References, Maths and P4C

References, maths and P4C

Association of Teachers of mathematics: A range of excellent resources available from www.atm.org.uk For example: Talking Mathematics, , Introduction to the Soroban Ball, D. 2003. Decoding Mathematics. ATM Bloomfield, A. and Vertes, B. 2005 People Maths: Hidden Depths ATM Movement and collaborative problem solving, develops interactive reasoning, negotiation. Watson, A and Mason, J 1998 Questions and Prompts for Mathematical Thinking. ATM Bills, C. Bills, L. Watson, A. and mason, J. Thinkers A range of examples questions, reasoning approaches eg always sometimes, odd one etc We can Work it Out.books 1 and 2 Collaborative Problem Solving for the mathematics classroom. Number without a worksheet for reception and year 1 ATM

Number Talk: Parrish, S. 2014 Number Talks: Helping Children build mental math and computational strategies, grades K to 5. California: Math Solutions

Brunel University project developing mathematical fluency in KS1 www.talkmathstalk.co.uk

Talk Maths Camden https://www.camdentds.co.uk/cms/v.asp?rootid=11&depth=1 Humphreys, C. and Parker, R. 2015 Making Number Talks Matter; Developing Mathematical Practices and Deepening Understanding; grades 4 to 10. Portland, Maine: Stenhouse Publishing.

Let’s Think Resources Let’s Think Through Maths for ages 5 -6 and 6 – 9 Thinking maths in the Primary School PCAME Available through GL Assessment http://www.gl-assessment.co.uk/products/lets-think-through-maths and information from the let’s think website: http://www.letsthink.org.uk

SMILE Maths SMILE: Whole Class Mathematics Projects. Collaborative project work for KS3 and 4 Quadrilaterals and Triangles p75 properties of shapes and justification https://www.stem.org.uk/elibrary/ Reasoning: Activities for developing thinking skills. SMILE Puzzles, ideas for reasoning and deciding Real Data. Statistics Projects for KS3 starting with hypotheses leading to enquiry and test. SMILE

1 First Steps mathematics downloads (diagnosing pupil misconceptions in mathematics) http://det.wa.edu.au/stepsresources/detcms/navigation/first-steps- mathematics/ Cross- Curricular If the World Were a Village by David Smith is a graphic portrayal of world demographics using a village of 100 people. (for example, 22 out of the 100 people speak a Chinese dialect). Many other stimulating activities relating to social and environmental issues can be found in Teaching Mathematics as if the Planet Matters. By Coles et. al. These include ‘The Fairtrade Game’ and ‘A Sustainable School’. The daily news provides numerous starting points for questioning and enquiry into environmental and social issues which makes the subject relevant and topical. See also Walsh, M 2008 10 Things I can do to Help My World Gutstein, E and Peterson, B eds. 2013 Rethinking Mathematics: Teaching Social justice by the Numbers. Milwaukee: Rethinking Schools.

The Librarian who Measured the Earth. By Kathryn Lasky tells the story of measurement of the diameter of the earth using measurement of the sun’s shadow.

OXFAM and Save the Children produce packs about food production and food security Go Bananas (OXFAM), Welcome to my World (Save the Children). These can be used as starters for data handling, display, comparisons, drawing conclusions etc. More links can be found on the SAPERE website www.sapere.org.uk under links and P4GC (Global Citizenship)

Maths events and longer projects. Loewenstein, J 2003 Maths all Week. London: BEAM Education A compendium of good ideas for longer projects connecting mathematical ideas to wider problems and the whole curriculum, within and outside the school.

