Young children's ability to use the balance strategy to solve for unknowns

Journal article

Warren, Elizabeth Anne and Cooper, Tom J.. (2005). Young children's ability to use the balance strategy to solve for unknowns. Mathematics Education Research Journal. 17(1), pp. 58 - 72. https://doi.org/10.1007/BF03217409
AuthorsWarren, Elizabeth Anne and Cooper, Tom J.
Abstract

This article examines students’ ability to use the balance model to solve for unknowns. A teaching experiment was conducted in four Year 3 classrooms. This experiment focused on exploring the application of the balance model as an analogue for representing equations and solving for unknowns. The teaching experiment promoted a shift by students towards viewing addition and subtraction equations in terms of equivalence, where the situation is viewed in a multi-directional way (i.e., balance). Initially the lessons were trialed by the researchers in two classrooms. The lessons were then implemented in a further two classrooms by two classroom teachers in conjunction with the researchers. Two weeks after the conclusion of the teaching experiment, a one-on-one interview was conducted with a random sample comprising twenty students with an average age of eight years. The interviews indicated that while the balance model did assist students reach solutions for finding unknowns, for some students further explicit teaching was required.

Year2005
JournalMathematics Education Research Journal
Journal citation17 (1), pp. 58 - 72
PublisherSpringer Netherlands
ISSN2211-050X
Digital Object Identifier (DOI)https://doi.org/10.1007/BF03217409
Scopus EID2-s2.0-67349233175
Page range58 - 72
Research GroupSchool of Education
Place of publicationNetherlands
Permalink -

https://acuresearchbank.acu.edu.au/item/88x3q/young-children-s-ability-to-use-the-balance-strategy-to-solve-for-unknowns

Log in to edit
  • 145
    total views
  • 0
    total downloads
  • 6
    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

Examining changes in young Aboriginal and Torres Strait Island students and their beginning primary school teachers’ engagement in the teaching and learning of mathematics
Miller, Jodie, Warren, Elizabeth and Armour, Danielle. (2020). Examining changes in young Aboriginal and Torres Strait Island students and their beginning primary school teachers’ engagement in the teaching and learning of mathematics. ZDM. 52(3), pp. 557-569. https://doi.org/10.1007/s11858-019-01077-1
Mathematical discourse when engaging in pattern generalisation: Considering semiotic systems in young Indigenous Australian students
Miller, Jodie, Warren, Elizabeth and Armour, Danielle. (2018). Mathematical discourse when engaging in pattern generalisation: Considering semiotic systems in young Indigenous Australian students. In In R. Hunter, M. Civil and B. Herbel-Eisenmann, N. Planas and D. Wagner (Ed.). Mathematical discourse that breaks barriers and creates space for marginalized learners pp. 213 - 234 Sense Publishers. https://doi.org/10.1163/9789463512121
Mathematics at the margins
Warren, Elizabeth Anne and Miller, Jodie. (2016). Mathematics at the margins Springer Nature. https://doi.org/10.1007/978-981-10-0703-3
Working together: Strategies that support cross-cultural engagement of Indigenous teacher assistants working in Indigenous contexts
Armour, Danielle, Warren, Elizabeth Anne and Miller, Jodie. (2016). Working together: Strategies that support cross-cultural engagement of Indigenous teacher assistants working in Indigenous contexts. Asia-Pacific Journal of Teacher Education. 44(5), pp. 421 - 435. https://doi.org/10.1080/1359866X.2015.1127324
Supporting English second-language learners in disadvantaged contexts : Learning approaches that promote success in mathematics
Warren, Elizabeth and Miller, Jodie. (2015). Supporting English second-language learners in disadvantaged contexts : Learning approaches that promote success in mathematics. International Journal of Early Years Education. 23(2), pp. 192 - 208. https://doi.org/10.1080/09669760.2014.969200
Young Australian Indigenous students generalising growing patterns: A case study of teacher/student semiotic interactions
