I don’t get it…..yet March 7, 2016Posted by Editor21C in Engaging Learning Environments, Primary Education, Secondary Education, Teacher, Adult and Higher Education.
Tags: curriculum, learning and the brain, learning theories, mathematics education, teacher education
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by Karen McDaid
I love mathematics and not just a little! I really love mathematics, but when I recall my mathematical school experiences, I do so with a fairly dispassionate attitude. Don’t get me wrong, it wasn’t that I disliked school mathematics. On the contrary, I quite enjoyed learning and grasped most mathematical concepts fairly quickly, which meant I met with a small but consistent degree of success in mathematics. I did alright in standardised tests, was about middle in the class, but I was not ‘smart’ in an academic sense, or at least I didn’t think so. In saying that, I was always more than happy to persevere with a challenging problem and wouldn’t let anything get the better of me.
On the other hand, Paula White, who became my friend in Year 4, was my antithesis. I thought Paula was very ‘smart’. She was awarded first in class many times throughout primary school. I admired her greatly and aspired to be as ‘smart’ as her. However, my observations of her as a learner through the years, even to my young self, were puzzling. Although she was top of the class in most of the mathematics tests we undertook, when facing a challenging mathematical problem where the solution was not immediately obvious, often the first words she said were, “I don’t get this” or “This is stupid”. By Year 8 Paula had slipped into a cycle of avoidance and her achievements in primary school were not reflected in high school. It seems to me now that she was so caught up in proving her capabilities and successes that she forgot, or couldn’t embrace, the opportunity to learn. I frequently wondered what made us so different.
Many years later as a teacher I noticed the same traits in several of my Stages 2, 3 and 4 (Years 4 to 8) students in the first few weeks of the year. Some were keen to tackle challenging problems or at least persevere with problems; others used Paula’s mantra to indicate their displeasure. What I found interesting was that there was absolutely no correlation between my primary and high school students’ defeatist attitude and their actual ability in mathematics. I knew they could achieve if only they would try. In more recent years, while teaching Mathematics to primary pre-service teachers at university I often heard Paula’s “I don’t get this” from the adult students with whom I was working. Many also subscribed to society’s misconception that a person is either born with a mathematical ability or they are not. Unfortunately, this misconception has created a culture where it is socially acceptable for someone to openly proclaim that they are ‘no good’ at mathematics and where the belief is that intelligence is fixed and unchangeable (Boaler, 2013).
So began my quest to understand what influences attitudes towards, and self-efficacy in mathematics. My aim was to see if it was possible to develop resilience, motivation and foster positive self-efficacy in my students and in the primary pre-service teachers with whom I work. I became particularly interested in the research of Carol Dweck at Stanford University into fixed and growth mindsets. Dweck (2006) describes a fixed mindset as a significant impediment to learning as it affects the ability of the learner to ‘believe’ in themselves and thus impacts their cognitive development. She also defines mindsets as a set of powerful beliefs that are in the mind and as such are changeable. Dweck argues that those who have a tendency towards a fixed mindset are rarely willing to persevere with challenges for fear they will expose their perceived deficiencies. She believes that this attitude turns people into ‘non-learners’ and an examination of the brain-waves of people with a fixed mindset demonstrated a loss of motivation when faced with challenging problems (Dweck, 2006). On the other hand, people who have a growth mindset are more open to challenges, give up less easily and believe that intelligence is malleable.
I found Dweck’s work fascinating and when reflecting on Paula’s behaviour, I realised that she had exhibited many fixed mindset behaviours as did some of my students. A study into motivation conducted by Blackwell, Trzesniewski and Dweck (2007) followed hundreds of students transitioning to 7th grade. The study found that students who had been identified as having a growth mindset were more motivated and achieved at a higher level than those with a fixed mindset in mathematics and the gap between them continued to increase over the following two years. When a growth mindset intervention was implemented in further studies, Blackwell et al (2007) and Good et al (2003) found that the achievement gap reduced further and in particular that the gap between girls and boys was significantly reduced.
In recent times there has been a lot of talk about brain plasticity, and both Dweck and Boaler acknowledge that intelligence is malleable. My challenge has been to move the immovable from ‘I don’t get it’ to believe that they can ‘get it’. So, how did all this knowledge contribute to my teaching and learning objectives in the mathematics classroom? Well it didn’t, at least not in the beginning. While my teaching philosophy has evolved over a number of years, I have always strived to create a classroom culture where students were learners, not just in name, but really enthusiastic, motivated and driven learners. No doubt this is every teacher’s goal! As such, I set high expectations and wanted students to feel safe to be risk takers. My teaching philosophy mirrored a growth mindset classroom.
So I was working within a growth mindset, unfortunately, that was just it! ‘I’ was working using a growth mindset. While I had taken the time to set up a classroom culture with my school students, I didn’t communicate my philosophy to my university students. I didn’t expect the school children to know what was in my mind; I clearly communicated and worked with them to create a safe learning space. What made me think that my university students would know what was on my mind? They didn’t know about the classroom culture that I was striving to achieve, yet they were part of the classroom community too.
“Just the words “yet’ of “not yet,” we’re finding, give kids greater confidence, give them a path into the future that creates greater persistence”.
(Carol Dweck, 2014)
While teaching time is finite, instead of rushing headlong into content in the first tutorial, I have found that spending twenty minutes setting up our classroom culture has been valuable for student engagement and for students’ self-efficacy in mathematics. I communicate my teaching philosophy and acknowledge that ‘we’ create the culture of the learning space. We discuss how our attitudes can set us up for success and take five minutes in small groups to discuss a time when we learned something well through hard work. We explore the notion of fixed and growth mindset and malleable intelligence. We set high standards for our learning and revisit this notion throughout the semester. No question is ‘dumb’ and mistakes are actively encouraged. I have learned to change my thinking and my language and that praise should be connected to behaviour rather than achievement.
This is my story, which changes according to student dynamics and as I continue to learn and adapt my teaching. I don’t claim that it will work for everyone, but I have seen a marked improvement in the effort and determination with which all students engage with the mathematics activities in class. Students have eagerly embraced replacing the statement ‘I don’t get it’ with ‘I don’t get it yet’. But one of the greatest and most powerful transformations is when you see a student who might have given up in the past, collaborate to work really hard on a mathematical problem and then suddenly they see the value in their effort and shout ‘I get it now!’
Blackwell, L.S., Trzesniewski, K.H., & Dweck, C.S. (2007). Implicit theories of intelligence predict achievement across an adolescent transition: A longitudinal study and an intervention. Child Development, 78. 246-263, Study 1.
Boaler, J. (2013). Ability and Mathematics: the mindset revolution that is reshaping education. FORUM, 55(1), Retrieved from http://www.youcubed.org/wp-content/uploads/14_Boaler_FORUM_55_1_web.pdf on 12th November 2015.
Dweck, C.S. (2006) Mindset: the new psychology of success. New York: Ballantine Books.
Dweck, C. S. (2014). The power of believing that you can improve. [Video/TED talk] Retrieved from https://www.ted.com/talks/carol_dweck_the_power_of_believing_that_you_can_improve/transcript?language=en
Good, C., Aronson, J., & Inzlicht, M. (2003). Improving adolescents’ standardized test performance: An intervention to reduce the effects of stereotype threat. Applied Developmental Psychology, 24, 645-662.
Growth mindset Videos
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