Math Mindsets

Lindsay Sirois, Student Achievement Officer The Literacy and Numeracy Secretariat

Math

I’m not very good at math.

Mindsets We currently live in a society where it is acceptable to be math phobic. We have embraced a culture of anxiety, stress and avoidance of mathematics. There is safety in this cohort, as many students, teachers, administrators, parents and the general population are members. How did this happen to a subject that the ancient Greeks viewed as beautiful and the key to unlocking the mysteries of the world? When and why did we develop such a closed mindset to learning mathematics? What are the implications for the students in our schools? As educators, we have the most powerful impact on student attitudes and achievement, and yet there is open admission at times of fearing mathematics. Many researchers are investigating this phenomenon. The consensus is that a closed or fixed mindset is an important element of the problem. Carol Dweck released a ground breaking book in 2006, Mindset: The New Psychology of Success. According to Dweck’s research, a person with a fixed mindset believes that they are either smart or not. People who have a fixed mindset believe they fail at tasks or make mistakes because they just aren’t smart enough. They may develop traits such as avoidance of challenges, problem solving evasion and lack of perseverance. In traditional mathematics classes, we have placed value on the fastest correct answer. This is a dangerous practice as it reinforces the concept of intelligence and the ability to learn as being fixed. Dweck’s research found that a fixed mindset is evident across all achievement ranges, with the highest proportion found in high achieving girls (Boaler, 2013). Educators and parents inadvertently contribute to this problem. How often have we heard, “You are so smart! Look at how fast you answered the question!” 6

Principal Connections • Fall 2014 • Volume 18 • Issue 1

When a student fails at a task or isn’t quick enough, a student (or adult) views this as a failure and surmise that they are not smart enough. We often reinforce this mindset in the classroom by ability grouping in mathematics problem solving settings. Students are highly perceptive to the fact they are judged and sorted on their abilities. Study after study indicates that this practice is deeply damaging and creates a fixed mindset in students (Boaler, 2013). In fact, the research shows, “mathematics classrooms influence to a high and regrettable degree, the confidence students have in their own intelligence. This is unfortunate both because math classrooms often treat children harshly, but also because we know there are many forms of intelligence and ways to be smart and math classrooms tend to value only one.” (Boaler, 2008) The opposite of a fixed mindset is a growth mindset. People who have a growth mindset demonstrate the following characteristics: embrace challenges, persist when faced with setbacks, see effort as the key to mastery, embrace constructive criticism and find inspiration in the success of others (Dweck, 2006). Failure is seen as an opportunity for growth, to learn and improve. A growth mindset can be taught to students and encouraged by the types of tasks students are provided. If students are given math questions that are closed and require right and wrong answers, the message that is communicated to students is that only a correct answer is valued. Offering more open tasks allows students to see the possibilities of high achievement and the opportunity to improve (Boaler, 2013). Jo Boaler, Professor of Mathematics at Stanford University, has applied Carol Dweck’s research to the study of mathematics. She is particularly concerned with the ways teachers treat mistakes in mathematics. The research is

I need to find another way to solve this problem.

Let me try to solve this by substituting other numbers.

clear – mistakes in mathematics are powerful opportunities to learn and grow. Brain research shows a plasticity of the brain to learn like a muscle. When a mistake is made and then used as a teaching point, new synapses are created. When an answer is correct, nothing happens. No new synapses. And for many students the reinforcement of a fixed mindset. One of the most powerful things a teacher can do to foster a growth mindset is to take the time to look at wrong answers. This is where the key learning in mathematics lie and it strengthens a growth mindset by modelling perseverance, effort and learning from criticism. Boaler states, “students and teachers should value mistakes and move from viewing them as learning failures to viewing them as learning achievements.” (Boaler, 2013)

repositioning their understanding of a topic based on what information their students provide them. This is a position of a growth mindset. The extensive learning by teachers in Ontario around problem-based learning in mathematics places the teacher as a co-learner along with the students. Often, even with in-depth preparation for a three-part lesson in mathematics teachers will be fascinated by a strategy a student used that they didn’t expect. When a teacher feels they hold all the knowledge and it is their job to impart it to students it takes them away from a growth mindset. They are less open to new learning and to seeing mistakes and constructive criticism as a key tool in teaching.

