After a fun and productive meeting with a couple of our undergraduate educators in my office last week, we shifted gears and started to talk about how very busy their own semesters were. One of them confided that they were committed to getting a good night’s sleep (Bravo!), and they had time for doing homework – mostly in the form of problem sets for engineering students in their first couple of years – but that they were having a hard time finding time to ‘study’. At that point I asked, “Isn’t doing a problem set ‘studying’?”
The brief conversation that followed reminded me that students sometimes compartmentalize tasks, experiences, and even related content information. And that ‘studying’ continues to mean finding large blocks of time to go over class notes and materials – often in passive, ineffective ways. It is what they are used to doing. Compartmentalization is often our default to get things done in a busy schedule. And we typically don’t support students in making those critical links and connections. But we can! When instructors are explicit about putting class activities, homework assignments, and topics into a larger context, and encourage complementary practices that prompt students to grapple with those connections, students become better, more self-directed learners, gain depth of understanding, new perspectives, and insight into their own thought processes. These powerful, under-used practices are reflection and metacognition.
This post will introduce the terms and share their value and some related links. Ultimately we suggest a practical way (and provide a worksheet to get started) to apply the ‘metacognitive cycle’ to problem sets so that the large amount of time students spend on these applications will become more efficient, deep- learning opportunities in which students actively retrieve, review and process course content while they apply their knowledge to solving problems.
Defining the terms
Whether we understand them in these specific terms or not, metacognition and reflection are critical parts of the ‘expert’ practitioner’s tool box. However, novice learners – early undergraduates – need to be instructed in the practice and the value of these tools. Generally, reflection is thinking back on an experience in order to process it and turn it into ‘knowledge’. In this way reflection can also be a version of ‘retrieval’ (pulling up information and working with it again, also a critical practice for making knowledge stick). Metacognition is most easily described as a type of reflection in which one examines the thought processes used during a task. So metacognition is ‘thinking about thinking. There is a lot of research on metacognition in the psychological literature and it is complex! Research suggests that adding metacognition to disciplinary teaching in the classroom where groups of students are solving problems can help them become better at solving open-ended problems and transferring that understanding to solving novel problems.
These higher order thinking skills are the goal of our disciplinary curricula, particularly in technical and applied sciences like engineering.
Applying the ‘metacognitive cycle’ to problem sets
Studying is most efficient when done in short, spaced, repeated, active, intervals. Interspersing topics, revisiting and actively engaging with the material several times before an assessment, has been shown to provide the best results. So, in a perfect world, we aren’t looking for large chunks of time to ‘go over notes’ or other more passive activities that are shown to not be very effective for learning. By adding a few extra minutes (30?) to the practice of ‘doing a problem set’, a student – ideally a group of students – can contextualize the problems they are solving in their growing conceptual understanding and make it an efficient, deep-learning study session.
The metacognitive cycle is broken into the following simple stages: planning (before beginning working on the problems in the set, gathering resources), monitoring (what is happening in ones thoughts while trying to apply knowledge to problem sets), and evaluation (how did it go, what was hard? what was learned? what do you need to ask at office hours or recitations?)
During the Planning Stage
Take a few minutes to look through the problems set and decipher the larger context of the problems there:
- List what you know about conceptual information that surrounds the problems and the associated equations that are being applied – retrieval
- Write 2 – 3 learning objectives. These are statements about what one should know by the successful completion of the problem set – goal setting. If they are not given in the assignment, it is your job as a learner to ‘figure them out’ from the types of problems in the worksheet – retrieval
- At the start of each question, ask “what information do I need to know in order to begin this question and why do I need it? “- reflection, retrieval and metacognition
During the Monitoring Stage
As you work through each of the problems in the set, be intentional about the choices you are making. Ask the ‘why’ questions:
- In a group or solo ask the question ‘why is this problem challenging?’. Responses to this question requires – reflection.
- Explain the decisions/processes that led to the solving of each part of a problem. Ask why did you/I make that choice in this part of the problem. Answers to these questions require – metacognition
During the Evaluation Stage
At the close of the problem set, or the part of it that was completed in one session, look through and remember the content that was applied, the processes and the decisions.
- Write a paragraph that summarizes (more detail is better) of what was learned and how ideas are connected and applied in the problems completed – reflection
- Make a list of topics/concepts/skills that still need work for good understanding and bring these to the next office hours or recitation section to get the support needed – goal setting
These suggested practices are the same ones that experts use without conscious effort! For someone new to material, reflection and metacognition and using the simple application of these learning strategies in work that is required as homework, will make it more relevant and expedite learning! Less additional time will be needed for ‘studying’, and the time spent studying will be more effective and efficient. This should help with time management and result in deeper understanding of disciplinary material. Start slow, and see how it works. Here is a worksheet to remind about guidelines while applying these strategies to problem sets. Let us know how it goes, and enjoy the process of becoming an expert!