# Demonstration lessons in mathematics education: Teachers' observation foci and intended changes in practice

Journal article

Clarke, Doug, Roche, Anne, Wilkie, Karina, Wright, Vince, Brown, Jill, Downton, Ann, Horne, Marjorie, Knight, Rose, McDonough, Andrea, Sexton, Matthew and Worrall, Chris. (2013) Demonstration lessons in mathematics education: Teachers' observation foci and intended changes in practice.

*Mathematics Education Research Journal.*25(2), pp. 207 - 230. https://doi.org/10.1007/s13394-012-0058-z

Authors | Clarke, Doug, Roche, Anne, Wilkie, Karina, Wright, Vince, Brown, Jill, Downton, Ann, Horne, Marjorie, Knight, Rose, McDonough, Andrea, Sexton, Matthew and Worrall, Chris |
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Abstract | As part of a teacher professional learning project in mathematics education, university mathematics educators taught demonstration lessons in project primary schools. These lessons were part of a “pre-brief, teaching, and debrief” process, in which up to eight teachers observed each lesson. Using brief questionnaires completed in advance of the lesson, during the lesson, following the debrief, and several weeks later, data were collected on teachers’ intended and actual observation foci and any anticipated changes in their beliefs and practices arising from the experience. There were several common themes in teachers’ intended observations, including a focus on questioning, catering for individual differences, and building student engagement. As evident in other research, teachers’ intended and actual observations gave greater attention to teacher actions and decision making than to student learning and thinking. In this paper, we situate demonstration lessons within teacher professional learning models, describe the features of our model, summarise teacher data, and discuss issues arising from our work. |

Keywords | teacher professional learning; demonstration lessons; observations; teacher change; pedagogical content knowledge; student learning |

Year | 2013 |

Journal | Mathematics Education Research Journal |

Journal citation | 25 (2), pp. 207 - 230 |

Publisher | Springer Netherlands |

ISSN | 1033-2170 |

Digital Object Identifier (DOI) | https://doi.org/10.1007/s13394-012-0058-z |

Scopus EID | 2-s2.0-84877010734 |

Page range | 207 - 230 |

Publisher's version | File Access Level Controlled |

Place of publication | Netherlands |

https://acuresearchbank.acu.edu.au/item/851z9/demonstration-lessons-in-mathematics-education-teachers-observation-foci-and-intended-changes-in-practice

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McDonough, Andrea Mary, Cheeseman, Jill and Ferguson, Sarah. (2012) Insights into children's understandings of mass measurement. In T Y Tso (Ed.).*Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education.*Taiwan: International Group for the Psychology of Mathemati.... pp. 201 - 208

##### Empirical evidence for Niss' implemented anticipation in mathematising realistic situations

Stillman, Gloria and Brown, Jill P.. (2012) Empirical evidence for Niss' implemented anticipation in mathematising realistic situations. In J. Dindyal, L. P. Cheng and S. F. Ng (Ed.).*Mathematics education: Expanding horizons.*Melbourne, Australia: Mathematics Education Research Group of Australasia. pp. 682 - 689

##### Editorial: To engage or not to engage

Stillman, Gloria and Brown, Jill. (2012) Editorial: To engage or not to engage.*Australian Senior Mathematics Journal.*26(1), pp. 1 - 5.

##### Important ideas in mathematics : What are they and where do you get them?

Clarke, Doug M., Clarke, David J. and Sullivan, Peter. (2012) Important ideas in mathematics : What are they and where do you get them?*Australian Primary Mathematics Classroom.*17(3), pp. 13-18.

##### Editorial: Envisioning the future of the mathematical sciences and mathematics teaching

Brown, Jill and Stillman, Gloria. (2012) Editorial: Envisioning the future of the mathematical sciences and mathematics teaching.*Australian Senior Mathematics Journal.*26(2), pp. 4 - 5.

##### Powerful pedagogical actions in mathematics education

Gervasoni, Ann, Hunter, Roberta, Bicknell, Brenda and Sexton, Matthew. (2012) Powerful pedagogical actions in mathematics education. In In B Perry, T Lowrie and T Logan, A MacDonald & J Greenlees (Ed.). pp. 193 - 218 Sense Publishers.##### The effects of creating rich learning environments for children to measure mass

Cheeseman, Jill, McDonough, Andrea and Ferguson, Sarah. (2012) The effects of creating rich learning environments for children to measure mass. In J Dindyal, L P Cheng and S F Ng (Ed.).*Mathematics education: Expanding horizons. Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia.*Australia: Mathematics Education Research Group of Australasia. pp. 178 - 185

##### Supporting teachers in choosing and using challenging mathematics tasks

Sullivan, Peter, Clarke, Doug M., Michels, Deborah, Mornane, Angela and Roche, Anne. (2012) Supporting teachers in choosing and using challenging mathematics tasks. In J. Dindyal, L. P. Cheng and S. F. Ng (Ed.).*Mathematics education: Expanding horizons. Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia.*Australia: Mathematics Education Research Group of Australasia. pp. 688 - 695

##### Students' proportional reasoning in mathematics and science

Dole, Shelley, Clarke, Doug, Wright, Tony and Hilton, Geoff. (2012) Students' proportional reasoning in mathematics and science. In T. Y. Tso (Ed.).*Proceedings of the 36th Conference of the International Group for the Psychology of Mathematics Education.*Taiwan: International Group for the Psychology of Mathemati.... pp. 195 - 202

##### Professional learning and action research: Early career teachers reflect on their practice

Scott, Anne, Clarkson, Philip and McDonough, Andrea. (2012) Professional learning and action research: Early career teachers reflect on their practice.*Mathematics Education Research Journal.*24(2), pp. 129 - 151. https://doi.org/10.1007/s13394-012-0035-6

##### Mathematical Modelling Challenge

Brown, Jill and Stillman, Gloria. (2011) Mathematical Modelling Challenge.*Vinculum.*26(4), pp. 16 - 19.

