In order to implement formative assessment well, Wiliam (2011) shares five key strategies. Three are particularly well-supported by manipulative-based instruction: classroom activities and learning tasks which elicit evidence of learning, activating learners as instructional resources for one another, and activating learners as owners of their own learning. In all three cases, by actively engaging students in the doing of mathematics, manipulatives provide a foundation which encourages discussion and student ownership of their work. This provides teachers with a vivid current picture of student understanding and guides teachers in determining appropriate next steps.
Building on the learning theory work of Piaget and Bruner, a solid history of research supports the regular use of manipulatives in classroom mathematics instruction. While children can remember, for short periods of time, information taught through books and lectures, deep understanding and the ability to apply learning to new situations requires conceptual understanding that is grounded in direct experience with concrete objects. It is also important to note the critical role of the teacher in helping students connect their manipulative experiences, through a variety of representations, to essential abstract mathematics. Together, excellent teachers and regular experiences with hands-on learning can provide students with powerful learning in mathematics.
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