About Perfect Times

Contact e-mail: wendy@perfect-times.co.uk

• Introduction
• What is Perfect Times?
• National Curriculum
• Perfect Times Encourages
• Components For Fluency
• Maths for the masses: Wendy Fortescue-Hubbard


Introduction

Perfect Times is now available for sale on the WEB, as a CD and as a set of cards, details of which can be found on this website.

Perfect Times is an innovation for teaching the automatic retrieval of multiplication and division facts, a learning tool that has been invented to help children become fluent in multiplication tables.

• the pupils to want to play many times, thus practising their times-tables;
• the game to be simple and fun to play so that they could practise at home, leaving school time free for learning other mathematics;
• to be able to assess their fluency without the traditional testing techniques and excessive associated marking;
• the pupils to be able to monitor their own progress without having to display their failure but being able to show their successes to their peers when they chose;
• the pupils to be able to work at their own level and pace.

The success of the game has travelled by word of mouth. For example, one teacher moving from an Education zone to a University purchasing 70 sets of the game to give to her student teachers.

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What is PerfectTIMES?

Perfect Times is a game based on particular packs of cards, one each for the times-tables. Each times-table pack is made up of a set of factor cards (the 1-12 cards) and the multiple cards(the answers to the multiplication table being played.

The design of Perfect Times makes it easy to distinguish between the various times-tables and between the Factor and Multiple cards. Each times-table is presented in a different colour you can see the difference between the Factor and Multiple cards as these are shades of the same colour, with the Factor card being the darker shade. The Factor numbers are printed in white, the multiple numbers in black.

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National Curriculum

Teachers have long recognised that fluency of multiplication and division facts is an important skill to possess; indeed, there has been a statutory requirement for pupils to know their multiplication tables since 1988. Currently the Orders for the National Curriculum (1995) state:

Pupils should be taught to:

• learn multiplication and division facts relating to the 2s, 5s, 10s and use these to learn other facts, eg double multiples of 2 to produce multiples of 4, and to develop mental methods for finding new results ...KS1 PoS Number
• know the multiplication facts to 10 x 10; develop a range of mental methods for finding quickly from known facts those that they cannot recall; use some properties of numbers, including multiples, factors ...KS2 PoS Number
• consolidate knowledge of number facts, including multiplication to 10 x 10, developing use of methods for finding quickly from known facts those that they cannot recall; use some common properties of numbers including multiples, factors ... KS3 and 4 PoS Number.

• mental recall of multiplication facts up to 10 x 10.

Despite this statutory requirement, a definition of what ‘mental recall’ means is not provided. This has led to a variety of definitions, set by individual teachers, which has caused problems for teachers in different schools where no standardisation exists. This is particularly apparent between primary and secondary schools and is exacerbated by the fact that some definitions include time elements and concepts of fluency whereas others do not.

Interpretations of ‘mental recall’ include:

• Accurately recalling multiplication facts when no time limit exists.
• Reciting a table sequentially, for example ‘two twos are four, two threes are six.’
• Saying a sequence of multiples, for example ‘two, four, six, eight...’
• Considering a child to be fluent in a particular table when they achieve a certain percentage in a written times-table test.
• Working out the answers using a mediation technique, such as working through the problem on paper or by using their fingers.
• Responding quickly to questions rapidly fired at them in front of their peer group.

Previously I have employed a variety of different methods for teaching children their tables. For example: singing to times-tables tapes; writing them out over and over again; saying their tables in sequence to me; rapid fire questions in front of peers; written tables tests; playing ‘fizz-buzz’; looking for patterns. Some techniques were more successful than others.

Through a survey amongst city centre shoppers, primary school children and teachers, it became apparent that some of these techniques were viewed as negative learning experiences. This was indicated by responses to the term ‘multiplication tables’ which included such words as ‘boredom’, ‘dread’, ‘fear’, ‘rote’, ‘difficult’, ‘pressure’, ‘embarrassment’ and ‘intimidation’. Further research has suggested that rapid response to number fact problems led to children displaying intense feelings of discomfort. This can leave a lasting impression and lead to negative attitudes towards mathematics in general.

Quite often there is pressure from parents, who, in their efforts to help their children, teach them the way that they were taught, often passing on associated attitudes. One proud mother once told me how she helped her son learn his tables: ‘He hates having a shower, so I make him say them correctly before he is allowed out.’ The results of this research can be read in my MSc Thesis entitled ‘Multiplication Tables: The Associated Issues” through the University of Plymouth.

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PerfectTIMES Encourages:

High levels of motivation
People pay most attention to those activities that are fun, regardless of their usefulness. Perfect Times allows the player to carry out a necessary activity whilst having a great deal of enjoyment. Perfect Times is a competitive game. The competition is more often the player against him or herself than against anyone else, but various games allow Perfect Times to be played in pairs, groups, or even teams (relays). Perfect Times motivates players to want to improve their score, encouraging high levels of practice.