##### Mathematical Modelling Challenge

Brown, Jill and Stillman, Gloria. (2011) Mathematical Modelling Challenge.*Prime Number.*26(4), pp. 15 - 16.

##### Modelling tasks: insight into mathematical understanding

Brown, Jill P. and Edwards, Ian. (2011) Modelling tasks: insight into mathematical understanding. In In G. Kaiser, W. Blum and R. Borromeo Ferri & G.Stillman (Ed.). pp. 187 - 197 Springer. https://doi.org/10.1007/978-94-007-0910-2_20##### Fostering professional learning communities beyond school boundaries

Scott, Anne, Clarkson, P. and McDonough, A. M.. (2011) Fostering professional learning communities beyond school boundaries.*Australian Journal of Teacher Education.*35(6), pp. 1 - 17. https://doi.org/10.14221/ajte.2011v36n6.2

##### Measurement matters: Fraction number lines and length concepts are related

Mitchell, Annie and Horne, Marj. (2011) Measurement matters: Fraction number lines and length concepts are related. In In J. Way and J. Bobis (Ed.). pp. 52 - 62 Australian Association of Mathematics Teachers.##### Mathematical Modelling and Applications

Stillman, Gloria and Brown, Jill. (2011) Mathematical Modelling and Applications.*Vinculum.*48(2), pp. 20 - 20.

##### Building preservice teacher capacity for effective mathematics teaching through partnerships with teacher educators and primary school communities

McDonough, Andrea and Sexton, Matthew. (2011) Building preservice teacher capacity for effective mathematics teaching through partnerships with teacher educators and primary school communities. In J. Clark, B. Kissane and J. Mousley (Ed.).*Mathematics: Traditions and [new] practices: Proceedings of the 2011 AAMT-MERGA conference.*Australia: AAMT and MERGA. pp. 508 - 514

##### Listening to children's explanations of fraction pair tasks: When more than an answer and an initial explanation are needed

Mitchell, Annie and Horne, Marj. (2011) Listening to children's explanations of fraction pair tasks: When more than an answer and an initial explanation are needed. In J. Clark, B. Kissane and J. Mousley (Ed.).*Mathematics: Traditions and [new] practices: Proceedings of the 2011 AAMT-MERGA conference.*Australia: AAMT and MERGA. pp. 515 - 522

##### 'Get down and get dirty in the mathematics': Technology and mathematical modelling in senior secondary

Stillman, Gloria and Brown, Jill. (2011) 'Get down and get dirty in the mathematics': Technology and mathematical modelling in senior secondary. In J. Clark, B. Kissane and J. Mousley (Ed.).*Mathematics: Traditions and [new] practices: Proceedings of the 2011 AAMT-MERGA conference.*Australia: AAMT and MERGA. pp. 711 - 718

##### The one-minute challenge

Clarke, Doug, Downton, A. and Roche, A.. (2011) The one-minute challenge.*Teaching Children Mathematics (print version).*17(6), pp. 342 - 349.

##### One-to-one student interviews provide powerful insights and clear focus for the teaching of fractions in the middle years

Clarke, Doug, Roche, Anne and Mitchell, Annie. (2011) One-to-one student interviews provide powerful insights and clear focus for the teaching of fractions in the middle years. In In J. Way and J. Bobis (Ed.).*Fractions: Teaching for understanding*pp. 23 - 31 Australian Association of Mathematics Teachers.

##### Percentages as a co-ordination class

Wright, Vince. (2011) Percentages as a co-ordination class. In J. Clark, B. Kissane and J. Mousley (Ed.).*Mathematics: Traditions and [new] practices: Proceedings of the 2011 AAMT-MERGA conference.*Adelaide, Australia: AAMT and MERGA. pp. 1081 - 1088

##### Some lessons learned from the experience of assessing teacher pedagogical content knowledge in mathematics

Roche, Anne and Clarke, Doug. (2011) Some lessons learned from the experience of assessing teacher pedagogical content knowledge in mathematics. In J. Clark, B. Kissane and J. Mousley (Ed.).*Mathematics: Traditions and [new] practices: Proceedings of the 2011 AAMT-MERGA conference.*Australia: AAMT and MERGA. pp. 658 - 666

##### Concerned about their learning: What matters to mathematics students seeking to study despite absence from school owing to chronic illness

Wilkie, Karina. (2011) Concerned about their learning: What matters to mathematics students seeking to study despite absence from school owing to chronic illness. In J. Clark, B. Kissane and J. Mousley (Ed.).*Mathematics: Traditions and [new] practices: Proceedings of the 2011 AAMT-MERGA conference.*Australia: AAMT and MERGA. pp. 786 - 794

##### Learning to measure length in the first three years of school

McDonough, Andrea Mary and Sullivan, Peter. (2011) Learning to measure length in the first three years of school.*Australasian Journal of Early Childhood.*36(3), pp. 27 - 35.

##### Editorial: To err is human

Brown, Jill and Stillman, Gloria. (2011) Editorial: To err is human.*Australian Senior Mathematics Journal.*25(2), pp. 4 - 5.

