Creating an Effective Mathematics Environment
Before instruction begins, it is important to create an effective classroom atmosphere in which learners feel safe and motivated to collaborate, cooperate and engage in the pursuit of mathematical understanding.
Research from the learning sciences indicates that successful learning happens when students are immersed in environments that are learner-centred, knowledge-centred and assessment-centred. In these environments, teachers are able to:
- attend to students' preconceptions and begin instruction with what students think and know
- organize mathematical knowledge around core concepts
- focus on what is to be taught, why it is taught and what mastery looks like
- provide daily opportunities to make students' thinking and learning visible as a guide for the teacher and student in learning and instruction
- encourage a culture of questioning, respect and risk-taking.
Adapted with permission from M. Suzanne Donovan and John D. Bransford, "Introduction," in M. Suzanne Donovan and John D. Bransford (eds.), How Students Learn: Mathematics in the Classroom (Washington, DC: The National Academies Press, 2005), p. 13.
Learner-centred classroom environments are those in which the knowledge, skills, attitudes and beliefs that learners bring to the educational setting are built upon.
Overall, learner-centred environments include teachers who are aware that learners construct their own meanings, beginning with the beliefs, understandings, and cultural practices they bring to the classroom. If teaching is conceived as constructing a bridge between the subject matter and the student, learner-centred teachers keep a constant eye on both ends of the bridge. The teachers attempt to get a sense of what students know and can do as well as their interests and passions—what each student knows, cares about, is able to do and wants to do.
(Bransford, Brown and Cocking 2000, p. 136)
Teachers who create learner-centred environments develop practices that include discovering what students think, discussing student misconceptions, and planning learning experiences that help students readjust their ideas and build stronger, more robust mathematical ideas and concepts. When students are allowed to make a mistake and then examine the consequences, they are more likely to develop deeper understandings and new knowledge.
Knowledge-centred learning environments tie student learning into the ideas that are central to the discipline of mathematics. In knowledge-centred environments, student learning focuses on fewer topics, but they develop a deeper understanding of the concepts and learn to communicate their understandings in a variety of ways (Newmann 2000).
One feature of a knowledge-centred learning environment is the focus on encouraging students to notice relationships and make connections between different facts, procedures and the underlying concepts they are learning. Another feature is the opportunities for students to solve challenging mathematical problems in ways that require them to wrestle with, grapple with, and even become temporarily frustrated, to get into the topic (Hiebert in Albert Shanker Institute 2005). Students share their ideas, improve on each other's ideas, challenge and be challenged, seek advice from peers, explain their thinking, provide evidence for their solutions, and explore evolving ideas and conjectures.
Assessment for learning and assessment as learning have been shown to improve teaching and learning. Traditionally, assessment practices have tended to emphasize the mastery of procedures and facts. Students in an assessment-centred classroom are routinely asked to demonstrate their understanding of important mathematical ideas that go beyond the application of algorithms. For more information on assessment, refer to Assessment.