Having undertaken various mathematical activities that emphasised mental mathematics with their children, class teachers and Numeracy project co-ordinators completed questionnaires that asked them to comment on their experiences with the work. Where possible teachers were asked to provide examples of the ways in which they had seen any improvement in children’s performance.

Children are more confident in using the correct mathematical term and understand that there is more than one way of expressing the same thing

More children are willing to attempt to explain their strategies using appropriate language. They realise that knowing the answer is not enough.

Children are able to discuss mathematical concepts to a higher level using the correct language

Children are more specific in their explanations

The confidence in and enjoyment of using mathematical language seems to improve understanding of and willingness to tackle a problem

The children are focusing on vocabulary and understand what they hear better

Children like the idea of a "new" word

They explain more logically, they are beginning to think more in patterns

This happens a lot more frequently in lessons, detailed answers are given and much discussion about alternatives ensues

Their vocabulary, including words such as product, mean, factor, multiple has increased due to the revisiting of these in the variety of games

There has been an improvement in their immediate recall of number bonds and tables which enables them to concentrate on the mathematical concepts involved in the problem

For number bonds they don’t use their fingers so much

Improvement seen, by quicker times in "Follow me" games and quicker responses to questions

They are answering questions quicker and work is more accurate

A few children have used knowledge of the 4 rules in problem solving and double check using reverse operations

When doing a topic on the Romans, children talked about tiles fitting together and shapes

When you revisit a curriculum area, recall of facts seems easier

There has been some improvement in basic number knowledge, but I feel more significant improvement relates to use of strategies built on from facts

E.g. 5 x 199 = (5 x 200) - 5

The tests have highlighted some gaps in learning/understanding

Oral work is a very useful tool, this has helped me to assess their understanding

With this oral work you are able to notice children who were hesitating and are now responding faster

You can see instantly areas of weakness and are able to plan appropriately to overcome these

It has helped identify children who have not understood what we have been doing in class, and those who have a clear understanding - therefore work is planned accordingly

Able to build on gaps in knowledge and emphasise work which causes problems

Mental and oral work has allowed me to better assess children’s knowledge - lack of skills and knowledge is often "hidden" in exercise books when they are working in groups

Mental/Oral work is a very quick and effective way of finding what they know. You can find out where the gaps exist and address the deficit promptly

Improved scores in tests

Improvement in SATs results

Children look for quicker ways to calculate now

Children are continually looking for new methods, always eager to share with others. They look for patterns and use knowledge more easily

They are now able to explain their methods more clearly, instead of saying "I just knew the answer"

Their explanations are clearer and they are adopting a wide variety of methods to solve the mental calculations

 

Comments related to other significant features of the project

Good listening skills are required for some of the games and the children have realised how important it is to listen

Children have needed to sustain concentration and improve their speaking and listening particularly for the "Follow me" games

Some children are now obviously listening to the full question e.g. "Draw a square with a triangle inside it"

Children do not ask so often what it means

Increased enthusiasm and confidence now, because they are experiencing success

Children are more prepared for listening and respond more successfully to questions

More children are drawn into the activity and concentration improves

They are able to comprehend language used in different contexts

They do not wish to be heard answering questions incorrectly hence an improved focus on what is being said, is developing throughout

Improved listening skills are seen in children by their greater attentiveness and improved behaviour

Yr. 2 children are asking to have questions repeated for clarification - whereas previously they would not have bothered or would not answer or would make a wild guess

Mental mathematics is now on daily planning, all staff have copies of activities. We used an INSET day to devise materials

The approach of using mental mathematics in all stages of our planning has been found to be very useful

Above all, the children have seen a fun side to learning maths through games

We will be including an extended range of vocabulary at the next revision of the Scheme of Work

Mental maths has become an integral part of our teaching and planning throughout the school

Mathematics Language is more specifically detailed

It is intended to ensure that the rest of KS3 children are covered by the project

I feel the whole school has benefited considerably and the strategies encouraged by the project are well embedded in teaching in the school

Numeracy units are being written into topic units in order to create relevant numeracy skills within areas of the curriculum

It made us focus at all stages on improving numeracy

The project has made the whole school rethink how it should plan its’ maths and the emphasis has moved towards more mental and oral approaches

Co-ordinator observed mental maths sessions, looked at results, discussed with year group

Mental maths was timetabled to ensure it happened

Mental maths was included in our curriculum planning

Looking at test results and analysing has been a useful monitoring tool

Co-ordinator has been given release throughout the year to observe mental maths activities and look at weekly plans etc.

Feedback to staff meetings

The first test showed gaps in children’s understanding of mathematical language. These were addressed in teaching sessions. Both subsequent tests showed improvement as has their work in the classroom

The sharing of games and activities with people from other schools and then being able to offer these ideas to colleagues has enriched our Scheme of Work.

I feel that I have learnt as much as the children in this numeracy project. It has greatly influenced my teaching of Maths. I have found the activities to be fun and they have helped me see Maths in a different way as a non-specialist

Have come away with many ideas to try out and for staff development and training

Teachers have been keen to receive fresh ideas to support their maths teaching

The cluster group meetings have also been enjoyable and worthwhile with the sharing of resources/ideas being a key factor in their value

Children really enjoy these sessions and are extremely enthusiastic

Children are quicker to stop chatting

They feel a lot more confident expressing relationships between numbers and describing numbers

Children are more flexible in their thinking

Children are better at holding concepts in their heads

Children are less anxious when formally tested

Different methods of solving numerical problems has been a big teaching point

It has been important to raise the children’s level of confidence; many felt threatened by oral questions and froze, even when they were perfectly capable of answering. I have noticed a greater willingness by children to take risks

Good preparation for implementation of Numeracy/Maths hour next year

"I have got better at working out sums in my head" ( said by a pupil and a teacher)

We were easily able to adapt the games for the SEN and EAL children and also to extend the more able

More able children have particularly enjoyed creating games

Less able children have generally enjoyed the activities and it has been possible to see their progress with the recording in games.

