The Early Career Framework states that teachers must learn that... Where prior knowledge is weak, pupils are more likely to develop misconceptions, particularly if new ideas are introduced too quickly.
In education, classrooms are comprised of students with various educational backgrounds. Each student in the classroom has his or her own understanding of mathematics and previous knowledge from past grade levels. However, sometimes these understandings contain misconceptions and educators must address them in order for their students to achieve mastery within an objective. In order to combat misconceptions early, educators must plan ahead for potential errors in the classroom and analyse what misunderstandings may occur that could potentially prevent a student from fully grasping a mathematical concept. In addition to this planning process, teacher must allow be able to differentiate between what errors should be addressed through a full class discourse and what errors should be addressed through individual corrections based on the type of conceptual understanding(s) that are essential to the given objective.
Every lesson holds the promise of both learning and mistakes. More often than not, the success of a lesson often hinges on the degree to which a teacher can turn these errors into learning. One of the keys to doing this well is Plan for Error, a daily planning exercise in which teachers anticipate student errors and their responses to them. Teachers who regularly do this increase their chances of taking action during the lesson to help students convert their misconceptions into mastery, their wrong answers into right. Through analysis of effective teachers’ techniques and deep planning and practice, participants in the session will strengthen skills with:
Anticipating student errors
Responding to those errors by:
Breaking it Down with prompts and questions to help students work their way to “right”
Engaging students in a deep study of errors to ensure they correct and learn from them
Addressing misconceptions in your lesson plans makes your teaching much better, but also much easier. Your students will have a better understanding of what you are teaching, leaving their preconceptions behind when they are incorrect. This technique can also reinforce preconceptions your students have that are correct.
Asking questions of your students, is one of the best ways to get to the bottom of your students' misunderstandings.
Incorporating this into your lesson plans will ensure that you address the misconceptions during teaching. In addition, you can add a place in your lesson plan template to ask questions to determine the misconceptions.
You may find the Article Inspection-Worthy Mistakes a useful article to read in relation to planning for misconceptions.
As experts in our own subjects we are all aware of the common misconceptions and misunderstandings that students make. In history for example, when working with dates, some students might mistakenly think for that 400 BC is more recent that 300 BC – the misconception being that the larger the number, the more recent it is.
Using our knowledge of these common misconceptions, we can anticipate where they will hold students back in our curriculum and plan for them accordingly.
Daisy Christodoulou in this blog post compares it to the planning for injury in high performance sport. She points out that a sport will have injuries that are more common than others. Coaches then establish training plans that mitigate the effects of that sport and reduce the frequency of that type of injury. Effective teaching, she argues, is the same principle.
It is perfectly possible to spend time identifying the common misconceptions that occur in a subject then planning activities that directly address these misconceptions.
[Further reading recommendations are indicated with an asterisk.]
Adesope, O. O., Trevisan, D. A., & Sundararajan, N. (2017) Rethinking the Use of Tests: A Meta-Analysis of Practice Testing. Review of Educational Research, 87(3), 659–701. https://doi.org/10.3102/0034654316689306 .
Agarwal, P. K., Finley, J. R., Rose, N. S., & Roediger, H. L. (2017) Benefits from retrieval practice are greater for students with lower working memory capacity. Memory, 25(6), 764–771. https://doi.org/10.1080/09658211.2016.1220579 .
Allen, B. and Sims, S. (2018) The Teacher Gap. Abingdon: Routledge. Baddeley, A. (2003) Working memory: looking back and looking forward. Nature reviews neuroscience, 4(10), 829-839.
Black, P., & Wiliam, D. (2009) Developing the theory of formative assessment. Educational Assessment, Evaluation and Accountability, 21(1), pp.5-31. Chi, M. T. (2009) Three types of conceptual change: Belief revision, mental model transformation, and categorical shift. In International handbook of research on conceptual change (pp. 89-110). Routledge.
Clark, R., Nguyen, F. & Sweller, J. (2006) Efficiency in Learning: Evidence-Based Guidelines to Manage Cognitive Load. John Wiley & Sons. Cowan, N. (2008) What are the differences between long-term, short-term, and working memory? Progress in brain research, 169, 323-338.
*Deans for Impact (2015) The Science of Learning [Online] Accessible from: https://deansforimpact.org/resources/the-science-oflearning/ . [retrieved 10 October 2018]. Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J., & Willingham, D. T. (2013) Improving students’ learning with effective learning techniques: Promising directions from cognitive and educational psychology. Psychological Science in the Public Interest, Supplement, 14(1), 4–58. https://doi.org/10.1177/1529100612453266 .
*Education Endowment Foundation (2018) Improving Secondary Science Guidance Report. [Online] Accessible from: https://educationendowmentfoundation.org.uk/tools/guidance-reports/ [retrieved 10 October 2018]. 29
Gathercole, S., Lamont, E., & Alloway, T. (2006) Working memory in the classroom. Working memory and education, 219-240.
Hattie, J. (2012) Visible Learning for Teachers. Oxford: Routledge.
Kirschner, P., Sweller, J., Kirschner, F. & Zambrano, J. (2018) From cognitive load theory to collaborative cognitive load theory. In International Journal of Computer-Supported Collaborative Learning, 13(2), 213-233.
Pachler, H., Bain, P. M., Bottge, B. A., Graesser, A., Koedinger, K., McDaniel, M., & Metcalfe, J. (2007) Organizing Instruction and Study to Improve Student Learning. US Department of Education.
Pan, S. C., & Rickard, T. C. (2018) Transfer of test-enhanced learning: Meta-analytic review and synthesis. Psychological Bulletin, 144(7), 710–756. https://doi.org/10.1037/bul0000151 .
Roediger, H. L., & Butler, A. C. (2011) The critical role of retrieval practice in long-term retention. Trends in Cognitive Sciences, 15(1), 20–27. https://doi.org/10.1016/j.tics.2010.09.003 .
*Rosenshine, B. (2012) Principles of Instruction: Research-based strategies that all teachers should know. American Educator, 12–20. https://doi.org/10.1111/j.1467-8535.2005.00507.x .
Simonsmeier, B. A., Flaig, M., Deiglmayr, A., Schalk, L., & Well-being, S. (2018) Domain-Specific Prior Knowledge and Learning: A Meta-Analysis Prior Knowledge and Learning. Accessible from: https://www.psycharchives.org/handle/20.500.12034/642
Sweller, J. (2016). Working Memory, Long-term Memory, and Instructional Design. Journal of Applied Research in Memory and Cognition, 5(4), 360–367. http://doi.org/10.1016/j.jarmac.2015.12.002 .
Willingham, D. T. (2009) Why don’t students like school? San Francisco, CA: JosseyBass. Wittwer, J., & Renkl, A. (2010) How Effective are Instructional Explanations in Example-Based Learning? A Meta-Analytic Review. Educational Psychology Review, 22(4), 393–409. https://doi.org/10.1007/s10648-010-9136-5 .