by Allyson Brown, Mathematics Department
I have just begun my twentieth year of teaching high school mathematics. During the course of these years, I have guided over 1200 students through some sort of math curriculum. Working with these students taught me three important lessons:
1. Student learning is improved when they are given the opportunity to explain concepts to other students.
2. When I assign group projects, students will divide the work in order to either minimize or maximize their own contribution.
3. Teenagers are more concerned with what their peers think of them than what I think of them.
My teaching style was best characterized by a combination of lecture and informal classroom discussion. I spent most of my professional time standing in front of the class, telling the students what they needed to know, and assigning problems that I would grade. I truly felt responsible for filling their brains with the content they would need and that they would perform in order to please me. When I was feeling creative, I would assign group projects and I expected them to work together and do their fair share. Hopefully you can see the disconnect between the lessons I was learning and the way I was teaching. After an informal summertime conversation about various teaching methods, I was introduced to the idea of team-based learning. Adapting Larry Michaelson’s team-based learning approach to the high school Algebra classroom turned out to be the way I could best teach students.
As the name, team-based learning, might imply, students are assigned to a team, with four-to-five students in the group. I make them as diverse as possible by considering several individual factors; I survey the students during the first class meeting and ask them about their performance in math classes last year, their opinion on their ability to lead or follow, and other basic information like gender, age, and whether they live on or off campus. Once the teams are set, they will remain intact for the duration for the semester. Team building is a crucial, early component of this class management, and I spend time in class offering them opportunities to get to know one another.
In order to prepare for this course, I broke the curriculum into eleven units, with titles typical to most Algebra 2 courses, such as Quadratics, Rational Expressions, and Equations. I determined the major themes for each unit and the types of application problems associated with that particular unit. Once the big ideas were noted, I determined the algebra skills necessary to acquire before tackling the more challenging questions. At the start of every unit, students will go through multiple days of skill building. During this period, every day follows the same template:
Step 1: Pre-class preparation – Students work independently on the material pertinent to the next class. This may include a reading, practice problems, or on-line research. They need to do whatever is necessary for them to come to class prepared for a quiz on the objectives.
Step 2: When they come to class, they will take an individual quiz (called iRAQ = individual readiness assurance quiz).
Step 3: Once their teammates have completed the iRAQ, they take the same quiz with their team (called gRAQ = group readiness assurance quiz). Teammates are encouraged to ask questions and provide help to each other. The teams receive immediate feedback on their performance on the gRAQ
Step 4: Following the gRAQ, I lead a class discussion clarifying any details still confusing the students.
The structure of the class changes once the students have covered the skill portion of the unit. Students are given challenging group problem sets. Well written GPS questions are significant to the unit of study as they require students to demonstrate a sophisticated understanding of the major themes. Questions should also try to force students to make a decision about something. Having students articulate the best first step when solving a complicated equation or the most common error when setting up a word problem forces students to discuss the process instead of focusing on an answer.
I provide the students with ample class time to work on this type of assessment. I have found that every student is engaged during these team discussions and, as a math teacher and expert eavesdropper, I love listening to their various arguments. Once the problem sets are submitted, I require simultaneous student presentations of their findings. Specifically, I randomly select one member from each team and send them to the board. I display the problem I want them to answer, they write down their team’s solution and then quickly look to see what the other teams have displayed. If the responses are different (which is often the case) and there was a decision to be made, I let the team representative at the board argue their team’s answer. This is usually a lively part of the class and a time when active learning is taking place. I have found that students that are not used to public speaking need extra encouragement and can learn valuable skills during this exercise. This public exchange of ideas also reveals those team members that are not fully prepared for class and encourages full participation on every problem of the GPS. The divide and conquer method is risky when each team member is equally likely to be the spokesperson for their team.
Peer feedback is a crucial element of team-based learning. I have found that teams benefit when there is a high level of participation from all members. Challenging questions are easier to answer when many minds provide input. Feedback from their teammates helps them gauge how their contributions are valued. Valuable input is only possible when students have put in the effort necessary to be at least familiar with the course skill content. In the most ideal situation, students would prepare for class and eagerly contribute to every team discussion. They would provide necessary support for weaker teammates and ask thoughtful questions, while providing insightful ideas, furthering their team’s efforts. When teenagers know that other teenagers are watching them and evaluating their contributions, their preparation is better and their participation increases. Students appreciate frequent opportunities to receive peer feedback and then the opportunity to alter their peer’s perception of their performance.
This class structure has revitalized my teaching. I love listening in on the team discussions and watching as every student engages with the material. Whether students are material experts or question askers, all of them are talking about the concepts and articulating their own understanding of the material in every class. Students are challenged by the concepts and by the social structure of working on a team. They are developing skills that enable them to take ownership of their own learning and they are practicing 21st century skills like public speaking, self-reflection, and inter-personal skills. In the end, I have set out to teach them Algebra 2, and I feel as though they have learned that and so much more.
Allyson Brown teaches Mathematics and coaches the St. Mark’s FIRST Robotics Team 3566. She holds a B.A. from Smith College and an M.A. from Teachers College. She is the head of Pine Oak House, where she lives with her husband and two young children.