Using manipulatives to support your child’s understanding in mathematics

Wyndham Park’s vision Our vision is to develop deep learning through everyone’s unique talents; giving each child a rainbow of experiences to take them through life.

The Elephant in the Classroom “Mathematics plays a unique role in the learning of most children – it is the subject that can make them feel both helpless and stupid. Maths, more than any other subject, has the power to crush children’s confidence, and to deter them from learning important methods and tools for many years to come.” Jo Boaler I’m sure if I asked you now what your experience of maths was like at school, there would be a mixed opinion in the room of people who had positive experiences and those of you who didn’t. I’m sure there would also be a split between those of you who like maths now and those of you who are scared of it. As our technology continues to develop, there is an increasing place for mathematics in the futures of your children. This means we have a responsibility to raise a generation of children who do not fear maths.

Positive encouragement “When you are working with your child on maths it is important to be as enthusiastic as possible about maths. This is hard if you have had bad mathematical experiences, but it is very important. Parents, especially mothers of girls, should never, ever say I was useless at maths! Research tells us that this is a very damaging message, especially for young girls.” Jo Boaler My biggest piece of advice from tonight is to encourage you to show your children that you like maths. That will be of more help to them than any workbook you can sit and do.

Aims of the National Curriculum The new curriculum aims that all children:  become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately. can reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language. can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

Manipulatives In maths, a manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name. The use of manipulatives provides a way for children to learn concepts in a developmentally appropriate, hands-on and an experiencing way. Manipulatives are used extensively throughout Wyndham Park.

Concrete, pictorial, abstract Concrete representation The enactive stage - a child is first introduced to an idea or a skill by acting it out with real objects. In division, for example, this might be done by separating apples into groups of red ones and green ones or by sharing 12 biscuits amongst 6 children. This is a 'hands on' component using real objects and it is the foundation for conceptual understanding. Pictorial representation The iconic stage - a child has sufficiently understood the hands-on experiences performed and can now relate them to representations, such as a diagram or picture of the problem. In the case of a division exercise this could be the action of circling objects. Abstract representation The symbolic stage - a child is now capable of representing problems by using mathematical notation, for example: 12 ÷ 2 = 6 The concrete-pictorial-abstract approach, based on research by psychologist Jerome Bruner, suggests that there are three steps (or representations) necessary for pupils to develop understanding of a concept. Reinforcement is achieved by going back and forth between these representations.

Numicon

Counting resources

Base 10 & place value counters

Maths passports Guide for parents to use at home with some key objectives at each stage. Opportunity to practise mental maths so are number based. Complete two boxes for each objective at home and then the third box will be completed in school. Use these targets to practise the different areas in fun and engaging ways.

“Education is not the filling of a pail but the lighting of a fire “Education is not the filling of a pail but the lighting of a fire.” William Yeats

Reasoning and applying Maths needs to be based in real-life contexts. In order to develop a love of maths in children, we need to make sure we are not misrepresenting the subject as pages of calculations. Mathematicians describe maths as the study of patterns whereas students describe maths as a list of rules and procedures that need to be remembered. Talking in maths is extremely important! Children need to be explain what they have done and why they have done it.

Games and ideas Keep maths fun! Sudoku puzzles, logic games etc. are far more valuable for helping children with their maths. Shopping – find me the cheapest tin of beans, calculate change Walking – house numbers, number of steps, cars driving by Cooking – doubling/halving quantities, measuring Board games and card games Problem solving questions Guess the number games Ask questions!

Clear the deck Objective: to practise number bonds to 10 with cards Remove the Jack, Queen, King and 10s from a pack of playing cards. Shuffle and deal out 9 cards in 3 rows of 3 (face up). Player A selects 2 cards that total 10 (and says the number fact). Keep going until no further pairs total 10. Replace cards that have been taken. Player B has a turn. The player with the most pairs of numbers to ten wins the game.

Basic, advancing and deep

Basic, advancing and deep activities Maths To add three 1 digit numbers Basic: complete number sentences using concrete apparatus to support calculation Advancing: answer word problems Deep: investigate whether there is a pattern when you add three odd numbers and explain findings

Maths reasoning test questions

End of KS1 expectations - maths

End of KS1 expectations – maths cont.