A Reflective Rubric-Creating Activity that Enhances Teachers’ Mathematical Habits of Mind

  • Scott A. Courtney College of Education, Health, and Human Services, Kent State University, Kent, Ohio, United States
  • Judy Benjamin College of Education, Health, and Human Services, Kent State University, Kent, Ohio, United States
Keywords: Mathematics teacher education, mathematical habits of mind, assessment tasks, teacher reflection

Abstract

As schools and teachers in the U.S. fine-tune their implementation of mathematics standards promoting college and career readiness, the number of support resources continues to expand. One resource focus experiencing significant growth involves sample items and tasks asserting alignment with the college and career ready mathematical content and practice standards. Such samples regularly identify both the content standards addressed and the mathematical habits of mind that students have the potential to engage in. Consistently absent are evaluation criteria articulating how engagement and demonstration of associated mathematical practices can be assessed, concurrent with content. The authors discuss the development of rubrics that attempt to faithfully assess the integration of mathematical content and practice standards and highlight the benefits to mathematics teachers, coaches, professional developers, and mathematics teacher educators of engaging in such reflective rubric-creating activities.

References

Achieve the Core. (2018). New York: Student Achievement Partners. Retrieved from https://achievethecore.org/

Arizona Department of Education. (2014). Arizona’s college and career-ready standards mathematics: Standards -Mathematical practices -Explanations and examples, High school grades 9–12. Retrieved from http://www.azed.gov/standards-practices/k-12standards/mathematics-standards/

Brahier, D. J. (2013). Teaching secondary and middle school mathematics (4th ed.). Pearson Education USA.

Brookhart, S. M. (1999). The art and science of classroom assessment: The missing part of pedagogy. ASHE-ERIC Higher Education Report (Vol. 27, No.1). The George Washington University, Graduate School of Education and Human Development. Retrieved from https://files.eric.ed.gov/fulltext/ED432937.pdf

Conference Board of the Mathematical Sciences. (2012). Mathematical education of teachers II. American Mathematical Society and Mathematical Association of America. Retrieved from https://www.cbmsweb.org/archive/MET2/met2.pdf

Courtney, S. (2017). What teachers understand of model lessons. Cogent Education, 4(1), 1-22. https://doi.org/10.1080/2331186X.2017.1296528

Covey, S. R. (2004). The seven habits of highly effective people: Powerful lessons in personal change. Free Press/Simon & Schuster.

Daro, P. & Burkhardt, H. (2012). A population of assessment tasks. Journal of Mathematics Education at Teachers College, 3(1), 19-25.

Education Development Center. (2016). Implementing the mathematical practice standards. Retrieved from http://mathpractices.edc.org/

Glasersfeld, E.V. (1995). Radical constructivism: A way of knowing and learning. Falmer London.

Illustrative Mathematics. (n.d.). Retrieved from https://www.illustrativemathematics.org/

Indiana Department of Education. (2017). Indiana Academic Mathematics Standards. Retrieved from https://www.doe.in.gov/standards/mathematics

Inside Mathematics. (2017). Retrieved from http://www.insidemathematics.org/

IXL Learning. (2018). IXL alignment to Common Core math standards. Retrieved from http://www.ixl.com/standards/common-core/math

Jonassen, D. H., & Strobel, J. (2006). Modelling for meaningful learning. In Hung, D., & Khine, M.S. (Eds.), Engaged learning with emerging technologies (pp. 1-27). Springer. https://doi.org/10.1007/1-4020-3669-8_1

Kentucky Department of Education. (2017). Kentucky academic standards with targets: High school – Algebra 1. Retrieved from https://education.ky.gov/curriculum/standards/kyacadstand/Pages/default.aspx

Mathematics Assessment Project. (2015). Shell Center for Mathematics Education at the University of Nottingham (Shell Center), the University of California, Berkeley (UC Berkeley). Retrieved from http://map.mathshell.org/materials/index.php

Meyer, D. (2017). Three-act math task bank. Retrieved from http://blog.mrmeyer.com/category/3acts/

Minnesota Department of Education. (2017). Minnesota comprehensive assessments (MCA). Retrieved from https://education.mn.gov/MDE/fam/tests/

Moskal, B. M. (2000). Scoring rubrics: what, when and how? Practical Assessment, Research & Evaluation, 7(3).