Miller, Jodie and Warren, Elizabeth. (2015). Young Australian Indigenous students generalising growing patterns: A case study of teacher/student semiotic interactions. 39th Conference of the International Group for the Psychology of Mathematics Education. Australia: International Group for the Psychology of Mathematics Education. pp. 257 - 264
Exploring ESL students' understanding of mathematics in the early years : Factors that make a difference
Miller, Jodie and Warren, Elizabeth. (2014). Exploring ESL students' understanding of mathematics in the early years : Factors that make a difference. Mathematics Education Research Journal. 26(4), pp. 791 - 810. https://doi.org/10.1007/s13394-014-0121-z
Supporting young ESL students from disadvantaged contexts in their engagement with mathematics : Teachers' pedagogical challenges
Warren, Elizabeth, Harris, Katherine and Miller, Jodie. (2014). Supporting young ESL students from disadvantaged contexts in their engagement with mathematics : Teachers' pedagogical challenges. International Journal of Pedagogies and Learning. 9(1), pp. 10 - 25. https://doi.org/10.1080/18334105.2014.11082016
Voices of reform from the classroom: Teachers' approaches to change
Noack, Margaret, Mulholland, Judith and Warren, Elizabeth. (2013). Voices of reform from the classroom: Teachers' approaches to change. Teachers and Teaching: Theory and Practice. 19(4), pp. 449 - 462. https://doi.org/10.1080/13540602.2013.770233
Enriching the professional learning of early years teachers in disadvantaged contexts: The impact of quality resources and quality professional learning
Warren, Elizabeth and Miller, Jodie. (2013). Enriching the professional learning of early years teachers in disadvantaged contexts: The impact of quality resources and quality professional learning. Australian Journal of Teacher Education. 38(7), pp. 91 - 111. https://doi.org/10.14221/ajte.2013v38n7.6
Exploring young students' functional thinking
Warren, Elizabeth, Miller, Jodie and Cooper, Thomas J.. (2013). Exploring young students' functional thinking. PNA. 7(2), pp. 329 - 336.
Enhancing teacher professional development for early years mathematics teachers working in disadvantaged contexts
Warren, Elizabeth and Quine, Janine. (2013). Enhancing teacher professional development for early years mathematics teachers working in disadvantaged contexts. In In L. English and J. Mulligan (Ed.). Reconceptualizing Early Mathematics Learning: Advanced Series in Mathematics Education pp. 283 - 307 Springer. https://doi.org/10.1007/978-94-007-6440-8_14
Young Australian indigenous students' effective engagement in mathematics: the role of language, patterns, and structure
Warren, Elizabeth and Miller, Jodie. (2013). Young Australian indigenous students' effective engagement in mathematics: the role of language, patterns, and structure. Mathematics Education Research Journal. 25(1), pp. 151 - 171. https://doi.org/10.1007/s13394-013-0068-5
A holistic approach to supporting the learning of young indigenous students: One case study
Warren, Elizabeth and Quine, Janine. (2013). A holistic approach to supporting the learning of young indigenous students: One case study. Australian Journal of Indigenous Education. 42(1), pp. 12 - 23. https://doi.org/10.1017/jie.2013.9
Male students' perspectives concerning the relevance of mathematics: Pilot study findings
Easey, Michael, Warren, Elizabeth A. and Geiger, Vince. (2012). Male students' perspectives concerning the relevance of mathematics: Pilot study findings. 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. 242 - 249
An exploration into growing patterns with young Australian Indigenous students
Miller, Jodie and Warren, Elizabeth. (2012). An exploration into growing patterns with young Australian Indigenous students. 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. 505 - 512
Understanding parent school choice: The development of a holistic theoretical model
McCarthy, Michael and Warren, Elizabeth. (2012). Understanding parent school choice: The development of a holistic theoretical model. Journal of Catholic School Studies. 84(1), pp. 24 - 35.
Exploration into cultural aspects of mathematical generalisation: young Australian indigenous students
Miller, Jodie and Warren, Elizabeth. (2012). Exploration into cultural aspects of mathematical generalisation: young Australian indigenous students. 12th International Congress on Mathematical Education. Australia: Ascilite.
