By Carmel Schettino, posted October 24, 2016 —

There are many different names for assessments—test, quiz, chapter test, quest, SLO (Student Learning Opportunity), Portfolio of Work, Knowledge Showcase—all of which mean the same thing to most students. When I started teaching with PBL, I found it difficult to align assessment practices with the learning goals of a PBL classroom (see my previous post). When students would do great work in class on their problem-solving or communication skills, I wanted to give them the feedback they deserved, to improve and to be supported in that work. Instead, without giving them that feedback, I felt like I was losing my integrity as a teacher.

To let my students know that major assessments are going to address both the use of content skills and the techniques of good problem solving, I call them problem sets. I tell students that they should expect some problems that they have seen before as well as others that have connections to what we have done. I’ll expect them to make those connections for themselves in class instead of at home.

I provide a study guide that gives an outline, by topic and page number, of the topics we have recently covered. Our problem-based curriculum is not compartmentalized, so students and I work together on a daily basis, categorizing the topics we are covering. Students also do metacognitive journaling on problems that stood out to them (i.e., they write about what was helpful in their learning and how it helped).

I grade problem sets with “Feedback before Grades with Revisions” (thanks to helpful people on #MTBoS for ideas and advice on this). I give a score for both initial conceptual understanding and initial skill ability, but students do not see their final grade until after completing the revisions. For example, my student Julia needed to find out if point C was equidistant from A and B, but she was confused about what that meant. Conceptually, Julia was thinking of slope instead of length, and skill-wise, she was manipulating the distance formula incorrectly. My feedback for her revisions was intended to make her aware of both of those errors. 

The next day, I was quite impressed with how, after reading my feedback, Julia was able to completely correct her work! The assessment was truly a learning experience as problem solving.

The rubric that I use to grade problems sets this year with “Feedback before Grades with Revisions” is on my website. This type of assessment didn’t change the overall average of four sections of geometry last year, but it allowed students to focus on their learning and not (as much) on their grades. I have remained true to the pedagogy and learning goals that are so important to me as a teacher and that I want students to gain from their experience in my classroom.

   With problem-based learning as her specialization, Carmel Schettino obtained a PhD in math education while teaching at the secondary level for more than twenty years. She is passionate about helping teachers grapple with the pedagogical and curricular questions that arise when PBL is brought into the math classroom. Her other areas of expertise include gender equity, discourse, technological implications and PBL's relationship to the Common Core. Schettino has consulted for a number of schools, has presented for NCTM (e.g., Annual Conferences 2015 and 2016) and has published articles with respect to PBL in the secondary mathematics classroom. Find her blog at carmelschettino.org, and contact her at [email protected].