One of the things I would like to do with my students is have them graph their understanding of different objectives and mathematical practices. This would help them visualize their progress at different points throughout the semester. It would also help me see where they know they need help. Both asking questions in class approaching a teacher after can be intimidating and a bit nerve-wracking for some, so I think this would be a very low-key and passive way for them to tell me how they think they’re doing. I imagine something like a y-axis of *levels of understanding*, including statements like “I do not understand this at all,” “I understand parts of this,” and “I fully understand this.” On the x-axis would be the different elements students have been exposed to.

While this would not be used to grade them, I would use it as an informal, formative assessment to help let me know what to reteach or which students needed intervention. I think another way this could help my students is to visually show them that they have, in fact, learned something over the course of the class. If they start with a graph at the beginning of the year with low levels of understanding and increase over the semester or year, they will be able to give a tangible answer to the question, “What have you learned this year?” It would also be useful to show parents during conferences as a way to illustrate (albeit self-reported) learning or during interventions to show which elements the student definitely struggles with. It would also be interesting to see if some students understand past elements better after applying them to newly learned material. There is no doubt that students need to learn certain information before moving on. But would the deliberate practice and application help increase that learning after they did move on? Also, I wonder if I were to measure their understanding immediately before and after breaks, would there be a drop in knowledge due to the time off?

This is an activity I would like to take class time to go over at least three times a year, though ideally it would be done once every month. I think it would be helpful to me as an informal, formative assessment and a good illustration of self-reported knowledge for students, parents, and administrators. Let me know what you think in the comments!

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I think this could be a great resource for any teachers.

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