Comparative Analysis of Mathematics Curriculum in Australia and Finland - Research Proposal Example

Comparative Analysis of Mathematic Curriculum in Australia and Finland Name: Course: College: Tutor: Date: INTRODUCTION Education systems are diverse across the world with variance beginning from the school curriculums to the particular subject syllabuses. The variation in the system help explains the development or decline in the performance in the various topics that are examinable to the different countries. One of the general subjects that have wide acceptance in school systems all over the world involves mathematics, which has a standard measure in the various theories and practical concerning its syllabus content. Symbols, equations, assumptions and theories concerning mathematics have over the time being international issues with methods and standards set at an international level. OVERVIEW BACKGROUND Two different system on the mathematical curriculum assessment two countries, Finland and Australia. The two countries have different mathematical curriculum systems based on the perspective in which they are viewed. The comparison relates to each countries syllabus difference in relation to the content of the subject, the strategies and measures employed to ensure success is achieved at the end of defined learning period. The curriculum also sets a topic for discussion, with the various methods of imparting knowledge to the students being a relevant issue that will show the variance among the two countries. The best approach of comparing the two nations about the mathematical curriculum would be best suited at the primary school level. The primary school level forms the backbone for the upper levels of education for every student, where they learn the basics of the different subjects. The basics involve formulae, methods, and concepts that explain the different functions that relate to mathematics. The comparison will be on the strengths that Finish Curriculum has showcased in the strategies and processes of teaching and learning mathematics in class, over that of the Australian curriculum. According to FCCS (1994), the strengths of the Finish curriculum lie in its ability to streamline the goals of both the teachers and the students in the process of teaching and learning mathematics respectively and which is achieved from the various student and teachers programs that have their focus on ensuring that mathematics is understood by the teachers first, in the different education programs offered for them in universities, and the students programs, aimed at sharpening the students skill on each academic level in and away from class. On the other hand, the report of ACARA (2010a, 2010b), show Australia to be in a struggle with the teaching and studying of mathematics on the curriculum. The curriculum emphasizes more on content rather than the method, processes, and strategies for educating and learning mathematics in class. It has, in turn, led to many students hating math due to perception that it is hard (Forgasz, et.al, 2003). LITERATURE REVIEW The organization of any curriculum in its selection and implementation requires relevance and consistency in this day and age. A comparative analysis on a curricula involves the isolation and analysis of a target set, with respect to a coverage and understanding of the characteristics of the specific curriculum (Porter, 2004). Content, as one of the major feature of a curricula, requires analysis of its description through isolation of the subject. The curriculum needs content analysis on its cognitive demand or performance expectation, which defines the knowledge needed by the students, provides procedure of how to go about gaining the knowledge and its importance to the students. Porter (2002, 2004) defines content as domain specific which has a declaration, procedure, tactics and a situation which targets the knowledge within the curriculum. Porter (2004) explains the intent of the curriculum as the content involved in the examining of the performance expectation, which showcases what the student needs to utilize, understand and know of the provided guidelines communicated through documents and academic material. Thus, the assessment of a curriculum with respect to performance expectation and content will help analyze most of the paper under intended curriculum which helps to reflect on the results of the content on documents and academic materials from the created and planned guidelines and assessments. The intended curriculum approaches best suites the analysis of Mathematic Curriculum. MATHEMATIC CURRICULUM ANALYSIS The analysis of the curriculum will have its basis on the set goals for the mathematic subject, the efforts employed by the teachers and finally the pupil efforts in the process of studying and understanding the subject (Aho, Pitkänen, and Sahlberg, 2006). This analysis will also be based on the policies and practices that will develop from the syllabus, institutions, and teachers in the process of growth and development of the pupils in the subject (mathematics). A better review of the curriculum would be with respect to the specific countries for analysis. FINLAND MATHEMATIC CURRICULUM ANALYSIS The Finnish mathematics curriculum has two critical features that require consideration and which impact the system that correlates the carrying out of mathematical education in the country (FCCS, 1994). Also, the two elements set the standards that mathematic instructions should be at, both locally and internationally for teachers and pupils, and they include the National School Curriculum itself and the teacher’s education at the university levels. They determine the education environment for both the teachers and the pupils during daily interactions between the two parties in a math class at school. a) National School Curriculum The Framework Curriculum defines the National School Curriculum for the Comprehensive