Repeating patterns: Strategies to assist young students to generalise the mathematical structure
Warren, Elizabeth, Miller, Jodie and Cooper, Tom. (2012). Repeating patterns: Strategies to assist young students to generalise the mathematical structure. Australasian Journal of Early Childhood. 37(3), pp. 111 - 120.
Supporting teachers' professional learning at a distance: A model for change in at-risk contexts
Warren, Elizabeth, Quine, Janine and De Vries, Eva. (2012). Supporting teachers' professional learning at a distance: A model for change in at-risk contexts. Australian Journal of Teacher Education. 37(6), pp. 12 - 28.
Plotting the use of oral language and rich mathematical representations of teachers in the early years of formal schooling
McDonald, Susan, Warren, Elizabeth and de Vries, Eva. (2011). Plotting the use of oral language and rich mathematical representations of teachers in the early years of formal schooling. In B. Ubuz (Ed.). 35th conference of the International Group for the Psychology of Mathematics Education: developing mathematical thinking. Ankara, Turkey: PME. pp. 209 - 216
Refocusing on oral language and rich representations to develop the early mathematical understandings of Indigenous students
McDonald, Susan, Warren, Elizabeth A. and DeVries, Eva. (2011). Refocusing on oral language and rich representations to develop the early mathematical understandings of Indigenous students. Australian Journal of Indigenous Education. 40(9), pp. 9 - 17. https://doi.org/10.1375/ajie.40.9
Play-based learning and intentional teaching in early childhood contexts
Thomas, Louise, Warren, Elizabeth A. and DeVries, Eva. (2011). Play-based learning and intentional teaching in early childhood contexts. Australasian Journal of Early Childhood. 36(4), pp. 69 - 75. https://doi.org/10.1177/183693911103600410
Engaging Indigenous children in mathematical learning in an early childhood setting
Warren, Elizabeth A., Thomas, Louise and DeVries, Eva. (2011). Engaging Indigenous children in mathematical learning in an early childhood setting. International Journal of Pedagogies and Learning. 6(2), pp. 97 - 107.
Years 2 to 6 students' ability to generalise: Models, representations and theory for teaching and learning
Cooper, Tom J. and Warren, Elizabeth A.. (2011). Years 2 to 6 students' ability to generalise: Models, representations and theory for teaching and learning. In In J. Cai and E. Knuth (Ed.). pp. 187 - 214 Springer.
Representations: Materials, language, and recording
Warren, Elizabeth A.. (2011). Representations: Materials, language, and recording. In In E. Cochrane (Ed.). pp. 98 - 121 Oxford University Press.
Young Indigenous Australian children's learning of mathematics: The influence of the role of teacher and teacher assistants
Warren, Elizabeth, McDonald, Susan and DeVries, Eva. (2011). Young Indigenous Australian children's learning of mathematics: The influence of the role of teacher and teacher assistants. Proceedings of the 2011 annual meeting of the American Educational Research Association (AERA). USA: American Educational Research Association. pp. 1 - 9
Pattern and structure
Warren, Elizabeth A.. (2011). Pattern and structure. In In E. Cochrane (Ed.). pp. 248 - 264 Oxford University Press.
An exploration of young students' ability to generalise function tasks
Warren, Elizabeth, Miller, Jodie and Cooper, Tom J.. (2011). An exploration of young students' ability to generalise function tasks. 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. 752 - 759
Algebraic thinking, pattern, and order
Warren, Elizabeth A.. (2011). Algebraic thinking, pattern, and order. In In E. Cochrane (Ed.). pp. 586 - 603 Oxford University Press.
Teaching mathematics and play-based learning in an Indigenous early childhood setting :early childhood teachers' perspectives
De Vries, Eva, Thomas, Louise and Warren, Elizabeth A.. (2010). Teaching mathematics and play-based learning in an Indigenous early childhood setting :early childhood teachers' perspectives. 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. 719 - 722
Pedagogies to support indigenous students' mathematics learning in rural and remote Queensland classrooms
Warren, Elizabeth A,, Baturo, Annette R. and Cooper, Tom J.. (2010). Pedagogies to support indigenous students' mathematics learning in rural and remote Queensland classrooms. In In Joseph Zajda (Ed.). pp. 161 - 184 Springer.
