Skip to main content

Part of the book series: The Enabling Power of Assessment ((EPAS,volume 3))

Abstract

A design-based research (DBR) approach was used to investigate how a mathematics geometry study which employed the principles of universal design for learning (UDL) within a discipline-based inquiry which embedded assessment for learning impacted student learning, and teacher learning and instructional designs. Qualitative and quantitative data informed the research findings and indicated: (i) all students showed significant improvement in achievement, (ii) all students made gains in the five strands of mathematical proficiency, (iii) all students can engage with difficult mathematical ideas when they are provided with assessment for learning, (iv) the principles of UDL permit teachers to break the stranglehold of the procedural script for teaching mathematics, (v) access to technology is a critical factor in an accessible mathematics classroom, (vi) introducing UDL and assessment for learning into the mathematics classroom is a disruptive innovation, and (vii) creating accessible mathematics classrooms, consistent with UDL and assessment for learning principles and practices, requires increased teacher knowledge and support for on-going professional development.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Mountain View School Division is a pseudonym.

  2. 2.

    These tasks were released in December 2006 in a document called PISA Released Items for Mathematics which can be found at www.oecd.org/dataoecd/14/10/38709418.pdf

  3. 3.

    These tasks were released in December 2006 in a document called PISA Released Items for Mathematics which can be found at www.oecd.org/dataoecd/14/10/38709418.pdf

References

  • Adams, R., & Wu, M. (Eds.). (2002). PISA 2000 technical report. Paris, France: Organisation for Economic Co-operation and Development (OECD). Retrieved from: http://www.pisa.oecd.org/dataoecd/53/19/33688233.pdf

  • Alberta Education. (2007). Mathematics kindergarten to grade 9 program of studies. Alberta Education. Retrieved from: http://education.alberta.ca/media/645594/kto9math.pdf

  • Assessment Reform Group. (1999). Assessment for learning: Beyond the black box. Cambridge, UK: Cambridge School of Education. Retrieved from: http://k1.ioe.ac.uk/tlrp/arg/AssessInsides.pdf

  • Bausch, M., & Hasselbring, T. (2005). Using AT: Is it working? Threshold, 2(1), 7–9.

    Google Scholar 

  • Bereiter, C. (2002). Design research for sustained innovation. Cognitive Studies: Bulletin of the Japanese Cognitive Science Society, 9(3), 321–327.

    Google Scholar 

  • Black, P. (2004). The nature and value of formative assessment for learning. Assessment for Learning Group. Retrieved from: http://www.kcl.ac.uk/content/1/c4/73/57/formative.pdf

  • Black, P., Harrison, C., Lee, C., Marshall, B., & Wiliam, D. (2002). Working inside the black box: Assessment for learning in the classroom. London, UK: King’s College London School of Education.

    Google Scholar 

  • Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education, 5(1), 7–71.

    Article  Google Scholar 

  • Bransford, J., Brown, A., & Cocking, R. (Eds.). (2000). How people learn: Brain, mind, experience and school. Washington, DC: National Academies Press.

    Google Scholar 

  • Carver, S. (2006). Assessing for deep understanding. In K. Sawyer (Ed.), The Cambridge handbook of the learning sciences (pp. 205–224). New York, NY: Cambridge University Press.

    Google Scholar 

  • CAST. (2013). Retrieved from: http://www.cast.org

  • Chappuis, S., & Stiggins, R. (2002). Classroom assessment for learning. Educational Leadership, 60(1), 30–43.

    Google Scholar 

  • Clifford, P., & Marinucci, S. (2008). Testing the waters: Three elements of classroom inquiry. Harvard Educational Review, 78(4), 675–688.

    Article  Google Scholar 

  • Darling-Hammond, L. (2008). Powerful learning: What we know about teaching for understanding. San Francisco, CA: Jossey-Bass.

    Google Scholar 

  • Davies, A. (2002–2003). Finding proof of learning in a one-to-one computing classroom. Courtenay, BC, Canada: Connections Publishing.