Schools (FCCS). The National School Curriculum’s first publication was in the year 1994 and was prepared by Finland’s National Board of Education which emphasized the importance of an education system which produces positive academic results at the end of the day. In particular, the Framework Curriculum Comprehensive Schools is a document that provided the contents with which the schools needed to partake in the process of teaching mathematical education (FCCS, 1994). The National School Curriculum, through the growth and development of the education system, undertook some changes in order to emphasize the spirit of constructivism. This was embedded in the curriculum by using the experience gained in life by both the student and the teacher to understand the content of the mathematics curriculum. The changes in relation to the perspective of the mathematics syllabus and teaching ensured that the document was more flexible than before, less centralized and adequately detailed on matters concerning responsibilities and procedures for teaching mathematics. As a result of the changes, the teacher’s responsibility shifted from just teaching to the writing and planning of the math curriculum making it easier to reflect upon when teaching due to the classroom experience gained over the years from interacting with students (NCCB, 2014). The changes involved include the problem-solving techniques in the subject, regarding both its methods and content, for example, practicality in the subject which require both the teacher and the student participation, in the process of understanding the various principles and logical requirements of mathematics (Kupari, 2004). In conclusion, the current National School Curriculum details the critical principles required to teach mathematics in schools found in Finland. b) Teachers Education at University Levels The general education curriculum system of Finland places a lot of emphasis on the role of a teacher in the performance of their duties in classrooms. Their knowledge of mathematics, together with their skills in the subject take priority because they determine the potential of the teacher’s ability to put the idea into practice in the process of solving different mathematical problems in the classroom (Krzywacki, 2009). The ability of achieving such effective and efficient teaching practices is the responsibility of the teachers as the university ensures that teacher graduates are competent in managing the curriculum content within the required time so that each student will comprehend the content. Thus the Finish teachers are viewed as having an enthusiastic attitude towards improving the level of education offered in the country attributed to the various programs in the universities. In conclusion, the education program for teachers which emphasizes on practicality and competence in the universities plays a vital role in the development of the mathematic curriculum in Finland. Merenuloto and Lehtinen (2004) argue that an understanding of the primary school mathematics creates an excellent background for pupils in the ever-changing scientific education for the next levels of school. AUSTRALIA MATHEMATIC CURRICULUM In contrast, the focus of mathematics in the Australian Curriculum approach to teaching places fundamental emphasis on the practicality of math and its usability (Ellis, 2005). It aims to enrich the employment prospects of students who have attained the skills necessary to practice the subject in the modern life and all democratic processes. The mathematics curriculum of Australia has two perspective goals for mathematics teaching in primary schools which are the practical point of view and the specialization perspective (Forgasz, 2005).These observations pave the way for the formulation of the mathematic curriculum which depends mainly on components that dictate processes and procedures involved in the teaching and understanding of mathematics. National Mathematic Curriculum The curriculum ensures that there is consistency in the foundation of mathematics (concepts, theories, formulae, and calculations) at all levels of the primary schoolings. The Australian curriculum is best assessed under the Australian Curriculum, Assessment and Reporting Authority (ACARA) as it gives an overview of the mathematical program on the set curriculum. The curriculum allows content collaboration (integration between content on one topic to another). The collaboration is done in the form of pictures, graphs and pie charts which provide illustrations and examples that assist the teachers in creating an enabling atmosphere so that the teacher’s interactions with the pupils results into a proper understanding of the curriculum content (ACARA, 2010a and 2010b). The Contents of the Australian Mathematic Curriculum The following provide the basis under which mathematics is assessed or evaluated by the teachers and pupils in primary schools. They include Achievement Standards, General capabilities, and Cross-curriculum priorities. 1. Achievement Standards Under the curriculum definition, achievement standards refer to the learning quality offered in a primary school (the knowledge, skill sophistication and depth of understanding). Achievement standards are used to assess a pupil before moving ahead to the next class. After an assessment of a student achievement on the performance standards, teachers become liable to judge of whether a student should proceed to the next level or not from the test scores (ACARA, 2010a, and 2010b). Furthermore, performance standards at early stages are organized in several work portfolios which represent specific topics such as fractions and numbers sub-strand. The work samples are explicit and have three different standards for each task assigned. The functions, specific features and achievement standards for each level of primary school are clearly outlined at the beginning of every stage/level in the school curriculum. The teacher makes an assessment of the student's progress is made after the grading of different mathematic tasks and a qualitative comment is necessary at the end of every academic primary education years (Hollingsworth, 2003). The qualitative comments are meant to help both the student and other tutors (such as guardians) understand their weaknesses in regards to different mathematical topics and hopefully work on them (ACARA, 2010a). 