Indigenous children's ability to pattern as they enter kindergarten/pre-prep settings :an exploratory study
Warren, Elizabeth and Miller, Jodie. (2010). Indigenous children's ability to pattern as they enter kindergarten/pre-prep settings :an exploratory study. 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. 594 - 601
Young Australian indigenous students: Engagement with mathematics in the early years
Warren, Elizabeth and De Vries, Eva. (2010). Young Australian indigenous students: Engagement with mathematics in the early years. Australian Primary Mathematics Classroom. 15(1), pp. 4 - 9.
Exploring four year old indigenous students' ability to pattern
Warren, Elizabeth and Miller, Jodie. (2010). Exploring four year old indigenous students' ability to pattern. International Research in Early Childhood Education. 1(2), pp. 42 - 56.
Power and authority in school and community: Interactions between non-Indigenous teachers and Indigenous teacher assistants in remote Australian schools
Warren, Elizabeth, Baturo, Annette R. and Cooper, Tom J.. (2010). Power and authority in school and community: Interactions between non-Indigenous teachers and Indigenous teacher assistants in remote Australian schools. In In Joseph Zajda and Macleans A. Geo-Jaja (Ed.). pp. 193 - 207 Springer. https://doi.org/10.1007/978-90-481-3218-8_11
Early childhood teachers' professional learning in early algebraic thinking: A model that supports new knowledge and pedagogy
Warren, Elizabeth. (2009). Early childhood teachers' professional learning in early algebraic thinking: A model that supports new knowledge and pedagogy. Mathematics Teacher Education and Development. 10, pp. 30 - 45.
Developing Mathematics Understanding and Abstraction: The case of Equivalence in the Elementary Years
Warren, Elizabeth Anne, de Vries, Eva and Cole, Antoinette. (2009). Developing Mathematics Understanding and Abstraction: The case of Equivalence in the Elementary Years. Mathematics Education Research Journal.
Developing literacy understandings :Examining the effects of engaging teacher aides in professional development
Young, Janelle Patricia and Warren, Elizabeth Anne. (2009). Developing literacy understandings :Examining the effects of engaging teacher aides in professional development. Standing Conference on University Teaching and Research in the Education of Adults (SCUTREA) 2009. Cambridge, UK: Standing Conference on University Teaching and Res.... pp. 1 - 9
Closing the gap: Myths and truths behind subitisation
Warren, Elizabeth Anne, de Vries, Eva and Cole, Antoinette. (2009). Closing the gap: Myths and truths behind subitisation. Australasian Journal of Early Childhood. 34(4), pp. 46 - 53.
Equivalence and equations in early years classrooms
Warren, Elizabeth Anne, Mollinson, Annette and Oestreich, Kym. (2009). Equivalence and equations in early years classrooms. Australian Primary Mathematics Classroom. 14(1), pp. 10 - 15.
Young Australian Indigenous students' engagement with numeracy: Actions that assist to bridge the gap
Warren, Elizabeth Anne and de Vries, Eva. (2009). Young Australian Indigenous students' engagement with numeracy: Actions that assist to bridge the gap. Australian Journal of Education.
Indigenous students' early engagement with numeracy :The case of Widgy and Caddy
Vries, Eva de, Young, Janelle Patricia and Warren, Elizabeth Anne. (2008). Indigenous students' early engagement with numeracy :The case of Widgy and Caddy. 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. 547 - 554
The impact of early numeracy engagement on four-year-old indigenous students
Warren, Elizabeth, Young, Janelle and De Vries, Eva. (2008). The impact of early numeracy engagement on four-year-old indigenous students. Australasian Journal of Early Childhood. 33(4), pp. 2 - 8.
Bridging the educational gap: Indigenous and non-indigenous beliefs, attitudes, and practices in a remote Australian school
Warren, Elizabeth, Cooper, Tom and Baturo, Annette. (2008). Bridging the educational gap: Indigenous and non-indigenous beliefs, attitudes, and practices in a remote Australian school. Educational Practice and Theory. 30(1), pp. 41 - 56.
