# Issues in the teaching of algorithms in the primary years

Book chapter

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.

Authors | Clarke, Douglas McLean |
---|---|

Editors | E. Clarke, L. Johansson and W. Lester |

Page range | 21 - 36 |

Year | 2004 |

Book title | International Perspectives on Learning and Teaching Mathematics |

Publisher | National Center for Mathematics Education |

ISBN | 9185143014 |

Permalink -

https://acuresearchbank.acu.edu.au/item/88043/issues-in-the-teaching-of-algorithms-in-the-primary-years

##### 23

total views##### 0

total downloads##### 1

views this month##### 0

downloads this month

*These values are for the period from 19th October 2020, when this repository was created.*

## Export as

## Related outputs

##### 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

##### 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

##### 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.

##### 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

##### 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.

##### 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

##### 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.).*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. 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

##### 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.

##### 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.).*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

##### 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.

##### 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.

##### 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