<p> References</p><p>Refs for international test scores Education Quality and Accountability Office (2010, December). Programme for International Student Assessment (PISA), 2009 highlights. Retrieved from http://www.eqao.com/NIA/PISA/PISA.aspx?Lang=E</p><p>Mullis, I. V. S., Martin, M.O., Foy, P. & Arora, A. (2012). Trends in International Mathematics and Science Study international results in mathematics. Chestnut Hill, MA: TIMSS & PIRLS International Study Center, Boston College. Retrieved from http://timssandpirls.bc.edu/timss2011/international-results-mathematics.html</p><p>+one more needed</p><p>General References on Learning Trajectories </p><p>Daro, P., Mosher, F.A. & Corcoran, T. (2011). Learning trajectories in mathematics: A foundation for standards, curriculum, assessment, and instruction (Report # RR- 68). Retrieved from Consortium for Policy Research in Education website: http://www.cpre.org/learning-trajectories-mathematics-foundation-standards- curriculum-assessment-and-instruction</p><p>Duschl, R., Maeng, S. & Sezen, A. (2011). Learning progressions and teaching sequences: A review and analysis. Studies in Science Education, 47(2), 123-182.</p><p>Empson, S. B. (2011). On the idea of learning trajectories: Promises and pitfalls. The Mathematics Enthusiast, 8(3), 571-596. </p><p>Popham,W.J. (2007).The lowdown on learning progressions. Educational Leadership, 64 (7), 83‐84. </p><p>Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145.</p><p>Stephens, M. & Armanto, D. (2010). How to build powerful learning trajectories for relational thinking in the primary school years. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the Future of Mathematics Education: Proceedings of the 33rd Annual Conference of the Mathematics Education Research Group of Australasia (pp. 523-530). Retrieved from http://www.merga.net.au/documents/MERGA33_Stephens&Armanto.pdf</p><p>Research In Learning Trajectories</p><p>Fosnot and Dolk’s Landscape of Learning</p><p>Fosnot, C.T. (2013). Contexts for learning mathematics: Investigating fractions, decimals and percents [Landscape of Learning Graphic]. Retrieved from http://www.contextsforlearning.com/grades4_6/landscapeLearning.asp Fosnot, C.T. & Dolk, M. (2001a). Young mathematicians at work: Constructing number sense, addition and subtraction. Westport, CT: Heinemann.</p><p>Fosnot, C.T. & Dolk, M. (2001b). Young mathematicians at work: Constructing Multiplication and Division. Westport, CT: Heinemann.</p><p>Fosnot, C. T. & Dolk, M. (2002). Young Mathematicians at Work: Constructing Fractions, Decimals, and Percents. Portsmouth, N.H.: Heinemann Press.</p><p>Fosnot, C. T. & Jacob, B. (2010). Young Mathematicians at Work: Constructing Algebra. Portsmouth, N.H.: Heinemann Press.</p><p>Lawson’s Primary Math Trajectories in Inquiry Classrooms </p><p>Lawson, A (in press, 2013 Fall) What to look for: Understanding student’s mathematical thinking Gr 1-2. Toronto: Pearson (Book, DVD, ebook) ISBN: 13: 978-0-321- 88717-7 (virtual samples will be available soon) </p><p>Lawson, A. (2013) Documenting the trajectory of children’s invented methods of calculation. Paper presented at the annual meeting of the American Educational Research Association, San Francisco (April 27- May 4.)</p><p>Cross, Woods and Schweingruber’s Teaching–Learning Paths </p><p>Cross, C.T., Woods, T.A. & Schweingruber (Eds.) (2009). Mathematics learning in early childhood: Paths toward excellence and equity. Washington DC: The National Academies Press. Retrieved from http://www.nap.edu/openbook.php? record_id=12519</p><p>Clements and Sarama's Learning Trajectories in Mathematics for Young Children </p><p>Sarama, J. & Clements, D.H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York: Routledge. </p><p>Szilágyi, J. , Clements, D. H., Sarama, J. (2013). Young children’s understandings of length measurement: Evaluating a learning trajectory. Journal for Research in Mathematics Education, 44 (3), 581 – 620. van den Heuvel-Panhuizen's Learning Trajectories for Calculation with Whole Numbers van den Heuvel-Panhuizen, M. (Ed.) (2008). Children learn mathematics: A learning- teaching trajectory with intermediate attainment targets for calculation with whole numbers in primary school. Rotterdam, The Netherlands: Sense Publishers. Retrieved from https://www.sensepublishers.com/media/161-children-learn- mathematics.pdf Confrey's Hexagon Map of Learning Trajectories </p><p>Confrey, J. (2008). A synthesis of the research on rational number reasoning: A learning progressions approach to synthesis. Paper presented at The 11th International Congress of Mathematics Instruction, Monterrey, Mexico.