The take-away from current research is simple.

For children to make sense of math, they must believe that they are capable of understanding and learning math.

There is a pervasive belief in our culture that being good at math is an innate ability. This has proven to be false. Researchers like Carol Dweck have worked hard to disprove this belief and according to Dweck (2006), people with a fixed mindset believe that our abilities and intelligence cannot be changed, while people with a growth mindset believe that our abilities can be changed through study, practice, and hard work. Mathematical confidence reflects this “growth mindset” or self-belief and includes a willingness to persevere, a positive attitude toward mistakes, a willingness to take risks, and self-reliance. Let’s look at each component closer.

Perseverance

Children’s mathematical confidence affects their approach to challenges and failure. Children with low self-confidence may fail or make a mistake and define themselves by that failure, deciding that they are not smart. When faced with a challenge, these children may get angry and give up because they feel they are not smart enough to figure it out.

On the contrary, students who see themselves as “smart” may believe that any struggle means that they are not smart. This may lead them to seek to preserve their sense of “smartness” by avoiding something that might take work. Children who possess mathematical confidence look at challenging math problems in a completely different way. Failure is a chance to learn and grow. It is a chance to reflect and think, “What can I do better next time?”

Children with mathematical confidence can persevere through challenging problems, trying and trying again until they figure them out. It is our job as teachers to help them gain this perseverance.

Valuing Mistakes

Fear of making mistakes and being labeled as “wrong” or “failing,” is one of the greatest obstacles to perseverance and to mathematical confidence. When students fear mistakes, it halts their ability to truly problem-solve. They are hesitant to try a strategy because they don’t know for sure that it will get them the right answer.

Children who have strong math confidence are unafraid to make mistakes. They know that mistakes are stepping-stones that help us learn. Jo Boaler, in her book Mathematical Mindsets, discusses brain research that shows how our brain grows and develops each time we make a mistake. When students solve a problem and get the answer right, no new neural pathways are formed.

However, when a student makes a mistake, synapses in the brain fire, forming new pathways and connections. Most surprisingly, new brain pathways are formed from making mistakes even when we don’t know we are making them (Boaler 2016). Boaler’s research shows us that children and adults learn most when they are challenged and make mistakes.

In a math classroom, mistakes should be celebrated as “great mistakes!” and learning opportunities, not looked at as simply wrong answers.

Taking Risks

To be successful mathematicians, young children also need to learn to be brave with new ideas. They need to feel confident enough to take risks, try new strategies, and share their thinking even when it contradicts that of others.

When students believe in themselves enough to take mathematical risks, they know that if one strategy doesn’t work, they can always try another. They feel confident that if they don’t get it right the first time, they’ll be able to figure out a way to solve the problem eventually. When a new, unfamiliar strategy is suggested, they are willing to give it a go. Helping students develop the confidence they need in math will allow them to take the risks necessary to truly make sense of mathematics.

Self-Reliance

When students feel brave as mathematicians, they do not rely on the teacher to tell them what to do or how to solve a problem. They do not look for confirmation of their answers but instead, check their own work and justify their thinking.

We as educators, need to help them develop the mathematical confidence to persevere through tough problems, embrace productive mistakes, and challenge themselves by trying new strategies and ideas without constantly looking to the teacher for the answers.

It is our responsibility as teachers to help set up a classroom environment that allows students to feel confident in their mathematical abilities as they persevere, make mistakes, and take risks with new ideas. When students possess this confidence, little stands in the way of their mathematical development.

Providing Educators With Resources:

Because the issue of student math pervasive and confidence is such a central factor for student success with math in their lives, it must also be explored in-depth. Teach & Kids Learn (TKL) has developed several comprehensive online courses for teachers which have been found to be very beneficial in addressing these issues in their classroom. Here are a few which you may want to consider:

• Creating Learning Classrooms for Today’s Students
• Creating Meaningful Math Engagement
• Creating Student Innovators
• Developing Mathematical Expertise in a Problem-Centered Classroom
• Developing Students’ Mathematical Habits of Mind
• Equalizing Mathematics through Differentiated Instruction
• Increasing Student Engagement and Motivation
• Increasing Student Engagement: Planning Outside the Box
• Supporting Mathematical Proficiency in Struggling Learners