In the article 5-Year-Olds Can Learn Calculus, the author Luba Vangelova, explains how children can be introduced to mathematics with the help from the more advanced fields of mathematics. Vangelova sparks the article by reviewing the common progression that used in the American education system today. The basics of counting, addition, subtraction, multiplication, division learned as in grammar schools. Then the transition to algebra, geometry, trigonometry and calculus which is considered the highest level of math in our current system in the United States of America. Math educator and curriculum designer Maria Droujkov stated that this common progression “has nothing to do with how people think, how children grow and learn, or how mathematics*…show more content…*

The idea is that rather than learning in a linear manner on the average sequential track, the student should use their natural instincts to learn mathematics and approach thesubject with a sense of play, spontaneity and adventure. Droujkova stated: “Studies [e.g., this one, and many others referenced in this symposium] have shown that games or free play are efficient ways for children to learn, and they enjoy them. They also lead the way into the more structured and even more creative work of noticing, remixing and building mathematical patterns.” The author explains that finding the appropriate path is dependent upon appreciating the ignored fact that “the complexity of the idea and the difficulty of doing it are separate, independent dimensions,” She goes on to state “Unfortunately a lot of what little children are offered is simple but hard—primitive ideas that are hard for humans to implement,” because they readily tax the limits of working memory, attention, precision and other cognitive functions. An example used was Building a trench with a spoon, which is a military punishment that involves many small, repetitive tasks that can be compared to doing 100 two-digit addition problems on a typical worksheet as made aware by

The idea is that rather than learning in a linear manner on the average sequential track, the student should use their natural instincts to learn mathematics and approach thesubject with a sense of play, spontaneity and adventure. Droujkova stated: “Studies [e.g., this one, and many others referenced in this symposium] have shown that games or free play are efficient ways for children to learn, and they enjoy them. They also lead the way into the more structured and even more creative work of noticing, remixing and building mathematical patterns.” The author explains that finding the appropriate path is dependent upon appreciating the ignored fact that “the complexity of the idea and the difficulty of doing it are separate, independent dimensions,” She goes on to state “Unfortunately a lot of what little children are offered is simple but hard—primitive ideas that are hard for humans to implement,” because they readily tax the limits of working memory, attention, precision and other cognitive functions. An example used was Building a trench with a spoon, which is a military punishment that involves many small, repetitive tasks that can be compared to doing 100 two-digit addition problems on a typical worksheet as made aware by

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