Mathematics Curriculum Analysis, Documentation and Origins - Essay Example

Educational Essay 1st December, Mathematics Curriculum Analysis Curriculum Analysis A curriculum analysis is a tool that helpsdevelop and monitor the learning of students. The goal of the analysis is to make the planned and improvised curriculum to meet the students’ requirements, create policy decisions regarding funding and implementation, pilot tests for the curriculum before implementation and determining the effectiveness and succession in reaching its goals. With a passage of time, this monitoring and instruction leads to more effective instruction. (Citation, year) there are four steps to this process: 1. Determining student requirements This step is the foundation of the curriculum analysis where the needs of the students are deliberated upon with questions like; does the set curriculum match the needs of the students? Does it fulfill the learning development level of their level? Incase the answers to these questions is no, it must be planned of what must done to meet up to the student criteria by considering developmental patterns, community needs, redundancy in existing criterion and student coursework. 2. Policy decisions What resources and material is required is decided in the policy decision making phase. The importance of the course information must be compared to the other topics already introduced in the curriculum. What beats the other topics will replace the older ones, as well as update and enhance previous courses to the advancements made in the schooling environment. Other factors include calculating the number of students who opt for the course, how many students are their in each class, what is their average amount per class. This way expenses and budgets can be emerged as well as planning out how to run the budget most cost effectively. 3. Pilot program Before the new curriculum developed is launched, it must be tested to see whether or not it will fulfill the goals for which it was made through testing it by a pilot program. This allows the developers to indicate accurately how the course is progressing, whether the amount of material provided is sufficient in terms of quality and quantity, and it will help detect any flaws or miscalculations that had not been brought to notice during development. This stage will help rectify all the problems by surfacing them through the pilot testing and will solve them before a large amount of funding be wasted. Genuine assessments and standardized testing will be used to achieve student achievement for e.g. student portfolios, containing each individual student’s records and assessments. Succeeding in this will give a positive sign to mainstream the curriculum throughout the school district and campuses, locally and internationally, so that each student can benefit from a standard program. For those analyses however that fail the pilot program, extensive deliberation and research must be done to evaluate and determine the causes of failure for e.g. insufficient resources to educate the ample amount of students (i.e. supply is less than demand). This assures planners of a better and brighter second attempt. 4. Implementation and Assessment When the curriculum has finally been developed, tested and improved, it must be implemented. Data collection must take place to further increase its efficiency. This is usually done through standardized testing as well as other common computation for e.g. portfolios and records, where needed. Projected goals can then be measured against achieving high quality academics for its student population. Curriculum Documentation and Origins A curriculum is systematically documented by isolating and analyzing targeted features of a specific curriculum. Basing our analysis solely on the subject of Mathematics, this analysis involves defining and isolating a particular set of content i.e. the topics and chapters and then analyzing the performance expectations and consumer demand which will describe students knowledge capacity. This has two main subdivisions i.e. Content Defined as declarative, procedural, tactile and situated knowledge targeted by the curriculum Performance Expectations Expectations of the student capabilities where he/she is expected to know and employ through instructional activities and assessments conducted according to course content Posner (YEAR) also makes distinctions regarding the four levels for which curriculum analysis may occur i.e. intended, enacted, assessed and learned. Level Primary Focus of Curricula Analysis Intended Curriculum Analysis is concerned with examining the content (e.g., declarative, procedural, tactile, and situated knowledge) and the performance expectations, which is the level at which a student is expected to know and use the content as it is communicated in the documents and materials created to give instruction and assessment Enacted Curriculum Analysis is concerned with examining the content and the performance expectations as it is enacted by the instructor in the classroom and in the learning contexts. Assessed Curriculum Analysis is concerned with examining the content and performance expectations represented by the tasks, questions, and performance tasks contained in assessment materials. Learned Curriculum Analysis is concerned with measuring the content and level at which learners enact the performance expectations in a targeted context. Defining a framework for measuring performance expectations Developers must team up and set a pre-defined list of priorities that must be met in order to achieve an accurate curriculum. The first step it to identify a framework for performance expectations that is accountable for the coursework and the subject itself. A perfect example or model for the framework is the Depth of Knowledge (DOK) as this model contains every level of the type of knowledge (procedural, declarative, tactile, and situative) that needs to be included in the syllabus or study curriculum. (Webb, 1997) In this model depicted as a table below, the knowledge and relevance increases with the increase in level. DOK Level Title of Level 1 Recall and Reproduction 2 Skills and Concepts 3 Short-term Strategic Thinking 4 Extended Strategic Thinking This table serves as the basis for all fields of study however considering our subject, Mathematics, this particular model was used to assign a DOK Level to each course