6.2: Learning from Others
The same empowerment and confidence in student ability and potential that teachers recognize in self-directed learners (see expectation 2.2: Self-Directed Learners and expectation 6.3: Empowering Students) can be applied collectively to cooperative learning. Sometimes as teachers it is easy to get caught up in demonstrations that depict “the right way.” When the insights of all students are recognized as important learning tools, often the demonstration of a failure is a more meaningful and relevant learning experience. When students can see and discuss why something doesn’t work, it is often easier to understand what has to change to make it right.
But the experience of failure, especially in the midst of peers, is not often one that adolescents value or appreciate. Students and teachers must have a level of trust in the abilities of one another to make lemons out of lemonade, that is, mistakes need to be rewarded as valuable diagnostics in the learning process. When I make mistakes in class, I often reiterate how easy it is to do so and then restate the correction. Students will make mistakes, too, and I want them to feel supported, not ashamed. Mistakes are part of growth and therefore part of learning (and certainly part of mathematics), and they should be valued in the classroom community by all students and teachers.
A classroom that truly functions as a community and values trust, respect, diversity, and risk can flourish by striving to learn from one another. In the classroom community, all students’ strengths and weaknesses come into play. In math, we can draw upon the strengths and weaknesses students possess in the areas of visualization, graphing and drawing, calculation, logic, peer familiarity, etc. When we design activities and assessments that allow them to work cooperatively, we engage them in activities that stimulate interest and provide opportunities for them to share and interact in an instructional manner. The teacher, as facilitator, is there to focus and encourage students in their cooperative efforts. When students work together to learn from one another, they benefit from the shared experiences of the participants and can later draw upon them when they are faced with a more solitary assessment.
While student teaching, I extended my mentor teacher’s class privilege of working together on assignments, because I saw value in encouraging students with different perspectives and levels of understanding to assist one another. Understanding deepens and questions arise from debates or misunderstandings that may not surface when students work alone or solely with the teacher. Then, when I took over the maternity leave at the end of the year, I went into a different classroom that had the desks arranged in clusters of five. On the first day, I surveyed the students in each class, and one of the things they liked most about what they had been doing prior to my arrival was the opportunity they had to work together in groups. However, the clusters bothered my because they all sat with their friends, and half the cluster always had their back to me during instructional time. I immediately rearranged the furniture into front-facing tables with desks pushed together that still allowed students to sit and work at the same table, but also focused the attention in a certain direction for better classroom management. Feedback Friday shows student appreciation for the directional changes and the continued cooperative learning that takes place in all of the classes.
The facilitator, whether student or teacher, must remain aware of the nature of the cooperative learning process. Facilitating means being flexible in direction and content while at the same time staying within the parameters of the discussion topic. The role of facilitator ensures that all thoughts, ideas and insights are presented and valued within the context of the discussion. To this end, it is imperative that students learn how to manage themselves both as participants and facilitators in small groups. There are many resources available to assist teachers in developing organizers, materials, and discussion protocols such as jigsaw, connections, or the final word. Teachers should be aware of these opportunities to prompt students in cooperative situations and stretch the meaning beyond the content into issues that address self-reflection, social conscience, cultural responsiveness, meeting exceptional needs and inclusion.
Did you notice the above link cites group size as a factor in management and organization as well? Some facilitators recognize the size of the group as a factor in the effectiveness of cooperative learning. A recent discussion in CoT seminar addressed this very point. While looking at a small school model, the question arose as to the nature of "small" schools, and whether or not size really matters. Are components of the learning community such as shared interest and experience, personalized attention, and authentic assessment more relevant? Our discussion remained focused on three areas: 1) small school vs. class size, 2) data that supports small school success, and 3) feasibility (resources, facilities, etc.). The overwhelming consensus among the seminar group was that size does indeed matter.
My mentor teacher and I share a philosophy about math education (see INTASC Standard #1 in his portfolio and expectation 4.1: Teaching for Problem-Solving), especially geometry. It is my belief that math is about the process, not the product. Accuracy is only a part of the expectation for students in my class. If mathematical professionals get the wrong answer, their bridges will collapse, but students are not far-sighted enough to care about that. The realization that the majority of our secondary math students are not on career paths into engineering or statistics should awaken teachers to the reason the content is still considered important for all students to learn. I always maintain, to peers, administrators and students alike, that math is really about "figuring stuff out." It is not about memorizing the quadratic formula or even solving for x.
I often write assessments (Chapter 10 test and Chapter 11 test) that help me gauge the process students go through to solve a problem. All right or all wrong is not an evaluative method in my class. Partial credit is always given for a good approach. The student that is inclined to make mathematical errors but begins by using sound logical methods should not be considered less of a math student that the one that plugs-and-chugs through a formula to get the right answer. Both strengths are important parts of mathematical content, and are fundamental to developing good problem-solving techniques. Allowing students to work cooperatively through both the set-up and the execution is an essential part of building confidence and skill in mathematics. And we all know that confidence is the greatest contributor to math anxiety and is a huge obstacle for many students to overcome alone.
Through my student-teaching and substituting experiences, I continued my mentor teacher's practice of allowing students to make corrections to their graded tests. Just like assignments, the process is a cooperative one. I formalized the process from having students use a blank page to submitting a Test Correction Form that required the student to describe what he had done wrong before proceeding through the correct method. My mentor teacher is going to use my form for future classes, because it enriches the learning that is intended to occur given the opportunity to make these corrections for credit.
Students and teachers both must realize the benefits of cooperative learning and the opportunities for enriched understanding and academic socialization. Classrooms that have an air of solitude and individual performance become competitive and non-developmental. When students and teachers are encouraged to work together cooperatively, both become better learners, both become better instructors.
