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Building Math Mindsets

Both parental guardians and educators have a profound impact on the mindset of children and teenagers as well as their beliefs about teaching and learning mathematics. 


Mindset

Those who value and praise performance as opposed to effort can inadvertently be promoting a fixed mindset in our learners. The type of feedback given to students - written, verbal and non-verbal - can also influence their attitudes and mindsets. Parental guardians and educators play a central role in demonstrating to children that everyone can learn, and that learning is the result of effort and application, not an inherent quality that some possess and others do not. 


What Is A Growth Mindset?

Growth Mindset is a belief system that suggests that one’s intelligence can be grown or developed with persistence, effort, and a focus on learning. Learners with a growth mindset believe that they can learn just about anything they set their mind to. The focus of a growth mindset individual is on learning, not on looking smart. 


Important Considerations: 

  • Praise
    • Every word and action send a message. It tells children how to think about themselves. Praise effort, resilience and hard work – not intelligence. An example of growth mindset praise is, “I like the way you tried all kinds of strategies on that math problem until you finally got it.”
  • Feedback, Persistence and Effort
    • A growth mindset means that a child will be open to feedback and welcome it. Parents and educators should use feedback to help students concentrate on improving their own performance, in small achievable steps. Remind students that if the work is not hard, they are not learning. Stress that intelligence is improved by effort and hard work and that we all learn in different ways and at different rates. 
  • Learning from Mistakes
    • Help students value mistakes. Let students know that you appreciate mistakes and it’s through mistakes that our brains grow. Thomas Edison said, “You must learn to fail intelligently. Failing is one of the greatest arts in the world. One fails forward to success.

Fixed Minset vs. Growth Mindset 

Here are some common characteristics of both a fixed vs. growth mindset is shared in the book Mindset: The New Psychology of Success by Carol Dweck:

​​Fixed Mindset

​Growth Mindset

​Leads to a desire to look smart and therefore a tendancy to:

  • avoid challenges
  • get defensive or give up easily
  • see effort as fruitless or worse
  • ignore useful feedback
  • feel threatened by the success of others 

As a result, they may plateau early and achieve less than their full potential.

​Leads to a desire to learn and therefore a tendancy to:
  • ​​​embrace challenges
  • persist in the face of setbacks
  • see effort as the path to mastery
  • learn from criticism
  • find lessons and inspiration in the success of others 

As a result, they reach even higher levels of achievement.


Dweck, C. (2006). Mindset The new psychology of success. How can we learn to fulfill our potential? USA: Ballantine Books. 
p.245

Tips For Developing A Growth Mindset

Instead of...

​Try Thinking...

​I'm not good at this.

​What am I missing?

​I give up.

​I'll use a different strategy.

​It's good enough.

​Is this really my best work?

​I can't make this any better.

​I can always improve.

​This is too hard.

​This may take some time.

​I made a mistake.

​Mistakes help me to learn.

​I just can't do this.

​I am going to train my brain.

​I'll never be that smart.

​I will learn how to do this.

​Plan A didn't work.

​There's always Plan B.

​My friend can do it.

​​I will learn from my friend.


Dweck’s research illustrates that a fixed mindset student believes their basic abilities, their intelligence, and their talents are just fixed traits. They have a certain amount and that’s that, and then their goal becomes to look smart all the time. A growth mindset student understands that their talents and abilities can be developed through effort, good teaching and persistence. They don’t necessarily think everyone’s the same or anyone can be Einstein, but they believe everyone can get smarter if they work at it (Morehead 2012). It is important to note that we all can possess each mindset in different situations and these terms should be applied to behaviours, actions, and attitudes rather than people.


Further Reading

If you are interested in reading further about Growth Mindset so you can develop this mindset for yourself and the children you surround yourself with, consider these books:


Beliefs About Teaching and Learning Mathematics

For the implementation of effective teaching and learning of mathematics, we must ensure a collective agreement in the belief that mathematics lessons should be centered on engaging students in solving and discussing tasks that promote reasoning and problem solving (NCTM 2009; National Research Council 2012a). Lessons should encourage student interactions and discourse, with the end goal of students being able to make sense of the mathematical concepts and procedures presented. An educator’s own beliefs about the teaching and learning of mathematics will directly influence the decisions they make about the manner in which they will teach mathematics. Educators need to reflect on their own beliefs to examine if their beliefs are productive or unproductive. Unproductive beliefs hinder the implementation of effective instructional practice or limit student access to important mathematics content and practices. 

The table below summarizes productive and unproductive beliefs about the teaching and learning of mathematics: 

Unproductive Beliefs

Productive Beliefs

Mathematics learning should focus on practicing procedures and memorizing basic number combinations.

​Mathematics learning should focus on developing understanding of concepts and procedures through problem solving, reasoning, and discourse.

Students need only to learn and use the same standard computational algorithms and the same prescribed methods to solve algebraic problems.

All students need to have a range of strategies and approaches from which to choose in solving problems, including, but not limited to, general methods, standard algorithms, and procedures.

Students can learn to apply mathematics only after they have mastered the basic skills.

Students can learn mathematics through exploring and solving contextual and mathematical problems.

The role of the teacher is to tell students exactly what definitions, formulas, and rules they should know and demonstrate how to use this information to solve mathematics problems.

The role of the teacher is to engage students in tasks that promote reasoning and problem solving and facilitate discourse that moves students toward share understanding of mathematics.

The role of the student is to memorize information that is presented and then use it to solve routine problems on homework, quizzes, and tests.

The role of the student is to be actively involved in making sense of mathematics tasks by using varied strategies and representations, justifying solutions, making connections to prior knowledge or familiar contexts and experiences, and considering the reasoning of others.

An effective teacher makes the mathematics easy for students by guiding them step by step through problem solving to ensure that they are not frustrated or confused.

An effective teacher provides students with appropriate challenge, encourages perseverance in solving problems, and supports productive struggle in learning mathematics.

Principles to Actions (2014), page 11​.