The middle grades offer unique challenges to the mathematics teacher, especially in this time of transition from traditional to reformed curricula and methods. The range and conceptual quality of mathematical knowledge that students have as they enter grades 5 and 6 vary greatly. Many students have been accelerated through textbooks, resulting in a high degree of proficiency at arithmetic computation but sometimes with little conceptual understanding of the underlying mathematics. Many other students will enter the middle grades with only rudimentary understanding of addition and subtraction. This disparity of skills and understanding creates a difficult dilemma for middle school teachers. Should they review the arithmetic that students have already experienced, or should they forge ahead to a higher level of more difficult mathematics? This decision need not be perceived as a dichotomy. Methods exist for exploring higher-order mathematical topics conceptually that allow understanding by students of varying knowledge levels whatever their base knowledge may be.
James A. Middleton and Marja van den Heuvel-Panhuizen
James A. Middleton, Marja van den Heuvel-Panhuizen and Julia A. Shew
Middle Grades Students Should be able to understand, represent, and use numbers in a variety of equivalent forms, including fractions, decimals, and percents. They should develop number sense for fractions and other representations of rational number. Students should also be able to represent such relationships in graphical form (NCTM 1989).
Angeliki Kolovou, Marja van den Heuvel-Panhuizen and Olaf Köller
This study investigated whether an intervention including an online game contributed to 236 Grade 6 students' performance in early algebra, that is, solving problems with covarying quantities. An exploratory quasi-experimental study was conducted with a pretest-posttest-control-group design. Students in the experimental group were asked to solve at home a number of problems by playing an online game. Although boys outperformed girls in early algebra performance on the pretest as well as on the posttest, boys and girls profited equally from the intervention. Implications of these results for educational practice are discussed.