The role of oral language in assisting young Australian Indigenous students' numeracy outcomes
Warren, Elizabeth Anne, Young, Janelle Patricia and de Vries, Eva. (2008). The role of oral language in assisting young Australian Indigenous students' numeracy outcomes. Changing Climates: Education for Sustainable Futures. Brisbane, Australia: Australian Association for Research in Education.
Generalising mathematical structure in Years 3-4 :A case study of Equivalence of Expression
Cooper, Tom and Warren, Elizabeth Anne. (2008). Generalising mathematical structure in Years 3-4 :A case study of Equivalence of Expression. In Olimpia Figueras, Jose Luis Cortina and Silvia Alatorre (Ed.). International Group for the Psychology of Mathematics Education: Proceedings of the Joint Meeting of PME 32 and PME-NA XXX. Morelia, Mexico: Cinvestav-UMSNH. pp. 369 - 376
Patterns that support early algebraic thinking in the elementary school
Warren, Elizabeth Anne and Cooper, Tom. (2008). Patterns that support early algebraic thinking in the elementary school. In Algebra and Algebraic Thinking in School Mathematics: Seventieth Yearbook pp. 113 - 126 National Council of Teachers of Mathematics.
Research empowering the researched :Reflections on supporting Indigenous teacher Aides to tutor mathematics
Underwood, Petrina, Warren, Elizabeth Anne, Cooper, Tom, Matthews, Chris and Baturo, Annette. (2008). Research empowering the researched :Reflections on supporting Indigenous teacher Aides to tutor mathematics. In Olimpia Figueras, Jose Luis Cortina and Silvia Alatorre (Ed.). Proceedings of 32nd Annual Conference of the International Group for the Psychology of Mathematics Education. The Joint Meeting of PME 32 and PME-NA XXX.. Morelia, Mexico: Cinvestav-UMSNH. pp. 137 - 144
Oral language, representations and mathematical understanding: Indigenous Australian students
Warren, Elizabeth and Young, Janelle. (2008). Oral language, representations and mathematical understanding: Indigenous Australian students. The Australian Journal of Indigenous Education. 37(1), pp. 130 - 137. https://doi.org/10.1017/S1326011100016173
The effect of different representations on Years 3 to 5 students’ ability to generalise
Cooper, Tom J. and Warren, Elizabeth A.. (2007). The effect of different representations on Years 3 to 5 students’ ability to generalise. ZDM. 40(1), pp. 23 - 37. https://doi.org/10.1007/s11858-007-0066-8
The use of a new mathematics text book scheme :support or impediment
Heirdsfield, Ann, Dole, Shelley and Warren, Elizabeth Anne. (2007). The use of a new mathematics text book scheme :support or impediment. AARE Focus 2007. Australia: Australian Association for Research in Education.
Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking
Warren, Elizabeth A. and Cooper, Thomas J.. (2007). Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking. Educational Studies in Mathematics. 67(2), pp. 171 - 185. https://doi.org/10.1007/s10649-007-9092-2
Current issues of vocational education and technical training in Australia
Warren, Elizabeth. (2007). Current issues of vocational education and technical training in Australia. Educational Practice and Theory. 29(2), pp. 81 - 92.
Repeating patterns and multiplicative thinking: Analysis of classroom interactions with 9 year old students that support the transition from known to the novel
Warren, Elizabeth and Cooper, Tom. (2007). Repeating patterns and multiplicative thinking: Analysis of classroom interactions with 9 year old students that support the transition from known to the novel. Journal of Classroom Interaction. 41(2), pp. 7 - 17.
Functional thinking in the year 1 classroom
Warren, Elizabeth and Benson, Samantha. (2007). Functional thinking in the year 1 classroom. Australian Primary Mathematics Classroom. 12(3), pp. 14 - 17.
