Say that again!: Mathematics, Assessment and our most vulnerable students

"Wait, can you say that again?" is I would say often to students as I walk past them during a classroom conversation. I felt like I heard something substantial, meaningful and impactful to my learning but also to my understanding of that particular student's learning. 

Photo Courtesy of Emory.Edu
The problem then became how do I assess what I just heard. Often times students weren't able to replicate their knowledge, understanding, or thinking on a "final assessment" that I would give them. Partially my fault because of the limited means of assessment that I provided, but I also wondered why the student(s) could not express what they did that particular time I walked by and listened in on their conversation? 
How do we assess our students understanding and thinking? Especially our students who are vulnerable or struggling learners. The best I can do is shed some light on this question. But in no way do I have the right answers or all the answers.

I've realized in my journey the importance of valuing and even using conversation and observations to assess some of my English Language Learners. I had no idea how to capture the learning or assess the thinking of those ELL students or even those students who have mathematics phobias. It was a difficult hurdle to overcome. 

Wien et. al (2011) note that "consciously recording small group conversations, to generate documentation and commit to examining what is generated" allows for an array of data that can be used to assess a students knowledge. If I add on the idea of observing and video recording for example our ELL or other struggling students, this gives them a prime opportunity to show their thinking of a mathematical concept. 

The data we gather, according to this document, could look a number of different ways: 

Image Courtesy of The Ontario Ministry of Education.
Capacity Building Series. Pedagogical Documentation Revisited (2015)

This all leads me to believe that designs, graphics, tables, drawings, numbers just to name a few are all valuable elements that can be used to assess a students thinking for the purpose of allowing them to be successful. Our ELL and struggling students need every opportunity for us to document their learning, so even they themselves can see their successes and achievements. 

Wien, C.A., Guyevskey, V., &Berdoussis, N. (2011). Learning to Document in Reggio-inspired Education. Early Childhood Research and Practice, 13(2).
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