objective; with the following that served as common guidelines and assessment for the invigilators: The DOK level should reflect the level of work students are expected to perform in order for the feedback to be deemed as acceptable The DOK level should reflect the complexes of the various processes required by the curriculum outline by its objectives, rather than its predictions The DOK level should be assigned based upon the wants and demands of the students and teachers Evaluators must consider the complexity of the task and information, conventional levels of prior knowledge for students at their specific grade level, and the mental thinking processes used to satisfy the requirements defined in the curriculum objectives Mathematics Mathematics is a key subject that is embedded in every field from biology to general sciences. It enables students to think and communicate quantitatively, indulge in problem solving, recognize situations where mathematics can be applied, and use appropriate technology such as calculators to verify answers and reasoning. This subject’s curriculum stresses upon the development of the student’s estimation, approximation and problem-solving skills with the help of examples that are relevant to the pupils experience. Class and group discussions, virtual experience with materials and activities, and active participant learning is widely encouraged for all age groups stressing upon the importance of the development of mathematical language. The enhancement of numerical skills is essential to every student’s life both in and out of the schooling and learning environment as they are essentially important for educational and personal matters through all walks of life. Mathematics Curriculum The Mathematics Curriculum is standard and made in a form that is understandable and apprehend-able for students world-wide in every level from Pre-K (preparatory-kindergarten) to high-school and above. It is presented in two distinct sections: skill development and topic list. The skills development section describes the skills that pupils should possess and develop as they study this subject in its mathematical procedure. These skills include: Applying and problem-solving Understanding and recalling Communicating and expressing Integrating and connecting Reasoning Implementing Understanding and recalling It also includes a number of sub-divisions which highlights the content outline that is to be included in the mathematics programme for every level. Each category contains a number of individual units which can be classified under these core-curriculum topics: Mathematical projects, assignments and activities Numbers (real, odd, even, negative, positive) Algebra and Arithmetic Mensuration and shapes Measures and Ratios Data Analysis and Configuration The Mathematics Curriculum was officially implemented in the early 2000’s all over the world in English to support an international audience. The advisory service of the Primary Professional Development Service (PPDS) continually supports and motivates teachers and principals of all school districts in their implementation of the subject as well as guides the school staff and board members to enhance and update the curriculum gradually with the advancements brought about in this field of study. Part I Q.1 The curriculum of mathematics was documented since 1999 and refined along the way with the progression of the topic in the proceeding years. This documentation began from accumulating the relevant and necessary topics without which human may seem to find difficulty, for which purpose this topics became necessary to teach to students. It is the foundation of education and lies in the study of every field from engineering and medical to business accounting and finance and economics. I have based my analysis on the Applied Mathematics for Business, Economics and the Social Sciences by Frank S Budnick. The state and national standards relevant to this curriculum is to focus on the topics being taught internationally and to standardize the language to English so that it is easily understood and learned by all. Q.2 This analysis focuses on the core topics that relate to every field of specialization. These chapters are listed below sequentially: Chapter 1 Basic Preliminaries Chapter 2 Linear Equations Chapter 3 Systems of Linear Equations Chapter 4 Mathematical Functions Chapter 5 Linear Functions and their Applications Chapter 6 Quadratic and Polynomial Functions Chapter 7 Exponential and Logarithmetic Functions Chapter 8 Mathematics of Finance Chapter 9 Matrix Algebra Chapter 10 Linear Programming (Introduction) Chapter 11 The Simplex and Computer Solution Methods Chapter 12 Transportation and Assignment Models Chapter 13 Introduction to Probability Theory Chapter 14 Probability Distributions Chapter 15 Differentiation Chapter 16 Optimization Methodology Chapter 17 Optimization Applications Chapter 18 Integral Calculus Introduction Chapter 19 Integral Calculus Applications Chapter 20 Optimization Functions of Several Variables Q.3 The limitations to be found can be the extent of intelligence and mathematical knowledge required to perform such complex mathematics and the limited use of calculator allowed to the pupil for these lengthy calculations. Part II The curriculum analysis meets the requirements of the standard equivalent education systems however neglects the fact that majority students lack the basic skills and understanding of this subject due to mental slowness or weakness. While many are very intelligent, some students fail to grasp the concepts of this subject within the first or second lesson and require further training hence hire tuition and enroll in private academies to overcome the areas in which they face trouble. The curriculum analysis should therefore highlight the topics that face most difficulty and hire qualified teachers who know how to tackle these areas of concern while maintaining a healthy learning atmosphere free from discrimination and judgment. Q.1 This curriculum in particular was developed by Budnick (1971) who with the help of certified teachers and professors (including himself) formed as a cast of characters who together developed this curriculum and put it to pen and paper creating a text book that was distributed and now used by students in all countries. The students of Rhode Island School (USA) were the subject targeted to meet. Q.2 This analysis was