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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Mountain View School Division is a pseudonym.
- 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.
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.
Bereiter, C. (2002). Design research for sustained innovation. Cognitive Studies: Bulletin of the Japanese Cognitive Science Society, 9(3), 321–327.
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.
Black, P., & Wiliam, D. (1998). Assessment and classroom learning. Assessment in Education, 5(1), 7–71.
Bransford, J., Brown, A., & Cocking, R. (Eds.). (2000). How people learn: Brain, mind, experience and school. Washington, DC: National Academies Press.
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.
CAST. (2013). Retrieved from: http://www.cast.org
Chappuis, S., & Stiggins, R. (2002). Classroom assessment for learning. Educational Leadership, 60(1), 30–43.
Clifford, P., & Marinucci, S. (2008). Testing the waters: Three elements of classroom inquiry. Harvard Educational Review, 78(4), 675–688.
Darling-Hammond, L. (2008). Powerful learning: What we know about teaching for understanding. San Francisco, CA: Jossey-Bass.
Davies, A. (2002–2003). Finding proof of learning in a one-to-one computing classroom. Courtenay, BC, Canada: Connections Publishing.
Design-Based Research Collective. (2003). Design-based research: An emerging paradigm for educational inquiry. Educational Researcher, 32(1), 5–8.
Dolan, R. P., & Hall, T. E. (2001). Universal design for learning: Implications for large-scale assessment. IDA Perspectives, 27(4), 22–25.
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.
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.
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.
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.
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.
Gilbert, J. (2005). Catching the knowledge wave? The knowledge society and the future of education. Wellington, New Zealand: NZCER Press.
Hattie, J. (2009). Visible learning: A synthesis of over 800 meta analyses. New York, NY: Routledge Press.
Hattie, J. (2012). Visible learning for teachers: Maximizing impact on learning. New York, NY: Routledge Press.
Jardine, D., Clifford, P., & Friesen, S. (2002). Back to the basics of teaching and learning. Mahwah, NJ: Lawrence Erlbaum and Associates.
Jardine, D., Clifford, P., & Friesen, S. (2008). Back to the basics of teaching and learning (2nd ed.). New York, NY: Routledge Press.
Kaplan, R., & Kaplan, E. (2007). Out of the labyrinth: Setting mathematics free. New York, NY: Oxford University Press.
Kelly, A., Lesh, R., & Baek, J. (Eds.). (2008). Handbook of design research methods in education. New York, NY: Routledge.
Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
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.
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.
Mighton, J. (2007). The end of ignorance: Multiplying our human potential. Toronto, ON, Canada: Knopf Canada.
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.
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.
Ritchhart, R., Church, M., & Morrison, K. (2011). Making thinking visible: How to promote engagement, understanding, and independence for all learners. San Francisco, CA: Wiley.
Robinson, V. (2011). Student-centered leadership. San Francisco, CA: Wiley.
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.
Rose, D. H., & Meyer, A. (2006). A practical reader in universal design for learning. Cambridge, MA: Harvard Education Press.
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.
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
Shanker Institute. (2005, May 5). From best research to what works: Improving the teaching and learning of mathematics: A forum. Washington, DC.
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.
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.
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.
Wiliam, D. (2011). Embedded formative assessment. Bloomington, IN: Solution Tree Press.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights 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)