##### Building teachers' expertise in understanding, assessing and developing children's mathematical thinking :The power of task-based, one-to-one assessment interviews

Clarke, Doug M., Clarke, Barbara and Roche, Anne. (2011) Building teachers' expertise in understanding, assessing and developing children's mathematical thinking :The power of task-based, one-to-one assessment interviews.*ZDM: The International Journal on Mathematics Education (print version).*43(6-7), pp. 901 - 913. https://doi.org/10.1007/s11858-011-0345-2

##### Investigating children's understanding of the measurement of mass

Cheeseman, Jill, McDonough, Andrea and Clarke, Doug. (2011) Investigating children's understanding of the measurement of mass. In J. Clark, B. Kissane and J. Mousley (Ed.).*Mathematics: Traditions and [new] practices: Proceedings of the 2011 AAMT-MERGA conference.*Australia: AAMT and MERGA. pp. 174 - 182

##### Editorial: Historical sources and historical development of statistical ideas

Brown, Jill and Stillman, Gloria. (2011) Editorial: Historical sources and historical development of statistical ideas.*Australian Senior Mathematics Journal.*25(1), pp. 4 - 6.

##### Pre-service secondary mathematics teachers' affinity with using modelling tasks in teaching years 8-10

Stillman, Gloria and Brown, Jill P.. (2011) Pre-service secondary mathematics teachers' affinity with using modelling tasks in teaching years 8-10. In In G. Kaiser, W. Blum and R. Borromeo Ferri & G.Stillman (Ed.). pp. 289 - 298 Springer. https://doi.org/10.1007/978-94-007-0910-2_29##### Linking multiplication and division in helpful ways for children

Downton, Ann. (2011) Linking multiplication and division in helpful ways for children.*Prime Number.*26(4), pp. 3 - 6.

##### The impact of two teachers' use of specific scaffolding practices on low-attaining upper primary students

Ferguson, Sarah and McDonough, Andrea. (2010) The impact of two teachers' use of specific scaffolding practices on low-attaining upper primary students. In L. Sparrow, B. Kissane and C. Hurst (Ed.).*Shaping the future of mathematics education: proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia.*Australia: Mathematics Education Research Group of Australasia. pp. 177 - 184

##### Turning ideas into modeling problems

Galbraith, Peter L., Stillman, Gloria and Brown, Jill P.. (2010) Turning ideas into modeling problems. In pp. 133 - 144 Springer. https://doi.org/10.1007/978-1-4419-0561-1_11##### School ties: Keeping students with chronic illness connected to their school learning communities

Wilkie, Karina and Jones, Anthony. (2010) School ties: Keeping students with chronic illness connected to their school learning communities.*International Federation for Information Processing (IFIP) Conference.*Semmering,Austria: International Federation for Information Processing. pp. 1 - 13

##### Challenging multiplicative problems can elicit sophisticated strategies

Downton, Ann. (2010) Challenging multiplicative problems can elicit sophisticated strategies. In L. Sparrow, B. Kissane and C. Hurst (Ed.).*Shaping the future of mathematics education: proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia.*Australia: Mathematics Education Research Group of Australasia. pp. 169 - 176

##### Using concept cartoons to access student beliefs about preferred approaches to mathematics learning and teaching

Sexton, Matthew. (2010) Using concept cartoons to access student beliefs about preferred approaches to mathematics learning and teaching. In L. Sparrow, B. Kissane and C. Hurst (Ed.).*Shaping the future of mathematics education: proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia.*Australia: Mathematics Education Research Group of Australasia. pp. 515 - 522

##### Teachers' extent of the use of particular task types in mathematics and choices behind that use

Clarke, Doug M. and Roche, Anne. (2010) Teachers' extent of the use of particular task types in mathematics and choices behind that use. In L. Sparrow, B. Kissane and C. Hurst (Ed.).##### Identifying challenges within transition phases of mathematical modeling activities at Year 9

Stillman, Gloria, Brown, Jill and Galbraith, Peter. (2010) Identifying challenges within transition phases of mathematical modeling activities at Year 9. In In R. Lesh, P. L. Galbraith and C. R. Haines & A. Hurford (Ed.).*Modeling students' mathematical modeling competencies: ICTMA13*pp. 385 - 398 Springer.

##### A teacher's perspective of interacting with long-term absent students through digital communications technologies

Jones, Anthony and Wilkie, Karina. (2010) A teacher's perspective of interacting with long-term absent students through digital communications technologies. In*Key Competencies in the Knowledge Society: IFIP TC3 International Conference KCKS 2010*pp. 187 - 192 Springer-Verlag.

##### Gap thinking in fraction pair comparisons is not whole number thinking :is this what early equivalence thinking sounds like?

Mitchell, Annie and Horne, Marj. (2010) Gap thinking in fraction pair comparisons is not whole number thinking :is this what early equivalence thinking sounds like? In L. Sparrow, B. Kissane and C. Hurst (Ed.).##### Students' opinions about characteristics of their desired mathematics lessons

Sullivan, Peter, Clarke, Doug and O'Shea, Helen. (2010) Students' opinions about characteristics of their desired mathematics lessons. In L. Sparrow, B. Kissane and C. Hurst (Ed.).##### 'Count me in' :Students with chronic illness continue mathematics study through connection with their teachers during absence

Wilkie, Karina. (2010) 'Count me in' :Students with chronic illness continue mathematics study through connection with their teachers during absence.*AARE Conference 2010.*AERA: Australia. pp. 1 - 17

##### The power of a single game to address a range of important ideas in fraction learning

Clarke, Doug and Roche, Anne. (2010) The power of a single game to address a range of important ideas in fraction learning.*Australian Primary Mathematics Classroom.*15(3), pp. 18 - 24.