made in an attempt to overcome the flaws in the education system being followed nationally and throughout the world and emphasizing on the student’s needs and requirements by consulting their issues and trying to overcome them by emerging a solution that would prove beneficial both for the teachers and students. Socially, it will students be more good with making judgments and communication. Economically, it will help students become efficient and accurate within the professions they wish to pursue ahead thus benefitting the working population. In political terms, it will help students debate equally with reasoning, accuracy and equality. Educationally, it’ll make the pupils more vigilant and wise especially in this subject which is essential for the foundation of learning. Q.3 The planning elements that dominated this analysis was the subject history, its content, its coursework details as well as the faculty available to teach these concepts clearly and precisely to the students. This was done with the help of the text-book, teacher guides, student curriculums and student surveys provided from the various institutions that follow this course line in their academic teachings. Part III The curriculum represents the value and importance of mathematics for every student’s development and learning skills and targets the main objectives that are focused on and emphasized. It has a broad perspective about the relevance of mathematics in all sorts of encounters and situations and without which a human would be handicapped with rationing, measurements and calculations. It also attempts to overcome the flaws and errors which students are facing regarding this particular subject, keeping in mind the best interest f the pupil as education is of first priority. Part IV The purpose of the curriculum is to teach students to vary and differ between two or more numbers, subjects or examples and apply arithmetical and algebraic formulae and quanta ions to their everyday life. Measurements and reason rationing is a basic tool used by every individual almost all the time from cooking (adding measured ingredients) to travelling (how much the car was purchased for, maintenance/fuel costs, mileage in km/hour) The aspects intended for training include fact finding, problem solving and communicative skills while research and analyzing and educational context are the chapters that are only taught as theory for e.g. factorization and matrices. These are taught for educational purposes however don’t apply to reality. The curriculum expresses its purposes at a high level, covering each and every topic with extensive research and detail to explain every large to each minute detail over what must be taught and it’s purpose of teaching. Mathematics is a wide scope and covers uncountable topics; however this must be refined and shortlisted to only those that seem most relevant and necessary to teach the students. The priorities and goals of this subject are to teach students how to vary between different elements and aspects met by future experiences that apply to the real world. Many students need proper thorough extensive training and virtual practice in order to grasp these concepts and learn how to apply them in their daily lives. The goal is to polish each student’s skills and brush them up so that they know how to deal with mathematical situations. The types of learning objectives that are included and emphasized on in the curriculum are: First and second degree variables Inequalities Rectangular coordinate systems Linear equations Graphical characteristics Slope intercept form Functions Quadratics, polynomials and rational equations Exponential, Logarithmetic functions Matrices and matrix operations Probability Measures of central tendency and variation Averages revenue cost and profit Statistics and calculus The primary ways in which the curriculum is represents the subject matter to the students is that of the old conventional ways i.e. the white boards and markers in the school classroom. Teachers who are specialized in the subject (usually PH.D’s) are hired to impart their knowledge of the subject to the students through a standard set pattern curriculum that must be followed and completed before the end year examinations or terminals. These teachers are certified and professionals who take out the time and effort to educate amateurs and refine their skills by practice, encouragement and patience. This faculty is to utilize their allotted time and make full use of their expertise so to avoid the need of extra help and coaching. A view of multicultural education is usually not included. This is due to discrimination and the arousal of unnecessary issues that can affect and offend people from diverse cultures. For this purpose, all biases and racism is eliminated so to maintain equality, respect and co-operation which are key elements for a safe and healthy learning environment. Multiethnic involves the emergence of different ethnicities of race, gender, cultures and beliefs. Internationally schooling usually follows this pattern as they have the most diverse and ranging population living together in one nation. For this purpose, I would prefer to choose the Multiethnic view over Assimilationist and Reconstructionist views for my analysis. It can be determined that students have met the standards of this curriculum by setting a grading system with a minimum (below average or failing) point to the passing and higher results. 