Blog: andypethan.com
Differentiation
We learn in class that instruction needs to be differentiated, but after the observations, I realized how completely different each student thinks and acts. One of the visible differentiators, race, has an effect on attitudes and social grouping. Another, socio-economic status, separates kids by how they dress and act. Cognitively, students are coming from many different places and hold different misconceptions about the topic under study. Socially, they respond differently to groups – both in how much they enjoy being grouped and how much work they can get done (they appear to be independent variables). They also fall at different skill levels in math. They are motivated in different ways. Finally, they have interests that are all over the map, and likely change week to week. There is a ton of diversity in the classroom – no two students think the same way.
My observations showed that many kids were bored throughout the class. With kids being so different and only one teacher existing up front, it is unlikely that many will find the lesson engaging. The class needs to be much more differentiated in order to keep everyone interested in the material. In order to achieve this kind of differentiation, I think the class needs to be run with a very different approach.
Approach
I personally have been most motivated in a project-based curriculum. When I am given latitude to choose a task within parameters, I often find the task interesting and relevant to my life. When the task requires learning a new skill, I am very focused and eager to learn, then immediately practice and apply, the new skill. Everyone in the class is doing different things in small teams, so differentiation is obvious, not something that happens to separate the “smart and dumb” kids. Sometimes, the group as a whole is responsible for the completion of a single task. In other groups, each person completes the task on their own, but the students cooperate to finish the work. Skills are learned in context and perseverance through failure is frequent. Direct instruction is appreciated, but only in small bursts on a need-to-know basis.
In math, there are applications that take minutes and others that take weeks to complete. Typical story problems rarely seem realistic and don’t require deep thinking. The goal in my classroom would be to use prompts or situations that require a few days of thought and action to complete. These problems have multiple correct solutions, as long as the approach can be justified. As students setup equations they cannot solve, they can come to the teacher as a group looking for direct teaching on the technique. Students can visually keep track of skills they learn with a “toolbox”, perhaps an envelope, full of cards that represent all of the skills they learned. Class content would be organized by the types of problems the skill is used for, not the chapter that Pearson decided to put it in.
This type of minds-on approach would be more likely to break the pattern of people who “don’t like math” or “can’t do math”. It would also add relevancy to the class days of the bored students. Since the focus is on application, how a student learns a specific skill is also more open-ended. They could use the teacher, a peer that already learned it, a YouTube video, a web-app, examples online, or even a textbook. Most likely, they would use a combination of these resources. It would take some experimenting to make sure students have enough practice to correctly learn the skills, but advances in software for learning math would be most likely to help track this.
Management
In order to have an active, differentiated classroom, basic management procedures would need to be followed on a daily basis. The start and end of each day would have to be generally consistent: look at the whiteboard for the first instruction (respond to the question or prompt, check homework, etc.) and pack up and sit quietly when a minute remained at the end of class. In the middle, the teacher needs a consistent, quiet way to call for attention. Interruptions for absent students, bathroom passes, turning in homework, and small logistical things need to taught explicitly and practiced so time is not wasted during the year. When students are in the middle of a project, they should be able to walk into class, know what to do, quietly transition into project teams, work, clean up, and leave without a teacher present. The classroom I observed had some of these procedures in place, but there were still frequent questions about small things that could have been automated. The more active a classroom will be, the less time there will be for teachers to micro-manage small student issues.
The room itself needs to be setup for cooperative and independent learning. There should be some tables, some desks, and furniture should be mobile. To keep the room neat, there should be a procedure for putting the room back to its initial state at the end. The classroom I observed did this very well.
Feedback
Kids don’t mind making mistakes. In games, kids play and screw up all the time. They lose a life, lose their gun, get swallowed by monsters, or get sent back to the start. Then they try again, knowing what not to do the next time. If they played for 20 minutes and then were sent back to the start for something they did wrong in the first minute, they would surely quit. To prevent the same situation in math class, students need to be taught how to check their work after every problem. If there is a mistake, they need to get help from another person (teacher or peer), a video, a solution guide, or some other source until they correct the mistake and understand what they did wrong. They need to keep trying again on progressively harder problems until they get the concept. Working in groups is one way to learn and fail with other people, offering assistance to others when you get concepts that they don’t. In the advanced math class in the middle school, peer teaching and frequent use of the solution guide helped most students understand the material with almost no teacher support required.
Original Field Notes