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

Conference item

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
AuthorsMitchell, Annie and Clarke, Doug
Abstract

Twelve students across Grades 2 to 6 were interviewed individually using a range of tasks, where the mathematical focus was a conceptual understanding of fractions. Careful listening established that despite giving a correct answer and appearing to have conceptual understanding, further probing sometimes revealed that the child had only a faulty procedural understanding. Similarly, success on one task did not guarantee success on a different but related task. Conversely, a task involving a continuous quantity enabled a child to move between discrete and continuous interpretations of fractional parts. This study supported the claimed advantages of one-to-one interviews over pen and paper tests, but also highlighted the importance of careful listening and the need for multiple tasks in the one mathematical domain in eliciting understanding.

KeywordsEducation Assessment and Evaluation;--Primary education
Year2004
PublisherJames Cook University
Web address (URL)http://www.merga.net.au/documents/RP432004.pdf
Open accessOpen access
Publisher's version
Page range367 - 373
ISBN1920846042
Research GroupSchool of Education
Place of publicationTownsville,Australia
EditorsIan Putt, Rhonda Farragher and Mal McLean
Permalink -

https://acuresearchbank.acu.edu.au/item/87452/when-is-three-quarters-not-three-quarters-listening-for-conceptual-understanding-in-children-s-explanations-in-a-fraction-interview

Log in to edit

Download files

Publisher's version
Mitchell_2004_When_is_three_quarters_three_quarters.pdf

  • 263
    total views
  • 131
    total downloads
  • 6
    views this month
  • 2
    downloads this month
These values are for the period from 19th October 2020, when this repository was created.