50 percent is usually bare minimum bar set for passing a subject. If the student obtains less than this, he/she has failed the course and will have to reappear to improve and pass the subject. If the student hits exact 50, he/she has bare minimally passed i.e. on the margin. And for those who attain higher, they achieve a good grade according to their specific percentage. The usual grading system involves the letters A-F with A being the highest and best possible score and F failing. For those pupils who fail to reach bare minimum passing criteria, the consequences for those students is the fact that they have been unable to clear their examinations, for which purpose they must clear the subject by repeating the course and will be held in the same grade until they do so; after which they will be promoted based on their performance. This is the worst case scenario for the student as not only will he/she lag behind from their former position and class fellows but will also sense the feeling of degradation and humiliation. For the teachers whose students have failed, the school board members may reconsider their stay in the school, depending upon the number of students they taught that had failed and also the complaints that may have (or may have not) been launched against the teachers foe e.g. student accusation of not understanding the teacher or the teacher indulges in some sort of favouritism. This can result to termination and destroy the reputation of the teacher as well as cause of unemployment. Schools that have a high rate of student failures too will loose their reputation and they may loose their position by parents transferring their children to a better institution which they consider better hence increasing the likelihood of the school shutting down due to poor quality services. From listing the points noted above, it definitely matters to adhere to the standards set as incase they have been disobeyed or not fulfilled in any way, it can result into a lot of trouble what so ever the reasoning for not meeting the requirements of the curriculum and institution. The curriculum is aligned with the standards as both are attained hand in hand and are incomplete without both processes done correctly together. The curriculum facilitates student understanding of the content and processes espoused by the standards developed in the curriculum. These are made keeping in mind the needs and requirements of the students. Portrayals of the nature and structure of the mathematics discipline are congruent between the curriculum and the standards as both go hand in hand and standards can only be achieved by following a certain curriculum; just as curriculum can only be taught by a standard set of conditions, rules and regulations including the system of rewards and punishments. Both are balanced with depth and breadth and each topic and chapter has a list of standards cited with it. Technology affects the content of the curriculum by making huge calculations without which finding results would be impossible such as the weather forecast or the stock exchange. Technology enables problem solving and result finding to become easy and accurate without the need of estimations and approximations as accurate results are obtained. Scientific and complex calculators make life easier to perform these calculations. Part V The assumptions that underlie the curriculums approach to purpose and content are the facts and figures that are attained from studying the subject of mathematics. This curriculum assumes and perceives to be the best method to teach students to handle numerical facts and figures and teach them of their usage and value in the world. Student course-outlines, teachers’ guidelines and student course curriculums underline the conceptions of learning, objectives, curriculum and teaching in the education system. It plays a very major hegemonic role in its purposes and content to a great extent as without mathematics, the world would be in uttered chaos. There would be no form of measurement and calculation hence this subject is of great importance and the curriculum must meet the current requirements and advancements to suffice for matters that once did not have a solution. Part VI The curriculum is organized in a sequential systematic way in which each the beginning chapters form the foundations by teaching basics and the proceeding relate to the previous chapters as their advanced form. In this way, students are alleviated of all difficulties by first adapting them to the foundation by grasping key factors and skills and gradually advancing to the harder levels so that the student does not suffer from lagging behind or mere confusion. Vertical and horizontal organization can be made to further enhance and improve the education systems for e.g. by hiring more qualified teachers, enabling training to the current ones to shape them up, and attaining more study material and activities such as employing a computerized information system that is interactive so the students have fun while studying. However all this would require a substantial amount of financing. In this way media is involved in the learning environment with added benefits such as slideshows and presentations that increase class participation and knowledge with less stress. Hence it can be said that technology plays a major role in the curriculum organization, especially with the rapid advancement in today’s technological era with educative and teaching applications that can be downloaded on to laptops, smartphones and smart tabs for on the go learning. The social and political implications of technology in curriculum organization include the financial background of the student as well as their government consent of using such techniques for education. Many students cannot afford such expensive gadgets to benefit from like the elite class, and some governments have restrictions due to security issues. For this reason, many students may suffer from various limitations that may restrict them in this case. It would decrease the likelihood of using tracking as many students will not be fortunate enough to avail such facilities and these students will be in majority. Part VII There may be the occurrence of psychological assumptions about the curriculum organization. Such can be the development of inferiority, low confidence and low self-esteem. Students who are underprivileged, or just average in studies may feel degraded and suffer from common health illnesses such as anxiety and stress. Teachers may also suffer from such issues due to newly hired teachers and professors who have better knowledge and skills than them for which purpose their class performance may be better than theirs. Other assumptions include the overall finance, performance and success of the curriculum revised and whether or not it will prove more beneficial and cost/effort worthy. Part VIII The curriculum should be implemented by a pilot test which will be a demonstration and low budget test to see whether or not the newly launched system will be an utter success or epic failure. This can be done by introducing the new syllabus to a few campuses only for a short time period and gather results of it after that time period to evaluate what must be done and what will be the next step. The temporal, physical, organizational and political requirements of the