First, let's talk about the issue broadly. One important thing to remember is that Math is culture. There exists default expectations about what a math class is and the roles for students and instructors. These default expectations are often unconscious -- we don't think about them. When you meet someone new or talk with your boss, you probably do not realize all of unconscious things you do (or don't do) in these interactions. Likewise, in a math class students have certain expectations that are almost always aligned to traditional instruction. Students expect instructors to show, and their job is to follow dutifully and write down notes and perform these tasks on exams.
IBL classes are aligned differently, of course. Students are asked to solve problems they do not know the answers to, to take risks, to make mistakes, and to engage in "fruitful struggle." These are all very different from normal expectations (as of today -- hopefully that will change).
Tools for making sure your students are on board are
- clearly defining students' role in the class
- providing a clear rationale for IBL (regularly)
- creating a safe and successful classroom environment.
Why IBL? Well there are lots of reasons. Research shows it's better for students. We are now in the era where information about anything is available on your cell phone, and one can run Wolfram Alpha on a cell phone, too! In other words, all lower-order thinking levels (as per Bloom's Taxonomy) are now nearly worthless due to advances in technology. Effective thinking is now where it's at. Thus, IBL is the way forward for students. This line of reasoning addresses items 1 and 2 above. What about 3?
The heart is the heart of the matter.
Telling people, "Medicine is good for you!" isn't sufficient. Students need to know that the instructor is their advocate for learning. Students need to see themselves as successful mathematicians (where they may never have thought this before in their lives). Thus it is important for students to struggle, but struggle within reason. It is suggested that IBL units start off at a basic level, where all students in the class can achieve some success. Then the problems should ramp up in difficulty as appropriate for your students. When in doubt, include more easy problems than less, especially at the beginning of the course and at the beginning of new material. The worst case scenario is that you spend a few extra minutes on them or just skip them entirely in class, and assign them as homework. There is no cost to including more problems.
In this sense, establishing a safe and successful classroom environment is asymmetrical. Erring on the side of being "tougher" is fraught with perils. First, you are going again previous experiences and the traditional classroom culture. Second, many students have negative attitudes about math. Third, telling students that are stuck to "just keep going" can lead to the perception that the instructor is not helpful, and thus not teaching. Struggle is good if the students feel that the struggle leads somewhere. This type of scenario is often the case for students writing negative comments on course evaluations. Students may in their minds understand that IBL is good for them, but they experienced too much frustration to truly enjoy the experience in their hearts. In other words, the experience was not an aesthetic experience.
I also note that saying that you told them is not enough. You need to know if the students feel it in their hearts. Look at them and see if they are enjoying the math and interacting positively.
Of course, there is good reason for students to struggle and perhaps not solve a problem. Such experiences are fruitful on many, many levels of learning. BUT this is something that should happen down the road, once students are off and running, enjoying math and doing math successfully in a positive and supportive learning environment. Training for a marathon has similarities to teaching an IBL course. You don't coach a new runner with hard interval training on day one followed by long 20-mile tempo runs. Athletes train by exerting an appropriate training load and recovering. Then they repeat and then move on to new things gradually. Math is no different. Tasks should match students' experiences and abilities and grow with them.
If you are not positive, how can your students be positive? If you never smile, why would your students smile back at you? Be positive! It's important to let your students know that they are working hard and progressing. I thank my students for their participation, and I try as best I can to make classes a supportive environment. Pointing out the good parts of solutions, ideas, and efforts should be a part of daily practice.
Start easy. Establish the learning culture from day 1. Build on positive class experiences to challenge students to do more and more.
General IBL Points
Some points you can use as a base for discussing IBL classes with your students. This is a list of talking points to help you find your own way of conveying the message that IBL is good for the mind.
- IBL is a student-centered method of teaching similar to the Socratic method. It requires more work for me (the instructor), but it's better for you. Research shows that students who are actively engaged learn better. While you may not be used to it, I'll do my best to make sure you are comfortable with it and will be successful in this class.
- One goal of IBL is to help students learn to think independently, and become a successful problem solver. In other words, a goal of IBL is to help you get better at thinking effectively. That's really what we will work on. And you can't learn to think effectively, if someone does all the thinking for you...
- IBL emphasizes the process of problem solving and theorem proving rather than the memorization of facts.
- IBL is not experimental. It has been employed successfully since the days of Socrates.
- The reason why books and other outside resources are not allowed is because we will discover the ideas ourselves. We will collectively work on the tasks and come up with our own ideas.
- It’s OK to be stuck. Being stuck is a noble state of mind. It means you are just about to learn something new!
- It’s OK to be frustrated. You’re doing fine -- try to slow down and enjoy the process. We'll get it eventually.
- Being stuck is natural. Whatever you do, don’t give up. If you're stuck, there has to be question in there that you can ask.
- What's the best way to learn to play the piano? Should you just watch videos of pianists? Do you need to do something else besides watch someone else play?
Teaching is more than content delivery. Addressing the learning challenges as part of the course is a good thing to do, and acknowledging where students are coming from and building a bridge for them to cross is a core component of effective IBL teaching.