Why is mathematics such a polarizing subject? Why is it acceptable to dislike math and be open about it? It is very rare that someone would admit to disliking reading or brag about not being good at it. This bravado is a deflection or a shield. If one states they are terrible at math, then they can’t be judged if asked to do it on demand. When splitting a bill in a restaurant, when figuring out how much tile to buy at the home improvement store and most unfortunately in schools. Many educators today remember math instruction as a time to learn algorithms and apply those procedures. Evaluation and assessment was based almost entirely on how well a student could recall and apply those procedures. Remember racing to the blackboard and waiting with chalk in your sweaty palm as the whole class watched and waited until you found out which times table you would be asked to record as fast as you could with the class watching? As Carol Dweck would say, we believed math was about how good or correct we were, not on what we learned and how much growth was exhibited. This message is still being heard today. When teachers participate in professional development, the idea is that teachers are always learning and

The same is true for educational leaders. A principal, who feels they don’t need to explore what makes an effective math program or doesn’t challenge traditional practices, is modelling those beliefs for staff. As a leader in an educational institution it is imperative that in the subject of mathematics, a growth mindset be first and foremost. A leader who colearns with staff and students is one who demonstrates the importance of being a lifelong learner. Principals who exhibit a growth mindset in mathematics are not always mathematicians but are people who are open to new learning. A Toronto principal commented recently about a math lesson she cotaught, “It was a disaster! It became clear very quickly that the students were well beyond the concepts. We had nothing to consolidate at first – but then we realized that it was OK. We didn’t get the results we were expecting, but we were able to use the student work as a starting point to further the student learning. We agreed that it was a good learning opportunity. We should expect more from the students and let them struggle rather than providing easy work during a co-learning experience. I think our ability to learn from this is vastly different than a Principal Connections • Fall 2014 • Volume 18 • Issue 1

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few years ago. Back then, we would have given up and said problem-based learning wasn’t effective. Now, we realized that we weren’t asking the right questions of our kids and pushing them hard enough.” In the past 10 years, there has been a remarkable change in the way Ontario schools treat mathematics. It has become a focal point of instruction. The mindset has gone from fixed to optimistically a growth mindset. Resources flow steadily into the hands of eager teachers who flock to social media to share what their students have come up with in class. Conferences like the annual Ontario Association of Mathematics Educators (OAME) are well attended, a prized event to hear researchers from around the world speak about mathematics and what can be done to help support teachers and students. So what can a principal who is fearful or phobic about math do to overcome this fear? It starts by admitting a fixed mindset about mathematics. Admitting that one is intimidated by math and that there is much to learn is a major step towards a growth mindset. Positioning oneself as a co-learner in a professional learning community or joining in a coteaching opportunity is an excellent way to break the ice. We don’t learn in isolation, and that is the wonderful thing about schools – there is a built-in community that embraces learners at all entry points. We need to change the culture of teaching and learning mathematics in Ontario. Jo Boaler was a key note speaker at the OAME 2014 conference. She received a standing ovation when she said that speed and silence are not signs of effective math learning. Math is exciting and frustrating and challenging. We need it to be all of these things and more. We need our students to learn to love math and persist in the face of wrong answers. In order for this to happen, adopting a growth mindset in mathematics is essential.

Thousands of Ontario students are returning to high school to upgrade their math skills in order to access college and university courses that value STEM skills. Future employment is at jeopardy for our young minds who don’t believe they are capable of taking pre-requisite courses to enter their field of interest. The Toronto Star reports that students are not encouraged to take these courses. The ‘lacklustre’ pursuit of STEM education is a crisis in the making (Nursall, 2013). Students were interviewed and commented that had educators stressed the importance of mathematics to their future they would not have to return to high school to upgrade their mathematics skills, while placing their future plans on hold. School is about learning, not about how quickly one grasps the concepts. So when a student receives a mark or evaluation, is it fair to ask: Are they being judged on the product or the journey? The connection can be made to the educator’s beliefs in their students’ abilities. When an educator has a fixed mindset about a student’s ability to learn, it narrows the opportunities for the student to achieve. When the educator believes that everyone’s ability to learn can grow and they provide the opportunities, students will achieve at high levels (Boaler, 2013).

References Ashcraft, M. H. (2002). Math Anxiety: Personal, Educational, and Cognitive Consequences. American Psychological Society, 181-185. Boaler, J. (1993). The Role of Contexts in the Mathematics Classroom: Do they Make Mathematics More "Real"? For the Learning of Mathematics, 12-17. Boaler, J. (2012, May). Don't let maths muddle you. Retrieved May 2014, from http://yano.co.uk: http://yano.co.uk/2012/05/dont-let-maths-muddle-you-2/ Boaler, J. (2012). Timed Tests and the Development of Math Anxiety. Education Week, 1-3. Boaler, J. (2013). Ability and Mathematics: the mindset revolution that is reshaping education. Forum, 143-152. Boaler, J. (2014). The Stereotypes That Distort How Americans Teach and Learn Math. The Atlantic, 1-5. Dweck, C. (2006). Mindset: The New Psychology of Succes. New York: Ballantine Books. Nursall, K. (2013, October 8). High School Students not taking science or math costing Canada millions: report. Toronto, Ontario: The Toronto Star. Popova, M. (2014, january 29). Fixed vs. Growth: The Two Basic Mindsets That Shape Our LIves. Retrieved May 5, 2014, from Brainpickings: www.brainpickings.org