Integrating Argumentation
Dr. Chepina Rumsey TEMBI 2 - Nov. 2015
Online Handout with Resources and Links
Common Core State Standards (CCSM) and the Eight Standards for Mathematical Practice (SMPs)
http://www.corestandards.org
Common Core Quick Tips
http://mathsolutions.com/landing/CC_Quicktips.html
SMP #3 Construct viable arguments and critique the reasoning of others.
What does SMP #3 look like?
http://www.heinemann.com/blog/smp3/
Vignettes at Illustrative Mathematics
https://www.illustrativemathematics.org/practice-standards/3
“Sean’s Numbers” video example of third graders
http://deepblue.lib.umich.edu/handle/2027.42/65013
How does Argumentation fit in with other subjects?
Depth of Knowledge Levels
http://education.ohio.gov/getattachment/Topics/Teaching/Educator-Evaluation-System/How-to-Design-and-Select-Quality-Assessments/Webbs-DOK-Flip-Chart.pdf.aspx
“Using Webb’s Depth of Knowledge to Increase Rigor”, by Gerald Aungst (2014), Edutopia
http://www.edutopia.org/blog/webbs-depth-knowledge-increase-rigor-gerald-aungst
Question Stems
http://svesd.net/files/DOK_Question_Stems.pdf
Hess’ Cognitive Rigor Matrix and Curricular Examples
http://www.stancoe.org/SCOE/iss/common_core/overview/overview_depth_of_knowledge/cognitive_rigor_matrix_math_science.pdf
Positive Classroom Norms
https://www.youcubed.org/wp-content/uploads/2015/09/Norms-Paper-2015.pdf
Visual Thinking Strategies
Resources for Tasks
https://www.illustrativemathematics.org
NRICH Enriching Mathematics
http://nrich.maths.org/teacher-primary
You Cubed
https://www.youcubed.org
Illuminations (National Council of Teachers of Mathematics)
http://illuminations.nctm.org/Default.aspx
Inside Mathematics
http://www.insidemathematics.org/problems-of-the-month/download-problems-of-the-month
Achieve the Core
http://achievethecore.org/dashboard/300/search/1/2/0/1/2/3/4/5/6/7/8/9/10/11/12
Articles and References
Barkai, R., Tsamir, P., Tirosh, D., & Dreyfus, T. (2002). Proving and refuting arithmetic claims: The case of elementary school teachers. Paper presented at the annual meeting of the International Group for the Psychology of Mathematics Education, Norwich, England.
Hersh, R. (1993). Proving is convincing and explaining. Educational Studies in Mathematics, 24(4), 389-399.
Gott, R., & Duggan, S. (2007). A framework for practical work in science and scientific literacy through argumentation. Research in Science & Technological Education, 25(3), 271-291.
Keith, A. (2006). Mathematical argument in a second grade class: Generating and justifying generalized statements about odd and even numbers. In S. Z. Smith & M. E. Smith (Eds.), Teachers Engaged in Research: Inquiry into Mathematics Classrooms, Prekindergarten-Grade 2 (pp. 35-68). Greenwich, CT: Information Age Publishing & National Council of Teachers of Mathematics.
Nussbaum, E. M. (2008). Collaborative discourse, argumentation, and learning: Preface and literature review. Contemporary Educational Psychology, 33, 345-359.
Ross, D., Fisher, D., & Frey, N. (2009). The art of argumentation. Science and Children, 47(28-31).
https://www1.maine.gov/education/esl/webinars/documents/Downs121310Artofargumentation.pdf
Rumsey, C. & Langrall, C. (in press). Key instructional strategies promoting mathematical argumentation. Teaching Children Mathematics
Rumsey, C. (2014). Communication and argumentation: A rich connection between language arts and mathematics. Kansas Journal of Reading. 30, 19-24.
Rumsey, C. (2013). A model to interpret elementary-school students’ mathematical arguments. In A. M. Lindmeier, & A. Heinze (Eds.), Proceedings of the 37th Conference of the International Group for the Psychology of Mathematics Education. (Vol. 4, pp. 121-128). Kiel, Germany.
Stylianides, A. J. (2007). The notion of proof in the context of elementary school mathematics. Educational Studies in Mathematics, 65, 1-20.
Toulmin, S. E. (1958). The uses of argument. Cambridge: Cambridge University Press.
Weber, K., Maher, C., Powell, A., & Lee, H. S. (2008). Learning opportunities from group discussions: Warrants become the objects of debate. Educational Studies in Mathematics, 68, 247-261.
Yackel, E. & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics Education, 27 (4), 458-477.
Yackel, E. (2001). Explanation, justification and argumentation in mathematics classrooms. Paper presented at the Conference of the International Group for the Psychology of Mathematics Education, Urtecht, The Netherlands.