    Google Scholar 

  • Design-Based Research Collective. (2003). Design-based research: An emerging paradigm for educational inquiry. Educational Researcher, 32(1), 5–8.

    Article  Google Scholar 

  • Dolan, R. P., & Hall, T. E. (2001). Universal design for learning: Implications for large-scale assessment. IDA Perspectives, 27(4), 22–25.

    Google Scholar 

  • Donovan, M. S., & Bransford, J. (2005). Pulling threads. In M. S. Donovan & J. Bransford (Eds.), How students learn: Mathematics in the classroom (pp. 569–590). Washington, DC: National Academies Press.

    Google Scholar 

  • Edyburn, D. (2006). Failure is not an option: Collecting, reviewing, and acting on evidence for using technology to enhance academic performance. Learning and Leading with Technology, 34(1), 20–23.

    Google Scholar 

  • Firchow, N. (2002). Universal design for learning: Improved access for all. Retrieved from: SchwabLearning.org http://www.schwablearning.org/articles.aspx?r=490

  • Friesen, S. (2006). Inside an accessible classroom. Unpublished manuscript.

    Google Scholar 

  • Friesen, S. (2009). Teaching effectiveness: A framework and rubric. Toronto, ON, Canada: Canadian Education Association. Retrieved from: http://www.cea-ace.ca/sites/cea-ace.ca/files/cea-2009-wdydist-teaching.pdf

  • Fuson, K., Kalchman, M., & Bransford, J. (2005). Mathematical understanding: An introduction. In M. S. Donovan & J. Bransford (Eds.), How students learn: Mathematics in the classroom (pp. 217–256). Washington, DC: National Academies Press.

    Google Scholar 

  • Galileo Educational Network. (2013). Discipline-based inquiry rubric. Retrieved from: http://www.galileo.org/research/publications/rubric.pdf

  • Gay, L., Mills, G., & Airasian, P. (2006). Educational research: Competencies for analysis and applications (8th ed.). New Jersey, NY: Pearson.

    Google Scholar 

  • Gilbert, J. (2005). Catching the knowledge wave? The knowledge society and the future of education. Wellington, New Zealand: NZCER Press.

    Google Scholar 

  • Hattie, J. (2009). Visible learning: A synthesis of over 800 meta analyses. New York, NY: Routledge Press.

    Google Scholar 

  • Hattie, J. (2012). Visible learning for teachers: Maximizing impact on learning. New York, NY: Routledge Press.

    Google Scholar 

  • Jardine, D., Clifford, P., & Friesen, S. (2002). Back to the basics of teaching and learning. Mahwah, NJ: Lawrence Erlbaum and Associates.

    Google Scholar 

  • Jardine, D., Clifford, P., & Friesen, S. (2008). Back to the basics of teaching and learning (2nd ed.). New York, NY: Routledge Press.

    Google Scholar 

  • Kaplan, R., & Kaplan, E. (2007). Out of the labyrinth: Setting mathematics free. New York, NY: Oxford University Press.

    Google Scholar 

  • Kelly, A., Lesh, R., & Baek, J. (Eds.). (2008). Handbook of design research methods in education. New York, NY: Routledge.

    Google Scholar 

  • Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.

    Google Scholar 

  • Leininger, M. M. (1985). Ethnography and ethnonursing: Models and modes of qualitative data analysis. In M. M. Leininger (Ed.), Qualitative research methods in nursing (pp. 33–72). Orlando, FL: Grune & Stratton.

    Google Scholar 

  • Meo, G. (2005). Curriculum access for all: Universal design for learning. Harvard Education Letter, 21(5). Retrieved from: http://www.edletter.org/past/issues/2005-nd/meo.shtml

  • Mighton, J. (2003). The myth of ability: Nurturing mathematical talent in every child. Toronto, ON, Canada: House of Anansi Press.

