Problem Solving in Mathematics GCSE or the Essay

Excerpt from Essay :

Problem Solving in Mathematics

GCSE or the General Certificate of Secondary Education is basically a system that is present in England, Northern Ireland and in Wales. In this system, a student is awarded an academic qualification based on the grades that they attain. The qualification that a person attains is equivalent to either a level 2 or Level 1 key skills qualification. Normally, a student can uptake as many subjects as he or she wants. However, different systems set a requirement for how many subjects or GCSEs a student must take. There is present an international system of IGCSE as well and these subjects can be up taken anywhere in the world. This was just a precise history of what exactly the GCSE system is all about. Interestingly enough, the GCSE system was not the first one of its kind. Prior to this, GCE and the English Baccalaureate System were also present.

The GCSE system as complicated as it is would defiantly require some sort of revision plan in all subjects. There is a revision plan designed which is specifically targeted to developing mathematical problem solving skills. Problem solving is an essential component of any subject and all the students must be able to have a good grasp over this. In Mathematics, problem solving isn't only required in word problems but the approach becomes necessary in solving equations as well. There were the choices of choosing between Number development in study skills or problem solving. When one thinks of math, then problem solving seems like the more appropriate skill required.

Problem solving in math

Problem Solving is made up of interpreting, reasoning, analyzing, predicting, evaluating and reflecting. In many countries, this concept is either a crucial component of school mathematics curriculum or an extended objective of the curriculum in many countries. Turning a student into skilled problem solvers requires a lot of disposition and skill. (Stacy, 2005) The students not only need mathematical knowledge but also require a lot of reasoning ability. That is to stay that the students should be able to come up with better heuristic ways of solving other problems as well. (Anderson, 2009) Along with having good skills in math and good reasoning abilities, the students should be able to work in good environment as well. The students should be confident and persisted. They should be able to organize their knowledge and then put it to good use.

One thing that should be highlighted is that problem solving itself cannot really be taught. Problem solving is taught and developed in the students by presented them with different problems. (Lester, Masingila, Mau, Lambdin, dos Santon and Raymond, 1994) In this approach, teachers mainly focus on different topics of math by going through them in a problem solving manner. It is the aim of the teacher to explain and develop a deep understanding of the topic or the problem. The students will only go on to solve the problem and work on the situation if they are well aware of the concept.

As mentioned earlier, there should be interaction between the students and interactions between the teacher and the student as well. (Van Zoest et al., "1994) This is one of the concepts that I am assuring is present in the course designed. Regardless of what the course or the curriculum, effective communication is what makes the entire course successful.

Apart from having a good relationship with the students, problem solving as a course become effective if the students are given a purpose. Since the 1970s, problem solving has been less subjective. That is to say that they are more focused and revolve more around the basic ideas. Students are explained the importance of mathematical reasoning and are given proof as well. This goes onto answer a very common query about math: Are we ever going to use this?

Problem solving skills are thus developed through better interactions and a sense of purpose in all the students learning it. Schoenfeld also went on to suggest that the students must meet these three criteria's of mathematical thinking. The students should go on to know the process of mathematization and abstraction to such an extent that they are not afraid to apply this knowledge. The tools that are developed in them such as tools of service and trade should be used in getting a good idea of the mathematical world. Lastly, it was recommended that problem solving should be developed within students so that they are motivated
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to reorganize the different themes taught to them through activity. With ideas such as these, the students only developed their own confidence but they are able to think mathematically. (Schifter and Fosnot, 1993) Problem solving is a guide for students to construct, analyze and alter their own ways and theories in math and in other subjects.

Curriculum Models

It should be noted that the content for any course is picked out on a vocational basis. That in short means that it is linked with what the student needs to know. In this scenario, it is mandatory that the students get a good review of all that they have learned. Not only does this scheme hopes to revise what the students have learned but also goes on to focus on areas where they still need some clarification. As mentioned earlier, problem solving is a complex skill and one needs clarification of concepts before he or she goes on to develop it further.

After the needs are looked at, the course should put its main objective on what the learning outcomes should be. Learning outcomes are basically what the learning class or the students would be able to do when the whole class is over. The objectives that are usually written out are done so with increasing level of specificity. (Davies, 1975) By starting from a very general objective and making way towards the specific targets of the course, the course managers can hope to cover a vast variety of goals and aims. In this way, the objectives and the targets are 'operationalised' and the entire course is directed in a very organized manner.

If hierarchies are applied to the targets and the objectives listed, then proper activities can be made that target the students. These activities can be in the form of lectures, assignments, quizzes and even assessments. Here the major idea is to start off with very simple objectives and targets and then move on to more complex tasks. This idea of starting from simple and then moving towards complex all falls under Bloom's taxonomy. (Bloom, 1956) It is up to whoever is designing the course to come up with outcomes or objectives based on the student population. This reflects on what their capabilities are, what it is that they need help with and how many the students can be actually achieved. The objectives model

The major obstacle is cleared when the students are able to steer easily through any tests or assessments thrown their way. Thus a curriculum model turns out to be exemplary or a good model where the assessment targets all the objectives in a very clear way and thus goes on to test all the objectives listed. If any student is not able to rightly fulfill an objective and answer it in a proper way, then it is solely the teachers or the curriculum planner fault. Many a times, what happens in schools or colleges is that when a curriculum is made, it is tested in a proper way by a group of typical students. These students can either be very diverse such that a certain group of children are not targeted.

This course that is made is for ages fourteen to nineteen years old. If a typical group of children were chosen for this curriculum, then they might belong to different race or casts however they would be in the aforementioned age group. After the typical students go through the objectives and give the proper feedback, the curriculum is then fixed to whatever alteration might be required. The Keller plan is a plan in which the students function at their own pace and once they have become skilled in a certain objective, they move on to the rest of the objectives.

Pedagogy theory

Pedagogy is basically the art and science of education. In the simplest terms, this can be defined as how the teachers teach and what the students learn. The major objectives of pedagogy are that whenever a teacher or any instructor is wishing to teach the students a certain course, the objectives should be met and the students should learn all the things taught to them. There are many factors that come between and affect the interaction that students and teachers might have. These could mean the instructive strategies and the own beliefs that a teacher has. Where every student has a different learning style, a teacher has a different teaching style as well. The teachers thought about the entire course holds a lot…

Sources Used in Documents:


Anderson, J. (2009) Mathematics Curriculum Development and the Role of Problem Solving. [E-Book] The University Of Sydney. Available Through: ACSA Conference 2009 Http://Www.Acsa.Edu.Au/Pages/Images/Judy%20Anderson%20-%20Mathematics%20Curriculum%20Development.Pdf [Accessed: 11th February 2013].

Bloom, B. (1971) Handbook Of Formative And Summative Evaluation Of Student Learning. New York: Mcgraw-Hill.

Boaler, J. (2002). Experiencing School Mathematics: Traditional And Reform Approaches To Teaching And Their Impact On Student Learning. Mahwah, N.J., L. Erlbaum.

Davies, I. (1975) Writing General Objectives And Writing Specific Objectives. In: Golby, M. Et Al. Eds. (1975) In Curriculum Design . 1st Ed. Open University Books .

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