2. General Capabilities The curriculum ensures that the general capabilities (knowledge, skills, dispositions, and behaviors) are part of the primary school math syllabus where the content aims to aid the pupils to live well and prosper in the twenty-first century (ACARA, 2010a and 2010b). The general capabilities under the Australian mathematic curriculum include the following: numeracy, literacy, critical and creative thinking, ethical understanding, personal and social capacity, and intercultural understanding (Forgasz et al., 2003). Under the mathematic curriculum, these general capabilities are important because they identify the available opportunities for adding richness and depth to the content of the primary school curriculum and also helps in the practical elaboration of the content on real life situations. 3. Cross-curriculum Priorities The priorities are responsible for the enrichment of the curriculum through contents that are considerable and focus on the different topics that cut across the different learning areas that relate to mathematics (ACARA, 2010a, and 2010b). The ability of the mathematics to relate to the various disciplines such as science (the percentage content of air in the atmosphere), history (the calculation of the important historical dates) and geography (the number of countries or states in a continent), has been embedded in the cross-curriculum process. These priorities include the ability of mathematics to assist in the generation of ideas and possible strategies in the event of a logical situation which requires thinking and immediate practical solutions. Also, Cross-curriculum priorities aid the pupil in becoming more inquisitive, organized and enthusiastic in exploring mathematics and its relation to another discipline by reflecting on their thinking and the particular processes (Forgasz, 2005). The cross-curriculum priorities are characterized by their ability to have a meaningful impact on the pupil in the course of learning mathematics in class. In conclusion, the Australian mathematic curriculum mostly focusses on the development of the learning process aimed at producing better results at the end of every academic year. The school curricula, apart from being result oriented, is task and workload specific with regards to the level of understanding assessed from a student’s achievements in class. METHODOLOGY A feasible method for attaining the required data for the improvement of the Australian mathematic curriculum require a comparative analysis. Therefore, the following discussion will look at the two curriculum in terms of their different perspective with regards to teaching and the understanding the subject. The analysis will reflect on the literature review of the two nations on their mathematic curriculum. COMPARATIVE ANALYSIS OF FINISH AND AUSTRALIAN MATHEMATIC CURRICULUM A comparative analysis of the above mathematic curriculum (Australia and Finland), will require an assessment under the Proficiency Strand Method of mathematics assessment which includes, Conceptual Understanding, Procedural fluency, Strategic competence, Adaptive reasoning and Productive disposition (Kilpatrick et al., 2001). Conceptual Understanding Watson and Sullivan (2008) and Kilpatrick et al. (2001), describe conceptual understanding by arguing that it first requires a proper description of the actions to be taken and the task relevance in the teaching of primary school students. They then define conceptual understanding as the process of being able to familiarize oneself with mathematical operations, formulae, and concepts. The Finish mathematic curriculum through its mandatory visual program such as the use of charts, graphs and pictorial representation in the National School Curriculum has been able to achieve a conceptual understanding (Kupari, 2004). Through such programs, Finish pupils have been able to build on the different concepts from scratch with everyday objects which not only aid in the visualization of a problem but also leaves a more permanent impression compared to classroom sessions. Consequently, the visualization of problems creates an ever alert learning environment whereas, in comparison, the cross-curriculum priorities of the Australian Curriculum mean that conceptual understanding is only superficially addressed by the curriculum. Therefore, the reason why the Australian mathematics curriculum does not adequately address the issue of conceptual learning is because of the open structure of the curriculum. It stipulates the need for the practical but not its necessity as compared to that of the Finish system making it less reliable for the students who learn from interacting with their environment. A practical approach to in the studying of the Australian mathematics to some extent plays the role of enabling conceptual understanding for the primary schools. Through understanding of the different progressive topics such as addition, multiplication or division in mathematics at the different primary school levels, a pupil can develop a concept with time after continued teaching and assessment over the academic year whereas, through the visualization program, Finnish pupil attains conceptual understanding much earlier. Procedural fluency This is also referred to by Watson and Sullivan (2008) as ‘mathematical fluency since the aims of procedural fluency on mathematics is to possess the necessary skills required for carrying out procedures efficiently, flexibly, accurately and appropriately. It also involves