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Our publications

                                                              

     

 

 

 

2024

 

2023

 

 

New!  

 

Carruthers, E. (2023). Early Years Teachers Perspectives on their Pedagogies of Play and Mathematics. Impact Journal. Issue 19.

 

Worthington, M., Dobber, M., & van Oers, B. (2023). Intertextuality and the advance of mathematisation in young children’s inscriptions. Research Papers in Education. 

 

Carruthers, E. (2023). 'I have a thousand ideas': Leading organic research & enquiry as a vehicle to drive a school's vision. BERA Research Intelligence 155, p. 16.  Summer 2023.

 

 

2022

 

Worthington, M. (2022). A paradigm shift for early childhood mathematics? Volgens Bartjens – ontwikkeling en onderzoek {Development and research: [Dutch teachers’ journal], 42(1), 50-57.

  
 Carruthers, E. (2022). The Pedagogy of Children's Mathematical Graphics: Teacher Perspectives. (Doctoral Dissertation). University of Bristol.

 

 

 

Carruthers, E. & Worthington, M. (2022). BLOG: Playful, play and children’s mathematics? Education Journal 486, 14. May 2022.

  
2021

Carruthers, E., Coles, A. & Rose, J. (2021). "Even bigger than this world!" Young children thinking about numbers through  their mathematical graphics. In O. Thiel., E. Severina & B. Perry (Eds.), Mathematics in early childhood: Research,  reflective practice and innovative pedagogy, (pp. 31-47). Routledge.

 

 

 

Worthington, M. (2021). The emergence and development of young children’s personal mathematical inscriptions: The evolution of graphical signs explored through children’s spontaneous pretend play. [Doctoral Dissertation]. Vrije Universiteit, Amsterdam. 

  
 Worthington, M., Carruthers, E., & Hattingh, L. (2021). “This is the safe. It has a number and no one else knows it”: Playing and mathematics. In O. Thiel, E. Severina & B. Perry (Eds.), Mathematics in early childhood: Research, reflective practice and innovative pedagogy (pp. 167-185). Routledge.

 

2020

 

Worthington, M. (2020). Young children’s graphical sign lexicons and the emergence of mathematical symbols. Review of Science, Mathematics and ICT Education 14(2), 65-83. 

 

Worthington M. (2020). Mathematical signs and their cultural transmission in pretend play. In A. MacDonald, Danaia L, & S. Murphy (Eds.), STEM education across the learning continuum (pp. 45-65). Springer Nature.

 

 

Carruthers, E. (2020). Mathematical teaching in nursery schools in England: Pretend play and democratic pedagogies. Review of Science, Mathematics and ICT Education 14(2), 25-41.

  
2019

Worthington, M., Dobber, M., & van Oers, B. (2019). The development of abstraction in the nursery. Educational Studies in Mathematics, 102, 91-110. 

 

2018

Worthington, M. (2018). Funds of knowledge: Children’s cultural ways of knowing mathematics. In V. Kinnear, M-Y Lai & T. Muir (Eds.), Forging connections in early mathematics teaching and learning (pp. 239-258). Springer.

 

2017

Carruthers, E. (2017). Early Years Mathematics. [Editorial] [Special issue, Early Years Mathematics]. Early Education Journal 83, Autumn, 3.

 

 

Carruthers, E. (2017). Children’s mathematics. Early Education Journal; [Special issue, Early Years Mathematics] 83, Autumn, 4-6.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2016

 

 

 

2015

 

 

 

 

 

 

 

 

2014

 

 

 

 

 

 

 

 

 

 

 

2013

 

 

 

 

 

 

 

2012

 

 

 

 

 

 

Carruthers, E. (2017). Open mathematics: Open minds: Children’s thinking and mathematics. Community Playthings.https://www.communityplaythings.co.uk/learning-library/articles/open-mathematics-open-minds 

 

Worthington, M. (2017). Respecting children’s personal symbolism. Early Education Journal; [Special issue, Early Years Mathematics]. 83: (Autumn), 13-15.

