In the U.S. many folks perceive there to be a "math ability" that one either has or does not have (

see Uttal's research). This actually does much harm to how we structure mathematics learning and limits achievement among students. As a teacher I constantly sought ways to engage students in making sense of mathematical concepts and relationships and believe that with few exceptions the majority of people can learn the mathematics in the K-12 curriculum. This was shown to be true among my students, many of whom went from believing mathematics to be a black hole of nonsensical symbols and rules to realizing the logical structure of mathematics and developing the power to reason mathematically to solve problems. This was possible in large part because I felt they were capable of making significant improvements to their knowledge of mathematics.

Important research from Carol Dweck and her colleagues at Stanford has shed light on the relationship between one's "mindset" toward ability (mathematical or otherwise) and the actions to which this leads in terms of opportunities to learn and feedback to learners. Ultimately, these have serious consequences on learning outcomes. The idea is this: if one believes ability to be fixed - a fixed mindset - this will lead to actions that a) serve to identify who is high-ability and not and b) provide feedback that reinforces ability status, directly and indirectly. The result - a few students are "smart" in mathematics while many others are not. The smart ones must strive to retain that labeling through "looking smart" (often at any cost) while the others see no reason to work at learning what they are being told is beyond their ability. The result is that actual learning among all students suffers.

What Dweck and colleagues found is that changing this script can have pronounced effects. Taking a "growth mindset" that views ability as derived more from effort than some innate quality leads to very difference choices about learning environment and feedback to learners. If one believes most all students can learn mathematics, those who are struggling to do so are in need of support. Feedback such as, "if you work hard at this you will improve" leads to greater motivation and, as their research has shown, greater success. For students who do well with mathematics, the feedback in the growth mindset tells them, "you made a good effort at this and have done well." This is critical because when the mathematics does get challenging (and it will!), these students will persist, putting in more effort, rather than look for ways to simply maintain their "looking smart" status (e.g., shortcuts, cheating, or bowing out).

See here for more about this work and suggestions for teachers and parents.

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