Last week, my colleagues and I – while taking a break from marking final exams – noticed that many students struggled to apply their skills during the multi-topic exams. We were surprised by this because students had previously demonstrated these skills in the unit tests throughout the year. As we discussed this, we realized that students had trouble moving from one topic to another. For example, students cross-multiplied fractions within an expression, not realizing that cross-multiplication only works in equations.

I do get to see my students again after they sit their final exam (a very worthwhile exercise, in terms of having students reflect on their work). When I showed them an expression and an equation on the board, they were able to explain the difference; however, they hadn’t noticed the difference when they took the exam. I shouldn’t have been surprised. Because I had taught each unit separately, they had never thought about the differences and similarities between equations and expressions or how the features of each one required that it be manipulated in a specific way.

Thinking ahead to next year, I want to be more purposeful in breaking down the barriers between the math skills and topics that are so often taught in isolation. This video in particular has inspired me to reorganize my units to be more conceptual.

By doing this, I hope to do a few things…

show students that a variety of skills can be applied in a given situation

give students exposure to topics that are similar but not exactly the same (like equations and expressions) so that they are better able to see and understand the particularities of each