##### Teacher change in response to a professional learning project

McDonough, Andrea, Clarkson, Philip and Scott, Anne. (2010) Teacher change in response to a professional learning project. In L. Sparrow, B. Kissane and C. Hurst (Ed.).##### Foundational ideas of measure :exploring length understandings

McDonough, Andrea. (2010) Foundational ideas of measure :exploring length understandings. In M. M. F. Pinto and T. F. Kawasaki (Ed.).*Proceedings of the 34th conference of the International Group for the Psychology of Mathematics Education.*Brazil: International Group for the Psychology of Mathemati.... pp. 289 - 296

##### Beginning the development of SAPP :self-analysis professional portfolio

Scott, Anne, Clarkson, Philip and McDonough, Andrea. (2010) Beginning the development of SAPP :self-analysis professional portfolio.*Proceedings of the 2010 annual conference of the American Education Research Association.*USA: American Educational Research Association. pp. 1 - 5

##### Creative connections to school: Teachers support the learning of students with chronic illness during absence

Wilkie, Karina and Jones, Anthony. (2010) Creative connections to school: Teachers support the learning of students with chronic illness during absence.*Australian Computers in Education Conference.*Australia: Australian Council for Computers in Education. pp. 1 - 10

##### Decimats: Helping students to make sense of decimal place value

Roche, Anne. (2010) Decimats: Helping students to make sense of decimal place value.*Australian Primary Mathematics Classroom.*15(2), pp. 4 - 12.

##### Developing Year 5 Students' Understanding of Density: Implications for Mathematics Teaching

Clarke, Doug, Hilton, Geoff, Dole, Shelley and Wright, Tony. (2009) Developing Year 5 Students' Understanding of Density: Implications for Mathematics Teaching. In Roberta Hunter, Brenda Bicknell and Tim Burgess (Ed.).*Crossing Divides: Proceedings of the 32nd Annual Conference of the Mathematics Education Research Group of Australasia.*Palmerston North, New Zealand: Mathematics Education Research Group of Australasia. pp. 153 - 160

##### Using a concept cartoon to gain insight into children's calculation strategies

Sexton, Matthew, Gervasoni, Ann Maree and Brandenburg, Robyn. (2009) Using a concept cartoon to gain insight into children's calculation strategies.*Australian Primary Mathematics Classroom.*

##### Students' fraction comparison strategies as a window into robust understanding and possible pointers for instruction

Clarke, Doug M. and Roche, Anne. (2009) Students' fraction comparison strategies as a window into robust understanding and possible pointers for instruction.*Educational Studies in Mathematics.*72(1), pp. 127 - 138. https://doi.org/10.1007/s10649-009-9198-9

##### Using a concept cartoon to gain insight into children's calculation strategies

Sexton, Matthew, Gervasoni, Ann and Brandenburg, Robyn. (2009) Using a concept cartoon to gain insight into children's calculation strategies.*Australian Primary Mathematics Classroom.*14(4), pp. 24 - 28.

##### Opportunities and challenges for teachers and students provided by tasks built around ''real'' contexts

Clarke, Douglas McLean and Roche, Anne. (2009) Opportunities and challenges for teachers and students provided by tasks built around ''real'' contexts. In R. Hunter, B. Bicknell and T. Burgess (Ed.).*Crossing Divides: Proceedings of the 32nd Annual Conference of the Mathematics Education Research Group of Australasia (MERGA).*Palmerston North, New Zealand: Mathematics Education Research Group of Australasia. pp. 722 - 725

##### Converting mathematics tasks to learning opportunities: An important aspect of knowledge for mathematics teaching

Sullivan, Peter, Clarke, Barbara and Clarke, Doug. (2009) Converting mathematics tasks to learning opportunities: An important aspect of knowledge for mathematics teaching.*Mathematics Education Research Journal.*21(1), pp. 85 - 105. https://doi.org/10.1007/BF03217539

##### Link and learn: Students connecting to their schools and studies using ICT despite chronic illness

Wilkie, Karina and Jones, Anthony. (2009) Link and learn: Students connecting to their schools and studies using ICT despite chronic illness.*Annual Conference of the Australian Association for Research in Education (AARE).*Australia: Australian Association for Research in Education. pp. 1 - 13

##### Preservice secondary teachers' competencies in proof

Brown, Jill Patricia and Stillman, Gloria. (2009) Preservice secondary teachers' competencies in proof. In Fuo-Lai Lin, Feng-Jui Hsieh and Gila Hanna (Ed.).*Proof and Proving in Mathematics Education: ICMI Study 19 Conference Proceedings.*Taipei, Taiwan: National Taiwan Normal University. pp. 94 - 99

##### Students provide information on affective domain and learning environment through interview

Horne, Marjorie. (2009) Students provide information on affective domain and learning environment through interview. In M. Tzekaki, M. Kaldrimidou and H. Sakonidis (Ed.).*In Search for Theories in Mathematics Education: Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education.*Thessaloniki, Greece: International Group for the Psychology of Mathemati.... pp. 185 - 192

##### Exploring the relationship between task, teacher actions, and the student learning

Sullivan, Peter, Clarke, Doug, Clarke, Barbara and O'Shea, Helen. (2009) Exploring the relationship between task, teacher actions, and the student learning. In M. Tzekaki, M. Kaldrimidou and H. Sakonidis (Ed.).*In Search for Theories in Mathematics Education: Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education.*Thessaloniki, Greece: International Group for the Psychology of Mathemati.... pp. 185 - 192