 

Worthington, M. (2017). Mathematics and symbolic meanings: From pretend play to problem solving. In J. Moyles, J. Georgeson & J. Payler (Eds.), Beginning teaching: Beginning learning (5th ed., pp. 131-143). Open University.

 

Worthington, M., & van Oers, B. (2017). Children's social literacies: Meaning making and the emergence of graphic symbols in pretence. Journal of Early Childhood Literacy 24(1), 1-29.

 

Worthington, M., & Van Oers, B. (2016). Pretend play and the cultural foundations of mathematics. European Early Childhood Education Research Journal 24(1). 51-66. 

 

Carruthers, E. (2015). Listening to children's mathematics in school. In B. Perry, A. Gervasoni & A. MacDonald (Eds.), Mathematics  and transition to school: International Perspectives (pp. 83-100). Springer.

 

Worthington, M. (2015). Mathematics and the ecology of pretend play. In J. Moyles (Ed.). The excellence of play (4th ed. pp. 237-249). Open University.

 

Worthington, M. (2014). Submission to the All Partly Political Group (APPG) on Maths and Numeracy. Final Report to the  government on 25th November 2014, in the house of Commons, Westminster. 

 

Worthington, M. (2014). Briefing paper for the APPG Maths and Numeracy Meeting. 25th June 2014, Portcullis House, Westminster.

 

Worthington, M. (2014). Early Years Policy Advice: Play and Pedagogy. Early Years: Policy advice and future research agendas. BERA/TACTYC, (pp8-9 prepared by M. Worthington.

 

Carruthers, E., & E. Butcher. (2013). Mathematics: Young children co-construct their mathematical enquiries. In P. Beckley (Ed.), The new Early Years Foundation Stage: Changes, challenges and reflections (2nd ed., pp. 91-104). Open University.

 

Worthington, M. & Carruthers, E.. (2013). Making quite a mark. Early Years Educator 13(2), 11.   

 

Worthington, M. (2012). Pretend play and mathematics: Informing the 'school readiness' debate. TACTYC, Reflecting on Early Years Issues. http://tactyc.org.uk/pdfs/MAULFRY-REFLECTIONS%202012.pdf

 

Carruthers, E. (2012). Are the children thinking mathematically? The pedagogy of children's mathematical graphics. In M. McAteer (Ed.), Improving primary mathematics teaching and learning (pp. 192-212). Open University.

 

 

Worthington, M. (2012). Children becoming expert symbol users. In M. McAteer (Ed.). Improving primary mathematics teaching and leaning (pp.39-57). Open University.

 

 

Worthington, M. (2012). The power of graphicacy for the young child. In T. Papatheodorou & J. Moyles. (Eds.), Cross cultural perspectives on early childhood (pp. 41-57). Sage.

 

2011

Worthington, M. (2011). Coomuniceren in rekentaal: Noodzakelijk voor kinderen in hun spel. [Communicating mathematically: 'Necessary' for children in their play]. Zone 1., 12-15. (Dutch teachers' magazine).

 

 

Carruthers, E., & Worthington, M. (2011). Understanding children’s mathematical graphics: Beginnings in play. Open University.

 

 

Carruthers, E., & Worthington, M. (2011). Developing children’s mathematical graphics: Supporting early mathematical learning. Open University.

 

 

Worthington, M. (2011). Young Mathematicians: Global learners. In E. Murphy (Ed.), Welcoming linguistic and cultural diversity in early childhood classrooms (pp. 83-100). Multi-lingual Matters.

 

Moyles, J., & Worthington, M. (2011). The Early Years Foundation Stage through the daily experiences of children. TACTYC Occasional Paper no. 1.

 

Carruthers, W. (2011). The importance of young children's mark-making: Beginnings, context, meaning and mathematics. The Foundation Stage Forum.

 

Worthington, M. (2011). From astronaut to calculations: Tracing children’s symbolic meanings. In J. Moyles, J. Georgeson & J. Payler (Eds.), Beginning teaching: Beginning learning in early years and primary education (4th ed., pp. 139-151). Open University.

