Mathematics is cumulative, requiring a progression of knowledge that builds upon previously learned skills. Unfinished learning occurs when students do not have prerequisite skills to understand more advanced concepts (Dorn, Hancock, Sarakatsannis, & Viruleg, 2020), resulting in an increased risk of math anxiety and fixed mindset (Montague & Jitundra, 2006). Unfinished learning has always existed, and the pandemic amplified its effects (Kuhfeld, Soland, Tarasawa, Johnson, Ruzek, & Liu, 2020). Math anxiety and fixed mindset conflate the effects of unfinished learning.
High leverage practices and growth mindset strategies accelerate learning. The Council for Exceptional Children (CEC) and CEEDAR Center identified 22 research-based High Leverage Practices (HLPs), and HLP #7 outlines ways teachers create positive, structured and predictable classrooms where all students thrive. Infusing growth mindset strategies further promotes academic courage, engagement and resilience (Dweck, 2010; Snipes & Loan, 2017; Tee, Leong, & Rahim, 2020; Yeagar, Romero, Paunesku, Hulleman, Schneider, Hinojosa, & Dweck, 2016). Preparing classroom materials aligned with classroom routines and learning goals creates structure. Essential grade level content and prerequisite standards provide a roadmap for learning and can be shared with students through self-monitoring checklists. Self-monitoring is a research-based strategy and is an essential component of HLP #9. Students self-evaluate their academic skills on a set of pre-established criteria (Rafferty, Raimondi, 2009; Rafferty, 2010; The IRIS Center, 2008), identifying skills they understand, skills they don’t understand yet, and improving students’ self-awareness and mindset. Self-monitoring checklists can be embedded into classroom routines, inspiring growth mindset and academic courage throughout the year.
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Get Ready to learn about ways to accelerate learning. To plan instruction that accelerates learning, the National Council on Teaching Mathematics (NCTM), National Council of Supervisors of Mathematics (NCSM) (2020), and National Council for Learning Disabilities (NCLD) (2021) recommend the following. First, identify power standards, which are essential standards and skills students need to achieve in sequential mathematics courses, other curricula, and life. Next, identify essential prerequisite skills related to prioritized power standards. For new content to make sense, students need to understand related prerequisite skills. Before every math unit, assess students understanding of essential prerequisite skills. Data about students’ strengths and needs informs instruction, which can be individualized for students with disabilities (NCLD, 2021). Finally, immediately before instruction, review critical prerequisite skills (NCTM, 2020). Prioritize teaching these skills and give students time to practice and engage with content until mastery (NCLD, 2021).
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Get Set to prepare your curriculum to accelerate learning. Virginia Department of Education resources can help teachers identify power standards.
VDOE Resources
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Go Explore High Leverage Practices and Growth Mindset Strategies that establish structured and respectful learning environments that boost academic courage and resilience. Enroll in TTAC’s free self-paced asynchronous professional learning session and create materials for the 2021-2022 school year. Included are resources to help administrators, teacher leaders, and instructional coaches scale up high leverage and growth mindset practices.
High Leverage Practices
Growth Mindset Strategies and Resources
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References
Dorn, E., Hancock, B. Sarakatsannis, J. & Viruleg, E. (2020). COVID-19 and student learning in the United s States: The hurt could last a lifetime. McKinsey & Company.
Dweck, C. S. (2010). Even geniuses work hard. Educational Leadership, 68(1), 16-20.
Flanagan, K. M., & Einarson, J. (2017). Gender, Math Confidence, and Grit: Relationships with Quantitative Skills and Performance in an Undergraduate Biology Course. CBE—Life Sciences Education, 16(3), ar47. https://doi.org/10.1187/cbe.16-08-0253
Kuhfeld, M., Soland, J., Tarasawa, B., Johnson, A., Ruzek, E., & Liu, J. (2020). Projecting the Potential Impact of COVID-19 School Closures on Academic Achievement. Educational Researcher, 49(8), 549–565.
Montague, M. & Jitundra, A. (2006) Teaching Mathematics to Middle School Students with Learning Disabilities. The Guilford Press.
McLeskey, J. (Ed.) (2019). High leverage practices for inclusive classrooms. New York: Routledge.
National Council of Teachers of Mathematics (NCTM) and National Council of Supervisors of Mathematics (NCSM). (2020, June). Moving Forward: Mathematics Learning in the Era of COVID-19.
Rafferty, L. A., & Raimondi, S. L. (2009). Self-Monitoring of Attention Versus Self-Monitoring of Performance: Examining the Differential Effects Among Students with Emotional Disturbance Engaged in Independent Math Practice. Journal of Behavioral Education, 18(4), 279–299. https://doi.org/10.1007/s10864-009-9092-7
Rafferty, L. A. (2010). Step-by-Step: Teaching Students to Self-Monitor. TEACHING Exceptional Children, 43(2), 50–58.
Snipes, J., & Loan, T. (2017). Growth mindset, performance avoidance, and academic behaviors in Clark County School District (REL 2017-226). Washington, DC: U.S. Department of Education, Institute of Education Sciences.
Tee, K. N., Leong, K. E., & Abdul Rahim, S. S. (2020). A Self-Regulation Model of Mathematics Achievement for Eleventh-Grade Students. International Journal of Science and Mathematics Education, 19(3), 619–637. https://doi.org/10.1007/s10763-020-10076-8
Yeager, D. S., Romero, C., Paunesku, D., Hulleman, C. S.,Schneider, B., Hinojosa, C., Dweck, C. S. (2016). Using design thinking to improve psychological interventions: The case of the growth mindset during the transition to high school. Journal of Educational Psychology, 108, 374–391.
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This e-Newsletter is a collaborative effort of the Virginia Department of Education Training and Technical Assistance Centers at George Mason University and James Madison University. This issue was prepared by the staff at the VDOE TTAC at George Mason University. For questions about content, please contact Catherine Martin (cmarti82@gmu.edu).
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