Posts Tagged ‘Out of the Labyrinth: Setting Mathematics Free

In our previous post, we discussed the need for less “teaching” and more “facilitating”. We talked in general terms about stepping out of the leader role and encouraging more discussion among the students with little intervention from us.  Others also are stressing the need for us to talk less. We realize that this is a somewhat radical notion for most classrooms and that many teachers would not know how this could work, so we would like to offer more specific ideas. One of the true benefits of the common core standards is that since we aim to go deeper and have fewer topics to cover, we now have the time, and indeed the directive from the standards of mathematical practice , to allow for meaningful discussions and to encourage students to rediscover their natural curiosity. The standards emphasize how we help students to learn at least as much as what we expect them to learn. We appeal to literature teachers to join us in these discussions since they have likely employed these methods when discussing novels, poetry, etc. They have much to share about constructing persuasive arguments and using deductive reasoning to communicate effectively, both in math classes and in their lives.

First, it should be noted that the arrangement of the furniture is often an impediment to student participation. The traditional rows of desks facing a teacher’s desk automatically forces students to look to the teacher for answers. Arranging desks in a circle, creating rows of concentric circles, if necessary, creates a more balanced atmosphere of equal opportunity among all participants. No more over-achievers in the front while the unengaged hide in the back! The facilitator’s desk should be unobtrusive in this arrangement, and in fact, it is best if the students must turn to see us, while looking to their peers first.English: MITIS students having s discussion

If this arrangement is new to them, students will likely be skeptical at first, especially the older they are. A great and necessary first activity is to write the ground rules, which should also be stressed before each discussion as long as is necessary. Ideally, the class would create and agree on these themselves, as they will have better buy in and an introduction to this discussion method, and typically they tend to be more stringent that we would ever be! Basically, it must be agreed that all responses are valid, and dismissing any thoughts is not allowed, as even a “wrong” answer can shed perspective. Be sure that the rules are posted in a prominent place within the classroom and posted on the course web page.

Following this activity with a group game, such as Sudoku on the board where the whole class can work together, can help break the ice and warm the class up to the idea of speaking more freely. It also gives the facilitator practice in allowing freer discussion, limiting questions/comments such as, “That’s an interesting observation. What led you to that conclusion? I’m not sure I follow that. How do you know that? Prove it to me!” Responses from other students are encouraged by the facilitator’s silence, though when encouragement is necessary, the facilitator can play the role of another student asking questions that are not too leading.  Putting oneself in the mind of the student automatically encourages inquiry. Even when there is a need to tone down the class, the facilitator could offer comments such as, “Wait, I want to understand Julie’s comment. Let’s back up to that one.”

Note that the facilitator may not always know the answers to questions that may arise during the discussion. If everyone is stumped, the appropriate reply is to solicit help in doing research, if they have the necessary skills, or just to say, “That is a great question, and I am not sure of the answer. I will get back to you all on this tomorrow.” And then follow through! We need to model the behavior we expect to see in our students, and students feel empowered when they have asked something that no one else, even the facilitator, can readily answer.

Once the class is more experienced and comfortable with this type of discussion, the facilitator can introduce more open-ended questions or even beginning with a claim, and allowing the students to take charge of the discussion. Choosing questions that are likely to cause a strong reaction will be more successful. A discussion might begin such as this:

Facilitator: Here are the results from a study that claim that playing video games causes the users to behave more violently. (Project study results on the board.)

Student1: No way! My friends and I all play those games and we aren’t stupid. We know the difference between fantasy and reality. That’s dumb!

Facilitator: Do you see something in the study that you think would lead to a false conclusion?

Silence, while facilitator gives time for them to digest the information on the board. Here is where it takes faith to know that they will say something! It’s easy to think that they are just waiting for guidance, but it’s up to us to dispel that notion with our silence.

Student2: How do they know that it isn’t just that violent people are more likely to play those games and give the rest of us a bad name?

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Bingo! From here, the discussion could take several different turns to how studies are conducted, random sampling, how to read results, etc., but always with the students driving the discussion and therefore remaining engaged. We strongly recommend the book Out of the Labyrinth: Setting Mathematics Free by Robert and Ellen Kaplan, founders of the, dedicated to fostering open inquiry into mathematics for all students. It’s a great resource for rethinking our approach to teaching and learning.

Be aware that this is not as easy as it sounds, and we are not advocating anarchy here. It takes thoughtful preparation to come up with good questions while allowing for flexibility in follow-up activities, and a willingness to loosen our control, admitting that we do not provide all the instruction. While we always have short-term goals and objectives, our ultimate goal is to create life-long learners. Implementing these strategies allows us to see this develop before our eyes as the classroom lights up with engagement and active learning.


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