Australian Indigenous Students :The role of oral language and representations in the negotiation of mathematical understanding
Vries, Eva de, Young, Janelle Patricia and Warren, Elizabeth Anne. (2007). Australian Indigenous Students :The role of oral language and representations in the negotiation of mathematical understanding. In Jane Watson and Kim 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. 775 - 784
Combining teaching experiments and professional learning: Conflicts between research and teacher outcomes
Lamb, Janeen, Cooper, Tom and Warren, Elizabeth. (2007). Combining teaching experiments and professional learning: Conflicts between research and teacher outcomes. Mathematics Education Research Journal. 19(3), pp. 73 - 92. https://doi.org/10.1007/BF03217463
Exploring an understanding of equals as quantitative sameness with 5 year old students
Warren, Elizabeth Anne. (2007). Exploring an understanding of equals as quantitative sameness with 5 year old students. In Jeong-Ho Woo, Hee-Chan Lew and Kyo-Sik Park (Ed.). Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, PME31, Seoul, Korea, July 8-13, 2007. Haifa, Israel: International Group for the Psychology of Mathematics Education. pp. 1 - 8
Using repeating patterns to explore functional thinking
Warren, Elizabeth and Cooper, Tom. (2006). Using repeating patterns to explore functional thinking. Australian Primary Mathematics Classroom. 11(1), pp. 9 - 14.
Teacher Professional Development in Patterns and Algebra :Being Sensitive to a Teacher's Zone of Proximal Development
Lamb, Janeen Therese, Warren, Elizabeth Anne and Cooper, Tom. (2006). Teacher Professional Development in Patterns and Algebra :Being Sensitive to a Teacher's Zone of Proximal Development. In Peter Grootenboew, Robyn Zvenbrergen and Mohan Chinnappan (Ed.). Identities; Cultures and Learning Spaces: Proceedings of the 29th Annual Conference of the Mathematics Education Research Group of Australasia. Adelaide, Australia: Mathematics Education Research Group of Australasia. pp. 543 - 550
Teacher actions that assist young students write generalizations in words and in symbols
Warren, Elizabeth Anne. (2006). Teacher actions that assist young students write generalizations in words and in symbols. In Jarmila Novotna, Hana Moraova and Magdelena Kratka (Ed.). Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Prague, Czech Republic: Charles University. pp. 377 - 384
Aim high - Beat Yourself :Effective mathematics teaching in a remote indigenous community
Cooper, Tom, Baturo, Annette, Warren, Elizabeth Anne and Grant, Edlyn. (2006). Aim high - Beat Yourself :Effective mathematics teaching in a remote indigenous community. In Jarmila Novotna, Hana Moraova and Magdelena Kratka (Ed.). Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. Prague, Czech Republic: Charles University. pp. 339 - 376
Supporting learning in early algebra :A model of professional learning
Warren, Elizabeth Anne. (2006). Supporting learning in early algebra :A model of professional learning. In Peter Grootenboew, Robyn Zvenbrergen and Mohan Chinnappan (Ed.). Proceedings of the 29th annual conference of the Mathematics Education Research Group of Australasia. Adelaide, Australia: Mathematics Education Research Group of Australasia. pp. 535 - 542
Investigating functional thinking in the elementary classroom: Foundations of early algebra reasoning
Warren, Elizabeth, Cooper, Tom and Lamb, Janeen. (2006). Investigating functional thinking in the elementary classroom: Foundations of early algebra reasoning. The Journal of Mathematical Behavior. 25(3), pp. 208 - 223. https://doi.org/10.1016/j.jmathb.2006.09.006
Comparative mathematical language in the elementary school: A longitudinal study
Warren, Elizabeth A.. (2006). Comparative mathematical language in the elementary school: A longitudinal study. Educational Studies in Mathematics. 62(2), pp. 169 - 189. https://doi.org/10.1007/s10649-006-4627-5
Patterns supporting the development of early algebraic thinking
Warren, Elizabeth Anne. (2005). Patterns supporting the development of early algebraic thinking. In P. Clarkson, A. Downton and M. Horne (Ed.). Proceedings of the 28th conference of the mathematics education research group of Australasia.. Melbourne, Australia: Deakin University Press. pp. 759 - 766
Lifelong learning and the reform of the teaching practicum in Australia
Chapman, Judith, Toomey, Ron, Gaff, Janet, McGilp, Jacqueline, Walsh, Maureen, Warren, Elizabeth and Willia, Irene. (2005). Lifelong learning and the reform of the teaching practicum in Australia. Asia-Pacific Journal of Teacher Education. 33(1), pp. 23 - 34.