curriculum include a qualified staff, sufficient material for each student, a class to test upon, and a control manager and school classroom to perform this test. It will also require the consent of the school board and state before this can be carried on. The probable costs will be great but so will its benefits as these expenditures will recover fast after parents see how successful and improving their child’s performance is. Hence the institutions following this curriculum, followed by its staff and students will all benefit greatly with students receiving quality education, parental satisfaction and a happy teaching workforce who will have the benefits of being paid incentives to boost their motivation and efforts. The extent to which the curriculum will be consistent and appropriate for the teachers attitudes, beliefs and competencies will be immense as not only will their work become easier with the help of technology but their job will become more fun and creative and this implementation can also give a slight bump in their salaries if they improve the overall performance of their class. The values embedded in this curriculum are mutual understanding, communication and co-operation with the elimination of all sorts of differences, biases and racism. People will learn to live as one whole community with respect for each others beliefs and values. This implementation helped the students discover their strengths and overcome their weaknesses. It helped them interact with other students and make close bonds with their teachers without any complaints. It allows the students to attain academic achievement and prosperity to further brighten their futures and careers. Part IX This curriculum analysis provides an understanding of how the education system can be implanted and evaluated from a complete learning point of view. It allows the student and teacher relationship to form on a higher level and helps both parties learn from an interactive education system which benefits all. It provides data on how many students are good or weak in the subject, how many teachers are preferred as better due to lesser complaints and better class performance, how many are willing and able to be a newbie to this newly introduced system. It can be concluded that this analysis will prove beneficial and successful and should therefore be fully launched and introduced to locally and internationally. The pilot test ha s proven a key factor in this process which helped as an instrument and suggestion advisor for collecting useful and informative data. These as well as other materials in the study have proven to attain equality among social, economic, cultural and ethnic groups as all humans are humans after all so each has a right to be educated in the same way. My only concern is that the government provides financial aid for those students who are underprivileged as every student deserves to learn from this education system. The approach to student evaluation in the curriculum manifests a measurement based and integrated based approach as it pertains what already existing data while integrating advancements to these already existing data. A neo-conservative or radical evaluation of the curriculum would look like the introduction of academics through government institutions run by forces such as the military force. It will ensure democracy and equal rights for all and promote American national interest in international affairs. Part X My judgment is that no matter how expensive the cost but education should be improved without a doubt as it is the key to success in this world. An individual is incomplete and illiterate without education and everyone has the right and deserves to attain academic knowledge. It has the drawback of being very costly to introduce however the overall benefits outweigh the costs as a better educated population will lead to a more efficient, educated and wealthy economy thus decreasing economic crisis such as poverty and unemployment. The strengths of this curriculum is the overpowering and extensive research, effort and dedication given into making the study of mathematics an interactive and indulging experience for both teachers and students. It allows pupils to become vigilant and inquisitive while taking interest in the subject, eliminating boredom and demotivation. Students also develop confidence and overcome their weaknesses by achieving satisfactory results after attending these extensive classes. Just as any system, imperfections and weaknesses too are very much present. Special care and attention must be given to the flaws that have been detected or are later surfaced in the mathematics curriculum. It should be aware that caution be taken while fulfilling the finance and expenditures as even the minutest details can result the economy in a huge loss. For this purpose a thoroughly revised budget plan must be induced. Also the staff hired should be thoroughly checked to ensure there are no problems in their teaching methods and that they deliver the lectures and lessons in the proper manner so that students do not face any confusions and misinterpretations. The dangers I would want to be cautious about during implementation would mostly regard the financial factors. I would fully ensure that the results obtained from all the evaluation and analyses are accurate in terms of reliability and validity and only after assured confirmation would I proceed to the next step thus increasing the likelihood of it being successful while eliminating possible errors. In order to adapt the curriculum to maximize its benefits and strengths and minimize its limitations and risks, it is essential to evaluate the curriculum analysis thoroughly by re-checking and opinion collection through interviews and surveys to judge whether this system satisfies the parents and guardians of the pupils, the pupils themselves and the teaching staff to further enhance and improve the education and academic system service being provided to their nations bright future and progressive success. Opinion generation is one of the most beneficial methods of fact collecting and judgment basing. This will ensure a safe, healthy and successive environment for the overall schooling system and will be used as an example for all schooling systems to adapt and imitate. Citations: Applied Mathematics for Business, Economics and the Social Sciences (Frank S. Budnick, 2011) Read More