|
Introduction
This numeracy pack can be used as an individually owned resource in accordance with the National Curriculum for children who require additional tuition. It is ideal for one to one, paired work or small groups of children.
Primarily it is aimed at those who perhaps have missed-out on the early building blocks of maths and have gradually fallen behind over time. It can be used both at school and home. The emphasis is placed on making maths real, fun, relevant and meaningful with the intention of developing a child’s confidence, independence and motivation.
Equally this pack could be useful to fast-track a child through the required learning stages of the National Curriculum or where simply reinforcement of mathematical skills is required.
The resource can be moved with the child as they transfer through each year-group, but also used at home to reinforce and compliment tasks undertaken in the classroom.
Alongside this, there is responsibility in that the child takes ownership and looks after the contents of the pack. Resources can be added-to and removed depending on progression.
The resources provide a foundation for understanding the mathematical world, the ability to reason and hopefully to give a child a sense of excitement and curiosity about the subject.
Maths is essential to everyday life. As children learn maths, they need to acquire fluency in procedures and develop a conceptual understanding if they are to be able to solve increasingly complex problems. Attitude and self-perception with regard to mathematical abilities commences very early-on, even before starting school and can have a significant impact on life choices. Creating links between numbers and a child’s environment helps to foster creative thinking and embed robust mathematical knowledge.
The contents list includes the resources suitable to provide a programme of activities. School and parents can decide which are likely to work best. The contents however are those that many children often need to refer back to, in order to grasp a concept, or to make sense of a problem by having the concrete tools to work through a process.
All of the resources are used as part of Key Stage 1 (year 1/ 2) and 2 (year 3/4) described in the National Curriculum. However, a child in year 4 to 6 may equally benefit from revisiting these areas. Furthermore, a child who is struggling in senior school may find some of the materials relevant to their stage of development. In other words, there is no defined entry and exit point.
Contents
 Shapes, 10 three dimensional;
Number cards, 0 to 100;
Counting bead string, 100 beads;
Cuisenaire rods, - connecting maths counting rods;
Connecting Unifix counting cubes;
Dice, 2;
Metric tape measure;
0-100 number line;
1000 grid square;
Multiplication wheel;
Fraction fan;
Negative number line -20 to +20;
Calculator;
Clock Face;
Maths vocabulary cards, set of 17; |
Shapes, 10 two dimensional;
Counting bead string, 100 beads;
Plastic money, notes and coins;
Connecting fraction tower equivalency cubes;
100 Counters, multi-coloured;
Geoboard and elastic bands;
Maths symbol, (Function cards) 9;
100 square grid A5;
Multiplication square A5;
White board grid, 120 square/20 square;
Coin fan;
Place value slider;
Electronic timer;
Geometry set, rule, protractor, set square;
Feelings/Reflection fan. |
 |
Click on image for larger view |
|
Mathematical Development
Prior to starting school, children are often using early maths skills throughout their daily routines and activities, notably in play, without even being of aware of it. Children learn such skills by building on their natural curiosity and having fun. Furthermore, young children are often exposed to stories and songs that use repetition, rhymes and numbers. Maths skills are just one part of a larger web of skills that children are developing in the early years, - including language, physical and social skills. Each of these areas is dependent on the other and vice versa. As a child enters school they will then access ongoing engagement that allows them to grasp:
An understanding of size, shape and pattern;
An ability to count verbally, (first forward, then backwards);
Number recognition;
More or less of a quantity;
An understanding of one-to-one correspondence, (i.e. matching sets, or knowing which group has four and which has five).
More advanced skills soon develop as children consolidate those early building-blocks and move through Key Stage 1. Crucial areas include:
Number Sense: an ability to count accurately, - first forward, then later, to count backwards. A more complex skill related to number sense, to see relationships between numbers, - adding and subtracting.
Estimation: guessing how much, or near to, - in quantity, size and measurement.The ability to make a good guess about the amount of size of something including the meaning of words or phrases like: more, less, bigger, smaller, more than, less than.
Representation: making mathematical ideas real by using words, pictures, symbols and objects, (like blocks).
Spatial sense: gaining an understanding of shape, size, space, position, direction and movement.
Measurement: investigating the length, height and weight of an object using units, including measurement of time
Patterns: numbers, shapes, images, - that repeat in a logical way. Patterns help children learn to make predictions, to understand what comes next, to make logical connections and to use reasoning skills.
Problem-solving: The ability to think through a problem, to recognise there is more than one path to the answer. It means using past knowledge and logical thinking skills to find an answer.
Throughout early schooling, children engage in a wide range of purposeful activities which involves them in different modes of mathematical learning, including playing, exploring and investigating, doing and observing, talking and listening, asking questions, reflecting, drafting, reading and recording. By giving children these skills in numeracy, they begin to make informed and responsible choices and decisions.
What then goes wrong for some children and why?
So why do children struggle? Why do they switch off or when does the pause button go on? Often children become stuck or dissociated with the real value and understanding of mathematical concepts.