Bowland Maths provides real-life problem-solving scenarios which develop skills of good thinking. http://www.bowlandmaths.org.uk NRICH maths: Resouces for investigative mathematics http://nrich.maths.org/frontpage Mathematics in the Making MiMa – an international project to promote collaborative mathematical problem solving, funded by the Life Long learning programme of the European Commission. Tool kit links below: www.mathematicsinthemaking.eu

Drama and Mathematics: Loewenstein, J. 2003 Maths all Week. London: BEAM, great range of mathematical applications. June suggests dramatizing stories with mathematical content Something Special for Me. Vera B Williams Treehorne’s Treasure. Florence Parry Heide Bed and Breakfast Star. Jacqueline Wilson

2 See also Cap-a-Pie The Trial of Girl A. Dramatic Enquiry, philosophical enquiry built into dramatic sequences. In particular see ‘The story of girl A’. http://www.cap-a-pie.co.uk/archive/the-trial-of-girl-a/

Mathematics and Science Concept Cartoons, Mathematics and Science Lynda Dunlop activities, many utilise mathematical data displays, arguments etc Science in Society, University of Ulster and P4C across the secondary Curriculum See CASE materials (Thinking Science) See Tim Sprod Discussions in Science.

More General sources of stimulus for questions: A number of Julian Baggini (2005) starters for enquiry have a mathematical theme, such as, ‘Squaring the Circle’ (p 70) and ‘Wheel of Fortune’ (p16). The Ultimatum Game: set up a few pairs with a sum of money, get them to play this game, watch how they react and use this as a stimulus for questions. http://en.wikipedia.org/wiki/Ultimatum_game National Stem Centre, mathematics resources https://www.stem.org.uk/elibrary/maths/

Thinking Through Series Higgins, S. Baumfield, V. Leat, D. 2003 Thinking Through Primary Teaching. Cambridge: Chris Kington Publishing fortune line and living graphs

Wright, D. and Taverner, S. 2008 Thinking Through Mathematics. Chris Kington Publishers

Curriculum Mapping : nrich . maths .org http://nrich.maths.org/curriculum The Nrich Maths Project Cambridge,England. ... documents can now be found by following the Curriculum links on the Primary and Secondary teacher pages. National Strategies : Primary Mathematics | STEM https://www.stem.org.uk/elibrary/collection/3428/national-strategies-primary- mathematics In 2003, the National Numeracy Strategy, including the Framework for Teaching, ... This set of materials, from the Primary National Strategy, arose through the ... Mathematics Framework - [ARCHIVED CONTENT] UK Government ... http://webarchive.nationalarchives.gov.uk/20110202093118/http:/nationalstrate gies.standards.dcsf.gov.uk/primary/primaryframework/mathematicsframework Feb 2, 2011 ... The National Strategies on the web ... Sections in Mathematics Framework ... Year 3 Blocks · Year 5 Blocks · SEN/LDD planning materials.

