Archived Information

State of the Art: Mathematics - July 1993

image omitted Teachers need to become "informed guides" to the learner.

Within the short space of these few minutes of classroom time, I faced a series of issues: how to get and maintain all my students' engagement, how to make sense of what Sean and Riba [students] were thinking, how to help them move toward appropriate and connected understandings of fractions. From moment to moment I was having to consider whether to praise, explain, solicit others' ideas, let an issue grow, or even stir up trouble in order to press on a crucial mathematical point. . .Day after day in my classroom, students say things I had never considered. Day after day they have trouble with ideas I used to think were simple. And day after day, these eight-year-olds catch me off guard with what captures their interest and what they reach for. 
                                           (Ball 1992, pp. 14-15)
Teachers who "guide" rather than "tell" transform student learning. The role of informed guide is much more difficult to assume than that of the lecturer. As teachers focus more on guiding their students' learning they need to know more mathematics. According to the Mathematical Association of America's A Call for Change.
Teachers need to recognize the relationship between what they teach and what is taught at other levels of school mathematics. They need, for example, to understand the close parallel among the development of integer arithmetic in the elementary grades, the algebra of polynomials in the middle and early high school curriculum, and the ideas of number systems explored later in high school....They should explore the relationships between geometry and algebra and the use of one to investigate the other. (Leitzel 1991, p.3)
Case studies indicate that teachers who have a good background in mathematics also add a richness to their lessons, involve students extensively in mathematical dialog, and capitalize on students' questions and discussions to weave and extend mathematical relationships. Such teachers guide their students to discover mathematical concepts and procedures. They do not list definitions and step-by-step procedures for students to memorize without understanding their meaning and function. Research indicates that classroom behavior is affected by an interplay among teachers' general and content-specific knowledge of mathematics, their understanding of how children think about mathematics, and their beliefs about mathematics and about how children learn it.
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[Mathematical discussion should be a daily part of classroom activity.] [Table of Contents] [Calculators, computers, and related technology can be effective tools in the teaching and learning of mathematics.]