Immediate corrective feedback
When learning to become fluent at times-tables, it is essential for errors to be corrected as quickly as possible. Incorrect responses must not be stored in the memory for too long or the bonding between incorrect facts may be stronger than for the correct facts. The state of correctness forms an integral part of the game; answers are checked at the end of each turn, mostly in less than one minute, thus giving immediate corrective feedback.

Use of a variety of mental methods
Facts are best committed to memory when the learner uses a variety of mental methods such as looking for patterns, using what the player knows to find the fact that is not known. Some examples are provided in the help menu attached to the game. The player soon abandons these methods of recalling facts and will make a conscious effort to learn them in order to gain reduced time scores. However, research has shown that where a learner has worked out for themselves ways of arriving at the answer (as opposed to reading or copying out), they will retain their tables more effectively.

Non-sequential learning
Being able to respond immediately to any multiplication question requires being able to have random access within the memory to those facts. Learning tables in sequence – 1 x 7, 2 x 7, 3 x 7, or as a list of multiples (7, 14, 21, 28 ...) often means that pupils have to work through a table to arrive at a correct answer. Random access is more easily acquired if facts are learned in a random fashion. In playing ‘Times Up’, the main Perfect Times game, both the Factor and Multiple cards are shuffled, randomising the sequence between turns.

Quantitative assessment of fluency
Assessment of fluency can be made through the player’s time scores this ican be seen as a score as the game is completed. Research has suggested that fluency for non computer card version is achieved when a player consistently has total time scores under 20 seconds over 10 rounds. This does depend on their reaction time.

For a small number of people the reaction time (the time it takes to place the factor card on the multiple card once the answer is known) is slow enough to produce times consistently above 20 seconds. In this case the player should play ‘Times Up’ using the factor cards from any two sets of times-tables, matching factor card to factor card (i.e. 1–1, 2–2, 3–3 etc.) The computer finds the median average score by putting the 10 reaction times in order; add the 5th and 6th times and divide by 2. This median average is then deducted from the players’s Total Time. If the total score is consistently under 8 seconds then the player can be assumed to ‘know’ the times-table. Further research is needed to verify the scores from the computer version as computers are now faster.

This system of assessing fluency offers a standardised, quantative measure of mental recall that can be understood by all.

Using Perfect Times for those with special needs
Players can work at their own level. Players are encouraged to compare improvements in their own score and not to compare their performance with others. Perfect

Times is suitable for use with players whose first language is not English and where perceived inability in learning the times-tables is a language rather than a mathematical problem.

Perfect Times not dependent upon the ability to write. Hence Perfect Times can be used with young children or those who have difficulty in writing.

Perfect Times has been used successfully with children who have hearing impairments.

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Components For Fluency:

Properties to help develop fluency

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Maths for the masses: Wendy Fortescue-Hubbard

FELLOWSHIP

STRICTLY EMBARGOED: 19th November 2001
Wendy Fortescue-Hubbard, a highly talented and energetic maths teacher, has received a NESTA Fellowship of £75,000 over three years to develop her talents as a national media personality who will help to popularise maths, making it exciting and accessible to people all age groups.

Devon-based Wendy has been teaching maths for the past fifteen years and has devoted much of her time to developing alternative approaches to teaching the subject to both children and adults. Her teaching methods have been acknowledged as exemplary by the teaching standards organisation, OFSTED. Wendy has taught in primary, secondary schools and supported Dyslexic students in their mathematics at University. Wendy also writes maths materials for an educational publisher, has invented and patented a game for teaching and assessing fluency of multiplication and division tables, advised Channel 4 on their 'Maths Programme', has presented Royal Institution masterclasses and researched in mathematics education.

Through out her career Wendy has demonstrated her gift for teaching and inspiring others in mathematics. This has not only been in the classroom but also outside the more usual framework, through mathematics clubs, for children and for parents, and residential maths courses

She is regarded by her peers as a mathematician with exceptionally good, inspirational people skills, who has a vision of maths as the popular science of the future.

However, Wendy feels that her gift for teaching mathematics would have more impact on a wider stage with a national audience of children and adults, helping them to understand and develop an enjoyment of maths.

NESTA's Fellowship will enable her to achieve her key aim which is to develop the skills, contacts and experience required to work in a range of media, from television to newspapers on a national scale.

Maths is a subject that can become a mental block to a great number of people early on in their education which can lead to problems later in their careers. Wendy's gift for the subject together with her drive and energy will help break down the barriers so many people have with understanding mathematics.

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