The classroom learning community

An Ethic of Care: Caring Classroom Communities that Are Focused on Mathematics Goals Help Develop Students’ Mathematical Identities and Proficiencies

From research studies we find that effective teachers facilitate learning by truly caring about their students‘ engagement (Noddings, 1995). They work at developing interrelationships that create spaces for students to develop their mathematical and cultural identities. They have high yet realistic expectations about enhancing students‘ capacity to think, reason, communicate, reflect upon and critique their own practice, and they provide students opportunities to ask why the class is doing certain things and with what effect (Watson, 2002). The relationships that develop in the classroom become a resource for developing students‘ mathematical competencies and identities.

Students want to learn in a ‗togetherness‘ environment (Boaler, 2008; Ingram, 2008). Teachers can make everyone feel included by respecting and valuing the mathematics and the cultures that students bring to the classrooms. Ensuring that all students feel safe allows every student to get involved. However, it is important that the caring relationships that are developed do not encourage students to become overly dependent on their teachers. Effective teachers promote classroom relationships that allow students to think for themselves, to ask questions, and to take intellectual risks (Angier & Povey, 1999).

Everyday classroom routines play an important role in the development of students‘ mathematical thinking. Effective teachers make sure that all students are provided with opportunities to struggle with mathematics for themselves. For example, simply inviting students to contribute a response to a mathematical problem may not achieve anything more than cooperation from students. Teachers need to provide students with expectations and obligations concerning who might speak, when and in what form, and what listeners might do (Stipek et al., 1998).

Teachers are the most important resource for developing students‘ mathematical identities (Cobb & Hodge, 2002). They influence the ways in which student‘s think of themselves in the classroom (Walshaw, 2004). In establishing equitable arrangements, effective teachers pay attention to the different needs that result from different home environments, different languages, and different capabilities and perspectives. The positive attitude that develops raises students‘ comfort level, enlarges their knowledge base, and gives them greater confidence in their capacity to learn and make sense of mathematics. Confident in their own understandings, students will be more willing to consider new ideas presented by the teacher, to consider other students‘ ideas and assess the validity of other approaches, and to persevere in the face of mathematical challenge.

Arranging for Learning: Effective Teachers Provide Students with Opportunities to Make Sense of Ideas both Independently and Collaboratively

An important role of the teacher is to provide students with working arrangements that are responsive to their needs. All students need some time to think and work quietly by themselves, away from the varied and sometimes conflicting perspectives of other students (Sfard & Keiran, 2001). At other times, partners or peers in groups can provide the context for sharing ideas and for learning with and from others. Group or partner arrangements are useful not only for enhancing engagement but also for exchanging and testing ideas and generating a higher level of thinking (Ding, Li, Piccolo, & Kulm, 2007). In supportive, small-group environments, students learn to make conjectures and learn how to engage in mathematical argumentation and validation (O‘Conner & Michaels, 1996). In particular, when groups are mixed in relation to academic achievement, insights are provided at varying levels within the group, and these insights tend to enhance overall understandings However, teachers need to clarify expectations of participation and ensure that roles for participants, such as listening, writing, answering, questioning, and critically assessing, are understood and implemented (Hunter, 2008).

Whole class discussion can provide a forum for broader interpretations and an opportunity for students to clarify their understanding. It can also assist students in solving challenging problems when a solution is not initially available. Teachers have an important role to play in the discussion. Focusing attention on efficient ways of recording, they invite students to listen to and respect one another‘s solutions and evaluate different viewpoints. In all forms of classroom organization it is the teacher‘s task to listen, to monitor how often students contribute, and to keep the discussion focused. When class discussion is an integral part of an overall strategy for teaching and learning, students provide their teachers with information about what they know and what they need to learn.

Building on students‘ thinking: Effective teachers plan mathematics learning experiences that allow students to build on their existing proficiencies, interest, and experiences. In planning for learning, effective teachers put students‘ current knowledge and interests at the centre of their instructional decision making. Informed by on-going assessment of students‘ competencies, including language, reading and listening skills, ability to cope with complexity, and mathematical reasoning, teachers adjust their instruction to meet the learning needs of their students.

With the emphasis on building on students‘ existing proficiencies, rather than remediating weaknesses and filling gaps in students‘ knowledge, effective teachers are able to be both responsive to their students and to the discipline (Carpenter, Fennema, & Franke, 1996). They understand that learners make mistakes for many reasons. Some mistakes happen because students have not taken sufficient time or care; others are the result of consistent, alternative interpretations of mathematical ideas that arise from learners‘ attempts to create meaning. To help students to learn from their errors, teachers organize discussions—with peers or the whole class—that focus students‘ attention on the known difficulties. Asking students to share a variety of interpretations or solution strategies enables learners to compare and re-evaluate their ideas.

Teachers who start where students are at with their learning are also able to design appropriate levels of challenges for their students. For low-achieving students, teachers find ways to reduce the complexity of tasks without falling back on repetition and busywork and without compromising the mathematical integrity of the activity (Houssart, 2002). In order to increase the task challenge in all classrooms, effective teachers put obstacles in the way of solutions, remove some information, require the use of particular representations, or ask for generalizations (Sullivan, Mousley, & Zevenbergen, 2006).