Too many concepts can result in weak foundations. Mathematics can place a significant demand on children: it requires the acquisition; organisation and access to knowledge; rules; techniques; skills and concepts with the aim of solving problems. It can be seen as a combination of organised knowledge and creative activity. It requires abilities in visual and verbal skills, spatial skills, linear and sequential skills. It requires large amounts of information to be stored and retained ready for swift and automatic access and retrieval from long-term memory. The language of mathematics is also full of challenges, - sometimes offering no support from context.
Many children it seems do not have adequate exposure to or an experience of exploring concrete number that surrounds them and unfortunately, within a relatively short period of time, are expected to record and quantify number onto paper without grasping those formative concepts. Foundations can therefore be easily shaken as children are encouraged to progress to computation and abstract reasoning.
From personal experience of working with children who struggle with maths, it is apparent that many experience significant difficulties in retaining and recalling information, ordering and sequencing, including the speed at which they process information. Areas where I have found children encounter problems relate to:
Counting objects, including moving forward and backwards;
Processing and memorising sequences;
Understanding the structure of the number system;
Understanding place value;
Confusion with fractions;
Combining and partitioning numbers;
Reciting times tables;
Learning number facts by heart;
Recall of fact derived strategies;
Calculations on paper;
Reading mathematical problem-solving tasks;
Abstract mathematical language;
Estimation;
Sequencing of time;
Confusions with left and right;
Reading data including graphs;
Drawing shapes.
Working Memory
Many children with maths difficulties often have weaknesses in retention and recall, - visually, spatially and auditory. This in turn causes difficulties with processing and their making sense of number. For instance, a child trying to add 10 and 12 mentally, has to hold both of the components and the sum in memory. Working memory difficulties can prevent the child from moving onto the next stage because they may have forgotten some or all of what is required.
Working memory ability is the capacity to hold and juggle information in short-term memory and if overloaded, information may be lost. There may also be inaccurate representations in long-term memory, in manipulation and sequencing data as well as difficulty with rote learning. Some children can struggle in learning the basic mathematical facts, particularly number bonds and times tables. Without those early building blocks, a child is likely to fall behind, which can impact significantly on self-esteem and motivation.
A poor working memory can have an impact on a child’s capacity to:
remember and carrying out instructions;
recall recently-learned vocabulary;
verbalise an answer even though they may know what they want to say;
remember facts, figures, technical/specialised vocabulary;
place things in order.
Sequencing
Another common challenge is a child’s capacity to sequence. They may find it hard to hold information in their head and re-order it. There may be a lack of automatic access to number facts and slow processing ability. This may include the concepts of left and right, more than and less than, bigger and smaller. Sometimes children can reverse numbers such as 25 as 52 and be unclear on how to begin a process. This includes directionality. The challenges of remembering processes and sequences, laterality and directions can be a significant struggle for those who are not confident with maths.
Processing Speed
Children with numerical differences can work much slower and take time to attend to, interpret, process and respond to incoming numerical tasks, thus hindering how much they may be accessing in the classroom. The rate at which a child learns often needs to be much slower and repetitive. A delay in speed of information processing may be evident when there is a delayed reaction to incoming information; reduced pace of work; reduced concentration span; slow reaction to information or instructions; reduced understanding and response to a continuous flow of material.
The Language of Maths
In order for a child to progress, a clear understanding of vocabulary and definitions linked to practical examples is vital. Language needs to be learnt and applied within a child’s environment not just at school but at home and in the community, so that it becomes meaningful.
A child is required to have a good basis of reading skills. Often children with literacy difficulties can experience similar challenges with interpreting the meaning of mathematical questions. It is essential therefore to be able to read the question accurately, to be able to decode the words and make sense of content. Mathematical reasoning for instance, requires breaking-down problems into a series of simpler sub-problems or steps; making decisions about gathering, processing and calculating to acquire new information; showing perseverance in finding solutions.
Confidence/ self-esteem and fear
Sometimes children crash and experience a block with maths, indicating mathematical anxiety. I’m not good at maths,… I can’t do… I don’t know what to do…. This situation can gradually build up and be self-reinforcing. The more a child has negative exposure to maths, the more this can lead to failure and low self-esteem, - a negative cyclical role begins to develop which becomes entrenched over-time. Positive affirmations are essential through a child’s learning experiences. Being able to identify success is crucial within every stage of learning. Developing a child’s strengths and feelings of positivity, correlates with encouraging curiosity, - the desire to enquire, understand and ask questions. This can only be promoted when a child feels good about themselves as a learner and able to identify successes.
As a child progresses, they need to feel safe to make a mistake. Rather than being exposed to negativity, they should be encouraged to have a go and will soon realise that making mistakes is part of the learning process. Positive affirmations such as ‘ I can…. ‘ ‘ I am…. ‘ I will….are crucial’.
