Demonstrating Thinking on Assessments in Mathematics

As we near the end of another school year, I find myself reflecting on my teaching practice over the last 10 months. A piece of "homework" we have been asked to complete has centered around assessments - reflecting on what we have done in our courses this school year. I know that one of my goals for next year is to investigate (and try) alternative ways to assess in mathematics, beyond just using a test. But before we get to that, I want to highlight a success I had on a test this year in my grade 9 (MPM1D) math course.

The unit we had just completed was on linear equations with a focus on graphing lines and determining the equation of a line given different pieces of information (2 points on the line, the graph, a line parallel and a point, etc.). The test addressed the main concepts/skills of the unit and we usually have 1 question that asks students to extend their knowledge in new ways.

Here is the example of the last question on the test.

Note: we had not discussed collinear points in class before the test - hence the definition of the word in the question.

I was amazed at the variety of solutions that students presented and how their thinking was visible but may not have matched the solution I had in mind. There were multiple ways to show their understanding!

Here are some examples of student solutions to this question:
Student #1:



Student #2:



Student #3:


It is clear in all of these solutions that the students have an understanding of what the slope of a line represents and they have not simply memorized the definition/formula. They were all able to apply their knowledge and clearly demonstrate their understanding of points on a line in relation to slopes.

Using VNPS in my classroom, I have been able to observe student thinking throughout the year. This type of question on a test shows that thinking is also possible to be seen on assessments. Furthermore, I sometimes get stuck trying to create "thinking" questions on test attempting to make them the "hard" questions on the test. This particular question helped clarify for me that these "thinking" questions do no have to be particularly harder than other questions. They should, however, be open-ended enough so that students have different entry points to the question that allows them to showcase their understanding of the content. This will be a lens that I will use when creating assessments next year!