##### There are more than part-whole strategies at work in understanding non-equal-parts fraction-area-models

Mitchell, Annie and Horne, Marjorie. (2009) There are more than part-whole strategies at work in understanding non-equal-parts fraction-area-models. In R. Hunter, B. Bicknell and T. Burgess (Ed.).*Crossing Divides: Proceedings of the 32nd Annual Conference of the Mathematics Education Research Group of Australasia (MERGA).*Palmerston North, New Zealand: Mathematics Education Research Group of Australasia. pp. 371 - 378

##### Making Sense of Partitive and Quotitive Division :A snapshot of Teachers' Pedagogical Content Knowledge

Clarke, Douglas McLean and Roche, Anne. (2009) Making Sense of Partitive and Quotitive Division :A snapshot of Teachers' Pedagogical Content Knowledge. In Roberta Hunter, Brenda Bicknell and Tim Burgess (Ed.).*Crossing Divides: Proceedings of the 32nd Annual Conference of the Mathematics Education Research Group of Australasia.*Palmerston Nth, New Zealand: Mathematics Education Research Group of Australasia. pp. 467 - 474

##### Concept Maps: Implications for the Teaching of Function for Secondary School Students

Brown, Jill Patricia. (2009) Concept Maps: Implications for the Teaching of Function for Secondary School Students. In R. Hunter, B. Bicknell and T. Burgess (Ed.).*Crossing Divides: Proceedings of the 32nd Annual Conference of the Mathematics Education Research Group of Australasia (MERGA).*Palmerston North, NZ: Mathematics Education Research Group of Australasia. pp. 65 - 72

##### Using mathematical tasks built around "real" contexts: Opportunites and challenges for teachers and students: The need for greater challenge and relevance for students in the middle years

Clarke, Doug and Roche, Anne. (2009) Using mathematical tasks built around "real" contexts: Opportunites and challenges for teachers and students: The need for greater challenge and relevance for students in the middle years.*Australian Primary Mathematics Classroom.*14(2), pp. 24 - 31.

##### Narrowing the gap :Empowering teachers and parents through understanding how children with Down syndrome develop mathematically

Brady, Josephine, Clarke, Douglas McLean, Gervasoni, Ann Maree, Clarke, Barbara and Faragher, Rhonda Muriel. (2008) Narrowing the gap :Empowering teachers and parents through understanding how children with Down syndrome develop mathematically. In Lorraine Graham (Ed.).*Proceedings of the 'Narrowing the Gap: Addressing Educational Disadvantage' Conference.*Armidale, Australia: SiMMER, University of New England. pp. 56 - 62

##### Ten practical tips for making fractions come alive and make sense

Clarke, Doug, Roche, Anne and Mitchell, Annie. (2008) Ten practical tips for making fractions come alive and make sense.*Mathematics Teaching in the Middle School.*13(7), pp. 373 - 380.

##### Developing understanding of triangle

Horne, Marjorie and Watson, Kelly. (2008) Developing understanding of triangle. In Olimpia Figueras, Jose Luis Cortina and Silvia Alatorre (Ed.).*Proceedings of the Joint Meeting of PME32 and PME-NA XXX.*Morelia, Mexico: Cinvestav-UMSNH. pp. 177 - 184

##### Fraction number line tasks and the additivity concept of length measurement

Mitchell, Annie and Horne, Marjorie. (2008) Fraction number line tasks and the additivity concept of length measurement. In M. Goos, R. Brown and K. Makar (Ed.).*Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia.*Brisbane, Australia: Mathematics Education Research Group of Australasia. pp. 353 - 360

##### The mathematics teacher as curriculum maker: Developing knowledge for enacting curriculum

Clarke, Doug. (2008) The mathematics teacher as curriculum maker: Developing knowledge for enacting curriculum. In In P. Sullivan and T. Wood (Ed.).*Knowledge and Beliefs in Mathematics Teaching and Teaching Development*pp. 133 - 151 Sense Publishers.

##### Using education research to inform Mathematics teaching in a school

Horne, Marjorie. (2008) Using education research to inform Mathematics teaching in a school. In Olimpia Figueras, Jose Luis Cortina and Silvia Alatorre (Ed.).*Proceedings of the Joint Meeting of PME32 and PME-NA XXX.*Morelia, Mexico: Cinvestav-UMSNH. pp. 81 - 86

##### Research into the teaching and learning of applications and modelling in Australasia

Stillman, Gloria, Brown, Jill Patricia and Galbraith, Peter. (2008) Research into the teaching and learning of applications and modelling in Australasia. In*Research in Mathematics Education in Australasia 2004-2007*pp. 141 - 164 Sense Publishers.

##### Understanding, assessing and developing young mathematical thinkers

Clarke, Douglas McLean. (2008) Understanding, assessing and developing young mathematical thinkers. In Mogens Niss (Ed.).*Proceedings of the 10th International Conference on Mathematical Education.*Roskilde, Denmark: Roskilde University. pp. 1 - 15

##### Children with down syndrome learning mathematics: Can they do it? Yes they can!

Faragher, Rhonda, Brady, Jo, Clarke, Barbara, Gervasoni, Ann and Clarke, Doug. (2008) Children with down syndrome learning mathematics: Can they do it? Yes they can!*Australian Primary Mathematics Classroom.*13(4), pp. 10 - 15.

