In my years at Michigan State University, I have learned that having a learning goal is one of the critical elements of lessons and assessments, research plans, presentations, and guiding your own learning. (I think this post is supported to some degree by All About Models.)
Learning Goals in Mathematics Lessons and Assessments
For teaching, learning goals are important in helping a teacher choose relevant and focused questions, tasks, and discussions. Sometimes learning goals can be too restricting, closing off the potential learning and interpretations. Deciding what the true take-away from a lesson should be, is incredibly difficult! A teacher needs to think about immediate mathematical needs of her students, as well as future needs – in future math classes, of course, but also for the future adults the students will become. Those adults need to be able to make sense of their world, think critically as consumers and citizens, and put their mathematics thinking to use in their future profession. Once a learning goal is chose, thinking critically about the assessment is also important and really questioning whether the kind of learning and thinking does the assessment test for is relevant to the learning goals. (Which comes first, the assessment or the learning goals?)
Learning Goals in Research Plans, aka “research questions”
In my time on research projects, especially Preparing to Teach Algebra, I have seen again and again how important it is to work for a while and then re-read the research questions. The research questions indicate what you hoped to get smarter about before the project began – they indicate your learning goals for the research. Dr. Sharon Senk told me over and over: “I think you need to go back to the research goals: Does your current analysis help or should you reorient and what we hoped to find out?”
Learning Goals for Presentations
A large part of my job as a research is “disseminating results of research.” In class or at conferences, it is tempting to – and almost impossible to avoid – sharing everything you have learned with the audience. Because it all is amazing and interesting – and, yes, the audience would be enthralled if they had several days of time to chat with you. I try to fight against that need because I have been the perpetrator and the victim of such presentations. I remember serving on a Math Education faculty search committee. A candidate visited and shared her dissertation – it seemed like the whole dissertation – in a 50 minute presentation. She had over 50 slides, and only managed to talk through a couple of them, because each slide had tiny graphs and figures. I think it was frustrating to her, but also to us – we wanted to understand something she shared, but she talked very fast and it was difficult to see any details on the slides. In my mind, I think of that example as my reason to focus on only a handful of take-aways from a presentation. (I fail sometimes.)
Learning Goals for Guiding your Own Learning (as a grad student … and beyond?)
As a fifth-year graduate student, I have spent a great deal of time in the past four years completely overwhelmed by a program requirement or course assignment. It is easy to lose sight of the meaning of these learning opportunities, and I believe that many faculty are not focused on the learning goals and many faculty would disagree on the learning goals if they talked about them. I have tried to choose a learning goal that each assignment could support, and have successfully navigated each (so far). I would strongly recommend to other graduate students to think deeply about potential learning goals – what will you get from each project or assignment? Then re-evaluate you work regularly to see if the project is getting too big or if you are steering off-course.
That said, it is not always possible to reconcile your chosen learning goals with the learning goals of your committee, other faculty, or other graduate students. Try to argue for you perspective, but be open to other interpretations. And remember that at the end of your program, you will have to defend the choices you make. If you had no choice but to let others make choices for you, it could be difficult to explain – so make sure to talk to others to make sense of those “other” choices.