Export as

Related outputs

Reflections on themes in professional contributions by David Clarke
Clarke, Doug, Stephens, Max and Sullivan, Peter. (2022). Reflections on themes in professional contributions by David Clarke. ZDM Mathematics Education. 54(2), pp. 457-465. https://doi.org/10.1007/s11858-021-01288-5
Using contextualized tasks to engage students in meaningful and worthwhile mathematics learning
Clarke, Doug and Roche, Anne. (2018). Using contextualized tasks to engage students in meaningful and worthwhile mathematics learning. The Journal of Mathematical Behavior. 51, pp. 95 - 108. https://doi.org/10.1016/j.jmathb.2017.11.006
Learning from lessons: Studying the structure and construction of mathematics teacher knowledge in Australia, China and Germany
Chan, Man Ching Esther, Clarke, David J., Clarke, Doug, Roche, Anne, Cao, Yiming and Peter-Koop, Andrea. (2018). Learning from lessons: Studying the structure and construction of mathematics teacher knowledge in Australia, China and Germany. Mathematics Education Research Journal. 30(1), pp. 89 - 102. https://doi.org/10.1007/s13394-017-0214-6
Understanding time: A research based framework
Thomas, Margaret, Clarke, Doug, McDonough, Andrea and Clarkson, Philip. (2016). Understanding time: A research based framework. In B. White, M. Chinnappan and S. Trenholm (Ed.). 39th Annual Conference of the Mathematics Education Research Group of Australasia. Australia: Mathematics Education Research Group of Australasia. pp. 592 - 599
Time: Assessing understanding of core ideas
Thomas, Margaret, McDonough, Andrea Mary, Clarkson, Philip and Clarke, Douglas McLean. (2016). Time: Assessing understanding of core ideas. In B. White, M. Chinnappan and S. Trenholm (Ed.). 39th Annual Conference of the Mathematics Education Research Group of Australasia. Australia: Mathematics Education Research Group of Australasia. pp. 600 - 607
Developing students' functional thinking in algebra through different visualisations of a growing pattern's structure
Wilkie, Karina Joyce and Clarke, Douglas McLean. (2016). Developing students' functional thinking in algebra through different visualisations of a growing pattern's structure. Mathematics Education Research Journal. 28(2), pp. 223 - 243. https://doi.org/10.1007/s13394-015-0146-y
Learning from lessons: Teachers' insights and intended actions arising from their learning about student thinking
Roche, Anne, Clarke, Douglas McLean, Clarke, David and Chan, Ching Esther. (2016). Learning from lessons: Teachers' insights and intended actions arising from their learning about student thinking. In B. White, M. Chinnappan and S. Trenholm (Ed.). 39th Annual Conference of the Mathematics Education Research Group of Australasia. Australia: Mathematics Education Research Group of Australasia. pp. 560 - 567
Changes in teachers' knowledge and beliefs about mathematics and mathematics teaching: A case study
Lomas, Laurinda and Clarke, Douglas McLean. (2016). Changes in teachers' knowledge and beliefs about mathematics and mathematics teaching: A case study. In B. White, M. Chinnappan and S. Trenholm (Ed.). 39th Annual Conference of the Mathematics Education Research Group of Australasia. Australia: Mathematics Education Research Group of Australasia. pp. 389 - 396
Supporting teachers in structuring mathematics lessons involving challenging tasks
Sullivan, Peter, Askew, Mike, Cheeseman, Jill, Clarke, Doug, Mornane, Angela, Roche, Anne and Walker, Nadia. (2015). Supporting teachers in structuring mathematics lessons involving challenging tasks. Journal of Mathematics Teacher Education (online version). 18, pp. 123 - 140. https://doi.org/10.1007/s10857-014-9279-2
Describing the nature and effect of teacher interactions with students during seat work on challenging tasks
Roche, Anne and Clarke, Douglas. (2015). Describing the nature and effect of teacher interactions with students during seat work on challenging tasks. Annual Conference of the Mathematics Education Research Group of Australasia (MERGA). Australia: Mathematics Education Research Group of Australasia. pp. 532 - 539
Pathways to professional growth : Investigating upper primary school teachers' perspectives on learning to teach algebra
Wilkie, Karina and Clarke, Doug. (2015). Pathways to professional growth : Investigating upper primary school teachers' perspectives on learning to teach algebra. Australian Journal of Teacher Education (online version). 40(4), pp. 87 - 118. https://doi.org/10.14221/ajte.2015v40n4.6
Students' willingness to engage with mathematical challenges :Implications for classroom pedagogies
Sullivan, Peter, Clarke, Doug, Cheeseman, Jill, Mornane, Angela, Roche, Anne, Sawatzki, Carly and Walker, Nadia. (2014). Students' willingness to engage with mathematical challenges :Implications for classroom pedagogies. In J. Anderson, M. Cavanagh and A. Prescott (Ed.). Curriculum in focus: Research guided practice (Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia). Australia: Mathematics Education Research Group of Australasia. pp. 597 - 604
Schools and Families in Partnership for Learning in Faith-Based Schools
Mitchell, Annie, Chapman, Judith, McNamara, Sue and Horne, Marjorie. (2014). Schools and Families in Partnership for Learning in Faith-Based Schools. In In J. D. Chapman, S. McNamara and M. J Reiss & Y. Waghid (Ed.). International Handbook of Learning, Teaching and Leading in Faith-Based Schools pp. 657 - 674 Springer. https://doi.org/10.1007/978-94-017-8972-1_38
Teaching mathematics effectively
Faragher, Rhonda and Clarke, Doug. (2014). Teaching mathematics effectively. In In M. Gaffney and R. Faragher (Ed.). Leading Improvements in Student Numeracy ACER Press.
The numeracy challenge: Student achievement, teacher quality, school leadership and system policy
Gaffney, Michael, Clarke, Doug and Faragher, Rhonda. (2014). The numeracy challenge: Student achievement, teacher quality, school leadership and system policy. In In M. Gaffney and R. Faragher (Ed.). Leading Improvements in Student Numeracy ACER Press.
Teaching strategies for building student persistence on challenging tasks : Insights emerging from two approaches to teacher professional learning
Clarke, Doug, Cheeseman, Jill, Roche, Anne and van der Schans, Stephanie. (2014). Teaching strategies for building student persistence on challenging tasks : Insights emerging from two approaches to teacher professional learning. Mathematics Teacher Education and Development Journal. 16(2), pp. 46 - 70.
