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Everything about school and work in the twentieth century was designed to create and reinforce separate subjects, separate cultures, separate grades, separate functions, separate spaces for personal life, work, private life, public life, and all the other divisions. Then the internet came along. Now work increasingly means desktop computer. Fifteen years into the digital revolution, one machine has reconnected the very things–personal life, social life, work life, and even sexual life–that we’d spent the last hundred years putting into neatly separated categories, cordoned off in their separate spaces with as little overlap as possible.

Digital games allow students to take an active role in their learning and see the visual connection between the game play and the math. The games also provide constant positive or corrective feedback that is "really hard for teachers to provide to individual kids,"

"We shouldn't look to old media such as a paper-and-pencil quiz as the arbiter of knowledge," Klein said. "If a student can do something smartly in a digital environment, that matters, that counts. Even if they can't yet introduce that in paper and pencil, that doesn't lessen the skill. ... It's just a different place for knowledge."

Even if students learn a concept with manipulatives and simultaneously learn it with written symbols, the two may remain separate, with students never drawing the connection between them

A simple review of key conclusions makes a few things clear. First, we must temper our endorsement of manipulatives in classrooms with some caveats; there are instances where manipulatives will not speed children’s learning, and may even slow it down. Second, the objects themselves should draw attention to whichever feature is meant to convey information, for example, the length of a rod if it is meant as an analogy to number. Third, teachers should provide instruction in the use of the manipulative so that this feature is salient to students, but teachers should not be so controlling that students are merely executing instructions without thinking. In addition, students are more likely to understand the concept the manipulative is meant to convey if that parallel is made explicit to them