Parents too have a significant role in helping their child to have an interest in maths and to make sense of their physical and social world; to build on previous experience and knowledge, to scaffold them as they strengthen problem-solving skills and reasoning processes, as well as representing, communicating and connecting with numerical ideas. Furthermore, it is vital that a child is given ample time and materials to revisit earlier concepts but also to engage in play, - a context in which they may explore and manipulate mathematical ideas with keen interest; learn through a range of appropriate experiences and teaching strategies.
My N Pack has a psychological underpinning by using a solution focused approach that aims to enable a child to see a way through the problems they experience in maths and to build skills to understand those that they may encounter in the future. It shows there are options and solutions as a means of making a difference to how they feel about maths and how to apply new skills.
By focusing on strengths, it is important to help a child develop good self-esteem, confidence and resilience. The approach puts the voice of the child at the centre of solution-sourcing, together with how they perceive themselves as a learner and how they would like the future to be. An emphasis is placed on collaborative talk and shared experiences throughout the activities. Having a key adult to work with, where an attachment is formed, - a trusting relationship where a child accesses emotional security and self-esteem, can only bring out the best.
A solution-focused approach offers proven ways of supporting an individual to overcome a whole range of difficulties, - by helping to identify strengths and achievements.
A key component of My N Pack is discussion, - talking about:
 What do you have to do
How are you going to do it
What resources do you need
How well do you think you did.
In addition:
I wonder what would happen if…?
Can you explain your thinking?
Why do you think that?
How does this link to other tasks you have worked on?
Semi Structured Questionnaire
My N Pack suggests you start with a semi-structured questionnaire, - before any engagement with learning tasks. It is optional. The aim is to extrapolate a child’s view and to build up a picture as to how they perceive themselves as a learner and what they are hoping to achieve. It is adaptable for the age of a child in Key stage 1 and 2. Generic questions may include:
What do you enjoy doing the most in school?
Tell me about your friends and what you like to do?
How do you learn best?
Tell me something that you are quite proud of?
Tell me what you enjoy doing the most?
What don’t you enjoy, can you tell me more about this?....
What help do you like and how does it help you in school?
Tell me where you sit and whether this helps you?
If you were stuck, who would you ask for help?
How confident do you feel about doing this?
Do you like working in a group?
Tell me what you do in group tasks?
What do you enjoy the most in maths?
What do you find difficult in maths?
If you get stuck, how do you know what to do?
Out of 10, how confident do you feel with your maths work?
Feelings Fan
The feelings fan is a useful resource in the pack to help a child communicate their understanding of a topic or feelings directly, visually and confidentially to the adult. It can be used at the start and or end of a session:
How did you feel about doing the activity, - very happy…… ok……worried….tell me more..
Do you understand everything…. some… none….
What made you feel like this face…. Why was that?....
My N Pack- Programme of activities
The following framework provides a basis for implementing the requirements of the updated National Curriculum and programme of activities.
In delivery, it is important to consider:
Presenting new information in small chunks, - no more than 20 to 30 minutes per day.
Setting limited but realistic targets.
Making learning multi-sensory.
Allowing plenty of time for recall.
Providing support materials to be used outside of the session.
Having materials on display.
Encouraging the use of memory, - what did you do… how did you do it…. tell me about……
Recognising numeracy in the environment and having fun for example, - point out the different shapes found around your home; shopping and
talking about the quantities of anything you buy; handling money and working out how much things cost; looking together for numbers on street signs and car registration plates
Organisation, - the child putting the equipment away.
Whoever works with the child, the general advice is:
Talk about and involve the child in the situations in which you use maths in everyday life;
Play games involving numbers and/or logic, such as card games, dominoes, darts, draughts, chess etc;
Stimulate the child’s thinking at times of boredom, (such as when travelling), with mental activities;
Refer to maths in the environment, stimulating exploratory skills and curiosity.
The main focus is to ensure that children develop confidence and fluency. This should involve working with whole numbers, words and the four operations. Children are encouraged to have access to practical resources and to use the associated vocabulary; to develop their knowledge and understanding of mathematics through practical activity, exploration and discussion. A child has to feel safe about making mistakes.
Key areas of focus are on:
Number and place value
Number ordering
Number sequences
Addition and subtraction
Division and multiplication
Money
Time
Shape
Position and movement
The suggested activities and resources are organised in a flexible format so that a child can go over early building-blocks to re-visit or consolidate knowledge. Maths is a highly inter-connected discipline. Children should therefore be taught to practice and then apply their skills to a range of problems, not only at school but in day to day activities at home. Such activities may be dependent on the programme being delivered at school and therefore serve to reinforce concepts and mathematical language. A child should be encouraged to make connections across mathematical procedures and concepts to ensure fluency, mathematical reasoning and competence in solving problems.
All of the activities are taken from the National Curriculum Programme of studies with a focus on Year 1 to 4. However a child in year 6 may benefit from consolidating earlier numeracy concepts.
The National Curriculum suggests certain activities and these are shown alongside more generic tasks.
Dr. Clare Boorn
Educational Psychologist.
|