Children were tested on 3 occasions within the academic year.

September this formed a baseline assessment

February a mid academic year assessment

June an end of year assessment

It was recognised that the transfer from Year 2 to 3 and Year 6 to 7 was a significant change for children. Therefore, to have a more accurate representation of the child’s performance it was desirable for the June test result to transfer with the child and become their baseline assessment for the new academic year, which also avoided any unnecessary re-testing. However, this was not a viable proposition, within the constraints of this project, for children transferring from Year 6 to 7. Thus in Year 3 only, teachers were given the option of not testing in September and using the Year 2 June test result as the baseline assessment for children in Year 3. New entrant children obviously had to complete a test in September.

The tests were administered orally

Each test had 3 sections

Number

Non Number

Problems

The total for each section was recorded on the child’s answer script so that teachers could have a detailed view of the child’s performance.

Optional Test Papers were introduced for the February and June tests, to be completed in addition to the Standard Test Papers. This was to provide questions to stretch the most able children. The guidance given to teachers for identifying which children should sit the Optional Test Papers was:

the most able "handful of children" or

children who dropped only 2 or 3 marks in the standard test that all children completed.

Mark schemes were provided for all test papers to try to standardise the allocation of marks. However teachers were encouraged to use their professional judgement, where appropriate, but ensure there was standardisation of marking within their school.

In order to test the fulfilment of the objective "quick recall of ……" time restrictions were introduced into the tests. There is a range of time allowed between questions, and again teacher’s professional judgement was expected. Recommendations were to allow 3 to 5 seconds for questions requiring instant recall and 15 to 25 seconds for more complex questions. Teachers discussed the strategies needed to deal with the time constraints with the children e.g.

listen to the question more carefully so you understand what is being asked on its first reading

learn the mathematical facts required so that you can perform mental calculations more efficiently

Following the completion of the tests and before children received any feedback on their achievement there was an option for children to complete a self-assessment pro-forma. This was to encourage children to reflect on what they had found easy/difficult in the test and to identify specific targets for themselves. This, as a method for raising children’s motivation and involving them in taking charge of their learning, is backed by research carried out by Dylan Williams and Paul Black, Kings College.

It should be noted that the Standard Test for each year group was to be completed by all children in that year group. Therefore teachers needed to explain the implications of this to some children.

Samples of the Standard Test Papers

                    1. What is two more than 5 ?

2. What is 7 take away 7 ?

3. What is half of 6 ?

4. Add 6 and 3 and 5 ?

5. Write down the number 81 ?

6. 10 add 6 equals ?

7. 30 subtract 5 is ?

8. How many tens are there in 34 ?

                    9. What is the next number 198, 199, 200 ?

10. Hold up the beaker diagram and write the words Less, Half and More on the board. How much water is in the beaker, Less than half full, Half full or More than Half full?

11. Draw a square then draw a circle on the left side of the square.

12. Hold up a clock face showing 9 o’clock. What time does the clock show ?

13. You need 50p to buy stickers, how many 10p coins do I need to give you?

14. If a strip of paper measuring 6cm long and another strip measuring 11cm long are stuck together, how long are the two strips together ?

                15. What would you measure the length of your finger in centimetres, metres, or kilogrammes ?

Pupil Self-assessment to be completed before any feedback of results or answers is given to children

The only information provided by the class teachers was the raw data i.e. children’s test results by section. This data was entered into the spreadsheet and all calculations (totals, percentages and targets) were built into the program. In addition the programs’ design automatically generated the "Progress comments" for each child.

The percentages calculated in the class summaries, at the bottom of the spreadsheet, were based upon those children who completed the relevant tests.

The aims of the spreadsheet were

to be a labour saving mechanism for teachers

to highlight children’s progress in detail

to provide a tool to identify the specific needs of a child or groups of children

to assist in the setting of targets for individual children

to facilitate the monitoring of children’s progress and achievement through testing, re-testing

Pip Huyton, using Microsoft Excel ’97, designed the Spreadsheet.

identify an individual child’s strengths and weaknesses in the 3 different sections of the test

monitor an individual’s progress in each section

obtain a target for the June test based on the child’s performance in the earlier tests

select a child or group of children whose test result and/or progress comment indicates the need for intervention strategies such as extension work, reinforcement or additional support

monitor the general performance of the class using the Percentage of Higher and Lower Achievers

help to ensure consistency of curriculum delivery

use the Charts as visual representations of children’s performance that can be discussed with relevant stakeholders i.e. parents, governors, etc.

Very useful for class teachers to focus on areas of individual children

Graph made easy reading

Valuable evidence to assess progress in different areas

Children liked the target setting as they were keen to improve their scores

Very useful in monitoring success of the teaching strategy

Where children have not improved the difference in their scores is generally small and teachers have attributed the decline to absence from school or poor test technique

Add SAT Teacher Assessment or Baseline Assessment from the previous Key Stage to give an additional indicator of progress and/or achievement

Include the child’s gender and ethnicity to monitor performance of specific groups

N.B.

All averages are mean averages.

The pupils participating in the project came from a variety of schools with widely differing intake profiles.

A copy of the Booklet can be obtained from Ann Longfield.  If you require further information about the project contact Rosemary or Pip Huyton.