Mathematics can pose significant challenges and obstacles to students who are in the early phases of their studies at university (Hernandez‐Martinez and Williams, 2013). This also includes engineering students, even though they, along with the rest of the engineering community, believe that the study of mathematics is indispensable to the study and practice of engineering (Sazhin, 1998). Students find the transition to university mathematics difficult for a number of reasons. One of these reasons is the lack of mathematical resilience, the subject of my discussion today. For this, I shall be relying on the work of Sue Johnston-Wilder and Clare Lee, who have popularized the concept of mathematical resilience within pre-university mathematics education.
An individual is said to be resilient if they achieve “good outcomes in spite of serious threats to adaptation or development”(Masten, 2001). Previously, educators and researchers believed that resilience was an attribute that only a few people possessed. However, Masten’s studies have since debunked this notion. Instead, her studies posit that, far from being exclusive, resilience is an ordinary trait that any individual can acquire. This new understanding renders invalid prevailing deficit models of intellectual ability. Indeed, using this new understanding, Yeager and Dweck (2012) have shown that the resilience of students improves when they are redirected to see intellectual ability as “something that can be developed over time with effort, good strategies, and help from others.”
Johnston-Wilder and Lee use the construct of mathematical resilience to describe “a learner’s stance towards mathematics that enables pupils to continue learning despite finding setbacks and challenges in their mathematical learning journey” (Johnston-Wilder and Lee, 2010). Often, learning mathematics is associated with negative emotions, such as avoidance, anxiety and helplessness (Lee and Johnston-Wilder, 2017). These negative emotions can be exacerbated by poor mathematics teaching methods, enduring cultural beliefs that mathematics is only for the gifted few, and fixed mindset beliefs that if someone is not good at mathematics, then there is no way they can improve their mathematical ability, even if there is good teaching and support (Lee and Johnston-Wilder, 2017). Mathematical resilience challenges these negative notions, and seeks to engender within the minds of learners the knowledge that that they can grow their mathematical abilities (Lee and Johnston-Wilder, 2017).
Characteristics of mathematically resilient students
There are four characteristics for students with mathematical resilience. These are growth mindset, personal value of mathematics, knowing that mathematics requires struggle and knowing how to recruit support in pursuing (Lee and Johnston-Wilder, 2017).
Growth mindset (Yeager and Dweck, 2012): The notion of growth mindset suggests that the brain is malleable. Consequently, students with a growth mindset believe that their mathematical abilities improve with practice, persistence and support from others (this includes peers and academic staff).
Value: Mathematically resilient students believe that mathematics is a valuable subject and is worth studying. Such values can be fostered within engineering by making explicit the connections between mathematics and engineering theory and practice.
An understanding of how to work at mathematics: Mathematically resilient students are aware that one has to persevere if they are to make progress in learning mathematics. They are aware that everyone experiences difficulties and challenges when learning mathematics; that mistakes are part of the learning process, and that one has to persevere and learn not to succumb to the negative emotions that are a part of learning something new.
Knowing how to gain support: Mathematically resilient students are aware that learning mathematics can be challenging, and that sometimes they need to seek support in order to get ahead. They are also aware of the support structures for mathematics within and outside their university. They are also aware, and adept, at constructively working and studying with each other.
Lessons for mathematics educators
Teaching mathematics is not just about delivering subject content. It is also about developing a supportive, inclusive, collaborative learning environment that challenges and encourages students to do the best they can. Indeed, achieving this is the holy grail of learning and teaching in engineering mathematics.
HERNANDEZ‐MARTINEZ, P. & WILLIAMS, J. 2013. Against the odds: resilience in mathematics students in transition. British Educational Research Journal, 39, 15.
JOHNSTON-WILDER, S. & LEE, C. 2010. Mathematical Resilience. Mathematics Teaching, 218, 38-41.
LEE, C. & JOHNSTON-WILDER, S. 2017. Chapter 10 – The Construct of Mathematical Resilience. In: XOLOCOTZIN ELIGIO, U. (ed.) Understanding Emotions in Mathematical Thinking and Learning. San Diego: Academic Press.
MASTEN, A. S. 2001. Ordinary magic: Resilience processes in development. American psychologist, 56, 227.
SAZHIN, S. 1998. Teaching mathematics to engineering students. International Journal of Engineering Education, 14, 145-152.
YEAGER, D. S. & DWECK, C. S. 2012. Mindsets That Promote Resilience: When Students Believe That Personal Characteristics Can Be Developed. Educational Psychologist, 47, 302-314.