the teaching of factual knowledge and concepts which can always be recalled from the mind and as such, this knowledge requires specifically used symbols or formulae and procedures. The specialized teaching within the Australian mathematic curriculum makes it suitable to achieve procedural fluency where a topic is taught to pupils in primary school beginning with essential basics then it's testing, and it is this repetitive nature which also allows an assessment of the understanding of and fluency in the topics. Consequently, the functional study of mathematics through continued assessment is what provides information with regards to the level of success of their curriculum which can then facilitate flexibility in the change of the curriculum. In contrast, the Finish curriculum encourages the personalization of mathematics teaching by teachers, that is, the teacher takes a personal interest in students who prove to be struggling with specific topics or questions in general. It ensures that procedural fluency is achieved among all students, both robust and weak in mathematics. In doing so, the country provides a standard for the mathematics to be taught at a young age and it, in turn, develops to become a culture of love of mathematic (Kupari, 2004 ). However, in both countries, the curriculum ensures that procedural fluency is addressed at all stages of the primary school levels, though the Finish curriculum has a better set up in relation to interactive studies which helps the student to deal with the issue. Strategic Competence It is the ability of a pupil to formulate and solve mathematical problems without difficulties. The process as argued by Turner (2010) states that it is a skill which has the characteristics of aiding the pupils to select or devise a strategy or plan that can solve mathematical problems from assigned tasks. As the Australian mathematics curriculum focuses on general capabilities, this facilitates strategic competencies where the skills necessary for solving mathematical problems in different environments are developed. Similarly, Features such as the creation of numeracy, literacy, critical and creative thinking, embedded in the Finnish Curriculum, are of importance to students in the acquisition of strategic competence. In retrospect, the Finish curriculum, through the development and growth of its primary school teachers while at university, equips them with the ability to create a school environment where strategic competence, its development, and implementation, are addressed first hand among teachers and pupils. The curriculum also ensures that the teachers, through the Finish National Curriculum, have a set plan for addressing strategic competence from the clearly defined aims of each topic under mathematics. Undoubtedly, the strategic competence for the both countries is addressed on equal terms by their specific curriculum and programs set for the development process of the students at each stage of primary school. Adaptive Reasoning This reasoning is defined by Watson and Sullivan (2008) as the capacity of a pupil to organize their thoughts logically through reflection, justification, and explanation. However, Australia mathematic has not adequately addressed adaptive reasoning in the curriculum, as its aims mostly target an understanding of the content rather than the creation of a thinking environment when solving mathematical problems. In contrast, the Finish curriculum, through the participation of the teachers in the creation of the mathematic curriculum, enables the teacher, who are always in contact with the pupils, to produce a program that ensures adaptive reasoning through the different primary school stages. Therefore, the interaction of the teachers with the student is instrumental in the making of the curriculum because they understand the students better than the educational authorities of the country. Productive Disposition The last assessment for the comparing these two national curriculums for mathematics as argued by Watson and Sullivan (2008) is productive dispositions, which is defined as the ability of a pupil to find sense in mathematics, its usefulness and worthwhileness as at the same time promoting efficiency in problem-solving. It also involves creating in primary students a positive attitude towards mathematics. In essence, the Finish mathematic curriculum, which promotes teacher’s ability to help the students learn mathematics has ensured that the productive disposition for primary school students is high. Not only has the curriculum fostered the understanding of maths, but the practical programs in the Finnish mathematic curriculum has also led to a general improvement in the success of students ranking in the top international competitions thus exemplifying a positive attitude mathematics in the country (NCCB 2014). However, the Australian curriculum has failed to address productive disposition by focusing on more content coverage more and understanding more rather than the general attitude of mathematics among students (Ellis, 2005). Conclusion Australia should strive to achieve the standards set for the mathematic curriculum in Finland which ensures that both the teachers and the primary school pupils are part of the curriculum and not only the content. The focus on university graduates (teachers) providing knowledge and information necessary for the understanding mathematics in Finland and are effective and efficient since the content coverage and the issues that relate to the teaching of the subject within the curriculum have been made critical when teaching in classes. However, any curriculum that concerns itself with educating primary school students needs to not only address the content but also the student’s attitude towards the content coverage such as those from Finland primary classes, which help teachers to also build on their attitude for teaching and creating an environment of positive attitude