Refs for International Test Scores

References

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

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

+one more needed

General References on Learning Trajectories

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

Duschl, R., Maeng, S. & Sezen, A. (2011). Learning progressions and teaching sequences: A review and analysis. Studies in Science Education, 47(2), 123-182.

Empson, S. B. (2011). On the idea of learning trajectories: Promises and pitfalls. The Mathematics Enthusiast, 8(3), 571-596.

Popham,W.J. (2007).The lowdown on learning progressions. Educational Leadership, 64 (7), 83‐84.

Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114–145.

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

Research In Learning Trajectories

Fosnot and Dolk’s Landscape of Learning

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.

Fosnot, C.T. & Dolk, M. (2001b). Young mathematicians at work: Constructing Multiplication and Division. Westport, CT: Heinemann.

Fosnot, C. T. & Dolk, M. (2002). Young Mathematicians at Work: Constructing Fractions, Decimals, and Percents. Portsmouth, N.H.: Heinemann Press.

Fosnot, C. T. & Jacob, B. (2010). Young Mathematicians at Work: Constructing Algebra. Portsmouth, N.H.: Heinemann Press.

Lawson’s Primary Math Trajectories in Inquiry Classrooms

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)

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.)

Cross, Woods and Schweingruber’s Teaching–Learning Paths

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

Clements and Sarama's Learning Trajectories in Mathematics for Young Children

Sarama, J. & Clements, D.H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York: Routledge.

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

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.

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.

Learning Trajectory Related Resources

Fosnot

Lawson

Building Blocks

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/

First Steps

Learning Trajectories in Curriculum Design

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

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

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

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

Australia Australian Council of Assessment and Reporting Authority (ACARA). (2013). The Australian curriculum: Mathematics. Retrieved from http://www.australiancurriculum.edu.au/Mathematics/Rationale

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

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

Victoria Curriculum and Assessment Authority (VCAA). (n.d.). The Australian curriculum in Victoria. Retrieved from: http://ausvels.vcaa.vic.edu.au/

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

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

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

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

The Vermont Institutes. (2008). Vermont Mathematics Partnerships Ongoing Assessment Project Fractions Framework. Retrieved from http://www.vermontinstitutes.org/index.php/vmp/ogap

The Vermont Institutes. (2008). Vermont Mathematics Partnerships Ongoing Assessment Project Multiplicative Reasoning Framework. Retrieved from http://www.vermontinstitutes.org/index.php/vmp/ogap

The Vermont Institutes. (2008). Vermont Mathematics Partnerships Ongoing Assessment Project Proportional Reasoning Framework. Retrieved from http://www.vermontinstitutes.org/index.php/vmp/ogap

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