The short, oversimplified background story is that mistakes are stigmatized (in the U.S.). Thus struggling in Math is equated by some students as a sign of being dumb or slow or that the teacher isn't doing a proper job. Traditionally math teachers present nice, clean solutions, and there are very few instances when students can witness the math process that actually is what makes us successful learners. It can be the case that a student has never experienced or witnessed what mathematicians do regularly. That is, the process of problem solving, inquiring, experimenting may all be unconnected from Mathematics.
Consequently, the IBL instructor who gets a group of such students must not only deal with the "regular" learning challenges that a math course presents, but also the legacy of underdeveloped/negative attitudes and habits of mind that promote learning. When these underdeveloped/negative components of the learning process come out is when students get stuck. Being stuck is both an opportunity and a risk. It takes courage (at least initially) for students to admit to being stuck and to then engage in problem solving. The risk to the students and teacher is when students are so frustrated and stuck that they shut down and stop learning. (In math speak, we want to avoid the boundary.)
What we can do as IBL instructors?
- Make sure students know and feel that it's okay to be stuck. "Are you guys stuck? Great! It's okay to be stuck! Let's use being stuck as an opportunity to work on our problem-solving skills... How can we break this problem down to a manageable size?..."
- Scaffold enough so that the students see your role as their advocate and facilitator in learning. It's better to error on the side or more scaffolding than less, early in the term. What this means is to provide enough hints/lemmas/basic examples so that students perceive themselves as progressing.
- Create a positive, relaxed class environment by using group work and visiting groups to check-in with individuals.
- Use (more) starter problems. One of the main roles of an instructor is selecting appropriate tasks. Giving several starter problems, where all students can get traction is important. Early in the term this is especially important, and the lower the level of the course the more important it is to have good entries into topics.
- Summarize, restate, and give alternative solutions here and there to provide the expert insight that students often gain from. When students have finished a section or unit, that is a wonderful opportunity to highlight all of the wonderful insights, ideas, and strategies that students learned. It's a way to make explicit progress and achievement, as well as review material.
- Marketing what IBL is and why it is good for students should be steady and ongoing. What this means specifically is clearly indicating that the goals of the course include handling being stuck, problem solving, communicating ideas with peers. These are in addition to the content goals. "The reason why we are doing these activities is so you get better at..."
- Consider employing reading assignments and journal writing. Such assignments can be especially useful in addressing beliefs and attitudes. Burger and Starbird have a book, "The Five Elements of Effective Thinking," that can be used in any math course as a supplement. Students can read a couple chapters at a time and write a one-page reflection paper on what they learned and how they might use the ideas in the class. Getting a second or third opinion in writing is very effective. It's one thing to get the message from class, and yet another when multiple sources support the same messages, thus providing more opportunities for students to take necessary steps towards successful learning.
If being stuck in class is explicitly a good thing, students' struggles are respected, and class activities are designed to take advantage of these opportunities in a positive spirit, then being stuck can be a positive force in learning!
Have ideas? Send the via email or post them in the comments.