towards the subject in the classroom. The contents are important for the general understanding of mathematics basics, what is mostly taught in primary school, but it is the attitude that sets the pace for understanding and appreciating math at the next level after the primary school, and hence the need to address it as early as possible in the study of mathematics. It will play a significant role in demystifying the perceptions that relate to mathematics such as how difficult it is to understand or comprehend. The Finnish Curriculum has showcased strength in the coverage of the mathematic content in primary school through visualization of problems relating to the subject in the curriculum. The level of its adoption, however, at the national level can be positive or negative depending on the level of precision of its adoption in a different nation. One of the major implication involves increased funding in the Education sector to incorporate features of the University education system of Finland. Increased funding will be necessary to train teachers to know the right procedures and methods to adopt while teaching mathematics at primary schools. Funds would also be necessary for the practical classes which require more than a classroom and a desk but also interactive material that can aid in the development of the students mind. The Finish Mathematic Curriculum will, however, add quality to any curriculum that is willing to spend in order to see the young minds prosper in mathematics and leave behind the misconceptions that relate to the comprehension of the subject. RECOMMENDATION Primary pupils from Finland seem to enjoy the mathematic lessons due to the attitude that they have acquired during classes. Kupari (1999) argued that mathematics was one of the most popular subjects among the 4th and 6th graders and which is also performed well in the respective classes. This not only shows the Finnish’s Curriculum effectiveness and efficiency in developing young minds (primary school children) but also its relevance in changing the Australian Curriculum to achieve the high standards and praise among the primary school pupils in regards to the mathematic curriculum. Australia should shift its focus of executing the mathematical curriculum under the following concepts: Teacher’s Education, Incorporating Practicality in Mathematics and Encouraging Personal Effort in Classrooms. Teacher’s Education One of the ways in which Australia can improve their Mathematic Curriculum in regards to that of the Finnish would be to give the teachers an independent role, that is, practice professionalism in education and teaching. This means that the teachers, during their university studies should be made aware of their role in impacting knowledge at primary schools with not only the content but also the environment they create during the lessons in class. The teachers should know how to assess a student in regards to their strengths and weaknesses in learning mathematics in class and focus on them. The shortcomings should be addressed whereas the strengths should be adopted as a means of familiarizing the student with the environment they understand more than the ones they do not. A focus on in-class assessment of students which are not for national level results should also be adopted by the Australian Curriculum so as to help the teachers assess the students better before a final assessment at the national level. This is because the teacher should understand their pupils better before focusing on the mathematic content of the curriculum which as its comprehension by pupil may vary with in a primary school. For Australia to adopt this new system it would reform from the core of the problem, which in this case is the ability of a teacher to create a proactive studying environment, they would need to implement policies that call for the Universities to also focus on the development of a child rather than the content only. Incorporating Practicality in Mathematics The Australian Curriculum can also adopt the Finish procedure of utilizing practicality in mathematic using the familiar objects or situations so as to create an inviting environment for the pupils. Practicality in mathematics helps the student to become comfortable during the lessons because it becomes easy to remember because of participation. Practicality in mathematics education in Australian Curriculum would develop their status in regards to success in maths by using contemporary examples rather than ones those which any mental pictures cannot be drawn from for primary school pupils. The implementation of practicality in Australian Mathematics Curriculum would call for the distribution of the mathematics lesson to incorporate practical as part of the learning schedule on the curriculum. This means that the Australian Education System requires a full review of the Curriculum before adopting a new one such as that of Finland. Encouraging Teacher’s Personal Effort in Classrooms Apart from practical mathematics, Krzywacki (2009) emphasizes the need for teacher’s commitment to educating young minds for future development rather than doing it for money. The Finnish teachers, apart from the guidance provided by the mathematic curriculum also take it as their initiative to see primary students prosper in the subject. This should also be the same for the Australian teachers who strictly focus on content completion more than the understanding of the pupils. In order to develop this concept in Australia, programs should be developed within the education system to provide guidance to the teacher in regards to mathematics matters and its curriculum. Reference ACARA (Australian Curriculum Assessment and Reporting Authority). (2010a). The shape of the Australian Curriculum: Mathematics. ACARA (Australian Curriculum Assessment and Reporting Authority). (2010b). The shape of the Australian Curriculum. 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