Teachers as Curriculum Leaders
Introduction:
For the purpose of this assignment, the syllabus under consideration is the mathematics syllabus and the outcome that is to be discussed shall be the level 3 outcome for topic N 3.2. This outcome shall take in consideration the students’ ability to add and subtract numbers that are either whole or in fraction. This is related to a problem solving scenario where the students are not just given the numbers to work on but they are given a word problem that they would have to interpret and then solve in order to understand how the rules of addition and subtraction would work in the real life situations. This paper shall take a look at this outcome in terms of the various conceptions of the curriculum that Eisner and Vallance have laid out in their paper entitled “Five Conceptions of Curriculum: Their Roots and Implications for Curriculum Planning.” Keeping this in mind, it is vital for us to understand that even though it is the children that present us with the outcome of a curriculum, it is the teachers’ job to lead them to it. It is thus very important for the teachers to be professional and that they undergo specific professional development programs.

Conceptions of Curriculum
1. The cognitive process approach to curriculum:
a. Pedagogy In this regard, the teachers would need to focus on ‘how’ to teach the students instead of what they are teaching. With respect to our outcome, it is imperative that the teacher teaches the children to extract the relevant information from a given worded problem and then to figure out whether the addition or the subtraction operator has to be used. This is sometimes very hard to convey to the children and the teachers must find a way in order to get through to the students. It is not just important that the children learns how to add and subtract after reading the problem, it is also important that the teacher finds the right means to get through to the students so that the student not just understands the final result, he/she also understands the procedure and how he/she came to the conclusion.
b. Students’ learning This conception works both ways: it provides the student with a better learning method and it also provides the teachers with an incentive to be better at what he/she is doing since more effort is also required. It enables the student to sharpen his/her intellectual process and also to determine a set of content-independent general cognitive skills that can be applied to learning virtually anything. The learner becomes an interactive part of an adaptive environment, which facilitates exceptional growth. Here, the task of the mathematics teachers become to identify the most prominent and efficient intellectual processes through which they could teach the concepts of addition and subtraction for the students.
c. Resources The biggest resource to be used for teachers here is past researches into this curriculum outcome. It is important that the teachers identify the right tools for this job. There have been many studies and researches into this problem of teaching mathematics to children and the success of the desired outcomes. “Outcome-based education has been of great interest to curriculum planners in the United Kingdom, Australia, Canada and New Zealand (Brady, 1996; Cullingford and Oliver, 2001;Kelly, 1990; Orpwood and Barnett, 1997). They not only advocated outcome-based national curriculum frameworks, but also boosted the use of information technologies within the school curricula” (Cheung and Wong 2002). The biggest finding of many of the researches that have been undertaken on the topic of teaching the right mathematics to the children is that most of the children tend to think of mathematics as a hurdle that they cannot cross. These problems are frustrating not only for the student, but also for the teacher. d. Classroom organisation It is important that the class is organized and the teachers and student work together to overcome all obstacles under this curriculum conception. The problem of teaching maths to children often is not the result of laziness or simple incompetence. While lack of effort in learning can lead to the same outcome, some students experience the problem even though they are working very hard to learn and remember their schoolwork. Recent research in mathematics instruction requires educators to rethink long-established beliefs about teaching, learning, and assessment. In particular, this research underscores the need for problem solving and higher level thinking in mathematics. Consistent with these recommendations, this chapter presents and illustrates four promising themes for mathematics instruction that have emerged from research. These themes--(a) providing a broad and balanced mathematics curriculum; (b) engaging students in rich, meaningful problem tasks; (c) accommodating the diverse ways in which children learn; and (d) encouraging students to discuss and justify their problem-solving strategies and solutions--suggest ways for rethinking the teaching and learning of mathematics in relation to the students of mathematics. (Atkins, 1999)