 

2010

Worthington, M. (2010). Play is a complex landscape: Imagination and symbolic meanings. In P. Broadhead, L. Wood & J. Howard (Eds.), Play and learning in the early years (pp. 127-144). Sage.

 

 

Carruthers, E., & Worthington, M. (2010). Children's mathematical graphics: Understanding the key concept. NRICH: University of Cambridge.

 

 

Carruthers, E. (2010). How children use graphics to support mathematical thinking. Early Years Educator (EYE). 39-44.

 

 

Worthington, M. (2010). “This is a different calculator – with computer games on”: Reflecting on children’s symbolic meanings in the digital age. In J. Moyles (Ed.), Thinking about play: Developing a reflective approach (pp. 179-196). Open University.

 

2009

Worthington. M. (2009). Fish in the water of culture: Signs and symbols in young children's drawing. Psychology of Education Review 33(1), 37-46.

 

 

Carruthers, E., & Worthington. M. (2009). A major new Early Years Mathematics Review recommends Children's Mathematical Graphics. Nursery World.

 

Carruthers, E., & Worthington. M. (2009). An early years CPD initiative for mathematics: The power of collaborative, 'grassroots' learning. Proceedings of the British Society for Research into Learning Mathematics 29(1), 25-30.

 

 

Carruthers, E., & Worthington, M. (2009). Children's mathematical graphics: Understanding the key concept. Primary Mathematics 13(3), 3-5.

 

 

Carruthers, E., & Worthington, M. (2009). Learning and development: mathematics - Marking time. Nursery World, 24-25. 

 

 

Carruthers, E. & Worthington, M. (2009). Children's mathematical development. In T. Bruce (Ed.), Early childhood: a guide for students. (2nd ed., pp. 165-179). Sage.

 

 

Carruthers, E., & Worthington, M. (2009). Key stage 1 Mathematics. In T. Bruce (Ed.), Early childhood: A guide for students (2nd ed., pp. 249-263). Sage.

 

 

DSCF (2009). Children Thinking Mathematically: PSRN essential knowledge for early years practitioners. [Elizabeth Carruthers and Maulfry Worthington were commissioned by the DCSF to write this publication].

 

2008

Carruthers, E., & Worthington, M. (2008). Children’s mathematical graphics: Young children calculating for meaning. In I. Thompson (Ed.), Teaching and learning early number (2nd ed., pp. 127-148). Open University.

 

 

Worthington, M. (2008). Children's Mathematical Graphics: Overview.  

 

 

Worthington. M. (2008). Playful pedagogy and transitions in children's mathematics. The Foundation Stage Forum.

 

Carruthers, E. (2008). The importance of children's mark making: Beginnings, context, meanings in mathematics. The Foundation Stage Forum

 

2007

Worthington, M. (2007). Exceptional children: Researching the young child's mathematics. Primary Mathematics: Maths Coordinator File 25: Early Years Issue. 5-11.

 

 

Worthington, M. (2007). "It's my birthday bridge": Multi-modal meanings through play. In: J. Moyles (Ed.), Beginning teaching: Beginning learning (pp. 131-141). Open University/McGraw Hill.

 

 

Worthington, M. (2007). Multi-modality, Play and children's mark-making in maths. In: J. Moyles (Ed.), Early years foundations: Meeting the challenge (pp. 253-269). Open University/McGraw Hill.

 

2006

Worthington, M. (2006). Creativity meets mathematics. Practical Pre-school 66, 10-11.

 

 

Carruthers, E., & Worthington, M. (2006). Children’s mathematics: Making marks, making meaning. (2nd ed.). Sage.

 

 

Worthington, M., & Carruthers, E. (2006). Mathematical Development. In T. Bruce (Ed.), Early childhood: A guide for students (pp. 146-154). Paul Chapman.

