Mathematics and Society - OS X Lion Server

DIDACTICSTEACHING VIA LAB APPROACHESIt is possible that in early laboratory lessons you will give much direction and exerciseconsiderable control, perhaps starting with a whole-group, teacher-led activity(e.g., fractions with paper'-folding).Later you might have several small groupsworking on the same lesson (e.g., fraction activities on geoboards with a whole-groupfollow-up.)Eventually, if all bas gone well and it fits the unit's objectives, differentlessons could be used at different stations.slow."The usual guideline is, "StartSee the teaching emphasis Lciboratory Approaches in Geometry and Visualization,Mathematics Resource Project, for more examples and suggestions for laboratoryapproaches.Once the students become accustomed to laboratory lessons, the teacher will bedoing these things:--Visiting groups to see whether they are working or are confused.-Asking questions and clarifying procedures, but not serving as an "answerbook."--Observing students as they work.-Encouraging group interaction.--Allowing students to attack the lessons in their own ways. (Sollje errors willoccur but may be caught by the students or exposed by the equiplljent or thedata. Besides, some "errors" may actually be good but unconventional ideaslI--Helping students connect the manipulative to the mathematics being illustrated.(Sometimes students seem to "learn" only the concrete device and not theconcept. )--Talking with other teachers (including librarians) about how to organizematerials.--Being patient.--Praising students for initiative, independence, cooperation, imagination, ••--Providing follow-up to emphasize an idea, to have groups share their findingsor methods of attack, or perhaps to have the students comment on what theylave learned about working in groups.Truly a new role is necessary for the teacher. In assuming such a roleit should also be clearly understood that the activity oriented mathematicsprogram places more, not less, responsibility on the teacher.In traditional(ly) oriented programs, mosf; curricular decisions aredictatedby the textbook. To a far greater extent, in the activity orient~ed program it is the teacher who must know how and what childPen need tolearn, and when they need to learn it.[Reys and Post, 1973, p. 230]IN PRAISE OF LAB LESSONSResearch support for laboratory lessons with middle schoolers has not beenclear-cut.Studies can be found which are highly supportive of laboratory approaches(e.g., Silbaugh, 1972; Schippert, 1965; McClure, 1972), but studies in which laboratorymethods fare no better (or worse) than conventional instruction can also be45