Introducing functional thinking in year 2: A case study of early algebraic thinking
Warren, Elizabeth and Cooper, Tom. (2005). Introducing functional thinking in year 2: A case study of early algebraic thinking. Contemporary Issues in Early Childhood. 6(2), pp. 150 - 162.
Young children's ability to generalize the pattern rule for growing patterns
Warren, Elizabeth Anne. (2005). Young children's ability to generalize the pattern rule for growing patterns. In H. Chick and J. Vincent (Ed.). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Melbourne, Australia: University of Melbourne. pp. 305 - 312
Queensland Indigenous students in rural and remote classrooms. Pedagogical practices in numeracy learning
Cooper, Tom, Baturo, Annette and Warren, Elizabeth Anne. (2005). Queensland Indigenous students in rural and remote classrooms. Pedagogical practices in numeracy learning. In J. Zajda and P. Ninnes (Ed.). Proceedings of the 23rd annual conference of the Australian and New Zealand comparative and international education society.. Armidale, Australia: Centre for Research on Education in Context, University of New England. pp. 154 - 165
Indigenous and Non Indigenous teaching relationships in the three mathematics classrooms in remote Queensland
Baturo, Annette, Cooper, Tom and Warren, Elizabeth Anne. (2005). Indigenous and Non Indigenous teaching relationships in the three mathematics classrooms in remote Queensland. In Helen Chick and Jill Vincent (Ed.). Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Melbourne, Australia: Melbourne University Press. pp. 262 - 272
Generalising arithmetic :Supporting the process in the early years
Warren, Elizabeth Anne. (2004). Generalising arithmetic :Supporting the process in the early years. 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. 425 - 432
Lifelong learning and the assessment and evaluation practices in some Australian faculties of education
Toomey, Ron, Chapman, Judith, Gaff, Janet, McGilp, Jacqueline, Walsh, Maureen, Warren, Elizabeth and Willia, Irene. (2004). Lifelong learning and the assessment and evaluation practices in some Australian faculties of education. Professional Development in Education. 30(2), pp. 225 - 243.
Indigenous students and mathematics: Teachers' perceptions of the role of teacher aides
Warren, Elizabeth, Cooper, Tom and Baturo, Annette. (2004). Indigenous students and mathematics: Teachers' perceptions of the role of teacher aides. The Australian Journal of Indigenous Education. 33, pp. 37 - 46.
Learning and teaching algebra
Warren, Elizabeth Anne and Pierce, Robyn. (2004). Learning and teaching algebra. In In B. Perry, G. Anthony and C. Diezmann (Ed.). Research in Mathematics Education in Australasia pp. 291 - 312 Post Pressed.
A review of research in learning and teaching algebra
Warren, Elizabeth Anne and Pierce, Robyn. (2004). A review of research in learning and teaching algebra. In In B. Perry, G. Anthony and C. Diezmann (Ed.). Research in Mathematics Education in Australasia pp. 291 - 321 Post Pressed.
Young white teachers' perceptions of mathematics learning of aboriginal and non-aboriginal students in remote communities
Doig, Shani, Baturo, Annette, Warren, Elizabeth Anne and Cooper, Tom. (2004). Young white teachers' perceptions of mathematics learning of aboriginal and non-aboriginal students in remote communities. 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. 239 - 246
The role of arithmetic structure in the transition from arithmetic to algebra
Warren, Elizabeth. (2003). The role of arithmetic structure in the transition from arithmetic to algebra. Mathematics Education Research Journal. 15(2), pp. 122 - 137.
Open-ended realistic division problems, generalization and early algebra
Coope, Tom and Warren, Elizabeth A.. (2003). Open-ended realistic division problems, generalization and early algebra. Proceedings of the 27th conference of the international group for the psychology of mathematics education. Honolulu, Hawaii: International Group for the Psychology of Mathemati.... pp. 245 - 253
Parent partnerships within Catholic school communities: Values underpins success
Warren, Elizabeth, Young, Janelle and Hanifin, Pam. (2003). Parent partnerships within Catholic school communities: Values underpins success. Journal of Empirical Theology. 4(1), pp. 63 - 80.
