Sunday, October 30, 2016

GROWTH MINDSET IN MATHEMATICS (II) - Developmental Mathematics

Drs. Benken and Li, along with Jorge Ramirez and Scott Wetendorf, conducted a study concerning students taking developmental mathematics courses in a large public comprehensive university setting. Their findings suggest a need for
re-evaluation of developmental mathematics courses to include student outcomes that focus on attitudes about mathematics in addition to content and skills.”
They note that
"math anxiety taxes and competes with resources that are normally used for working memory,"
thus impeding development of a positive mathematical identity.

Carnegie Foundation estimates that 60 percent of the nation’s 13 million community college students are unprepared for college-level courses and must enroll in at least one developmental course (see the article Pathways to Improvement). Currently 27% of incoming California State University students arrive unprepared for college-level mathematics, as noted in the recent CSU Academic Senate Quantitative Reasoning Task Force Report. These staggering numbers illustrate a broader problem of effectiveness of mathematics education in the United States (see the Slate Article, What's Wrong with Math Education in the US). According to the most recent results of the Program for International Student Assessment (PISA), the U.S. 15-year old students place 35th out of 64 tested countries in mathematics proficiency.

The Carnegie Foundation programs utilize the growth mindset principles specifically to developmental mathematics in a framework called Productive Persistence. There are several excellent resources on their website, for example:
You can also watch an excellent lecture on productive persistence by Dr. Rachel Beattie
Finally, please explore an excellent website With Math I Can. Watch this emotional video describing importance of students’ mindset in mathematics
and sign this pledge to help every student succeed in math.

Tuesday, October 25, 2016


This blog is intended as a resource for STEM faculty interested in applying the new psychology of success and growth mindset in their teaching practices (learn more about the growth mindset on Carol Dweck's Mindset Online) Research demonstrates that
thinking about intelligence as changeable and malleable, rather than stable and fixed, results in greater academic achievement.
(Source: American Psychological Association)
Very recently, Yeager Group at UT Austin published groundbreaking results suggesting that teaching freshman students so called lay theory, which conveys a message that
challenges in the transition to college are common and improvable and, thus, that early struggles should not suggest a permanent lack of belonging or potential,
improves retention and significantly reduces achievement gap when delivered to entire incoming freshman class. (Source: Proceedings of the National Academy of Sciences). These results generated national attention with editorials in the Wall Street Journal and the New York Times.

The growth mindset concept is pertinent to specific psychological interventions as well as to a host of teaching methods, advising approaches, institutional policies (such as academic probation) and an overall "institutional culture." There is increasing evidence that growth mindset is key to teaching STEM, as described in this US News & World Reports article. Please follow this blog for resources and insights for learning about and applying growth mindset in higher education.


Thomas Westenholz, the founder of Positive Edge Program, authored a short article on how to use growth mindset to motivate students, including a list of five easy ways to use growth mindset in improving students’ motivation.

Here, I linked each of Westenholz' five “easy ways” to various related on-line resources. Many of these resources would be great to show to your students.
  1. Introduce growth mindset in your classes: TED Talk by Eduardo Briceno, and Carol Dweck speaks at Stanford University.

  2. Use mistakes as a learning opportunity: Celebrate Mistakes, an on-line lesson for teachers

  3. Administer positive praise: A Study on Positive Praise and Mindsets
    Disclaimer: while growth mindset emphasizes “process over product,” praising effort alone or telling students "you can do anything" does not improve performance. Please see an excellent Edutopia article on “false growth mindset.”

  4. Show students examples of past failures: Famous Failures

  5. Help students find value in learning: Trevor Ragan's The Learning Machine


Malcolm Ocean is the founder of a company called “Complice,” advertised as a “startup changing how people relate to their ambition.” He offers an interesting essay on “applied growth mindset”, in which he recognizes the difference between knowing what growth mindset means and using it consistently in your learning. He suggests that applying growth mindset consistently requires practice, which can be done in part by shifting the language you use from fixed to growth mindset.

There are several on-line resources useful to reinforce growth mindset language:
Finally, I encourage you to read an essay by the Lenox Academy Assistant Principal, commenting on the value of building growth mindset culture in schools, and watch the short video below of teachers describing their experiences teaching with a growth mindset program called Brainology.


Growth mindset has a special place in mathematics education.  Fostering growth mindset reduces stereotype threat and can help narrow both racial and gender achievement gaps.  For example, recent PLOS ONE article suggests that gender-dependent decisions to drop out of STEM (following a calculus I class) might be dictated by beliefs rather than abilities.  See also this introduction to stereotype threat on dePaul University's Learning in Progress.

In the November issue of Scientific American, Dr. Jo Boaler, Professor of Mathematics Education at the Stanford Graduate School of Education, argues that
An emphasis on memorization, rote procedures, and speed impairs learning and achievement in mathematics.  
Dr. Boaler is a cofounder of Youcubed, a company providing large array of growth mindset resources for K-12 teachers - some of them certainly applicable to college-level mathematics.
The video below is an excerpt of an interview with Carol Dweck and Greg Walton in which they discuss some strategies for and effects of encouraging a growth mindset in learners.

Drs. Carol Dweck and Greg Walton talk about Growth Mindset from Character Lab on Vimeo.