Downsend School, Epsom Lodge, Leatherhead, 'Children's Mathematical Graphics: Moving into Calculations'. 21st April 2010.

'Today has helped me extend my maths passion – on what's already in place. I shall add resources outdoors and provide somewhere for the children to display their own marks - more mark-making provision. Resources such as calculators, rulers, weights etc., accessible with writing materials.'

' I have only positive comments about the day – it was very informative, with lots of new ideas, such as having paper within arm's reach and a reminder to enjoy our observations!'

'It was very useful to start off discussing play – what it is and how to observe and use… inside and out! The importance of talking with the children to find out their past experiences and their understandings. Value all graphics, give opportunities to make graphics all over and places for children to display and share them. Ask children, listen, guide, record progress. For me this takes children into their 'ZPD'. Thanks!

'Thank you! Today gave me a clearer understanding of children's mathematical graphics and lots of useful ideas to implement in the classroom.'

'Extremely useful and meaningful to use the taxonomy and go through the children's examples – so that now I shall be able to do this in my class. Now I understand the difference between recording and representing! Inspiring!'

'Thank you! A very informative day. This has changed the way I will think about maths in the classroom and I will begin to make some changes. Lots of useful ideas to use in class. It made me open my mind to letting children experiment and explore their own thinking on paper.'

'A very interesting and informative day – hopefully a start of change and a move away form worksheets! I'm going to find a board for the children to use for their mathematical graphics and put paper out everywhere. Thank you for sharing your wealth of experiences.'

'Very inspirational – thank you so much. Hopefully all the children will benefit form the new ideas. I shall definitely develop a Graphics Corner! Must relax and have more fun with the children and more mental thinking problems.'

'Thank you for an exciting course. It was interesting to look at children's graphics from such an early age. I certainly look forward to putting things into place next year when I join reception.'

Brent LA: 'Children's Mathematical Graphics: Moving into Calculations.' 22nd April 2010.

'Today has helped me think about my focus as a teacher. I'm going to think about resources that challenge and focus more on observations. The tutor was really responding to our needs – lots of opportunities to ask questions.'

'Excellent course – it's made me more aware of mathematical graphics, and the way children represent their own thinking. I'm going to try never to miss an opportunity when I've observed one, or question.'

'A really good day. I'm going to encourage mathematical graphics in 'writing' areas and pose problems for children to solve. I'm going to put maths resources in all areas and also paper and pens.'

'I shall inform other members of staff about the objectives from the session and develop and improve my own practice. Excellent.' (MaST teacher).

'The day met the objectives very well. I shall be more vigilant about children's mathematical graphics and continually be ready to respond to opportunities that arise.'

'Excellent day. I'm going to be more flexible in my teaching of maths and not so prescriptive! I shall encourage children to 'put something down to show…'.

'I shall continue to use children's mathematical graphics in classroom practice and disperse to Foundation / KS1 staff. Excellent.'

Redcliffe Children's Centre, Bristol, 'An introduction to Children's Mathematical Graphics': March 2010

'Very enjoyable – it was well presented and allowed for good group reflective work. It was useful to have an understanding of children's mathematical graphics, which will help me develop my practice. A really good day! Gave me lots of useful information to help develop my practice.'

'Useful to consider the differences between recording and representing; being given time to reflect and talk about examples and to think about developing a focus for maths. I'd like to know more about practical ways to develop the ethos that encourages children's mathematical graphics and ways to model effectively. A great day!'

'It helped me understand how 'recording' focuses on products and not on thinking. The taxonomy was useful – interesting to look at children's examples in relation to it. It was good to be given the book! I'd be interested to spend more time looking at the link between recording, product, thinking, etc., Great and informative day – thank you!'

'I enjoyed the day, especially discussions with other reception teachers, the examples of graphics and understanding 'mathematical graphics' and assessing their conceptual understanding. The day helped me understand the difference between 'recording maths' and representing [mathematical thinking]. Thank you very much! Can we form a cluster of interested people to continue this exploration of graphics?

'It was useful to moderate the mathematical graphics; to explore recording, I enjoyed today very much, especially children's thinking and modelling mathematics. The discussion with others about children's graphics and the tour of the Centre were very useful. A great day!'

'I enjoyed today very much – the chance to discuss ideas with teachers; practical ideas for encouraging children to represent their thinking and ways of moving children's thinking forward.'

'It was really helpful to learn about children's mathematical graphics and the distinctions between recording and representing. Helpful to network and compare experiences with peers. I'd like to know more about maths / calculations strategies to model. I'll looking at EYFS and explore ways to encourage children to develop mathematical thinking, especially problem-solving and calculation (e.g. how to resource areas inside and out). I enjoyed the day!'

'It was most inspiring and I learn a lot! Discussions with other practitioners was really useful and helped me think about trying to make maths more open. Lovely to see the Children's Centre! An excellent day!'

'Very informative. I found it helpful to hear from actual teachers form the Centre giving their examples and the taxonomy is very useful for assessment. I enjoyed the tour of the Centre.'

'I found a whole different way of looking at 'recording'. The case studies were really useful and realistic and I see that children don't always need to be writing maths in the 'correct' (horizontal) way. It was useful to network and to have a clear definition of what children's mathematical graphics are. The day gave me time to reflect.'

'Very enjoyable. It was really useful to listen to staff involved at Redcliffe and to hear the 'stories' behind the graphics shown, also the discussions with other teachers were helpful.'

'Yes thanks! Sharing practice, Emma and Carole's input and clarification of terms were all really helpful. I'd like to know more about all or any of this!'

'A really good day. It helped me re-establish what I'm looking for with maths and I got ideas from other teachers. Enjoyed looking around the Centre.'

