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Chris Harrow

Demonstrating Competence by Making Mistakes - National Council of Teachers of Mathematics - 0 views

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    "Demonstrating Competence by Making Mistakes"
Chris Harrow

Fluency Without Fear - 0 views

  • The English minister’s mistake when he was asked 7 x 8 prompted calls for more memorization. This was ironic as his mistake revealed the limitations of memorization without ‘number sense’. People with number sense are those who can use numbers flexibly. When asked to solve 7 x 8 someone with number sense may have memorized 56 but they would also be able to work out that 7 x 7 is 49 and then add 7 to make 56, or they may work out ten 7’s and subtract two 7’s (70-14). They would not have to rely on a distant memory. Math facts, themselves, are a small part of mathematics and they are best learned through the use of numbers in different ways and situations.  Unfortunately many classrooms focus on math facts in unproductive ways, giving students the impression that math facts are the essence of mathematics, and, even worse that the fast recall of math facts is what it means to be a strong mathematics student.
  • I learned math facts through using them in different mathematical situations, not by practicing them and being tested on them.
  • Math facts are a very small part of mathematics but unfortunately students who don’t memorize math facts well often come to believe that they can never be successful with math and turn away from the subject.
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  • For about one third of students the onset of timed testing is the beginning of math anxiety (Boaler, 2014).
  • when students are stressed, such as when they are taking math questions under time pressure, the working memory becomes blocked and students cannot access math facts they know (Beilock, 2011; Ramirez, et al, 2013).
  • Many people will argue that math is different from other subjects and it just has to be that way – that math is all about getting correct answers, not interpretation or meaning. This is another misconception. The core of mathematics is reasoning – thinking through why methods make sense and talking about reasons for the use of different methods (Boaler, 2013).
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