##### Competencies in argumentation and proof :A comparative study of future mathematics teachers from Australia, Germany and Hong Kong

Schwarz, Bjorn, Vale, Colleen, Brown, Jill Patricia, Stillman, Gloria, Kaiser, Gabriele, Buchholtz, Nils and Leung, Issic. (2008) Competencies in argumentation and proof :A comparative study of future mathematics teachers from Australia, Germany and Hong Kong. In Gabriele Kaiser (Ed.).*Discussion Group 14: International Comparisons in Mathematics Education.*Monterrey, Mexico: International Commission on Mathematical Instruction. pp. 1 - 6

##### Sprouting of dopamine terminals and altered dopamine release and uptake in parkinsonian dyskinaesia

Lee, Joohyung, Zhu, Wen-Mei, Stanic, Davor, Finkelstein, David, Horne, Marj, Henderson, Jasmine, Lawrence, Andrew, O'Connor, Louise, Tomas, Doris, Drago, John and Horne, Malcolm. (2008) Sprouting of dopamine terminals and altered dopamine release and uptake in parkinsonian dyskinaesia.*Brain: a journal of neurology.*131(6), pp. 1574 - 1587. https://doi.org/10.1093/brain/awn085

##### Focusing Year 8 students on self-regulating their learning of mathematics

McDonough, Andrea Mary and Sullivan, Peter. (2008) Focusing Year 8 students on self-regulating their learning of mathematics. In Merrilyn Goos, Ray Brown and Katie Makar (Ed.).*Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia.*Brisbane, Australia: Mathematics Education Research Group of Australasia. pp. 337 - 343

##### Eliciting growth in teachers' proportional reasoning :Measuring the impact of a professional development program

Dole, Shelley, Clarke, Douglas McLean, Wright, Tony, Hilton, Geoff and Roche, Anne. (2008) Eliciting growth in teachers' proportional reasoning :Measuring the impact of a professional development program. In Merrilyn Goos, Ray Brown and Katie Makar (Ed.).*Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia.*Brisbane, Australia: Mathematics Education Research Group of Australasia. pp. 163 - 170

##### Future teachers' professional knowledge on argumentation and proof: A case study from universities in three countries

Schwarz, Bjorn, Leung, Issic K. C., Bucholtz, Nils, Kaiser, Gabriele, Stillman, Gloria, Brown, Jill Patricia and Vale, Colleen. (2008) Future teachers' professional knowledge on argumentation and proof: A case study from universities in three countries.*ZDM.*40(5), pp. 791 - 811. https://doi.org/10.1007/s11858-008-0150-8

##### The case of mathematical proof in lower secondary school :Knowledge and competencies of pre-service teachers

Brown, Jill Patricia, Stillman, Gloria, Schwarz, Bjorn and Kaiser, Gabriele. (2008) The case of mathematical proof in lower secondary school :Knowledge and competencies of pre-service teachers. In Merrilyn Goos, Ray Brown and Katie Makar (Ed.).##### Year Six Fraction Understanding :A Part of the Whole Story

Clarke, Douglas McLean, Mitchell, Annie and Roche, Anne. (2007) Year Six Fraction Understanding :A Part of the Whole Story. In J Watson and K Beswick (Ed.).*Mathematics: Essential Research, Essential Practice. Proceedings of the 30th Annual conference of the Mathematics Education Research Group of Australasia..*Adelaide,Australia: Mathematics Education Research Group of Australasia. pp. 207 - 216

##### Early notions of functions in a technology-rich teaching and learning environment (TRTLE)

Brown, Jill Patricia. (2007) Early notions of functions in a technology-rich teaching and learning environment (TRTLE). In J Watson and K Beswick (Ed.).*Mathematics: Essential Research, Essential Practice. Proceedings of the 30th Annual conference of the Mathematics Education Research Group of Australasia..*Adelaide, Australia: Mathematics Education Research Group of Australasia. pp. 153 - 162

##### A framework for success in implementing mathematical modelling in the secondary classroom

Stillman, Gloria, Brown, Jill Patricia, Edwards, I. and Galbraith, Peter. (2007) A framework for success in implementing mathematical modelling in the secondary classroom. In J Watson and K Beswick (Ed.).*Mathematics: Essential Research, Essential Practice. Proceedings of the 30th Annual conference of the Mathematics Education Research Group of Australasia..*Adelaide, Australia: Mathematics Education Research Group of Australasia. pp. 688 - 707

##### Helping Teachers to assess students' readiness to learn Mathematics

Sullivan, Peter and McDonough, Andrea Mary. (2007) Helping Teachers to assess students' readiness to learn Mathematics. In Peter L. Jeffery (Ed.).*AARE 2006 International Education Research Conference Engaging Pedagogies.*Melbourne, Australia: Australian Association for Research in Education. pp. 1 - 9

##### Challenges in formulating an extended modelling task at Year 9

Stillman, Gloria and Brown, Jill Patricia. (2007) Challenges in formulating an extended modelling task at Year 9. In H. Reeves, K. Milton and T. Spencer (Ed.).*Mathematics: Essential for learning, essential for life Proceedings of the 21st Biennial Conference of the Australian Association of Mathematics Teachers Inc..*Adelaide, Australia: Australian Association of Mathematics Teachers. pp. 224 - 231

##### Identifying challenges within transition phases of mathematical modelling activity at Year 9

Stillman, Gloria, Brown, Jill and Galbraith, Peter. (2007) Identifying challenges within transition phases of mathematical modelling activity at Year 9.*Conference Proceedings Of the Thirteenth International Conference on the Teaching of Mathematical Modelling and Applications.*International Conference on the Teaching of Mathematical Modelling and Applications. pp. 1 - 10

##### Ten key principles from research for the professional development of mathematics teachers

Clarke, Douglas McLean. (2007) Ten key principles from research for the professional development of mathematics teachers. In In G. C. Leder and H. J. Forgasz (Ed.).*Stepping Stones for the 21st Century: Australasian Mathematics Education Research*pp. 27 - 37 Sense Publishers.

