Key Stage 1 in the maintained schools is the legal term for the two academic years of schooling in the United Kingdom and Wales. Previously it was known as year 1 and year 2, this is when the children are between the age of 5 and 7. The key stage mostly covers pupils in their infant schools but also in some cases it might cover part of primary or first school. Mathematics is the study of space, shape, quantity and change, these is one of the subjects that poses a lot of difficulty to this infant learners. Mathematics formulates patterns, resolve the falsity or truth of conjectures through mathematical proofs.
Education act defines the term as the duration which begins with the normal school and starts at the age of six and end at the same time as the time as the school year where a larger number of students attain the age of seven. The purpose of this term is to define the group of students who must follow the National Academic Curriculum’s programmes. All students in this Key stage must follow a special programme which has ten statutory areas of study; these areas are always set out in the National Curriculum website. They include: Mathematics, English, Science, design and communication Technology, Music, History, Art and design, Geography, and physical education. Religious education is also statutory, non statutory frame work set out in the same web site is not necessarily followed. After this stage, pupils in UK aged 7 in their second year are assessed using a programme of assessment commonly known at the SATs. They cover only Science, Mathematics and English (Spooner, 2002).
Mathematics and shapes
Set of numbers and functions in many mathematical objects produce different internal structures as a consequence of relations and operations that are defined on the set. Mathematics is then applied to study the properties of those individual sets and later expressed in form of structures. This is the reason why laying a good foundation in mathematics is always important as it paves way to the later complex solution which are solved using the basis laid in the introduction of the subject to the individual. This calls for a detailed analysis on how to deal with the inefficiencies which may lead the pupils from not getting the targeted information. We are going to look at the mathematical errors and misconceptions in reference to shapes in mathematics for the pupils in Key stage 1 ear 2 (Doreen, 2010).
Mathematical errors and misconceptions
This report deeply examines the recent research done on the teaching approaches aiming to minimise the common mathematical misconceptions and errors made by Key stage 1 year 2 (primary- aged children). It targets whether applying teaching techniques which seek to root misconception as well as common errors is likely to be fruitful. Different teaching approaches are looked into based on dialogue, discussion and challenges existing among children’s mathematical constructions. Changes and choices in mathematics teaching techniques carry with them strategies which not only aim at the teaching practise but also a continues review of the teaching role within the foundation stages ( key stage 1 and 2) to have a firm setting (Spooner, 2002).
This analysis is ideal for primary trainees as it practically guides them in handling children’s misconceptions and common errors. It main aim is making them gain a deeper understanding on the challenges encountered when a good foundation is not laid at the early development of the concerned children. When this happens the individual child encounters difficulties throughout his or her cause (Doreen, 2010).
Difference between mathematical misconceptions and errors
The teacher’s response in handling errors in mathematics requires diagnostic terms: various responses will be suitable depending with the frequency of the error observed.
An error may result as a result of many reasons; misrepresentation of text or symbol, carelessness, lack of relevant knowledge or experience related to that concept/ learning objective/mathematical topic, inability or lack of awareness in looking at the answer given or as a result of misconception. Different mathematicians consider view of mathematical error or knowledge to be principally generated from the surface of knowledge: a good example is the pupil’s response to a task procedural and the only way to correct errors is by through the teacher providing alternative corrections (Scribd, 2011).
In addition, the nature of the task chosen by the relevant teacher should not be definite for children making errors. Considerations must be to the technicality or complexity of the task, that is; it should be sufficiently challenging but not too challenging. The nature of the task in reference to task translation should also be considered (Scribd, 2011).
Causes of mathematical misconceptions and errors
In this case, the children lack the importance of being keen in what they are doing thus the mind becomes reluctant, leading to poor judgement. This can be rectified by changing the mode of teaching; also the teachers should create awareness to the pupils of the importance of mathematical elements such as shapes, as they also help in evaluating the level of thinking of individual pupils (Hodson, 2008).
Lack of relevant knowledge
Teachers should work harder in equipping the children with all the basic knowledge, by so doing the children will gradually are in a position to handle more complex shapes as knowledge piles up. This will lay a good foundation in the decision making of the child as far as mathematical concepts are concerned because he or she has the knowledge and what is required of him/her is to understand the task (Hodson, 2008).
Problem in interpreting or reading
These challenges result from the incapability of a child to understand. Problems related to interpretation can only be handled through teacher’s effort to expose the children to different shapes and by so doing confidence is created within them. Having in mind that these are young children, repetition is the only key to meet this challenge (Hasen, 2011).
Misapplication of mathematical rule
This arises from lack of enough knowledge or exposure. When impacting a certain skill in the mind of little children, the teacher should put all effort in making sure that the concept is understood. It can by met through practise, frequent evaluation and emphasis (Hodson, 2008).
Error and misconceptions in reference to shape
The first mathematical aspect that young pupils explore is shape. This is to enhance them interact with the three dimensional world and later begin to understand its content. It also hence them to learn and understand their position in space and how hey are related to other objects. After they have learnt of the basics of shape they can later learn of the two dimensional position of their world and this helps in spatial reasoning development (Alice Hansen, 2011).
Early Years Foundation Stage’s Statutory Framework (DCSF, 2007) mainly aims at developing children’s ability to name and recreate patterns with shapes. Space and shape as well as measures, together forms Objective Target 3 of England’s National Curriculum. It aims at understanding properties of different shapes, applying and using shape and understanding properties of movement and position. Key stage 1 pupils aim at developing the language of space and shape while those in Key stage two aim at evaluating two and three dimensional shapes and their characteristics (Scribd, 2011).
Although this is among the first topics that children meet in the early encounters with mathematics, teachers should take it serious as it a complex subject. This awareness should be made to teachers (complexity of the subject) in order to help the children in identifying the challenges related to shapes. From their tender age, they begin to draw, this slowly brings sense to their 3 dimensional world through a two dimensional representation. That kind of representation is a form of language which is more convectional than the written or spoken language (Alice Hansen, 2011).
By being able to identify, analyse and later discuss different errors and misconception with the children, these opportunities will be easily used as they portray themselves through an excellent assessment. It makes it easy to evaluate the performance of the children as they levelled; they all have equal knowledge on the subject matter. Teachers at this level should ensure that this level ground is met to avoid laying down a poor foundation.
Shapes are critical in development of mathematics as they down the foundation of the next more complex level. This calls for more time and emphasis to make sure that adequate time the pupils grasp all that is required for them to avoid difficulties in understanding more complex tasks. Also the teaching modes should be looked at to ensure that the technique used best suits the subject, this aims at optimising the level of comprehending as well as interpreting.