Curriculum
The educational theorist Larry Cuban separated the concept of curriculum into four distinct areas, which were official, taught, learned and tested curriculum. The taught curriculum is that which teachers choose to teach, with the choice being independent of the state recommendations, which is the official curriculum. The learned curriculum is that which goes beyond the education revealed in test scores. This includes the knowledge and experiences acquired by the child through the classroom environment. The learned curriculum is largely based upon the processes modeled by the teacher, as the child will learn how to process information in certain ways, and appropriate behaviors to the classroom. The learned curriculum is therefore more inclusive than the taught curriculum, which does not take these extra influences into account. The outcomes of the learned curriculum are often not intentional, where both taught and tested curriculums are planned. The tested curriculum is that which is subject to testing, and is a limited part of the overall curriculum which is taught by teachers and learned by pupils (Cuban, 1995).
The relationship between the curriculums and how subjects are taught will have an impact upon student achievement, particularly if one curriculum is permitted to dominate the others. For example, the taught curriculum is often based upon the teachers' own knowledge, beliefs about how a subject should be taught, and interests in certain subjects (Joseph, 2000: 4). If this were allowed to dominate the teaching then there is the possibility that this would lead to some areas of a subject not being taught, either due to lack of knowledge on behalf of the teacher or personal preference. Allowing tested curriculum to dominate could also adversely affect the students' achievement, as students' may have poor understanding of the taught and learned curriculum and still achieve good test results if the emphasis is placed on tested curriculum. It is considered that tested curriculum is often meaningless unless taught and learned curriculums are also taken into consideration (Joseph, 2000: 4). Therefore it is important that the curriculums be integrated to achieve optimal results (Glatthorn, 2000: 133).
The presentation of learned, tested and taught curriculum may be illustrated through the curriculum at the school for sixth grade mathematics. The curriculum of the unit in which 'measurements' is taught will be examined, which spans six weeks of the semester. The presentation of the three curriculums is outlined in the following table:
Unit Component
Taught Curriculum
Learned Curriculum
Tested Curriculum
Standard measurement tools and units
Why specific units and tools are used to measure specific attributes
How the measurements may be used in real world situations - e.g. engineering
How to choose between different measurements which are available
Methods for measurement
Language relating to measurement
The units and tools which are used for measurement
Mathematical manipulation of measurements
Precision in measurement
The degree of precision in measurements depends on the tool used
Why there are differences between different tools
How to decide on whether precision is appropriate to the task
The degree of precision which is necessary given the situation
Specifying numbers to a given precision
Comparing relationships through ratios
Why ratios are useful
How ratios are used in the real world for comparing things - e.g. maps
What types of relationships it is appropriate to compare through ratios
How to write down ratios
How to calculate ratios
Amherst Public Schools, n.d.)
Section 2
The role and purpose of the Vermont State Board of Education is to ensure attendance of pupils at school and records of attendance are maintained. They are also responsible for ensuring that there are standards set for student performance and that all students meet these standards. The State Board of Education is also responsible for administering adult education programs, disbursement of funds to schools and ensuring equal access for all to education (Department of Education, 2007).
The strategic plan which has been put in place to meet these goals has five major points:
Support high-quality, innovative instruction to improve student achievement
Provide and promote high-quality educational leadership
Promote safe and positive learning environments
Build department capacity to best support external needs
Practice and promote effective use of all resources (Department of Education, 2006)
At the grade 8 level, there are five standards which are applicable:
Arithmetic, number and operation concepts
Geometry and measurement concepts
Functions and algebra concepts
Data, statistics and probability concepts
Mathematical problem solving and reasoning applications
Each of these standards is accompanied by a set of measurable objectives. For example, to assess arithmetic, number and operations concepts, the measurable objectives used include the pupil being able to demonstrate an understanding of the relative magnitude of numbers, being able to accurately solve problems involving proportional reasoning and applying properties of numbers. These criteria would be assessed and supported through documentation as evidence. To assess the overall depth of knowledge of each pupil, the attainment of each measurable objective is compared to a standardized chart in order to assess the level of achievement reached (Department of Education, n.d.). The Department of Education Web site also supplies teachers supplementary materials which outline the required knowledge which must be demonstrated by the pupil to attain each measurable objective.
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