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In fact, 'proof and proving are fundamental to doing and knowing mathematics; they are the basis of mathematical understanding and essential in developing, establishing, and communicating mathematical knowledge' (Stylianides, 2007, p. 289).
"Play Works" designed by Roto Studio, a firm in Dublin, Ohio, is devoted to fostering not only literacy, but also mathematical understanding and what Dr. Hirsh-Pasek calls "cultural literacy": hence the "Mona Lisa".
But Jevons worked on the limits of his mathematical understanding, and many ideas that he foreshadowed were not developed until decades after his death.
Seventy-three percent of PTs witnessed improvement in their students' mathematical understanding, and the students did not readily give up on solving a mathematical task.
The original HIF was employed in control areas, and HIF has not been widely employed due to its level of mathematical understanding and the necessity of a good modeling of the system.
The episodes show that is possible to create a micro-learning ecology where regular students are seriously involved in mathematical discussions, ground their mathematical understanding and strengthen their relational framework.
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They found during math talk they could determine students' mathematical understandings and misunderstandings.
The six areas of learning are: mathematical understanding; scientific and technological understanding; human, social and environmental understanding; understanding the arts and design; understanding physical health and well-being; and understanding English, communication and language.
Technology supporting computations and representations (e.g., geometric figures, graphs of functions, or animations) provides interactive tools and makes key relations for mathematical understanding more transparent and tangible.
A pretest and posttest were created to contain questions that would test for mathematical understanding on equations and inequalities using Glencoe Math: Your Common Core Edition CCSS [5] as a resource.
This has implications for strategy use and mathematical understanding because, for example, reversing combinations (e.g., 5 and 2 into 2 and 5) is much easier to perform when manipulating multiple objects at once than by subsequently manipulating one object after another.
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