mistaks Mistakes are important 4 four for learning!
This critical advice for educators and parents from one Stanford University educator comes at a time when the push for getting it all correct seems to be the controversial focus of many school systems.
Mathematics Education professor Jo Boaler, presenting her work through a series of online courses and Webinars entitled “How to Learn Math: For Teachers and Parents” insists that labeling students with test scores and grades is detrimental to their educational development. She believes that all students can achieve in mathematics at high levels if we create environments that are conducive to learning and allow students to take risks, delve into complex problems, and make mistakes. Boaler wants teachers, schools, and high-stakes decision makers (including education officials at The White House) to understand the findings of a decade’s worth of research on the brain and learning that provide a clear picture of how to best support the mathematical development of children. I had the opportunity to listen in on a Webinar she held last week, entitled “Mathematics Teaching Ideas for the Common Core with Prof. Jo Boaler,” sharing strategies for effectively implementing these standards.
On being “smart”
Findings show that 15-year olds world-wide who took the PISA (Programme for International Student Assessment) and did well had a common attribute—they were learners who were confident in their abilities; showed evidence that they looked at the big picture and made connections when solving problems; and did not rely on memorization. “The fact that large proportions of students in most countries consistently believe that student achievement is mainly a product of hard work, rather than inherited intelligence, suggests that education and its social context can make a difference in instilling values that foster success in education.” OECD, 2012
Students who understand that hard work results in high-achievement are what Carol Dweck, author of Mindset: The New Psychology of Success, describes as having a “growth mindset.” This belief that “smartness” increases with hard work differs from a fixed mindset, which assumes that you are either smart (which cannot be changed) or you are not. The ideas compare as: “He’s good at math because he’s a smart kid” (fixed mindset) vs. “She’s good at math because she works hard” (growth mindset.) The notion that certain children (and adults) are smart at math, Boaler feels, is the root cause of underachievement in the United States. She calls it “the elephant in the classroom“—something that no one openly states in schools, yet most or many believe. Students with a fixed mindset have been found to focus on the grade and often shut down to understanding because they are “not good at math” and keep getting everything wrong. In studies she has conducted, students with a fixed mindset labeled “smart” have even been found to later on choose the easier, less-challenging problem over the more complex one.
The new evidence that has come out of brain growth research actually show that when learners with a growth mindset make mistakes in a trusting environment, synapses are fired off that help them learn more. It’s the struggle in trying to solve the problem that makes the mind grow. What’s even more interesting, is that when students get the answer correct brain studies have shown that absolutely no brain growth occurs. In “Unlocking Students Math Potential: 5 Research Results to Transform Math Learning,” Boaler states that “we want students to be making mistakes in math, and we should not be giving students work that they get mainly correct.” And in other research she has written, when a teacher simply writes on a paper “I believe that you can do this,” improvement in student achievement occurs.
The new Common Core standards are actually developed to promote thinking and understanding in mathematics. They give “more time for depth and exploration than the curricula it has replaced by removing some of the redundant methods students will never need or use.” (from “The Stereotypes that Distort How Americans Teach and Learn Mathematics” ) In prof. Boaler’s Webinar, she presented strategies for integrating Common Core into the mathematics classroom that support achievement for all students. They included:
- Provide plenty of time for mathematical discussions in order to give students access to a deeper level of understanding.
- Structure group works so that all students equally participate in the process, with clearly defined roles and multi-dimensional activities. (The book Designing Groupwork by Cohen and Lotan, presents the strategy of complex instruction. New edition pre-order for July 18.)
- Use diagnostic assessments that support engagement, help students improve, and are constructive vs. using grading systems that most often stop learning. Studies have show when grades stop and diagnostic comments are provided, achievement improves. She recommends that if grades are necessary, grade participation instead.
- Structure mathematical problems to be complex in nature and give students a space to learn. When students are continually provided problems that are a series of closed questions, students do not grow and develop into mathematical thinkers. The understanding becomes that math class is not a place to think, but to perform. Students need to have opportunities to learn something vs. having to continually demonstrate what they know.
- Time tests are damaging and do not develop mathematical thinking. This information has even been published by the NCTM (National Council on Teaching Mathematics) in their April 2014 newsletter.
- Tell students that mistakes are great. In Make Math Fun, Boaler encourages parents to share the research with their children. “It is important both to celebrate mistakes and tell children their brain is growing when they make them.“
To learn more about Jo Boaler’s work and her quest to get students to believe that they can achieve high levels in mathematics and engage in mathematics, visit her non-profit organization entitled YouCubed.
Image courtesy of KROMKRATHOG/ FreeDigitalPhotos.net.