Effective mathematics learning environment

An effective mathematics learning environment is one in which students and teachers interact in ways that allow students to have an opportunity to maximize how much they learn. There are a variety of ways in which students and teachers interact in a learning environment. Some interactions result in student learning, however, others have very little effect on student learning. Classroom discussions, teacher and student initiated questions, cooperative group work, peer tutoring and a host of other feedback systems such as assignments, examinations and electronic response systems such as the personal response system (PRS) and the personal data assistant (PDA) are instructional strategies that provide a measure of two-way communication in which information about what is taught and what is learned is exchanged between two people.

 On the other hand, there are instructional strategies in which students sit passively in classrooms where there is one-way communication – from teacher to students. On many college and university campuses, for example, the professor operates as the proverbial “sage on the stage” and the didactic lecture is the modal way of teaching. And although the lecture is an efficient method for transmitting information from a teacher to a large group of students, telling information to someone does not mean that learning takes place. In order to determine whether learning is occurring – in fact, to ensure that learning is taking place, there must teacher-student assessment interactions along with the instructional interactions.

Assessment interactions between students and teachers occur when teachers gather information about student learning and use that information help students better understand concepts and principles and apply knowledge, not just learn facts. This type of assessment interaction referred to as formative assessment is defined as follows: Formative assessment is a process used by teachers and students during instruction that provides feedback to adjust ongoing teaching and learning to improve students’ achievement of intended instructional outcomes (Council of Chief School State Officers, 2008). It is clear from this definition that formative assessment is a process. It is a process that may employ tests or various other types of assessments, but it may also employ interactive instructional strategies such as classroom discussions, assignments, homework, quizzes, projects, investigations, electronic response systems or oral questions to gauge and improve student learning (Angelo & Cross, 1993; Fennell, 2006).

Creating an interactive learning environment inside the mathematics classroom in which students are engaged in mathematics learning can be challenging. Students may experience discomfort about their own level of mathematics content knowledge and may shy away from participating openly in class discussions or responding to teachers’ oral questions. Further, the complex negotiation of teacher talk, student talk, and classroom dynamics while remaining on-task requires certain skills and know-how. In some models of “best practices” in mathematics teaching and learning, these classroom dynamics are viewed as a social endeavor (Cobb & Bauersfield, 1995) in which the classroom functions as a learning community where thinking, critiquing, debating, disagreeing and agreeing are encouraged. When these dynamics work well, the result can be the creation of a learning environment in which critical thinking and quantitative reasoning develop, student learning thrives, and students take increasing responsibility for their own learning.