesn't know numbers. We stopped because I felt he was not ready for the task yet.

We looked at the large numbers on the windows pointed to each one (1,2,3,4,5) while he showed me the same number on our worksheet. He recognised them and pronounced them right. Then we tried again, this time I picked the numbers at random. He called 3 ( 5), and 5 he called (4). We counted 1 to 5 rotely again, then pointed to 2, asked what it's called. He got it right, pointed to 1 and he was right but when I pointed to 5 again he called it 3. We concluded by rote counting 1 to 5 and pointing to the large numbers on the window.

Next I gave him 7 dinosaurs to count. He touched them without moving any aside and counted 1,2,3,4,5,6,7- - -10

Child C - Can you tell me what these numbers are?

1 4 2 3 5 6 8 10 9 7

1st attempt correct correct correct correct #

Child C recognised numbers 1, 2, 3, 4 at random very well. When we got to 5, he counted the numbers on the window and said 6. I asked him to try again, then he said 2. I showed him the number 2 and number 5. But he was adamant and tried to convince me I have written 2 upside down. I brought the large 2 and 5 from the window showed him the difference and turned the number 5 upside down. We talked about the shape and how it is written. It was now time for assembly and we had to conclude the session with him. Before we finished, he was only able to count up to 5 dinosaurs on a 1.1 basis.