TouchTimes vs Penn DOT Permit Practice Test

TouchTimes lets children learn multiplication through powerful, embodied approaches. By using two-handed gestures to create and manipulate their own factors and products, children build a strong sense of multiplicative meanings and relationships. TouchTime’ hands-on approach makes abstract ideas concrete, letting students literally "grasp" mathematical concepts. TouchTimes offers two complementary experiences: In the Grasplify World, children first create, with the fingers of one hand, some form of unit, and then—through one or more taps of the other hand—create a "unit of units,"" a product. The Grasplify World enables experiences of multiplication that go beyond approaches based on additive thinking and repeated addition. In the Zaplify World, children create simultaneous bolts of lightning—horizontal from one hand, vertical from another. Orange sparks appear where these bolts cross as a product of the lightning-bolt factors. (These terms may also be displayed numerically.) This dynamic model of multiplication emphasizes the commutative property of multiplication and the symmetry of multiplicative factors, and gives learners conceptual and geometric building blocks for understanding multiplicative relationships. Neither a repetitive drill-and-practice worksheet nor a rigid "level-driven" game, TouchTimes is a mathematics exploration environment designed to allow students to discover, pose and examine their own questions and understandings. Since TouchTimes displays the product that results from any multiplicative expression, learners focus less on how to compute than on how multiplicative relationships work, and on how, with their hands, to coordinate and combine multiplicative factors into given multiplicative products. Learners also encounter and work with numbers, symbols and equations, and move back and forth between symbolic/numeric forms and more visual, haptic, and tactile representations of multiplicative relationships. As children begin to learn about multiplication, TouchTimes is the perfect environment to solidify that understanding and help them generalize patterns beyond their ability to count and compute. Based on contemporary research understandings of how children learn mathematics, and developed by the Tangible Mathematics Learning Project in the Faculty of Education at Simon Fraser University, TouchTimes is intended for use in school and at home; in small groups, or in 1:1 pairings of a learner and a parent or teacher. Website: http://www.touchcounts.ca/touchtimes Reach us anytime at: tangible.mathematics@gmail.com

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