I am a firm believer that methods and reasoning for assessment need to be consistent with the philosophical and pedagogical styles and theory by which any class is run. For me, this means using assessment methods that are diverse and in which a student’s voice is heard and valued. Problem solving methods are valued and students can feel empowered at the same time that I am able to assess the skills that students need to move forward and feel like they have accomplished something.
How do students gain a sense of mastery in this type of assessment when problem solving is such a gradual experience? Problem solving also has been discussed in research as such an ambiguous phenomenon to assess as well. Some researchers believe that there is an algorithmic method than can be taught and assessed, while others believe that it is a skill that comes with mentorship and cognitive apprenticeship.
In a PBL course, our assessments are entitled “problem sets” instead of “tests.” We do this purposefully because students enter the class with the concept of a test being something where their knowledge is being tested of an algorithmic process (completing the square, using the quadratic formula, etc.), but not necessarily in context. Also, students usually believe that the “test” they are taking is on a finite amount of material (e.g. a test on Chapter 5 – Conic Sections). Although problem sets are also on a certain amount of material, students are held responsible for all prior knowledge that has been covered at all times. Problems encountered on these types of assessments are similar to problems encountered on homework, which have been discussed in class, journal entries have been written, and follow up problems have been solved. On the problem set, however, a different aspect may be added.
Problem sets are done individually, in partners, in class, at home, with laptops, with graphing calculators and with journals as resources, and many different combinations of all of these possibilities. The diversity in the set-up is necessary for students to be able to show their best work at different times throughout the year. Since students have different learning styles, they also have different ways in which to be able to show their best work. Since some of the problems depend on knowing material from the beginning of the year, or past knowledge, memorization is not the focus for assessments, but application and learning for understanding is.
Other Methods of Assessment
Not all assessment is for problem solving or learning for understanding. Quick Quizzes check for algorithmic processes (writing equations of lines, applying formulas, etc.). Grading journal entries checks for procedural understanding and communication skills. Assessing daily class participation with a grading rubric shows students how important communication about mathematics is and values their input in the discussion on a daily basis. Staying true to your pedagogical theory is key to letting students understanding your assessment philosophy. You can find samples of journal entries under Research ->Metacognitive Journaling.
Student Feedback and Self-Assessment
I also have been doing some work with student self-assessment, feedback and critical thinking rubrics. I have students fill out this Student Self-Report on Class Contribution sometime in the middle of the term and I attempt to give them my take on their question-asking and listening skills so that they can see if their perspective on what they are doing in class and the way that I view their work in this area are actually the same. Since class contribution counts as a whole test grade for me, I want to make sure they get some feedback in this area throughout the term and year.
Here are some samples of problem sets and quick quizzes for you to understand more about my assessment style.