How to Build Confidence and Problem-Solving Through Mathematics

As a math tutor, I have lots of experience helping students who are struggling to increase their math confidence. I’ve found that these students decide early on that “math just isn’t my thing”, but nothing could be further from the truth. The real struggle, I think, has much more to do with a lack of math confidence when it comes to problem-solving.

When you think about a math problem, there are so many places mistakes can be made. Not only do you have to know all the steps, but you have to know the correct order of those steps, as well as how to execute each one without making any mistakes. A lot is riding on it, so students understandably get frustrated and quickly lose confidence if things aren’t going their way.

How can you avoid the frustration and maintain self-confidence? Below are some of the techniques I use.

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1. TRY THE QUESTION YOURSELF.  I always like it when the students try a problem first, and then ask me how to do it as a last resort. When they attempt it alone, more often than not, they know what to do – they just need an expert or a tutor to be with them to assure them they’re doing it the right way. Receiving instant expert feedback is good for diagnosing where the issue is in their understanding of the concept, and it also provides positive reinforcement. Everyone likes being told they’re doing a good job, right? It is also important that the feedback be descriptive. The more descriptive it is, the quicker the students will come to see exactly what made them successful. This builds math confidence.
2. WALK THROUGH IT STEP-BY-STEP.  Typically, before doing any of the actual homework problems, I will give students a couple of examples similar to the ones they’ve brought in. We walk through them together step-by-step, and as we break it down, I ask them, “So what do you want to do here?” and “Why do you want to do that?” By having them explain their thought process, they start to see where the holes in their understanding are. As the holes get filled, their math confidence improves. This leads me to…
3. TEACH SOMEONE ELSE.  This is my favorite way to build math confidence. Explaining helps immensely with understanding. If students are missing certain foundation elements, that will hinder their future learning and prevent them from mastering any new material that comes up in school. If your student is struggling, sit down with them and ask them to explain some problems to you as if you were learning the material for the first time. When they are forced to break a problem down into its simplest terms, it reinforces those foundation concepts that are so important.
4. LEARN SHORTCUTS.  Another effective approach is teaching shortcuts. Kids come in all the time complaining about solving problems that are not inherently difficult, but are made so because they have a rigid approach to problem-solving – an inability to see the problem from a different perspective. They know only one route to the solution. Math is very flexible though, and when students learn there are multiple ways to solve a problem, it becomes much more enjoyable. If one method doesn’t work, they can always try another.
5. LEARN THE APPLICATIONS.  Something many teachers fail to do for their students is teaching them how to apply what they are learning to the “real world.” I dread being asked, “When am I ever going to use this in my life?” (even though I know I asked it many times myself). As I said earlier, math is very flexible. If you look hard enough, you can find it anywhere. As students advance in their mathematics education, they will undoubtedly find that most of the material they learn in school is not used by the general population. BUT…the whole reason we learn math in school is to improve our ability to solve problems. We solve problems every day, but mathematics is just a formal, algorithmic way of doing it. Math is so much more interesting when you realize how much of your life is determined by underlying equations and formulas.
6. PRACTICE.  Last but not least, practice. Students don’t like it, but this is the single best way to increase math confidence. Students can listen to lectures all day long, but there’s really no way to test their knowledge aside from applying it to actual problems. To be good at math, just like anything, you have to practice every day. Spending an extra 20 minutes each day doing practice problems – or supplementing the school lectures with videos on sites like Khan Academy – add up to almost two and a half hours per week. Students will feel more prepared for tests and quizzes, and feeling prepared is vital to increasing confidence. The extra practice will pay dividends over time in the form of better grades, better test scores, and more scholarship money.

As far as confidence goes, there is no substitute for feeling prepared and being self-reliant. However, if your child is struggling in math (or any subject), consider finding a tutor who can give a boost to their self-esteem.