3 Some Story Books to use with mathematics (related curriculum) and P4C sessions Allen, P. 1980 Mr Archimedes’ Bath. London: Puffin Books. Anno, M and Anno M. 1983 Anno’s Mysterious Multiplying Jar. Paperstar Books Baker, J. 1987 Where the Forest Meets the Sea. London: Walker Baker, J. 2002 Window. London: Walker Books. Baker, J. 2010 Mirror. London: Walker Books. Banyai I. 1995 Zoom Viking Children’s Books. Bradman, T. 2009 Michael. London: Andersen Press Brown and Weisgard 1990 The Important Book. Perfection Learning. Browne, A. 1989 The Tunnel. London: Walker Browne, A. 1995 Willy the wimp. London: Walker Browne, A. 2008 Little Beauty. London: Walker Books. Browne, A. 2008 Changes. London: Walker Carle, E. 1992 The Very Hungry Caterpillar London, Mantra Lingua. Clement. R. 1995 Counting on Frank. Toronto: Houghton Miffin Donaldson, J and Scheffler, A. 2005 The Gruffalo’s Child. Macmillan Donaldson, J and Scheffler, A. 2002 Night Monkey, Day Monkey. Macmillan. Foreman, M 1972 Dinosaurs and all that Rubbish. London: Puffin. Gaiman, N. 2003 The Day I Swapped My Dad for a Goldfish. London: Bloomsbury. Gravett, E. The Rabbit Problem. London: Macmillan Holzwarth 1994 The Story of Little Mole Who Knew it was None of his Business. London: Pavilion Children’s Books Hutchins, P. 1970 Clocks and More Clocks New York: Aladdin. Hutchins, P. 1983 You’ll Soon Grow into Them, Titch: Greenwillow. Hutchins, P. 1986 The Doorbell Rang New York: Greenwillow Books. International, A. 2008 We are all Born Free: London, Francis Lincoln Books. Lasky, K. 1994 The Librarian Who Measured the Earth. New York: Little Brown Lesieg, T 1957 Wacky Wednesday New York: Random House Lobell, A. 1971 Frog and Toad Together. New York: Harper Collins Lord, J. 1972 The Giant Jam Sandwich London: Red Fox. Milbourne, A and Riglietti, S 2007 How Big is a Million? London: Usborne. Minne, B. 2002 The Best Bottom. Barkeley: Mill and Cookies Press. Pinczes, E. 1995 A Remainder of One New York: Houghton Mifflin Co. Sayre, A and Sayre, J. One is a Snail, Ten is a Crab. London:Walker Books Serres, A. 2009 I Have the Right To be a Child. London: Phoenix Yard. Smith, D. J. and Adams S. 2004. If the World Were a Village. London: A and C Black Publishers. Scieszka, J and Smith, L 1995 Maths Curse. London: Penguin. Smith D J and Adams S. 2004 If… London: Wayland. Thompson, C. 1994 The Paperbag Prince. London: Red Fox Thompson, C. 1996 The Tower to the Sun. London: Red Fox UNICEF 2000 For Every Child. London: Random House. Ungerer, T. 2009 The Moon Man. Phaidon Press. Velthuijs, M. Frog and the Stranger. London: Andersen Press. Velthuijs, M. 1995 Frog is a Hero. London: Andersen Books. Walsh, M 2008 10 Things I can do to Help My World London: walker Books

4 Wehrli, U. 2003 Tidying up Art. New York: Prestel. Wormell, C. (2003) Two Frogs. London: Red Fox Willems, M 2008 Edwina, The Dinosaur Who Didn’t Know She was Extinct. London: Walker Books Williams, K. Four Feet, Two Sandals. Cambridge, UK: Eerdmans Books Zolotow, C. 1969 When the Wind Stops. Harper Trophy.

General References

Abbott, E. A. (1987) Flatland: A romance of Many Dimensions. Harmondsworth, Middlesex: Penguin Books.

Boaler, J. 2016 Mathematical Mindsets: Unleashing Students’ Potential Through Creative Math, Inspiring Messages and Innovative Teaching. San Francisco: Josey- Bass.

Bird, M. 1983. Generating mathematical activity in the classroom. Leicester: The Mathematical Association. Downloadable from: http://www.stem.org.uk/elibrary/maths/

Bird, M. H. (1991) Mathematics for Young Children: An Active Thinking Approach. London: Routledge

Buxton, L. 2001 Sums for Smart Kids. London: BEAM

Coles, A. Barwell, R. Cotton, T. Winter, J. and Brown, L. 2013 Teaching Secondary Mathematics as if the Planet matters. Abingdon, Oxon: Routledge.

Cunningham, R. and Smith, J. (2012), P4C in Mathematics, in (L. Lewis and N. Chandley, eds.) ‘Philosophy for Children Through the Secondary Curriculum.’ pp68-91. London: Continuum.

Du Sautoy, M. 2010 The Number Mysteries. London: Fourth Estate.

Dweck, C. S. 2006 Mindset: The new psychology of success. New York: Balantine

Fielker, D. Extending Maths Ability Through Whole Class teaching.

Gray, E and Tall, D. 1994 Duality, Ambiguity and Flexibility: A ‘Proceptual’ view of simple arithmetic. Journal for Research in Mathematics Education. 25(2), 116-140.

Gregory, M. et. Al. 2008 Philosophy for Children: Practitioner Handbook. Montclair State University.

Loewenstein, J. 2003 Maths all Week. London: BEAM

Mottershead, L. 1977 Sources of Mathematical Discovery. Oxford: Basil Blackwell.