e. Assessment and reporting Under this conception, the teachers should make sure that the students should (a) learn to value mathematics, (b) become confident in their ability to do mathematics, (c) become mathematical problem solvers, (d) learn to communicate mathematically, and (e) learn to reason mathematically. To accomplish these goals, the council advocates, teachers should decrease their emphasis on complex paper-and-pencil computation, rote memorization of rules and formulas, written practice, "one answer, one method," and teaching by telling. These recommendations for school mathematics are grounded in constructivist theory (e.g., Cobb & Bauersfeld, 1995; Noddings, 1990) and stem from a broad research base in mathematics education (Grouws, 1992).
f. Curriculum design This conception calls for the most basic of curriculum design that the Standards of the National Council of Teachers of Mathematics (NCTM; 1989, 1991, 1995) calls for strategic shifts in mathematics instruction for all students. In essence, these shifts involve a movement toward higher level mathematical reasoning and problem solving, and involve rethinking long-established beliefs about teaching, learning, and curricular practices. Common practice in both general and special education classrooms, however, still reflects a narrow emphasis on computation. This focus is also mirrored in diagnostic teaching and evaluation thrusts (Heshusius, 1991). Not only are such perspectives on instruction and assessment incompatible with the vision of the Standards, but they are also contrary to the findings of recent research about mathematics teaching and learning (e.g., Carpenter, Fennema, Peterson, Chiang, & Loef, 1989; Englert, Tarrant, & Mariage, 1992; Resnick, 1987, 1989; Thornton & Bley, 1994). The National Council of Teachers of Mathematics (1989) proposed five goals for rethinking mathematics teaching and learning.
g. Formal structure of the school and culture of the school Since the teacher needs to be really skilled and professional under this conception, it is important that they attend a Professional Development Program. These programs teach a teacher to help create a learning environment in which students learn to share ideas, work together cooperatively, tolerate differences, disagree agreeably, and take risks. This is like the approach to knowledge production John Dewey (1929) sought—one that empowers teachers with greater understanding of complex situations rather than seeking to control them with simplistic formulas or cookie-cutter routines. It also helps the teachers in understanding how to use Interactive Student Notebooks that allow students to use various writing and graphic techniques to organize and process information. Throughout the past, teachers have been learning new methods of assessment of a class, thereby reaching a higher level of student achievements.
i. The way in which teachers work One of the ways in which the teachers can make themselves better apt at teaching the children is by going through professional developmental programs themselves. The teaching and policy making community has been performing research to establish some effective professional development methods for the past twenty years now. This extensive research has helped institute many “key lessons and principles that can help inform the planning of professional development programs in all areas, including those focused on technology integration. In summaries of the lessons from research, Sparks and Hirsh (1997) describe a shift in effective staff development, away from one-day in-service presentations to professional development that is designed to be an integral, ongoing part of teachers' lives, focused on improving student learning outcomes, based on inquiry into teaching and learning, and built on interactions within professional learning communities.” (NeirTec) It has been noted that teachers trained in professional development programs are very effective with students teachers and are much more likely to enter and stay in teaching than their peers prepared in traditional four-year programs (Andrew and Schwab 1995)

