An Extensive Variety Of Expertise Knowledge Education Essay

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During my PGCE placement, I have utilized an extensive variety of expertise knowledge, assessment, teaching and learning approaches from Part 1. I believe that this is essential in terms of offering the most excellent teaching to students. Having repetitive, predictable and non-contemporary approaches are to compromise the usefulness of teaching and reduce the chance of accomplishing the learning objectives.

It is vitally important to understand that the students under the guidance of the teacher will not frequently learn at the same speed as the other students. Likewise, the students will not comprehend or uniformly understand mathematical ideas. For that reason, it is significant to adapt my methods to support each individual as best as possible. By implementing my method of teaching I would not only provide with an a explanation that suits most of the students as well as make it more comfortable for me to teach, so that I will be able answer the questions that students asks, and many examples are explained as follows:

Teaching approaches

During my first placement of my PGCE course, I attempted to build on or challenge/test students in my lessons to take full responsibility as much as possible for their own performance by making them involve in projects and tasks which permit them to plan, produce and either self-assess or peer assess mutually. This approach not only provides assistance from a well-built support group, and also it lowers the fear of students who may sense isolation and hesitant when doing challenges in Mathematics. Mathematics is like learning a new language the more we practice we get better at it. So by giving more exercises in a such a way that it is more interactive and fun which involves all of the pupils attention, will not only give way to the pupils understanding the topic more, but also provide with an attraction towards the class.

A lot of lesson planning went towards developing the perception of community and teamwork within the classes. At the beginning of each teaching topic, I summarized what my expectations were in terms of approach, behavior and outcomes. At this initial period, I did not want to consider talking about the qualitative outlooks, as I was being afraid of intimidating the students who were less certain; instead I summarized the outlook of how the mathematics task would be represented as and what the evaluation was to be at the end of the lesson. I was ascertained to distinguish that the challenges I showed to the pupils would not be simply and academic beside the point.

I planned two lessons concentrating on area and perimeter at the same time. As part of my first lesson which is shown here detailed focuses the way the actual application of an example in the classroom might progress in surprising techniques and to specify how significant pedagogical subject knowledge is in managing with this.

I started by studying the concept of area where I stressed on the definition of Area - "Area measures the space inside a shape, so the number of squares inside the shape" (Colin Foster, 2003). I asked the pupils to annotate a rectangle with an area of 20cm2 in their books on squared paper and to cut the rectangle out. My choice of this task was called a "reversed" open task, was by most suitably given to the pupils who had worked with area previously, especially the formula of area for the rectangles. Before long after the instruction the resulting conversation occurred in the middle of a student and me (Miss Arun):

S: Can I do a square?

Miss Arun: Is a square a rectangle? … What's a rectangle?

S: Two parallel lines

Miss Arun: Good but two sets of parallel lines … and what else does a rectangle have?

S: Four right angles.

Miss Arun: Better …(I point to the square the student has drawn) so is that a rectangle?

S: Yes.

Miss Arun: Right! … But has this got an area of 20?

S thinks: Erm… no.

Miss Arun nods: Okay! … (and leaves student to think).

It is not distinct whether my original choice of 20 was made with any understanding of geometrical suggestions however the smoothness where I moved from area dimension to three-dimensional problems showed with positive consideration to the properties of geometry and yet again needed perceptive approach to the pedagogical subject knowledge of both the dimension and three dimensional areas. I also showed the useful practise of questioning to stimulate understanding from the pupil. Following this I talked to my class about the properties of rectangles.

Next I invited a pupil to come to the front of the class with her cut out rectangle of dimension of 5 by 4, and proved that it has an area of 20cm2. The student led the class by discussing how multiplying the length and the width together is similar to counting squares and therefore calculates the area. I then used the student's cut out rectangle as an example to emphasize the connection between the theoretical definition of area and the calculation. I carried on as I knew the students needed to recognize that the area formula "L x W" is only applied to particular shapes.

Miss Arun: When [the first student] mentioned that is how you find the area of a shape, is she completely right?

(Another student answers)

S: That's what you do with a 2D shape.

Miss Arun: Yes, 2D shape like this shape … what kind of shapes would it not work for?

(More students answer)

S: Triangles…

S: A circle.

I questioned more as it provokes out that the formula "L x W" only works for rectangles.

A pupil then implied on a rectangle with dimensions of 10 by 2 as another example with an area of 20cm2, therefore at this point I made sure that all the pupils had picked either dimensions of 4 by 5 or 10 by 2. The pupils were asked for more possibilities and they proposed the initial examples however turned at 90°, simultaneously with dimension of 1 by 20 - this dimension had not been mentioned before.

On the interactive whiteboard using Smart Notebook, I showed rectangles with numbers on the sides. I asked the pupils to search for a pattern in the rectangles displayed, and then interestingly the pupils discussed the factors of 20. I continued to talk about the topic:

Miss Arun: Can you find any more numbers that give an area of 20?

I waited with an attitude of ambiguity. The students gave me no response.

Miss Arun: No? How do we know that there isn't any more numbers giving an area of 20?

