their authentic counterparts. Virtual versions of concrete manipulatives typically used in mathematics education include base 10 blocks, Cuisenaire rods, and tangrams. Many available virtual manipulatives are paired with structured activities or suggestions to aid implementation in the classroom.

Visual/holistic level refers to a level of thinking that occurs when children have formed schemes, or mental “patterns,” for these shape categories. It refers to the ability of preschoolers to learn to recognize a wide variety of shapes, including shapes that are different sizes and are presented at different orientations. They also learn to name common three-dimensional shapes informally and with mathematical names (“ball”/sphere, “box” or rectangular prism, “rectangular block” or “triangular block,” “can”/cylinder). They name and describe these shapes, first using their own descriptions and increasingly adopting mathematical language.

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