##### Eliciting positive student motivation for learning mathematics

Sullivan, Peter and McDonough, Andrea Mary. (2007) Eliciting positive student motivation for learning mathematics. In J. Watson and K. Beswick (Ed.).##### Facilitating middle secondary modelling competencies

Galbraith, Peter, Stillman, Gloria, Brown, Jill Patricia and Edwards, I. (2007) Facilitating middle secondary modelling competencies. In In C. Haines, P. Galbraith and W. Blum et al. (Ed.).*Mathematical modelling (ICTMA12): Education, engineering and economics*pp. 130 - 140 Horwood Press.

##### Making Connections Science and Mathematics :The MC SAM Project

Clarke, Douglas McLean, Hilton, Geoff, Wright, Tony and Dole, Shelley. (2007) Making Connections Science and Mathematics :The MC SAM Project. In U.H. Cheah, Y. Wahyudi and R.P. Devadson (Ed.).*Refining Learning Culture for Sustainability (Proceedings of the 2nd International Conference on Science and mathematics Education.*Penang, Malaysia: SEAMEO RECSAM. pp. 184 - 194

##### Young children developing place value understandings

Horne, Marjorie and Livy, Sharyn. (2006) Young children developing place value understandings. In Jarmila Novotna, Hana Moraova and Magdalena Kratka (Ed.).*Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education.*Prague, Czech Republic: Charles University. pp. 313 - 320

##### Looking through zones at the teacher's role in technology-rich teaching and learning environments (TRTLE's)

Brown, Jill Patricia. (2006) Looking through zones at the teacher's role in technology-rich teaching and learning environments (TRTLE's). In C. Hoyles, J-b. Lagrange and L. H. Son (Ed.).*Digital technologies and mathematics teaching and learning: Rethinking the terrain, Proceedings of the seventeenth ICMI Study: 'Technology revisited'.*Hanoi, Vietnam: International Commission on Mathematical Instruction. pp. 56 - 65

##### Manifestations of affordances of a technology-rich teaching and learning environment (TRTLE)

Brown, Jill Patricia. (2006) Manifestations of affordances of a technology-rich teaching and learning environment (TRTLE). In J. Novotna, H. Moraova and M. Kratke (Ed.).*Proceedings of the 30th annual conference of the International Group for the Psychology of Mathematics Education (PME),.*Prague, Czech Republic: International Group for the Psychology of Mathemati.... pp. 241 - 248

##### Defining moments in the graphing calculator solution of a cubic function task

Brown, Jill and Stillman, Gloria. (2006) Defining moments in the graphing calculator solution of a cubic function task.*Nordisk Matematikkdidaktikk (Nordic Studies in Mathematics).*11(3), pp. 57 - 84.

##### Fractions as division: The forgotten notion?

Clarke, Doug. (2006) Fractions as division: The forgotten notion?*Australian Primary Mathematics Classroom.*11(3), pp. 4 - 10.

##### When successful comparison of decimals doesn't tell the story

Roche, Anne and Clarke, Douglas McLean. (2006) When successful comparison of decimals doesn't tell the story. In J. Novotna, H. Moraova and M. Kratka (Ed.).*Proceedings of the 30th Conference of the International Group of Psychology of Mathematics Education.*Prague, Czech Republic: Charles University. pp. 425 - 432

##### Identifying key transition activities for enhanced engagement in mathematical modelling

Galbraith, Peter, Stillman, Gloria Ann and Brown, Jill Patricia. (2006) Identifying key transition activities for enhanced engagement in mathematical modelling. In P.Grootenboer, R. Zevenbergen and M. Chinnappan (Ed.).*Identities, cultures and learning spaces, Proceedings of the Twenty Ninth annual conference of the Mathematics Education Research Group of Australasia (MERGA).*Adelaide, Australia: Mathematics Education Research Group of Australasia. pp. 237 - 245

##### Perhaps the decision of some students not to engage in learning mathematics in school is deliberate

Sullivan, Peter, Tobias, Steve and McDonough, Andrea Mary. (2006) Perhaps the decision of some students not to engage in learning mathematics in school is deliberate.*Educational Studies in Mathematics.*62(1), pp. 81 - 99. https://doi.org/10.1007/s10649-006-1348-8

##### Student Engagement in the Middle Years :Describing Influences and Possible Teacher Actions

Prain, Vaughan, Sullivan, Peter and McDonough, Andrea Mary. (2006) Student Engagement in the Middle Years :Describing Influences and Possible Teacher Actions.*Australian Association for Research in Education 2005 Conference Papers.*Melbourne, Australia: Australian Association for Research in Education. pp. 1 - 8

##### A longitudinal study of children's mental computation skills

Clarke, Douglas McLean, Clarke, Barbara and Horne, Marjorie. (2006) A longitudinal study of children's mental computation skills. In J. Novotna, H. Moraova and M. Kratka (Ed.).*Proceedings of the 30th Conference of the International Group of Psychology of Mathematics.*Prague, Czech Republic: Charles University. pp. 329 - 336

##### Assessing student understanding of fractions using task-based interviews

Clarke, Douglas McLean, Roche, Anne, Mitchell, Annie and Sukenik, Michal. (2006) Assessing student understanding of fractions using task-based interviews. In J. Novotna, H. Moraova and M. Kratka (Ed.).*Proceedings of the 30th Conference of the International Group of Psychology of Mathematics Education.*Prague, Czech Republic: Charles University. pp. 337 - 344