S: You could put half by 40.

Miss Arun: Oh! You have now gone into decimals. We are going to have many factors of 20 with decimal numbers in, won't we?

I was aiming only on whole numbers and, consequently some disagreement about stressing the factors of 20. I knew the pupil's unexpected response was important and to what level of the curriculum it would relate. My open choice of questioning allowed this extension to start, though it was not my intention nevertheless, I decided not to engage in this part, although it might have been a beneficial use of the 20cm2 example because I just wanted to go on to examples that were different. As an alternative I utilised the 20cm2 example to aim on the pursuit for all the factors of 20. This study of the 20cm2 example took the first fifteen minutes of the lesson. I then had pupils redo the exploration for rectangles with a different area of 16cm2. I used this example to focus the procedure of finding factors, and to emphasise "a square is a rectangle".

I reminded on what they had studied on, and then told the pupils about the perimeter and how to calculate it for rectangles. I helped the class to calculate the perimeter of rectangles that are of different dimensions but of the same area of 16cm2 and showed that shapes may have the same area however they do not always have the same perimeter. I returned to the examples with the area of 20cm2 and the perimeter for each rectangle was worked out to focus on the aspects in perimeter.

My last and final task for the lesson was planned for the pupils to work in pairs to search for lots of shapes and not only rectangles, but limit to contiguous squares having an area of 12 cm2 and establish the perimeters. I showed a spider diagram of the centre part saying "What is the connection between perimeter and area?" on the board and let pupils to talk and explore this activity for roughly five minutes. They were to jot down what they had in mind.

I went around the classroom and interfered with their work to assist them to develop approaches to work in a systematic way and teach them to note the perimeters of each shape. Five minutes later, I discussed that there were "many" possible shapes. As a class we discussed at the work from a group and then questioned pupils to concentrate on discovering a shape of biggest perimeter and a shape of smallest perimeter. The one hour lesson finished with a last minute quick discussion of the students' outcomes, which highlighted the shapes of small perimeters were more compact. Also shifting one of the squares on a shape not including altering the number of contiguous edges will not change the perimeter.

My conclusion was that the area and perimeter can have similar or different numbers; two shapes can have different perimeters but have the same area.

These learning objectives were accomplished through three examples.


Reflection on my practice at my teaching placement was, without a doubt, the most essential method I had acquired during my PGCE course. Reflection on my practice at my teaching placement was, without a doubt, the most essential method I had acquired during my PGCE course. This utilized entirely to the assessment and evaluation of my own work and to the students. By initializing a scheme of checking and reviewing, in the perspective of the national curriculum, students are encouraged to be analytical and perceptive in the middle of a task of their individual work. The value of initializing this scheme is important. The students are not only given confidence to break down and reassess smaller chunks of their work but they can amend mistakes or have the tendency to tangent or set off activities in which, revising for a considerable examination, this activity could be particularly detrimental to the management of their time.

I have experienced the benefits by making use of a mixture teaching approaches and strategies being both the practitioner in addition to the students: engaging students in the creation and evaluation of activities, a combined ownership is began and a common sense of principle is produced.

It must be ensured that I must have a deep theoretical understanding of area and perimeter, and show rich pedagogical subject knowledge for teaching.

Given the important examples to the learning and teaching procedure, never-the-less time must be crucially spent utilising this perception to an exploration of examples and also the pedagogical propositions. I have learnt how to alter examples to make them more theoretically difficult or simpler, to create counter examples or to show a different approach. I used my opportunity from my placement to involve with examples, to trial them with students and to learn how to successfully adapt them to assemble needs of different kinds.

In each and every one of the parts in area and perimeter, it must be necessary to have an in depth discussion of the mathematical connections in addition to the mathematical topics and also finding how an example illustrates these connections. As a final point, there needs to be a discussion of how to apply the examples in the classroom, therefore the examples develop achieving, educational objects that show the preferred general principle. If these points were lacking, the chances for learning presented by examples may possibly go unconvinced.

Wendy's feedback that relates to you: You use no references in this section.


Tanner , H. & Jones, S. (2000) Becoming a Successful Teacher of Mathematics London: RouteledgeFalmer - spelling

Orton, A. (2004) Learning Mathematics: Issues, Theory and Classroom Practice. Continuum

Johnston-Wilder, S. & Mason, J. (2005) Developing Thinking in Geometry. Paul Chapman

Johnston-Wilder, S. & Pimm, D (eds) (2005) Teaching Secondary Mathematics with ICT. Maidenhead: Open University Press

Education Week: Evaluating Teacher Evaluation [WWW Document], 2012. . URL [Accessed 11 November] - who is the author?


Peer Review of Teaching [WWW Document], 2012. . URL [Accessed 11 November] - what is this? Who are cte at uwaterloo in California?


See plagiarism

My references - Keep the references above they need citing. So far I have cited one! I need to cite more! Here are the websites I used: - I used this pdf and changed words - this book, I have cited in the assignment as (Collin Foster, 2003) - and this book

These references were used from the pdf I got: