For the last several days they had been solving systems of linear and nonlinear equations and inequalities. When isolated, these aren't complicated topics.Today they needed to apply what they had been practicing into a single problem. This is called linear programming, a technique of combining several constraints or restrictions to (usually) find a maximum profit or a minimum cost in business.
Sounds interesting? It is! This is one of my favorite topics because it makes connections for students between what they are learning and how it applies in the "real" world. Today I decided to present the material differently.
Using SMART amp (a digital whiteboard called a workspace that allows students to collaborate in the same workspace from their own device), I gave them the problem, defined key terms, which lead them step-by-step through the solution of the problem.
Each pair of students shared one workspace. Whatever one wrote, the other could see. By request, I let two pairs work together.
The students were quickly intimidated by the problem. Too many words, too many numbers, and no obvious way to connect all the information. To compound the difficulty, the teacher wasn't telling them what to do or how to do this. How did I expect them to solve a problem they had never seen before? Students were calling me to come help them and to answer all their questions.
I walked around the room to listen to the discussions. It seemed when I stopped to listen, the questions and conversation would be aimed at me. Rather than answer, I asked more questions to guide their discussion. As the end of the period neared, there were anxious shouts to "just tell us how to do this!"
As one student was ready to give up, I told him that one day his boss will give him a project to work on but the step-by-step instructions wouldn't be included. That would be his job - to figure out the problem then come up with the best solution. I assured him
- He wouldn't be done after one attempt.
- He wouldn't be able to figure it out on his own.
- He would need to collaborate and brainstorm with others.
- He would need to ask questions to better understand the problem.
- He would need to listen to others even if their ideas were different from his.
- He would need to work hard only to find after hours of work that he and his team were way off.
- He would need to refocus, and try again using the last solution to help find a better solution. .
- And the most important thing is he couldn't quit just because the problem seemed impossible.
I have bright, motivated students who want to do well. If I tell them how to do a problem, they will solve that problem well. They rely on their notes or text to help them with the tough homework problems. There's always a solution with a little bit of effort. Today was different.
Today my students were upset because I wouldn't "help" them. Oh, but I was helping them . . . not only helping them with today's problem but for the ones to come . . . later. Today I realized I need to do this more often.
Tomorrow they will share their ideas and solutions and be reassured that they were close. Some figured it out: seven 6-ton and two 10-ton trucks.
Next day's follow up
I thought about how my students left the room yesterday. They weren't all happy and some were super frustrated. I knew we had to have a conversation.
As soon as she walked into class, a girl who had been especially frustrated (and almost rude) came up to me and apologized for her behavior the previous day. That was a great way to start class.
I let my students know that I realized there was frustration and confusion and that it was ok to feel that way. I gave them my reasons for doing what I did (listed above) and I began to see heads nodding.
This really shows how important communication is. I don't believe I have to explain everything that I do and reasons why with my students but there are days when it is necessary. Now that my students have a better understanding, we can move on.
Tomorrow they will share their ideas and solutions and be reassured that they were close. Some figured it out: seven 6-ton and two 10-ton trucks.
Next day's follow up
I thought about how my students left the room yesterday. They weren't all happy and some were super frustrated. I knew we had to have a conversation.
As soon as she walked into class, a girl who had been especially frustrated (and almost rude) came up to me and apologized for her behavior the previous day. That was a great way to start class.
I let my students know that I realized there was frustration and confusion and that it was ok to feel that way. I gave them my reasons for doing what I did (listed above) and I began to see heads nodding.
This really shows how important communication is. I don't believe I have to explain everything that I do and reasons why with my students but there are days when it is necessary. Now that my students have a better understanding, we can move on.