</p><p>Confrey, J. , Maloney, A. , Nguyen, K ., Mojica, G. , & Myers, M. (2009). Equipartitioning/splitting as a foundation of rational number reasoning using learning trajectories. Paper presented at The 33rd Conference of the International Group for the Psychology of Mathematics Education, Thessaloniki, Greece.</p><p>Learning Trajectory Related Resources</p><p>Fosnot</p><p>Lawson</p><p>Building Blocks</p><p>TurnOnCC Generating Increased Science and Math Opportunities (GISMO) Research Team (n.d.). Learning trajectories for the K-8 Common Core Math Standards. Retrieved from http://www.turnonccmath.net/</p><p>PRIME</p><p>First Steps</p><p>Learning Trajectories in Curriculum Design</p><p>Quebec Ministère de l’Éducation, Loisier et Sport Québec. (n.d.). Progression of learning in elementary school [Video]. Retrieved from http://www.mels.gouv.qc.ca/progression/index_en.asp</p><p>Ministère de l’Éducation, Loisier et Sport Québec. (2009). Progression of learning mathematics. Retrieved from http://www.mels.gouv.qc.ca/progression/mathematique/pdf/math_en_sectionCom .pdf</p><p>Ministère de l’Éducation, Loisier et Sport Québec. (2001). Quebec education program, preschool education, elementary education: Chapter 6 Mathematics, science and technology. Retrieved from http://www.mels.gouv.qc.ca/DGFJ/dp/programme_de_formation/primaire/pdf/edu cprg2001/educprg2001-061.pdf</p><p>Ministère de l’Éducation, Loisier et Sport Québec. (2011). Quebec Education Program Frameworks for the Evaluation of Learning, Mathematics, Elementary School. Retrieved from https://www7.mels.gouv.qc.ca/dc/evaluation/index_en.php? page=mathematics-pri#crit%E8re22</p><p>Australia Australian Council of Assessment and Reporting Authority (ACARA). (2013). The Australian curriculum: Mathematics. Retrieved from http://www.australiancurriculum.edu.au/Mathematics/Rationale</p><p>New South Wales (NSW) Department of Education and Training (2010) K-10 Mathematics continuum [Poster]. Retrieved at http://www.curriculumsupport.education.nsw.gov.au/primary/mathematics/k6/cont inuum/index.htm</p><p>Victoria Curriculum and Assessment Authority (VCAA). (2013) The AusVELS curriculum. Retrieved from: http://ausvels.vcaa.vic.edu.au/Print/AusVELS.pdf? d=M&l=F&l=1&l=2&l=3&l=4&l=5&l=6&l=7&l=8&l=9&l=10&e=0&e=1&e=2&e=3&e =4&e=5</p><p>Victoria Curriculum and Assessment Authority (VCAA). (n.d.). The Australian curriculum in Victoria. Retrieved from: http://ausvels.vcaa.vic.edu.au/</p><p>Victoria Curriculum and Assessment Authority (VCAA). (2012) The Australian curriculum: Mathematics scope and sequence. Retrieved from http://www.vcaa.vic.edu.au/Documents/auscurric//Maths_scope_and_sequence_ AusVELS.pdf</p><p>Government of Victoria Department of Education and Early Childhood Development (n.d.). Matheamtics developmental continuum. Retrieved from http://www.education.vic.gov.au/school/teachers/teachingresources/discipline/ma ths/continuum/pages/mathcontin.aspx?Redirect=1</p><p>United States National Governors Association Center for Best Practices, Council of Chief State School Officers. (2010). Common Core State Standards: Mathematics. Washington, DC: National Governors Association Center for Best Practices, Council of Chief State School Officers. Retrieved from http://www.corestandards.org/Math</p><p>National Research Council. (2001). Knowing what students know: The science and design of educational assessment. Pelligrino, J., Chudowsky, N., & Glaser, R., (Eds.). Washington, DC: National Academy Press. Retrieved from http://www.nap.edu/openbook.php?isbn=0309072727 The Vermont Institutes. (2013). Vermont Mathematics Partnerships Ongoing Assessment Project. Retrieved from http://www.vermontinstitutes.org/index.php/vmp/ogap</p><p>The Vermont Institutes. (2008). Vermont Mathematics Partnerships Ongoing Assessment Project Fractions Framework. Retrieved from http://www.vermontinstitutes.org/index.php/vmp/ogap</p><p>The Vermont Institutes. (2008). Vermont Mathematics Partnerships Ongoing Assessment Project Multiplicative Reasoning Framework. Retrieved from http://www.vermontinstitutes.org/index.php/vmp/ogap</p><p>The Vermont Institutes. (2008). Vermont Mathematics Partnerships Ongoing Assessment Project Proportional Reasoning Framework. Retrieved from http://www.vermontinstitutes.org/index.php/vmp/ogap</p><p>US Department of Education. (2008). The Final Report of the National Mathematics Advisory Panel. Retrieved from http://www2.ed.gov/about/bdscomm/list/mathpanel/reports.html</p>