'Thinking through examples with colleagues and lead practitioners and listening to the work of teachers at Redcliffe and research of others (Elizabeth and Maulfry) was really helpful. Very enjoyable day.'

'The moderation of children's mathematical graphics, exploring recording and [versus examples of] children's thinking and ways to model mathematics were all helpful to me.'

'A very inspiring day – I enjoyed it very much so! I liked the whole idea of having paper, pens etc., available for children's representations, just as I do in the making areas. It helped me understand how children can represent their thinking! Looking forward to getting to grips with it all!'

'It was helpful discussing ideas with others and gave me confidence. I like seeing examples of real life maths and the discussions and assessment with others was helpful. It's encouraging to see how children can use their graphics to solve problems. Thank you for a very interesting day and tour around the Children's Centre.'

'I liked the concept of 'open' activities that have real meaning for children. The idea of having paper and pens 'within reach' was useful and the day helped me recognise children's mathematical graphics. It gave me confidence and ideas to develop open activities and I was really pleased to have a day aimed at Reception teaching. Thank you!'

Weston College, BA Hons Course: Early Years - seminar: Feb 2010

'I very much enjoyed the session - the information relates to the work we are doing on our degree. It was really helpful to see how you can use children's mathematical graphics as evidence. It backed yup my previous knowledge and extended it.'

'I loved it! It was great - well presented and enjoyable. It was all useful and interesting, but most of all the examples of children's mathematical graphics. The session helped with my module 'symbolic representation', but most of all my practice as EYP. I'd like to learn more about different aspects of drawing. Thank you so much for sharing your knowledge with us.'

'I really enjoyed the session - especially the way the information and examples 'open-up' the mind: they give you a different way of thinking. It certainly overlaps all areas of the curriculum.'

'Enjoyed this morning's session very much - all of it was useful and of interest. It's really given me more confidence in mathematics in the class where I work. With practice I hope I will be able to recognise children's mathematical graphics. I enjoyed the session a lot. I am the one who avoids mathematics if I can. Thank you for the session.'

'It was an enjoyable session - and especially useful and interesting to analyse the children's examples. It really supports what we're doing on our course.'

Bristol: Redcliffe Children's Centre, Feb 2010: "An Introduction to Children's Mathematical Graphics – the Williams' Maths Review: Teachers share their insights"

"Thank you both very much for a great course today. It has opened up a new area of understanding for me and does seem to bridge the gap in the EYFS Calculating strand of PSRN where children are arranging objects with intent and categorising objects according to properties - and then they are suddenly using numbers to solve problems. This makes visible their thinking and development from the real physical world to abstract symbolism. Now I recognise it I need to work on how to support and extend it."

"A very informative course that made me more aware of the graphics already happening. I enjoyed discussions with other colleagues, examples of mathematical graphics and the challenging questions. A very stimulating thought provoking day!"

"I very much enjoyed the day – especially lots of practical examples, the theory behind concepts and the range of practitioners. It would be helpful to know more about problem solving and marks and their meanings. I'd like to have more training – practical ideas for assessment with foundation stage."

"It was helpful to hear the distinction between recording maths and representing (mathematical thinking). I enjoyed seeing all the examples of children's mathematical graphics and discussions. I'd like to know more about how to extend children's thinking – understand the valuing children's meaning and have examples of how it was extended. Thank-you."

"I really enjoyed the day, especially the discussions of examples, listening to case studies and key points of pedagogy). A really interesting day – thank to all!"

"I enjoyed today very much, it was very relaxed and comfortable and very informative. Really helpful seeing examples of mathematical graphics, discussions with practitioners, hearing about the CM network group, and the website for further information. I'd like to know more about moving from informal to formal recording."

"Yes – a really good day. It was really helpful to see all the examples of mathematical graphics, the case studies, and to have key points of pedagogy."

"I enjoyed the course very much. Learning about the difference between 'recording' and 'representing' maths was really helpful and I enjoyed the tour around the children's centre, especially looking at planning methods – and talking to other practitioners. It would be really helpful to know more about calculation."

"I enjoyed today, especially the ideas on resources and the case studies. I'd like to know more about using children's graphics as evidence for assessment."

"A great day – very interesting – lots to think about! It was really valuable to see all the examples of mathematical graphics, focusing on children's mathematical thinking and children making connections through their making."

"I enjoyed today and was please to have the Network meeting information. The course helped me think about the representation of mathematical thinking and validation of own ethos."

"I'd like to know more about children's mathematical graphics across Key Stage 1 and the formal nature of maths and calculation. "It was an informative, interesting, and necessary day, emphasising the value of really listening to children – building on their maths, importance of modelling on a daily basis."

"I enjoyed the day – lots of practical ideas, raising the profile of mathematics. Inspiring talking to others. I'd like more of an understanding of 'representing quantities that are not counted'."

"I enjoyed today's course and found it helpful listening to the teachers' case studies and having group discussions. The course gave me time to think and discuss and I enjoyed looking around the nursery setting. I'd like to know more of an understanding of 'representing quantities that are not counted'."

"I found today's course enjoyable, especially linking theory to practical examples, talking to other professionals about feelings on maths and looking round the nursery setting. I'd like to have a better understanding of the taxonomy of children's mathematical graphics."

"The day was very informative. It was great having lots of examples to look at of children's work, having a list of publications to look at further, and the opportunity to talk with other colleagues."

"A very thought provoking day - good to engage the brain in other things! Very pleasing, interesting day!. The presentation case study by Carole and Emma was very inspiring, and discussion of the teachers' examples and where they fitted (on the taxonomy)."

"An enjoyable day - really good balance between practical and theoretical approach. It was helpful to have all the examples of practice and discussion in groups. I'd like to know more about connecting children's graphics to more formal development of maths."

Comments from teachers' and practitioners' course evaluations, 2008-2009