Young children's understanding of equals: A longitudinal study
Warren, Elizabeth Anne. (2003). Young children's understanding of equals: A longitudinal study. In Neil Pateman, Barbara Dougherty and Joseph Zilliox (Ed.). Navigating between theory & practice PME27. Honolulu, Hawaii USA: CRDG College of Education - University of Hawaii. pp. 379 - 386
Introducing equivalence and inequivalence in year 2
Warren, Elizabeth and Cooper, Tom. (2003). Introducing equivalence and inequivalence in year 2. Australian Primary Mathematics Classroom. 8(1), pp. 9 - 14.
Language arithmetic & young children's interpretations
Warren, Elizabeth. (2003). Language arithmetic & young children's interpretations. Focus on Learning Problems in Mathematics. 25(4), pp. 22 - 35.
Arithmetic pathways towards algebraic thinking: Exploring arithmetic compensation in year 3
Warren, Elizabeth and Cooper, Tom. (2003). Arithmetic pathways towards algebraic thinking: Exploring arithmetic compensation in year 3. Australian Primary Mathematics Classroom. 8(4), pp. 10 - 16.
Number combinations and arithmetic structure: Implications for early algebra
Warren, Elizabeth Anne. (2003). Number combinations and arithmetic structure: Implications for early algebra. In L. Bragg, C. Campbell and G. Herbert (Ed.). Mathematics Education Research: Innovation; Networkings; Opportunity: Proceedings of the 26th Annual Conference of the Mathematics Education Research Group of Australia. Melbourne, Australia: Mathematics Education Research Group of Australasia. pp. 712 - 719
Collaboration and sharing as crucial elements of professional development
Warren, Elizabeth Anne, Nisbet, Stephen and Cooper, Tom. (2003). Collaboration and sharing as crucial elements of professional development. In In A. Peter-Koop, V. Santos-Wagner and C. Breen et al. (Ed.). Collaboration in Teacher Education: Examples from the Context of Mathematics Education pp. 23 - 40 Kluwer Academic Publishers.
Lifelong learning and teacher education
Chapman, Judith, Toomey, Ron, McGilp, Jacqueline, Walsh, Maureen, Warren, Elizabeth Anne and Gaff, Janet. (2003). Lifelong learning and teacher education Melbourne, Australia: Australian Teacher Education Association.
Learning for life
Walsh, Maureen Patricia, Chapman, Judith Dorothy, McGilp, Jacqueline, Toomey, Ron and Warren, Elizabeth A.. (2003). Learning for life. In In bFrank Crowther (Ed.). Teachers as Leaders in a Knowledge Society pp. 69 - 80 Australian College of Educators.
Literacy and numeracy in the home: Parents supporting children's learning
Young, Janelle Patricia and Warren, Elizabeth Anne. (2002). Literacy and numeracy in the home: Parents supporting children's learning. In Bill Cope and Mary Kalantzis (Ed.). Learning for the Future: Proceedings of the Learning Conference 2001. Melbourne, Australia: Common Ground Publishing. pp. 369 - 376
Arithmetic and quasi-variables: A year 2 lesson to introduce algebra in the early years
Warren, Elizabeth Anne. (2002). Arithmetic and quasi-variables: A year 2 lesson to introduce algebra in the early years. In A. Cockburn and E. Nardi (Ed.). International Group for the Psychology of Mathematics Education: Proceedings of the 26th Annual Conference. Norwich, England: University of East Anglia. pp. 369 - 376
Children's understanding of 'turn arounds'
Warren, Elizabeth. (2002). Children's understanding of 'turn arounds'. Australian Primary Mathematics Classroom. 7(1), pp. 9 - 13.
Parent and school partnerships in supporting literacy and numeracy
Warren, Elizabeth and Young, Janelle. (2002). Parent and school partnerships in supporting literacy and numeracy. Asia-Pacific Journal of Teacher Education. 30(3), pp. 217 - 228.