As parents we encourage our children to try many different activities such as sport and music. As they learn the skills needed for each activity, we are there to provide support and offer encouragement when it becomes challenging. When it becomes difficult, we hope that they don’t give up, instead they make a commitment to overcome the challenge through patience, persistence and practice. Success happens when they overcome each challenge and they feel a sense of accomplishment.
How well our children overcome these challenges depends on their mindset. When faced with a challenge, or indeed failure, students with a growth mindset increase their effort to improve and complete the task successfully. The lessons they learn along the way to success provide them with the toolkit they need to help them achieve success throughout life. “The Iceberg Illusion” is a great illustration that shows us that success is just the tip of the iceberg, it is what is below the surface that defines our success. This is what we should be most proud of. Success in maths requires the use of the same toolkit.
One barrier many of our boys have is a fixed mindset about mathematics. How often have you heard your son say, “I just can’t do maths”, “I am not a mathematical kind of person”, or words to this effect. Our challenge as teachers and parents is to overcome this barrier, to encourage our boys to have self-belief and the idea that everyone can learn even the most complex of mathematical procedures, if they are prepared to persevere. Teaching a growth mindset creates motivation and productivity. Boys with a growth mindset believe that effort creates success, talents can be developed, and great abilities can be built over time. They are resilient and view mistakes as an opportunity to develop and think about how they learn. All of which are attributes of a lifelong learner.
The power and Value of Mistakes
Many mistakes are made in a maths class. It is how our boys deal with those mistakes that determines ongoing success in maths. Mistakes are opportunities to learn and improve. Mistakes cause our brain to spark and grow. Psychologist Jason Moser studied the impact that making mistakes has on the brain (Moser et al, 2011). The brain has two potential responses when we make a mistake. The error-related negativity (ERN) response is increased electrical activity when the brain experiences conflict between a correct response and an error. Error positivity (Pe) response is a brain signal reflecting conscious attention to mistakes. This occurs when there is awareness that a mistake has been made and conscious attention is given to the mistake. Moser’s study showed that we don’t have to be aware of making a mistake for our brain to spark. At a time of struggle, our brain is challenged, and this is the time when the brain grows the most.
Research has shown that the brain reacts with greater ERN and Pe responses when a mistake is made than when the answer is correct. More importantly, brain activity is greater following a mistake in individuals who have a growth mindset than for individuals with a fixed mindset. Those with a growth mindset have a greater awareness of errors than those with a fixed mindset, so they are more likely to review and correct errors. Mistakes are not only opportunities for learning, as we consider the mistakes, but also times for our brain to grow, even if we don’t realise a mistake has been made. Mistakes should be valued and not seen as a weakness.
Studying for Mathematics
Studying is not cramming for the upcoming maths exam. There is a need to be motivated to study mathematics effectively. That is, setting aside time for ongoing review of learning the mathematical concepts and techniques taught. So, how do you study mathematics?
1. Once a week, read through your notes and textbook carefully.
2. Take notes, writing a summary of the ideas you remember from class or from what you are reading. Make notes in your summary book.
3. Once you’ve finished your summary book, close the summary book, take a blank sheet of paper and write an explanation of the ideas as if you were teaching a friend. Writing and rephrasing the ideas forces you to clarify the ideas in your own mind. It is also extremely useful for exposing gaps in your understanding, which you can then remedy by rereading the relevant parts of the text and/or asking questions.
Learning mathematics requires the patience to take small steps and make certain that you understand each step before continuing. Many small steps add up to a large result.
Some more tips for Success in Mathematics
1. Do your homework. Don’t ever think of homework as a choice. It’s the most important way that you practice and master the concepts taught in class. Have a regular time and place for completing homework and revision.
2. Get help fast. If something is difficult, seek as much help as possible as quickly as possible. You can access help from many places. You could go to your notes or textbook, ask a friend, search for tutorials from your online textbook or via the internet. Teachers are also available for extra help. Straighten out misunderstandings before they start to snowball.
3. Don’t swallow your questions. Questions are the vehicle by which we learn. If you have one, ask it. Chances are that many of your classmates have the same question. Saying it out loud will help you, your classmates, and the teacher. Asking good questions is a lifelong skill, and school is a safe place to practice. The more questions we ask, the easier it gets.
4. Analyse and understand every mistake. Our culture has become perfection- focused, and it’s tempting to ignore our mistakes. Students want to pass over a mistake made on homework or a test, to just let it go. But it’s important to fix mistakes and understand why they were made; otherwise we’re doomed to repeat them. Take time to figure out the thinking behind a mistake and figure out how to do it right.
5. Find a friend to be your study partner. We all have reasons for legitimate absences. So, find a friend who will take good notes when you’re gone and will call that night to fill you in on the homework. This is good practice for the real world, where building positive relationships is necessary to thrive. In senior school, it’s a good idea to have a study group to practice for tests.
As parents and teachers, we need to provide a positive environment, modelling by example and not imposing on our boys one’s own negative experiences with mathematics. We should consider how we model or not model positive associations to mathematics.
As the boys continue their mathematics journey, I would encourage them to believe in themselves, to consider how they could adapt a growth mindset to increase motivation, productivity and positive outcomes and use the suggestions outlined above to help them be successful in mathematics.
Head of Mathematics – Senior School