Developing student's functional thinking in algebra through different visualisations of a growing pattern's structure
Wilkie, Karina J. and Clarke, Doug. (2014). Developing student's functional thinking in algebra through different visualisations of a growing pattern's structure. In J Anderson, M Cavanagh and A Prescott (Ed.). Curriculum in focus: Research guided practice (Proceedings of the 37th annual conference of the Mathematics Education Research Group of Australasia). Australia: Mathematics Education Research Group of Australasia. pp. 637 - 644
Teachers' views of the challenging elements of a task
Cheeseman, Jill, Clarke, Doug, Roche, Anne and Wilson, Karen. (2013). Teachers' views of the challenging elements of a task. In V Steinle, L Ball and C Bardini (Ed.). Mathematics Education: Yesterday, Today and Tomorrow (MERGA36). Australia: Mathematics Education Research Group of Australasia. pp. 154 - 161
Teachers' decisions about mathematics tasks when planning
Sullivan, Peter, Clarke, David, Clarke, Doug and Roche, Anne. (2013). Teachers' decisions about mathematics tasks when planning. In V. Steinle, L. Ball and C. Bardini (Ed.). Mathematics Education: Yesterday, Today and Tomorrow. Melbourne, Australia: Mathematics Education Research Group of Australasia. pp. 626 - 633
Teachers and observers learning from demonstration lessons in mathematics education
Clarke, Doug, Roche, Anne and Knight, Rose. (2013). Teachers and observers learning from demonstration lessons in mathematics education. In A. M. Lindmeier and A. Heinze (Ed.). Mathematics learning across the life span. Germany: International Group for the Psychology of Mathematics Education. pp. 44 - 44
Teaching with tasks for effective mathematics learning
Sullivan, Peter, Clarke, Doug and Clarke, Barbara. (2013). Teaching with tasks for effective mathematics learning Springer Science and Business Media. https://doi.org/10.1007/978-1-4614-4681-1
Primary teachers' representations of division: Assessing mathematical knowledge that has pedagogical potential
Roche, Anne and Clarke, Douglas M.. (2013). Primary teachers' representations of division: Assessing mathematical knowledge that has pedagogical potential. Mathematics Education Research Journal. 25(2), pp. 257 - 278. https://doi.org/10.1007/s13394-012-0060-5
Demonstration lessons in mathematics education: Teachers' observation foci and intended changes in practice
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
The four-three-four model: Drawing on partitioning, equivalence, and unit-forming in a quotient sub-construct fraction task
Mitchell, Annie. (2012). The four-three-four model: Drawing on partitioning, equivalence, and unit-forming in a quotient sub-construct fraction task. 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. 513 - 520
Reasoning in the Australian Curriculum: Understanding its meaning and using the relevant language
Clarke, Douglas, Clarke, David and Sullivan, Peter. (2012). Reasoning in the Australian Curriculum: Understanding its meaning and using the relevant language. Australian Primary Mathematics Classroom. 17(3), pp. 28 - 32.
Choosing tasks to match the content you are wanting to teach
Sullivan, Peter, Clarke, David and Clarke, Douglas. (2012). Choosing tasks to match the content you are wanting to teach. Australian Primary Mathematics Classroom. 17(3), pp. 24 - 27.
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.
The four-three-four model: Drawing on partitioning, equivalence, and unit-forming in a quotient sub-construct fraction task
Mitchell, Annie. (2012). The four-three-four model: Drawing on partitioning, equivalence, and unit-forming in a quotient sub-construct fraction task. 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. 513 - 520
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
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.
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
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 Way, Jenni and Bobis, Janette (Ed.). Fractions : Teaching for understanding pp. 23-32 Australian Association of Mathematics Teachers.
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
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
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.). 33rd Annual Conference of the Mathematics Education Research Group of Australasia. John Curtin College of the Arts, Fremantle, Western Australia, Australia 03 - 07 Jul 2010 Australia: Mathematics Education Research Group of Australasia. pp. 414 - 421
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.). 33rd Annual Conference of the Mathematics Education Research Group of Australasia. John Curtin College of the Arts, Fremantle, Western Australia, Australia 03 - 07 Jul 2010 Australia: Mathematics Education Research Group of Australasia. pp. 531 - 538
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.
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
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
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
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.
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.
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.
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
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.). 30th annual conference of the Mathematics Education Research Group of Australasia. Wrest Point Hotel Casino, Hobart, Tasmania, Australia 02 - 06 Jul 2007 Adelaide,Australia: Mathematics Education Research Group of Australasia. pp. 207 - 216
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.
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
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
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
Written algorithms in the primary years: Undoing the good work?
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
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.
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.
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 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.
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.
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