EFFECTIVE PEDAGOGY IN MATHEMATICS
1. An ethic of care
Caring classroom communities that are focused on mathematical goals help develop students’ mathematical identities and proficiencies.
Research findings
Teachers who truly care about their students work hard at developing trusting classroom communities. Equally importantly, they ensure that their classrooms have a strong mathematical focus and that they have high yet realistic expectations about what their students can achieve. In such a climate, students find they are able to think, reason, communicate, reflect upon, and critique the mathematics they encounter; their classroom relationships become a resource for developing their mathematical competencies and identities.
Caring about the development of students’ mathematical proficiency
Students want to learn in a harmonious environment. Teachers can help create such an environment by respecting and valuing the mathematics and the cultures that students bring to the classroom. By ensuring safety, teachers make it easier for all their students to get involved. It is important, however, that they avoid the kind of caring relationships that encourage dependency. Rather, they need to promote classroom relationships that allow students to think for themselves, ask questions, and take intellectual risks.
Classroom routines play an important role in developing students’ mathematical thinking and reasoning. For example, the everyday practice of inviting students to contribute responses to a mathematical question or problem may do little more than promote cooperation. Teachers need to go further and clarify their expectations about how students can and should contribute, when and in what form, and how others might respond. Teachers who truly care about the development of their students’ mathematical proficiency show interest in the ideas they construct and express, no matter how unexpected or unorthodox. By modelling the practice of evaluating ideas, they encourage their students to make thoughtful judgments about the mathematical soundness of the ideas voiced by their classmates. Ideas that are shown to be sound contribute to the shaping of further instruction. Caring classroom communities that are focused on mathematical goals help develop students’ mathematical identities and proficiencies.
Caring classroom communities that are focused on mathematical goals help develop students’ mathematical identities and proficiencies.
Research findings
Teachers who truly care about their students work hard at developing trusting classroom communities. Equally importantly, they ensure that their classrooms have a strong mathematical focus and that they have high yet realistic expectations about what their students can achieve. In such a climate, students find they are able to think, reason, communicate, reflect upon, and critique the mathematics they encounter; their classroom relationships become a resource for developing their mathematical competencies and identities.
Caring about the development of students’ mathematical proficiency
Students want to learn in a harmonious environment. Teachers can help create such an environment by respecting and valuing the mathematics and the cultures that students bring to the classroom. By ensuring safety, teachers make it easier for all their students to get involved. It is important, however, that they avoid the kind of caring relationships that encourage dependency. Rather, they need to promote classroom relationships that allow students to think for themselves, ask questions, and take intellectual risks.
Classroom routines play an important role in developing students’ mathematical thinking and reasoning. For example, the everyday practice of inviting students to contribute responses to a mathematical question or problem may do little more than promote cooperation. Teachers need to go further and clarify their expectations about how students can and should contribute, when and in what form, and how others might respond. Teachers who truly care about the development of their students’ mathematical proficiency show interest in the ideas they construct and express, no matter how unexpected or unorthodox. By modelling the practice of evaluating ideas, they encourage their students to make thoughtful judgments about the mathematical soundness of the ideas voiced by their classmates. Ideas that are shown to be sound contribute to the shaping of further instruction. Caring classroom communities that are focused on mathematical goals help develop students’ mathematical identities and proficiencies.
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