National Governors Association Center for Best Practices, Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. National Governors Association Center for Best Practices, Council of Chief State School Officers. Retrieved from http://www.corestandards.org/Math/

Nebraska Department of Education. (2015). Nebraska’s college and career ready standards for mathematics. Retrieved from https://www.education.ne.gov/math/

New York City Department of Education. (n.d.). WeTeachNYC library. Retrieved from https://www.weteachnyc.org/resources/

Partnership for Assessment of Readiness for College and Careers (PARCC). (2012). PARCC item development, Invitation to Negotiate (ITN) 2012-31, Appendix G: Project terms and definitions. Retrieved from http://www.myflorida.com/apps/vbs/adoc/F28718_AppendixPagesITN201231PARCCItemDevelopmentFinal.pdf

Partnership for Assessment of Readiness for College and Careers (PARCC). (2017a). PARCC Mathematics Evidence Table Algebra I (EOY). Retrieved from https://parcc-assessment.org/mathematics/

Partnership for the Assessment of Readiness for College and Careers (PARCC). (2017b). PARCC model content frameworks: Mathematics, Grades 3-11 (Version 5.0). New Meridian Corporation. Retrieved from https://parcc-assessment.org/model-content-frameworks/

Piaget, J. (1962/2000). Commentary on Vygotsky’s criticisms of Language and thought of the child and judgment and reasoning in the child. (L. Smith, Trans.; Original work published in 1962). New Ideas in Psychology, 18(2-3), 241-259. Retrieved from https://lchcautobio.ucsd.edu/wp-content/uploads/2015/10/Piaget-19622000-Commentary-on-Vygotsky.pdf

Rosenbaum, D. A. (1972). The theory of cognitive residues: A new view of fantasy. Psychological Review, 79(6), 471-486. http://dx.doi.org/10.1037/h0033548

Salomon, G., Globerson, T., & Guterman, E. (1989). The computer as a zone of proximal development: Internalizing reading-related metacognition from a reading partner. Journal of Educational Psychology, 81(4), 620-627. http://dx.doi.org/10.1037/0022-0663.81.4.620

Salomon, G., Perkins, D. N., & Globerson, T. (1991). Partners in cognition: Extending human intelligence with intelligent technologies. Educational Researcher, 20(3), 2-9.https://doi.org/10.3102/0013189X020003002

Schön, D. A. (1983). The reflective practitioner. New York: Basic Books.

Smarter Balanced Assessment Consortium. (2018). The mathematics summative assessment blueprint. The Regents of the University of California. Retrieved from https://portal.smarterbalanced.org/library/en/mathematics-summative-assessment-blueprint.pdf

Smarter Balanced Assessment Consortium. (2015). Content Specifications for the summative assessment of the Common Core state standards for mathematics. The Regents of the University of California. Retrieved from https://portal.smarterbalanced.org/library/en/mathematics-content-specifications.pdf

Stanford Center for Assessment, Learning and Equity. (2013, September). edTPA secondary mathematics assessment handbook. Board of Trustees of the Leland Stanford Junior University. Retrieved from http://edtpa.aacte.org/

Steffe, L. P., & Thompson, P. W. (2000). Interaction or intersubjectivity? A reply to Lerman. Journal for Research in Mathematics Education, 31(2), 191-209. https://doi.org/10.2307/749751

Sztajn, P., Marrongelle, K.A., Smith, P., & Melton, B. L. (2012). Supporting implementation of the Common Core State Standards for Mathematics: Recommendations for professional development. Raleigh, NC: Friday Institute for Educational Innovation at North Carolina State University. Retrieved from https://pdxscholar.library.pdx.edu/cgi/viewcontent.cgi?article=1157&context=mth_fac

Thompson, P. W. (2013). In the absence of meaning. In K. Leatham (Ed.), Vital directions for research in mathematics education (pp. 57-93). Springer. https://doi.org/10.1007/978-1-4614-6977-3_4

Thompson, P. W. (2008). Conceptual analysis of mathematical ideas: Some spadework at the foundations of mathematics education. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano & A. Sépulveda (Eds.), Proceedings of the Annual Meeting of the International Group for the Psychology of Mathematics Education, (Vol 1, pp. 45-64). Morélia, Mexico: International Group for the Psychology of Mathematics Education (PME).

Wiggins, G., & McTighe, J. (2005). Understanding by design (2nd ed.). Alexandria, VA: Association for Supervision and Curriculum Development.

Published
2018-09-03
Section
Articles