2. Curriculum Technology Approach
a. Pedagogy This approach, as its name suggests, focuses on the medium that is used in order to convey the contents of the curriculum to the children. In the context of our learning outcome, we can say that the usage of computer software and animations is one of the technologies that can be used in order to give a more visually perceptive representation of the problem that the children are trying to solve. In this approach, the knowledge of the teacher is communicated in order to facilitate the learning of the students. In our context, the technology is not just using computers; it can also be to use certain psychological measures, such as reinforcing behavior and feedback mechanisms, in order to teach the most effective way of solving the mathematics problems. It is important that the teacher assumes a very systematic approach and become extremely predictable so that the students do not have any problems when determining the right path to the solution of worded arithmetic problems.
b. Students’ Learning Some of the themes that the teachers have to keep in mind while conducting mathematical education with the technology approach to children with the outcome of teaching them word problems involving arithmetic would include the following. Providing a broad and balanced mathematics curriculum; Engaging students in rich, meaningful problem tasks; Accommodating the diverse ways in which children learn; and Encouraging students to discuss and justify their problem-solving strategies and solutions. In essence, these themes embrace the philosophy that students benefit from rich, challenging programs that promote mathematical thinking.

c. Resources The main resources to be used in this approach would be the various technological equipment such as computers, etc.
d. Classroom organisation Cooperative learning should be encouraged, as this continues to prove its effectiveness in many facets of mathematics education. Not only does cooperative learning promote achievement with many levels and types of students but as students work together in groups, communication and interpersonal-relations skills are refined. Students in small groups are more involved with the subject matter and with one another than they are in whole-group mathematics contexts.
e. Assessment and reporting In accordance with the current mathematics syllabus for years 1 to 10, we find that the outcomes that are usually desired by the teachers are not met, not because of any deficiency on the students’ part but because the teachers are not competent enough. Many teachers who are still engaged in the older, more traditional styles of teaching do not really help the children develop the right skills for solving mathematical problems. There are those, however, who follow a more modern and more efficient style of teaching as proposed by Dewey, Jerome Bruner and C.S. Lewis. Their ideas about teaching and the methods of teaching something to students revolutionized the way that teachers teach. Before these people exerted their ideas, a typical classroom was a boring place and the method of teaching in a class a monotonous and tedious affair. The students would not really grasp what was going on in the class because of the mundane methods employed by the teachers. The ideas of such like Dewey and Bruner paved a way for a new insight into teaching.

f. Curriculum design The curriculum designed should focus on the use of software and other applications in order to teach children that mathematics can be fun and joyful.

3. Self-actualization approach
a. Pedagogy It is important that the students feel a sense of achievement once they have completed the task and the desired outcome has been reached. The student must feel that the curriculum has been designed in order to foster the specific growth of that one child only. The child must find his/her way to personal liberation and development through the contents of the curriculum. Being proficient in mathematics and being able to extract the relevant arithmetic information from the worded problem is sure to give the students a boost in their self esteem when they feel that they have indeed achieved something. If a student feels that he/she has in fact achieved something from this particular outcome of our curriculum, then only can we be sure that all the requirements for the completion of the learning objectives have been made.
b. Students’ Learning This approach is more didactic and student centered, which is what is meant by the pedagogy of the curriculum. The children perceive their success when the outcome holds true for them. Thus a student learns that if he/she can solve an arithmetic word problem, he/she is satisfied. This also ties in with the students’ learning abilities as this outcome allows for the children to learn a lot of things that they will face in the latter years of their lives. Our worded problems provide the basis for the understanding of other social problems that the students are likely to face in their latter years. All the mathematical problems that we are to ensue in the older stages of our lives usually stem from the proper wording and their proper interpretations of the ongoing events. This learning objective of teaching the children to interpret the correct arithmetic meaning from the problem enables them to be able to comprehend the mathematics behind many of the situations that they are likely to incur. Some examples include the calculation of stock dividends and the basic conceptual understanding of many of the physical as well as chemical laws. In our context, our outcome provides a link for the student to comprehend the basic mathematical procedures in the context of the real world problems that they are likely to face.
c. Classroom organization It is imperative that the teachers include the students in the study and discussion about mathematics. For instance, Bruner introduced his ideas about the nature of learning and spoke about his observations of a teacher-student environment. His ideas depicted a large improvement on the ways that these tow groups should interact. He identified such notions as the students’ potentials for growth, their levels of interest in educations and the students’ analytical abilities. Dewey, like Lewis, was an advocate of an informal way of teaching to the students so that the students would learn more. His ideas worked to expand Bruner’s ideas about the nature of students and incorporated the characteristics of the students into his theory of the best way to teach them. Dewey stressed that a healthy and friendly student-teacher interaction and a sound learning environment was necessary to maximize the amount of education that a student could receive.
e. Curriculum design The curriculum designed under this conception would be different from the ones designed in other conceptions on the basis that this would provide more for the personal development of the students. But at the same time, it should be familiar to all educators. “Behavioral objectives, time on task, sequential learning, positive reinforcement, direct instruction, achievement testing, mastery in skills and content, and teacher accountability are essential concepts used in practice and research. The measured curriculum should neither be condemned nor used exclusively to direct curriculum practice and research. It must be recognized for its strengths and limitations. It is compatible with some of the major educational outcomes valued by society-a store of knowledge about the world, command of the basic processes of communication, and exposure to new content areas. But this conception and design of curriculum cannot accomplish everything students are expected to learn” (Klein).
f. The way in which teachers work The teachers should involve themselves more with the children under this conception and try to work more on a one-to-one basis to make the most of this curriculum design. They have to make sure that the teacher and the children are able to communicate with each other on a level that allows both of them to exchange the information effectively.

Work Cited

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