    Google Scholar 

  • Mighton, J. (2007). The end of ignorance: Multiplying our human potential. Toronto, ON, Canada: Knopf Canada.

    Google Scholar 

  • Newmann, F., Bryk, A., & Nagaoka, J. (2001). Authentic intellectual work and standardized tests: Conflict or coexistence? Chicago, IL: Consortium on Chicago School Research. Retrieved from: http://ccsr.uchicago.edu/sites/default/files/publications/p0a02.pdf

  • Organisation for Economic Cooperation and Development (OECD). (2000). Programme for international student assessment: Sample tasks from the PISA 2000 assessment: Reading, mathematical and scientific literacy. OECD Publishing.

    Google Scholar 

  • Organisation for Economic Cooperation and Development (OECD). (2005). Formative assessment: Improving learning in secondary classrooms. Policy brief. OECD Publishing. Retrieved from: http://www.oecd.org/edu/ceri/35661078.pdf

  • Research Points. (2006). Do the math: Cognitive demand makes a difference. Research Points, 4(2). AERA.

    Google Scholar 

  • Ritchhart, R., Church, M., & Morrison, K. (2011). Making thinking visible: How to promote engagement, understanding, and independence for all learners. San Francisco, CA: Wiley.

    Google Scholar 

  • Robinson, V. (2011). Student-centered leadership. San Francisco, CA: Wiley.

    Google Scholar 

  • Rose, D., & Meyer, A. (2002). Teaching every student in the digital age: Universal design for learning. ASCD. Retrieved from: http://www.cast.org/teachingeverystudent/ideas/tes/

  • Rose, D., Meyer, A., & Hitchcock, C. (Eds.). (2005). The universally designed classroom: Accessible curriculum and digital technologies. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Rose, D. H., & Meyer, A. (2006). A practical reader in universal design for learning. Cambridge, MA: Harvard Education Press.

    Google Scholar 

  • Rothberg, M., & Treviranus, J. (2006). Accessible e-learning demonstrations using IMS accessibility specifications. In ATIA National Conference, Orlando, FL. Retrieved from: http://ncdae.org/activities/atia06/presentations.cfm

  • Sawyer, K. (2006). The Cambridge handbook of the learning sciences. New York, NY: Cambridge University Press.

    Google Scholar 

  • Scardamalia, M. (2001). Getting real about 21st century education. The Journal of Educational Change, 2, 171–176. Retrieved from: http://ikit.org/fulltext/2001getting_real.pdf

    Google Scholar 

  • Shanker Institute. (2005, May 5). From best research to what works: Improving the teaching and learning of mathematics: A forum. Washington, DC.

    Google Scholar 

  • Stiggins, R., Arter, J., Chappuis, J., & Chappius, S. (2004). Classroom assessment for student achievement: Doing it right – Using it well. Portland, OR: Assessment Training Institute.

    Google Scholar 

  • Stigler, J., & Hiebert, J. (1999). The teaching gap: Best ideas from the world’s teachers for improving education in the classroom. New York, NY: The Free Press.

    Google Scholar 

  • Swain, J., & Swan, M. (2007). Thinking through mathematics: Research report. NRDC. Retrieved from: http://www.maths4life.org/uploads/documents/doc_296.pdf

  • The Alberta Teachers’ Association (ATA). (2003). Trying to teaching, trying to learn: Listening to students. Edmonton, AB, Canada: The Alberta Teachers Association.

    Google Scholar 

  • Wiliam, D. (2011). Embedded formative assessment. Bloomington, IN: Solution Tree Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sharon Friesen .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Friesen, S. (2016). Assessment for Learning in a Math Classroom. In: Scott, S., Scott, D., Webber, C. (eds) Leadership of Assessment, Inclusion, and Learning. The Enabling Power of Assessment, vol 3. Springer, Cham. https://doi.org/10.1007/978-3-319-23347-5_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-23347-5_6

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23346-8

  • Online ISBN: 978-3-319-23347-5

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics