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Give babies a set of blocks, and they will build and order them, fascinated by the ways the edges line up. Children will look up at the sky and be delighted by the V formations in which birds  \nfly. Count a set of objects with a young child and then move the objects and count them again, and they will be enchanted by the fact they still have the same number. Ask children to make patterns with colored blocks, and they will work happily making repeating patterns—one of the most mathematical of all acts. Mathematician Keith Devlinhas written a range of books showing strong evidence that we are all natural mathematics users and thinkers.1 We want to see patterns in the world and to understand the rhythms ofthe universe. But the joy and fascination young children experience with mathematics are quickly  \nJo Boaler is a professor of mathematics education at Stanford University. The author of numerous books and research articles, she is the faculty director of Youcubed. This article is excerpted with permission of the publisher, Jossey-Bass/Wiley, from Mathematical Mindsets: Unleashing Students’Potential through Creative Math, Inspiring Messages and Innovative Teaching, by Jo Boaler. Copyright (c) 2015 by Jo Boaler. All rights reserved. This book is available wherever books and e-books are sold.  \nreplaced by dread and dislike when they start school mathematics and are introduced to a dry set of methods they think they just have to accept and remember.  \nIn Finland, one of the highest-scoring countries in the world on PISA (Program for International Student Assessment) tests, students do not learn formal mathematics methods until they are 7 years old. In the United States, students start much earlier, and by the time they are 7, they have already been introduced to algorithms for adding, subtracting, multiplying, and dividing numbers, and been made to memorize multiplication facts. For many students, their first experience of math is one of confusion, as the methods do not make sense to them. The inquisitiveness ofour children’s early years fades away and is replaced by a strong belief that math is all about following instructions and rules.  \nThe best and most important start we can give our students is to encourage them to play with numbers and shapes, thinking about what patterns and ideas they can see. In her autobiography, Sarah Flannery, who won Europe’s Young Scientist of the Year Award in 1999 for inventing a new mathematical algorithm, talks about the way she developed her mathematical thinking from working on puzzles at home with her dad, and how these puzzles were more important to her than all of her years of math class.2  \n28 AMERICAN EDUCATOR | WINTER 2018–2019  \nSuccessful math users have an approach to math as well as mathematical understanding that sets them apart from less successful users. They approach math with the desire to understand it and to think about it, and with the confidence that they can make sense of it. Successful math users search for patterns and relationships and think about connections. They approach math with a mathematical mindset, knowing that math is a subject of growth and that their role is to learn and think about new ideas. We need to instill this mathematical mindset in students from their first experiences of math.  \nResearch has shown definitively the importance of a growth mindset—the belief that intelligence grows and that the more you learn, the more mathematical pathways you develop. But to erase math failure, we need students to have growth beliefs about themselves and accompany them with growth beliefs about the nature of mathematics and their role in relation to it. Children need to see math as a conceptual, growth subject that they should think about and make sense of.  \nWhen students see math as a","cbCair0KePcxkafk","https://ap.wps.com/l/cbCair0KePcxkafk","pdf",351201,"English","# Developing Mathematical Mindsets\n## The Need to Interact with Numbers Flexibly and Conceptually\n## Early Childhood and Natural Engagement with Math\n## Growth Mindset and the Nature of Mathematics\n## Developing Mindsets Through Play and Sense Making\n## Fixed vs. Procedural Mindsets in Early Schooling\n## Number Sense","[{\"question\":\"Why do children enjoy mathematics before school?\",\"answer\":\"Children are naturally fascinated by patterns, counting, and relationships in the world. The text describes how play with objects, shapes, and puzzles supports conceptual engagement.\"},{\"question\":\"How does early schooling affect students’ mathematical attitudes?\",\"answer\":\"The text explains that early formal instruction focused on dry methods and memorization can replace curiosity with confusion, dread, and a belief that math is only about following rules.\"},{\"question\":\"What is a “mathematical mindset” according to the text?\",\"answer\":\"It involves approaching math with understanding, confidence, and the desire to search for patterns and connections. Students see math as a growth subject and their role as thinking and making sense.\"}]","Developing Mathematical Mindsets - The Need to Interact with Numbers Flexibly and Conceptually | PDF",18]