In my classes I tend to focus heavily on the personal and social aspects of student development, by having discussions about their motivations for being in school, sharing their past anxieties, picking project topics that interest them, and other activities that address the affective domain. While this appears to be effective in helping students change their attitudes toward math in particular and school in general it seems disconnected from helping students learn the actual content. While my students often form a cohesive community and begin to utilize resources, they seem to lack independence and learn things almost entirely through others’ explanations. It appears to me that a form of dependence seems to develop, where students are not able to work alone and are not developing the skills that would allow them to teach themselves.
Moreover, I am not convinced that the content learning happening in my classes is very deep or substantial. Mostly they gain proficiency in the more rote skills like Algebraic manipulation.
While I do think most of my students become more comfortable doing mathematics and begin to change their attitudes about college, the range of problems that they are able to solve is limited to specific, identifiable “types” they come to recognize and are able to repeat a learned procedure. When confronted with problems of a completely different character, but involving the same mathematics, students have a very difficult time beginning.
All of this has caused a shift in my own ideas about the role of the teacher in the classroom. Building on Vygotsky’s view of learning as a “social-cognitive interactive process” which is socially mediated by ”more competent others”, I can see how the concept of teaching and learning as an apprenticeship arises. In an apprenticeship, the expert collaborates and interacts with the learner in a social context, both modeling for and challenging the student. “Through this social learning process, learners’ cognitive structures—the ways in which learners think—are shaped” (Schoenbach, Greenleaf, et. al., 1999). As the learner becomes more proficient, the expert can decrease the level of support and structure necessary for the learner to successfully accomplish the tasks. This positions the teacher both as a practitioner that attempts to make their mental habits transparent, but also one who facilitates metacognitive conversations about making sense of the mathematics, including its personal, social, cognitive and knowledge-building dimensions. My interpretation is that the teacher can create routines that allow students to teach themselves, a skill that goes far beyond a single course.
This approach flushes well with my ‘Freirean’ sensibilities, which prefer to empower students as actors capable of changing their own lives. In the article Insiders vs. Outsiders, Sheila Tobias argues that helping students build metacognition is a ‘bottom up’ approach which views the students not as deficient, but as competent individuals who are merely “outside the conventions, rituals, and expectations of discourse in that field” (275). These outsiders must be enlisted in discovering their own cognitive processes and pathways to learning. Through instructor modeling, practicing and reflecting on the learning process with peers, students can begin to develop their own metacognitive abilities and learn to teach themselves by engaging with texts.
In Reading Across the Divide, author David Donahue makes an observation that speaks directly to me: ”Many teachers avoid engaging students in texts and teach content by other means” (Greenleaf et al., 2001). For my students this manifests itself as a series of handouts, and lectures, which essentially replace the text as the source of information. In fact, the text in certain classes has become almost superfluous aside from being a source of problems to work on. While I think resources like videos and tutorial websites can be great for students, I don’t see them as a means to develop their long-term ability to self-teach. Donahue further describes my experience when he states “many secondary content area teachers are unconscious of their own strategies as expert discipline-based readers and feel ill-prepared to help their students who struggle to make meaning from texts.” The result is that we avoid teach students how to comprehend text. Teaching reading comprehension strategies requires that the teacher be conscious of their own strategies for comprehending texts and solving problems. This is not something I have ever thought about in a conscious, systematic manner. And now that I have begun to think about it, I find that my methods for making meaning of texts is quite complex, circuitous and in some ways still a mystery to me. In order to model and coach students toward higher-level functioning, I must learn about and document my own processes.
Building RA routines into my classroom may be challenging at first, but the potential seems enormous. Through effective modeling and the development of routines that help students discover, develop and share their mental processes, I am convinced students can become both independent and collaborative learners. The challenges will be in discovering my own process in order to make it visible to students and in learning to adapt these strategies to the peculiarities of each course. The process of grounding my mathematics courses more firmly in text will take time, but I’m hoping the result will be students that can turn mistakes and confusion into learning experiences as opposed to obstacles.
Michael Hoffman has been teaching transfer and developmental math courses to community college students in different districts for the better part of three years. Before starting at Cañada College, Hoffman worked as an instructional aide in the Skyline Learning Center where he did intensive one-on-one tutoring with students enrolled in calculus, linear algebra, and statistics as well as developmental math courses such as pre-algebra and algebra. He also taught developmental algebra as well as calculus and pre-calculus throughout his graduate education at San Francisco State University and taught algebra to returning adults through the Program for Adult Continuing Education at Berkeley City College.