A couple of weeks ago I wrote a piece about student portfolios, specifically a subtracting integers portfolio my students were about to create. Their media of choice is Explain Everything. Now that the projects are trickling in I’m discovering conceptual errors which I might have overlooked on a traditional paper-pencil assessment. Here’s an example:
While the screenshot does capture the number line error when subtracting a positive number, I’m drawn to the student’s voice and explanation, “Since 2 is negative I move to the right.” The portfolio is no longer a thing to grade, there’s a human being behind that work and I can see and hear her. Her portfolio submission has instead become a formative assessment.
This next problem demonstrates further confusion. Here 2 is negative, but she moves to the left.
The student below, on the other hand, has mastered subtracting integers. She begins by demonstrating the number line movements, explains why she moved to the right, then proceeds to show its equivalence by adding the opposite.
When solving this equation the student admitted to a lot of guess and check, however I’m not bothered by the extra practice she got from doing the problem.
After introducing this slide she explained how she turned it into an addition problem by adding the opposite.
Then she solved.
So far my favorite student created real world problem is:
Only three projects have been submitted thus far, but I’m anticipating most of my time will be spent giving feedback rather than issuing grades. I don’t feel comfortable grading something that’s a work in progress. In terms of time, the portfolios run between 6 and 7 minutes each. I really need to front load the time now so it will be easier later when the students apply the integer rules to negative fractions and decimals.
Here’s another project I looked at this morning. How much conceptual understanding does this student have? He provides no explanation and relies on adding the opposite to demonstrate the number line. Also, he only provided a screenshot of the equivalence problem with no explanation of how it was solved.