Status & Mindset Interventions
In her book Strength in Numbers: Collaborative Learning in Secondary Mathematics, Ilana Horn writes: “Judgements about who is smart based on prior achievement or social categories violate a fundamental principle of equity and are consequential: learning is not the same as achievement” (2012, p.20). The resources below were curated to help you redefine "smarts" in math, disrupt status divisions, develop growth mindsets, and foster a collaborative math community.
Anticipatory Planning
How often does your planning for math involve searching for the "best" problem and then thinking about how you want to teach the problem? It's safe to say this is how most of us approach(ed) lesson planning. The problem with this approach, however, is that it is teacher focused and neglects to consider how students might perceive and respond to the problem. Conversely, anticipatory planning focuses planning efforts on imagining how students might respond to a problem and using that information to plan questions that will push and clarify student thinking and build understanding by sequencing and connecting approaches students are already using.
If you've ever tried to facilitate constructivist math learning in your classroom and it fell short of your expectations, it's likely because the key factor, anticipatory planning, was missing! The template below can help you prepare to facilitate constructivist math learning in your classroom. Grab a planning buddy and give it a try!
Anticipatory Planning
How often does your planning for math involve searching for the "best" problem and then thinking about how you want to teach the problem? It's safe to say this is how most of us approach(ed) lesson planning. The problem with this approach, however, is that it is teacher focused and neglects to consider how students might perceive and respond to the problem. Conversely, anticipatory planning focuses planning efforts on imagining how students might respond to a problem and using that information to plan questions that will push and clarify student thinking and build understanding by sequencing and connecting approaches students are already using.
If you've ever tried to facilitate constructivist math learning in your classroom and it fell short of your expectations, it's likely because the key factor, anticipatory planning, was missing! The template below can help you prepare to facilitate constructivist math learning in your classroom. Grab a planning buddy and give it a try!
References
Boaler, J. (1997). When even the winners are losers: Evaluating the experiences of “top set” students. Journal of Curriculum Studies, 29(2), 165-182
Boaler, J. (2006) How a Detracked Mathematics Approach Promoted Respect, Responsibility, and High Achievement. Theory into Practice 45(1), 40–46.
Boaler, J. (2014). Fluency without fear: Research evidence on the best ways to learn math facts. YouCubed at Stanford University. Retrieved from http://www.youcubed.org/wp-content/uploads/2015/03/FluencyWithoutFear-2015.pdf
Boaler, J. (2015, May 7th) Memorizers are the lowest achievers and other Common Core math surprises. The Hechinger Report. Retrieved from: http://hechingerreport.org/memorizers-are-the-lowest-achievers-and-other-common-core-math-surprises/
Boaler, J. & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers’ College Record, 110, 608-645.
Boaler, J., William, D., & Brown, M. (2000). Students’ experiences of ability grouping—dis- affection, polarisation and the construction of failure. British Educational Research Journal, 26(5), 631–648.
Bohrnstedt, G. W., Zhang, J., Park, B. J., Ikoma, S., Broer, M., Ogut, B., (2018). Mathematics Identity, Self-Efficacy, and Interest and their Relationships to Mathematics Achievement: A Longitudinal Analysis, prepared for Indiana University Identity Conference, Bloomington, IN, April 13-14, 2018. American Institutes for Research.
Brill, S., & McCartney, A., (2008). Stopping the Revolving Door: Increasing Teacher Retention. Politics and Policy 36: 750-774.
Carpenter, T. P., Fennema, E., & Franke, M. L. (1996). Cognitively guided instruction: A knowledge-base for reform in primary mathematics instruction. The Elementary School Journal, 97(1), 3–20. https://doi.org/10.1086/461846
Gray, E., & Tall, D., (2007). Abstraction as a natural process of mental compression, 19, 23–40.
Gutiérrez, Rochelle. (2000) Advancing African-American Urban Youth in Mathematics: Un-packing the Success of One Math Department. American Journal of Education 109(1), 63–111.
Gutiérrez, R. (2012). Embracing Nepantla: Rethinking "knowledge" and its use in Mathematics teaching. Journal of Research in Mathematics Education, 1, 29-56
Lee, J., (2002). Racial and ethnic achievement gap trends: Reversing the progress toward equity? Educational Researcher, 31(1), 3-12.
Moser, J., Schroder, H. S., Heeter, C., Moran, T.P., & Lee, Y. H. (2011). Mind your errors: Evidence for a neural mechanism linking growth mindset to adaptive post error adjustments. Psychological Science 22, 1484-1489.
Organisation for Economic Cooperation and Development (2014), PISA 2012 Results: What Students Know and Can Do – Student Performance in Mathematics, Reading and Science (Volume I, Revised edition, February 2014), PISA, OECD Publishing. http://dx.doi.org/10.1787/9789264201118-en
Rose, H., & Betts, J. R. (2004). The effect of high school courses on earnings. Review of Economics and statistics, 86(2), 497-513.
Solomon, Y., (2007). Not belonging? What makes a functional learner identity in undergraduate mathematics? Studies in Higher Education, 32(1), 79-96
Yeager, D., Bryk, A., Muhich, J., Hausman, H., & Morales, L. (2013). Practical Measurement. Retrieved from http://www.carnegiefoundation.org/resources/publications/practical-measurement/