Super Wrong, Kinda Right
Learning to be Creatively Incorrect
Amber G. Candela
Zandra de Araujo
Mitchelle M. Wambua
and Colleagues
Samuel Otten
Faustina Baah
Learning is very strongly spurred by…
Alvidrez, M., Louie, N., & Tchoshanov, M. (2024). From mistakes, we learn? Mathematics teachers’ epistemological and positional framing of mistakes. Journal of Mathematics Teacher Education, 27(1), 111–136.
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Yet, the vast majority of class time is spent on correct solutions.
Strategies for promoting productive mistakes
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Strategies for promoting productive mistakes
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Plan
Super Wrong, Kinda Right
Try Your�Own
Our Broader Project (PDPD)
Debrief & Discuss
Super Wrong, Kinda Right
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PROBLEM:
WRONG ANSWERS
Super Wrong!
Kinda
Right
PROBLEM: A Boeing 787 Dreamliner typically travels at about 1,680 miles in three hours. About how long should it take a 787 to travel from Orlando, Florida, to Seattle, Washington, nonstop, which is about 2,564 miles?
WRONG ANSWERS
Super Wrong!
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Right
PROBLEM:
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Super Wrong!
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Right
Come up with a wrong answer. Where would you put it and why?
107 ✕ 51
PROBLEM:
WRONG ANSWERS
Super Wrong!
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Right
Come up with a wrong answer. Where would you put it and why?
Find the area.
WRONG ANSWERS
Super Wrong!
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PROBLEM:
Find the area.
Answer #1
33m
Answer #1
88m2
Answer #1
67m
Answer #1
109m2
Place each of these wrong answers on the continuum. Justify your placement.
WRONG ANSWERS
Super Wrong!
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Come up with a wrong answer. Where would you put it and why?
PROBLEM:
Find the equation of the line that passes through the points (3, 2) and (6, -4).
PROBLEM:
WRONG ANSWERS
Super Wrong!
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Right
Where would you put Aaliyah’s answer and why?
Find the equation of the line that passes through the points (3, 2) and (6, -4).
Aaliyah got the following answer: y = -2x
Find the equation of the line that passes through the points (3, 2) and (6, -4).
Super Wrong Kinda Right
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Alternative Approach
Find the equation of the line that passes through the points (3, 2) and (6, -4).
Super Wrong Kinda Right
❤
Alternative Approach
Why Try Super Wrong, Kinda Right?
Encourage wrong answers as an opportunity for student creativity
Help students develop a deeper conceptual understanding
Encourage student participation, with low floor for entry
Other thoughts?
Create Your Own
Think of some content you are teaching soon, or a topic you know to be challenging for students.
What is a problem that you could start by using “Super Wrong, Kinda Right”?
What do you think students might say in response?
Instructional Nudges
Super Wrong, Kinda Right
My Messy Idea
Confidence Meter
Reversals
Leave a Trace
Rewrite to Reveal
And more!
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Dr. Zandra de Araujo
The PDPD Team
zdearaujo@coe.ufl.edu
Dr. Samuel Otten
ottensa@missouri.edu
Dr. Amber Candela
candelaa@umsl.edu
Dr. Paul Wonsavage
wonsavagef@coe.ufl.edu
Dr. Mitchelle Wambua
wambua@wustl.edu
Maria Stewart
mntkd@umsystem.edu
Faustina Baah
fa6nz@umsystem.edu
Olumide Banjo
olumidebanjo@missouri.edu
Build from Teachers’ Existing Practice
Provide Options for Teachers
Small Suggestions for Improvement
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Instructional Nudges
Nudge Teacher’s Instructional Practice
Improve Student Outcomes
Generate Knowledge about Incremental PD
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Discussion
What are your thoughts on…
PracticeDrivenPD.com >> Presentations >> NCTM 2024
Samuel Otten, ottensa@missouri.edu
Faustina Baah, baahf@missouri.edu
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Thank you!
This work was supported by the National Science Foundation (award #2101508) though any opinions, findings, and conclusions expressed here are those of the authors and do not necessarily reflect the views of the NSF.
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References
Alcala, L. (2015). My Favorite No: Learning from mistakes. The Teaching Channel. https://learn.teachingchannel.com/video/class-warm-up-routine
Cortina, J. L., & Višňovská, J. (2023). Designing instructional resources to support teaching. In T. Lamberg & D. Moss (Eds.), Proceedings of the forty-fifth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 15-26). Reno, NV: University of Nevada.
Dougherty, B., Bryant, D. P., Bryant, B. R., & Shin, M. (2016). Helping students with mathematics difficulties understand ratios and proportions. Teaching Exceptional Children, 49, 96-105.
Krutetskii, V. A. (1976). The psychology of mathematical abilities in schoolchildren (J. Kilpatrick & I. Wirszup, Trans.). Chicago, IL: University of Chicago Press.
Liljedahl, P. (2020). Building thinking classrooms in mathematics, grades K-12: 14 teaching practices for enhancing learning. Corwin Press.
Lithner, J. (2008). A research framework for creative and imitative thinking. Educational Studies in Mathematics, 67, 255-276.
Otten, S., de Araujo, Z., Candela, A. G., Vahle, C., Stewart, M. E. N., Wonsavage, F. P., & Baah, F. (2022). Incremental change as an alternative to ambitious professional development. In A. E. Lischka, E. B. Dyer, R. S. Jones, J. N. Lovett, J. Strayer, & S. Drown (Eds.), Proceedings of the forty-fourth annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1445–1450). Nashville, TN: Middle Tennessee State University.
Otten, S., Cirillo, M., & Herbel-Eisenmann, B. A. (2015). Making the most of going over homework. Mathematics Teaching in the Middle School, 21, 98–105.
Otten, S., de Araujo, Z., & Baah, F. (2024). Mathematical tasks from 141 secondary algebra lessons: A preponderance of procedures without connections.
Rittle-Johnson, B., & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. Journal of Educational Psychology, 99, 561-574.
Rittle-Johnson, B., & Star, J. R. (2011). The power of comparisons in learning and instruction: Learning outcomes supported by different types of comparisons. Psychology of Learning and Motivation: Cognition in Education, 55, 199-226.
Star, J. R. (2016). Improve math teaching with incremental improvements. Phi Delta Kappan, 97(7), 58–62.
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