Conversations and observations in the math class

 Have you heard of triangulation of data?  Triangulation of data involves collecting evidence from multiple sources over time. When you hear triangulation, if you think of a triangle, you are bang on!

Essentially, as math teachers, we need to collect data that extends beyond student products.  We will only be able to truly assess our students' understanding if we go beyond the typical pencil to paper tests, quizzes, assignments...etc. that we are used to seeing in math classes. 

First let's look at the 3 components of assessment here.  I believe that we are all familiar with the idea of products: this is anything that a student produces (quiz, test, assignment, homework...etc.)  all too often, students' understanding is assessed solely on their production.  We need to go a little further to evaluate their understanding. This leads us to conversations:

Conversations imply exactly what you think, talking to students or rather, students talking to you.  Conversations can happen through student-teacher conferences, they can happen in a group context, they can happen on an individual basis. In a group context, you may want to present a particular problem to a group and listen to how the students go about talking through the problem.  Sometimes, rather than testing a student, I have them record a quick video using screencastify or flipgrid explaining

how they've solved a problem.  This lets me know what level of understanding they have achieved.   Particularly in this day and age of remote learning.  Students can easily have an older brother or sister help with math problems and I wouldn't necessarily know.  However, they certainly would not be able to explain how to solve a math problem if they didn't understand it. 

Observations, which we make every day in class, are valid forms of assessment. I think that too often, we feel that we need PROOF of a student's level of achievement.  Observations allow us to assess students' understanding on a daily basis.  I use a very simple Google Form to track observations.  This allows me to open a Google Sheets attached to this form and search through the observations made over time.  You can choose to observe a few particular students each day and you can add in any observations more spontaneously.

Why is this important?  Have you ever taught a student who was an active, engaged participant who did very well in class but bombed the tests?  So have I.  There are all kinds of reasons that students might not do very well on a test.  Perhaps your student has a learning disability, perhaps your student had a rough morning/night, perhaps your student just has generalized testing anxiety.  Whatever the reason, each student deserves to be evaluated on their understanding of a concept, not the product of their understanding on a concept.  In order to really assess a student's understanding, we need to delve deeper than tests.

For more information, check out this video by MISA London Region Professional Network: Assessment of Learning: Triangulation of Assessment