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Reasoning and Proving Across Mathematics
Course Description
Course Description
Examine the role of reasoning and proving across the mathematical domains. Investigate student conceptions of proof and the appropriate curriculum treatment of topics related to conjecturing, justifying, and generalizing. Design instructional and assessment tasks that elicit student thinking and formulate ways to move student thinking forward in mathematically productive ways.
Essential Questions
Essential Questions
What is reasoning, justification and proof?
How do middle and high school students benefit from engaging in reasoning and justification?
How can teachers support the development of students’ capacity to reason and justify?
Required Text
Required Text
Arbaugh, F., Smith, M., Boyle, J., Stylianides, G. J., & Steele, M. (2018). We reason & we prove for all mathematics: Building students’ critical thinking, grades 6-12. Corwin.
Course Location
Course Location
Multnomah Education Service District
11611 NE Ainsworth Cir, Portland, OR 97220
-or- Online synchronous via Zoom
Course Schedule
Course Schedule
Dates: Monday, 6/24/2024 through Friday, 6/28/2024
Time: 8:30 am - 4:00 pm
Online and Print Resources
Online and Print Resources
Carpenter, T. P., Hiebert, J., Fennema, E., Fuson, K. C., Wearne, D., & Murray, H. (1997). Making sense: Teaching and learning mathematics with understanding. Heinemann. [excerpts on tools and tasks]
Coffland, D. A. (2012). Closing in on proof. Mathematics Teaching in the Middle school, 17(8), 494-500.
Common Core Standards Writing Team. (2022). Progressions for the Common Core State Standards for Mathematics. Institute for Mathematics and Education, University of Arizona. https://mathematicalmusings.org/wp-content/uploads/2023/02/Progressions.pdf.
Healy, L., & Hoyles, C. (2000). A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31(4), 396-428.
Keazer, L. M., & Menon, R. S. (2016). Reasoning and sense making begins with the teacher. Mathematics Teacher, 109(5), 342-349.
Ko, Y. Y., Yee, S. P., Bleiler-Baxter, S. K., & Boyle, J. D. (2016). Empowering students' proof learning through communal engagement. Mathematics Teacher, 109(8), 618-624.
Krebs, A. S. (2005). Take time for action: Studying students' reasoning in writing generalizations. Mathematics Teaching in the Middle School, 10(6), 284-287.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Author. http://standards.nctm.org.
National Governors Association Center for Best Practices and Council of Chief State School Officers (2010). Common core state standards for mathematics. Author. http://www.corestandards.org/Math.
Stylianides, G. J. (2008). An analytic framework of reasoning-and-proving. For the Learning of Mathematics, 28(1), 9-16.
Yopp, D. A., & Ellsworth, J. L. (2017). Generalizing and skepticism: Bringing research to practice. Mathematics Teaching in the Middle School, 22(5), 284-292.
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