# Understanding; assessing and developing young children's mathematical thinking

Conference item

McDonough, A., Clarke, Doug and Clarke, Barbara. (2003). Understanding; assessing and developing young children's mathematical thinking.

*9th National Conference of the Association for Mathematics Education of South Africa.*Cape Town,South Africa: Association for Mathematics Education of South Africa. pp. 11 - 31

Authors | McDonough, A., Clarke, Doug and Clarke, Barbara |
---|---|

Abstract | At Australian Catholic University and Monash University, preservice mathematics teachers are required to conduct and analyse one-to-one mathematics assessment interviews with primary-aged children. The assessment tool is drawn from the Early Numeracy Research Project, where it was used with over 11,000 children in Victorian schools. The interview assesses content from Number, Measurement and Geometry, in an interactive, hands-on format, with children’s responses and strategies determining the path through the interview protocol. Follow-up discussion in class enabled preservice teachers to explore appropriate pedagogies that build upon what had been learned from the interviews. The research described in this chapter sought to investigate the effectiveness of this process. Interviews and written questionnaires were the data sources. Analysis of the data suggested that teachers were more aware of the kinds of strategies that children use including their variety and relative level of sophistication, and that the interview and subsequent discussion stimulated preservice teachers to reflect upon appropriate classroom experiences for young mathematics learners. |

Keywords | Preservice teacher education; Mathematics education; One-to-one interview; Children; Questioning; Listening; Reflection |

Year | 2003 |

Journal | Proceedings of the 9th National Conference of the Association for Mathematics Education of South Africa |

Publisher | Association for Mathematics Education of South Africa |

Publisher's version | File Access Level Controlled |

Page range | 11 - 31 |

Place of publication | Cape Town,South Africa |

https://acuresearchbank.acu.edu.au/item/87zv5/understanding-assessing-and-developing-young-children-s-mathematical-thinking

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Clarke, D.. (2005). Written algorithms in the primary years: Undoing the good work? In M. Coupland, J. Anderson and T. Spencer (Ed.).*Making mathematics vital (Proceedings of the 20th biennial conference of the Australian Association of Mathematics Teachers).*Adelaide, Australia: Australian Association of Mathematics Teachers. pp. 93 - 98

##### Professional development as a catalyst for changes in beliefs and practice :perspectives from the Early Numeracy Research Project

McDonough, Andrea Mary and Clarke, Barbara. (2005). Professional development as a catalyst for changes in beliefs and practice :perspectives from the Early Numeracy Research Project. In P. Clarkson, A. Downton and D. Gronn (Ed.).*Proceedings of the annual conference of the Mathematics Education Research Group of Australasia.*Melbourne, Australia: Mathematics Education Research Group of Australasia. pp. 521 - 528

##### Mathematics teaching in grades K-2: Painting a picture of challenging; supportive and effective classrooms

Clarke, Douglas McLean and Clarke, Barbara. (2004). Mathematics teaching in grades K-2: Painting a picture of challenging; supportive and effective classrooms. In In R. N. Rubenstein and G. Bright (Ed.).*Perspectives on the Teaching of Mathematics (66th Yearbook)*pp. 67 - 81 National Council of Teachers of Mathematics.

##### Investigating young children's beliefs about mathematics and learning :The use and value of a range of creative interview tasks

McDonough, Andrea Mary. (2004). Investigating young children's beliefs about mathematics and learning :The use and value of a range of creative interview tasks.*ICME-10 Proceedings Editor: Mogens Niss Administrative editor: Elin Emborg ICME-10 Proceedings.*Copenhagen,Denmark: International Commission on Mathematical Instruction. pp. 1 - 1

##### Making mathematics challenging and enjoyable in the middle years

Clarke, Doug. (2004). Making mathematics challenging and enjoyable in the middle years.*Australian Journal of Middle Schooling.*4(1), pp. 1 - 8.

##### Students' perceptions of factors contributing to successful participation in mathematics

McDonough, Andrea Mary, Sullivan, Peter and Harrison, Robyn Turner. (2004). Students' perceptions of factors contributing to successful participation in mathematics. In M. J. Hoines and A. B. Fugelstad (Ed.).*Proceedings of the 28th Conference of the International group for the psychology of mathematics education.*Bergen, Norway: Bergen University College. pp. 289 - 296

##### Issues in the teaching of algorithms in the primary years

Clarke, Douglas McLean. (2004). Issues in the teaching of algorithms in the primary years. In In E. Clarke, L. Johansson and W. Lester (Ed.).*International Perspectives on Learning and Teaching Mathematics*pp. 21 - 36 National Center for Mathematics Education.

##### When is three quarters not three quarters? Listening for conceptual understanding in children's explanations in a fraction interview

Mitchell, Annie and Clarke, Doug. (2004). When is three quarters not three quarters? Listening for conceptual understanding in children's explanations in a fraction interview. In Ian Putt, Rhonda Farragher and Mal McLean (Ed.).*Mathematics Education for the third millennium: Towards 2010, Proceedings of the 27th annual conference of the Mathematics Education Research Group of Australasia.*Townsville,Australia: James Cook University. pp. 367 - 373

##### When does the successful comparison of decimals reflect conceptual understanding?

Clarke, Douglas McLean and Roche, Anne. (2004). When does the successful comparison of decimals reflect conceptual understanding? In Ian Putt, Rhonda Farragher and Mal McLean (Ed.).*Mathematics Education for the Third Millennium: Towards 2010 (Proceedings of the 27th Annual Conference of the Mathematics Education Research Group of Australia).*Townsville,Australia: James Cook University. pp. 486 - 493

##### Using questioning to elicit and develop children's mathematical thinking

Clarke, Barbara and Clarke, Douglas McLean. (2004). Using questioning to elicit and develop children's mathematical thinking. In In G.W. Bright and R.N. Rubenstein (Ed.).*Perspectives on the teaching of mathematics*pp. 5 - 10 National Council of Teachers of Mathematics.

##### Encouraging perseverance in elementary mathematics

Clarke, Doug and Clarke, Barbara. (2003). Encouraging perseverance in elementary mathematics.*Teaching Children Mathematics.*

##### An issue in teaching and learning subtraction: What's the difference?

Clarke, Doug. (2003). An issue in teaching and learning subtraction: What's the difference?*Australian Primary Mathematics Classroom.*8(3), pp. 4 - 11.

##### Assessing and developing measurement with young children

Clarke, Douglas McLean, Cheeseman, Jill and McDonough, Andrea Mary. (2003). Assessing and developing measurement with young children. In In D. H. Clements and G. Bright (Ed.).*Learning and Teaching Measurement*pp. 68 - 80 National Council of Teachers of Mathematics.

##### Describing the practice of effective teachers of mathematics in the early years

McDonough, Andrea Mary and Clarke, Doug McLean. (2003). Describing the practice of effective teachers of mathematics in the early years. In N. A. Pateman, B. J. Dougherty and J. Zilliox (Ed.).*Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics.*Honolulu, Hawaii, USA: International Group for the Psychology of Mathematics Education. pp. 261 - 268

##### Naïve and yet knowing: Young learners portray beliefs about mathematics and learning

McDonough, Andrea M.. (2002).*Naïve and yet knowing: Young learners portray beliefs about mathematics and learning*[Thesis]. https://doi.org/10.4226/66/5a8e4d814b7aa

##### Understanding assessing and developing young children's mathematical thinking: Research as a powerful tool for professional growth

Clarke, Doug. (2001). Understanding assessing and developing young children's mathematical thinking: Research as a powerful tool for professional growth.*24th Annual MERGA Conference.*pp. 11 - 29