 

 

Worthington, M., & Carruthers, E. (2006). Key Stage 1 Mathematics. In T. Bruce (Ed.), 

Early childhood: A guide for students (pp. 204). Paul Chapman.

 

2005

Carruthers, E., & Worthington, M. (2005). Making sense of mathematical graphics: The development of understanding abstract symbolism. European Early Childhood Education Research Association Journal, 13(1), 57-79.

 

 

Worthington, M. (2005). Issues of collaboration and co-construction within an online  discussion forum: Information ecology for Continuing Professional development. Issues of collaboration and co-construction within an online discussion forum: Information ecology for Continuing Professional Development, Reflecting Education, 1(1-2), 76-98. http://reflectingeducation.net/index.php/reflecting/article/view/15/22

 

 

Worthington, M. (2005). Reflecting on creativity and cognition: Visual representations and mathematics in early childhood - some evidence from research. Reflecting on creativity and cognition: Visual representation and mathematics in early childhood - some evidence from research, Reflections – TACTYC, https://tactyc.org.uk/pdfs/Reflection-worthington.pdf

 

2004

Carruthers, E., & Worthington, M. (2004). Young children exploring early calculation, Mathematics Teaching 187, 30-34.

 

2003

Worthington, M., & Carruthers, E. (2003). Children’s mathematics: Making marks, making meaning. Paul Chapman.

 

 

Worthington, M. (2003). Children make many meanings with their marks, Hundred Languages (South West), 8-10.

 

 

Worthington, M., & Carruthers, E. (2003). Research uncovers children's creative mathematical thinking, Primary Mathematics 7(3). 21-25.

 

Worthington, M., & Carruthers, E. (2003). Becoming bi-numerate: a study of teachers’ practices concerning children’s early ‘written’ mathematics. Unpublished article.

 

Worthington, M. & Carruthers, E. (2003). Teachers’ practices concerning children’s early ‘written’ mathematics: worksheets or children’s own mathematical graphics? Paper presented at the European Early Childhood Education Research Association (EECERA) Conference, September 2003 at University of Strathclyde, Glasgow, (unpublished).

 

 

Worthington, M. (2003). Creativity and mathematics: practitioner perceptions. Practical Preschool, 66, 10-11.

 

1999 

Carruthers, E. (1999). It all adds up: The numeracy strategy approach in reception classes. It all adds up: The Numeracy Strategy approach in Reception classes,

Nursery World

 

1998

Worthington, M., (published as Hayton) & Carruthers, E. (1998). Emergent mathematics: A collaborative approach. Emergent Mathematics: A collaborative approach, Mathematics Teaching 162, 11-15.

 

 

Carruthers, E. (1998). A pattern of children's learning incumber - a developmental theory, Mathematics Teaching 162, 15 -17.

 

 

Worthington. M. (published as Hayton) (1998). Emergent mathematics: Personal views of learning, Mathematics Teaching 162, 17.

 

 

Worthington, M. (1998). Solving problems together: Emerging understanding. Mathematics Teaching 162, 118-19.

 

1997

Worthington, M., & Murchison, P. (1997). Mathslines: A Mathematical framework for Four-Year-Olds. Devon Curriculum Advice.

 

 

Carruthers, E. (1997). Talking numbers - a developmental link between literacy and numeracy,  Early Education, 5-6.

 

 

Carruthers, E. (1997). A number line in the nursery - a vehicle for understanding children's  number development, Early Years 18(1). (Autumn), 9-14.

 

 

Carruthers, E. (1997). A pattern of children’s learning in number: A developmental theory. Mathematics Teaching 198, 15-17.

 

 

Carruthers, E. (1997). Number: A Developmental Link between Literacy and Numeracy: A Case-study of a Child from Twenty to Forty-four Months, M.Ed. Dissertation, University of Plymouth (unpublished).

 

1996

Worthington, M. (published as Hayton)., & Carruthers, C. (1996). Emergent and developmentally appropriate learning: the relationship to personal views of learning. Primary Practice 5, 16 -17.

 

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