### Inductive and Cooperative Learning

I'm a huge fan of inductive learning and group work. I was frustrated in High School when I was graded on how well I worked in a group, or when I was forced to cooperate even at the cost of efficiency. Group work can be great, though, insofar as it excites students to explore, gives them opportunities to teach their peers, and fosters social development. Inductive learning is also great, especially because is is the things learned inductively that are most often remembered. My astronomy teacher routinely made me mad by refusing to lecture and tell us how the stars and moon moved in the sky. He realized that if he told us, we'd just forget it, whereas if we figured it out on our own, we'd understand it and remember it. We learned a lot less in his class, but we probably retained more.

I'm not tempted to assign only group work or inductive lessons, but I do want to incorporate it as much as possible into my teaching. Yesterday, I was teaching the students how to find the area of trapezoids and triangles. We had learned how to find the area of rectangles by multiplying the length by the width, and we had learned that a parallellogram can be rearranged to make a rectangle, too. For the trapezoid and triangle, I gave them a mini-lab in which they drew each shape, labelled their edges, and then cut them out to make a parallelogram. The hardest part, which none of them got, was using their labes from their original drawings to make a formula for the area. I then showed the class where the new formulas come from and how these shapes are related to rectangles and parallelograms.

I would say that the activity was successful, although I was incredibly nervous about it. I have been spending a huge amount of energy being very strict with my class so that students know that no speaking is acceptable without permission. We only had enough scissors for half of the students, though, so I had to let them work with partners. I was afraid that the class would erupt in chaos. Luckily, we made it through with only a moderate amount of noise. They definitely enjoyed themselves and learned, but my fear is that letting them do such an activity undermines the atmosophere of quiet that I'm trying to impose.

Is this an inevitable trade-off? Fun, enthusiastic, creative learning versus ordered, disciplined, productive learning? I don't know. I do know that I'm going to be very hesitant to assign group work until I've established very clearly an orderly classroom. This'll be tough because all of the best lessons I've seen and thought of involve lots of active participation, cooperation, and exploration.

I'm not tempted to assign only group work or inductive lessons, but I do want to incorporate it as much as possible into my teaching. Yesterday, I was teaching the students how to find the area of trapezoids and triangles. We had learned how to find the area of rectangles by multiplying the length by the width, and we had learned that a parallellogram can be rearranged to make a rectangle, too. For the trapezoid and triangle, I gave them a mini-lab in which they drew each shape, labelled their edges, and then cut them out to make a parallelogram. The hardest part, which none of them got, was using their labes from their original drawings to make a formula for the area. I then showed the class where the new formulas come from and how these shapes are related to rectangles and parallelograms.

I would say that the activity was successful, although I was incredibly nervous about it. I have been spending a huge amount of energy being very strict with my class so that students know that no speaking is acceptable without permission. We only had enough scissors for half of the students, though, so I had to let them work with partners. I was afraid that the class would erupt in chaos. Luckily, we made it through with only a moderate amount of noise. They definitely enjoyed themselves and learned, but my fear is that letting them do such an activity undermines the atmosophere of quiet that I'm trying to impose.

Is this an inevitable trade-off? Fun, enthusiastic, creative learning versus ordered, disciplined, productive learning? I don't know. I do know that I'm going to be very hesitant to assign group work until I've established very clearly an orderly classroom. This'll be tough because all of the best lessons I've seen and thought of involve lots of active participation, cooperation, and exploration.

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