##### Examining the changed role of numeracy coordinators

Clarke, Douglas McLean and Cheeseman, Jill. (2006) Examining the changed role of numeracy coordinators. In P. Grootenboer, R. Zevenbergen and M. Chinnappan (Ed.).*Identities; Cultures; and Learning: Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia.*Canberra, Australia: Mathematics Education Research Group of Australasia. pp. 123 - 130

##### Affordances of a technology-rich teaching and learning environment

Brown, Jill Patricia. (2005) Affordances of a technology-rich teaching and learning environment. In P. Clarkson, A. Downton and D. Gronn (Ed.).*Building Connections, Theory, Research and Practice: Proceedings of the 28th Annual Conference of the Mathematics Education Research Group of Australasia.*Adelaide, Australia: Mathematics Education Research Group of Australasia. pp. 177 - 184

##### Algebra revisited

Horne, Marjorie. (2005) Algebra revisited. In M. Coupland, J. Anderson and T. Spencer (Ed.).*Making Mathematics Vital: The Proceedings of the Twentieth biennial conference of the Australian Association of Mathematics Teachers Inc..*Adelaide, Australia: Australian Association of Mathematics Teachers. pp. 308 - 315

##### 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

##### Identification of affordances of a technology-rich teaching and learning environment (TRTLE)

Brown, Jill Patricia. (2005) Identification of affordances of a technology-rich teaching and learning environment (TRTLE). In H. Chick and J. Vincent (Ed.).*Proceedings of the 29th annual conference of the International Group for the Psychology of Mathematics Education (PME).*Melbourne, Australia: International Group for the Psychology of Mathemati.... pp. 185 - 192

##### The effects of number knowledge at school entry on subsequent number development: A five-year longitudinal study

Horne, Marjorie. (2005) The effects of number knowledge at school entry on subsequent number development: A five-year longitudinal study. In P. Clarkson, A. Downton and D. Gronn (Ed.).*Building connections: Research; theory and practice (Proceedings of the 28th annual conference of the Mathematics Education Research Group of Australasia).*Melbourne, Australia: Mathematics Education Research Group of Australasia. pp. 443 - 450

##### Longer is larger - or is it?

Roche, Anne. (2005) Longer is larger - or is it?*Australian Primary Mathematics Classroom.*10(3), pp. 11 - 16.

##### Gender and mathematics

Horne, Marjorie, Vale, Colleen and Forgasz, Helen. (2004) Gender and mathematics. In In B. Berry, G. Anthony and C. Diezmann (Ed.).*Research in Mathematics Education in Australasia; 2000-2003*pp. 75 - 100 Post Pressed.

##### 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.

##### Early Gender Differences

Horne, Marjorie. (2004) Early Gender Differences. In Marit Johnsen Hoines and Anne Berit Fuglestad (Ed.).*Proceedings of the 28th Conference of the International group for the psychology of mathematics education.*Bergen, Norway: Bergen University College. pp. 23802 - 25993

##### 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

##### Enabling teachers to perceive the affordances of a technologically rich learning environment for linear functions in order to design units of work incorporating best practice

Brown, Jill Patricia. (2004) Enabling teachers to perceive the affordances of a technologically rich learning environment for linear functions in order to design units of work incorporating best practice. In W. C. Yang, S. C. Chu and T. de Alwis (Ed.).*Proceedings of the 9th Asian Technology Conference in Mathematics.*Singapore, Singapore: Advanced Technology Council in Mathematics Inc. pp. 242 - 251

##### 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.

##### Class grouping for mathematics: What do we know?

Horne, Marjorie. (2004) Class grouping for mathematics: What do we know? In In E. Clarke, L. Johansson and W. Lester (Ed.).*International Perspectives on Learning and Teaching of Mathematics*pp. 395 - 410 National Center for Mathematics Education.

##### 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

##### A difficult function

Brown, Jill. (2004) A difficult function.*Australian Mathematics Teacher.*60(2), pp. 6 - 11.

##### 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.

##### Teacher approaches to graphing a difficult cubic function

Brown, Jill Patricia. (2004) Teacher approaches to graphing a difficult cubic function. In I. Putt, R. Faragher and M. 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: Mathematics Education Research Group of Australasia. pp. 111 - 118

##### 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

##### Can the notion of affordances be of use in the design of a technology enriched mathematics curriculum?

Stillman, Gloria, Brown, Jill Patricia and Herberts, Sandra. (2004) Can the notion of affordances be of use in the design of a technology enriched mathematics curriculum? In I. Putt, R. Faragher and M. 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: Mathematics Education Research Group of Australasia. pp. 119 - 126

##### 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.

##### Properties of shape

Horne, Marj. (2003) Properties of shape.*Australian Primary Mathematics Classroom.*8(2), pp. 8 - 13.

##### 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.

##### Gender differences in the early years in addition and subtraction

Horne, Marjorie. (2003) Gender differences in the early years in addition and subtraction. In N. A. Pateman, B. J. Dougherty and J. Zilliox (Ed.).*Proceedings of the 2003 Joint Meeting of PME and PMENA.*Honolulu, United States: Curriculum Research and Development Group - University of Hawaii. pp. 79 - 86

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

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

##### 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

##### Defining moments in determining a complete graph in a graphing calculator teaching and learning environment

Brown, Jill Patricia. (2003) Defining moments in determining a complete graph in a graphing calculator teaching and learning environment. In L. Bragg, C. Campbell and G. Herbert (Ed.).*Mathematics Education Research: Innovation, networking, opportunity. Proceedings of the 26th annual conference of the Mathematics Education Research Group of Australasia (MERGA).*Geelong, Australia: Mathematics Education Research Group of Australasia. pp. 168 - 175

##### 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