How a Math Tutor Can Help Your Child Master Critical Thinking Skills

Last Updated on June 1, 2022 by Thinkster

According to The Foundation for Critical Thinking, “critical thinking is a way of thinking – about any subject, content, or problem – in which the thinker improves the quality of his or her thinking by skillfully analyzing, assessing, and reconstructing it. Critical thinking is self-directed, self-disciplined, self-monitored, and self-corrective thinking. It presupposes assent to rigorous standards of excellence and mindful command of their use. It entails effective communication and problem-solving abilities, as well as a commitment to overcome our native egocentrism and sociocentrism.”

Young students are not usually taught how to think critically until they reach high school (or even college), yet it’s one of the core skills they’ll need throughout their academic career and beyond.

So how can a math tutor help your child master the art of critical thinking? And why does your child even need critical thinking in the first place?

What Exactly are Critical Thinking Skills and Why Does Your Child Need Them?

Solving a puzzle

Often, children read their textbooks and write down notes without ever questioning the “why” behind what they’re learning.

The Earth isn’t flat
There are capital cities in each state in the US.

So when most children learn a new math concept, they are expected and get used to being given a specific formula to follow, providing the steps they must complete in order to arrive at a correct answer.

But what happens when students encounter a math problem that seems a little different or a bit harder than the simple, repetitive ones they’ve been practicing?

That’s where most young children get stuck.

Students may have an idea of why they need to perform certain steps to get an answer, but they lack a true understanding of the concepts necessary to solve a similar problem in different contexts.

They miss the ability to think critically, develop an understanding to unpack a problem so that they can solve it, and become unable to think rationally about what to do next. This also includes the ability to engage in independent thinking, which is the ability to do something independently without asking for help.

In short, using critical thinking to solve a problem is just the opposite of using memorized steps to solve a problem. Applied to math homework, it requires that students:

  • Understand the logical connections between different math concepts
  • Solve math problems systematically
  • Identify, create and evaluate different ways of solving a problem
  • Avoid common mistakes
  • Connect relevant concepts to each other in order to tackle harder problems
  • Analyze and reflect on why and where they went wrong

Instead of solely focusing on the answer, critical thinking focuses students to understand what problem needs to be solved, determine what paths and solutions are available, and analyze and evaluate the most efficient methods to solve the problem. Unfortunately, not everyone uses Critical Thinking when solving problems. According to the National Institutes of Health, “in order to think critically, there must be a certain amount of self-awareness and other characteristics present to enable a person to explain the analysis and interpretation and to evaluate any inferences made.” Students trained to think critically automatically start to understand that there are multiple approaches to solving a problem and develop confidence in their abilities to find solutions to problems they encounter.

This shows them that anything can be solved – any geometry problem, algebraic equation, word problem, or calculus question – if you understand the why behind the math.

Rather than becoming frustrated when they encounter an equation that stumps them, they then begin to get creative and attack the problem head-on. It’s not about the answers they know as much as it is about the way in which they find those mathematics answers.

Even better, once your child learns this new approach to problem-solving, they will have the tools to continue to develop their critical thinking skills for the rest of their life.

So how can an online math tutor help your child master these critical thinking skills?

Here’s How a Thinkster Math Tutor Develops Critical Thinking Skills in their Students

Thinking about a chess move

While tutors and math help websites can aid your child with practicing a math concept, not all of them are able to develop those valuable critical thinking skills.

Here at Thinkster, we do things differently.

We are firm believers that thinking is the foundation of learning. Everything an online tutor does is meant to spark this “thinking” – because that’s what makes us understand the “why” behind everything. Here’s how they light that spark:

First, All Math Tutors Begin with an Assessment of Your Child’s Skills.

Instead of sticking your child on the standard common curriculum for their grade, Thinkster students start by taking a skills assessment test to find out their strengths and weaknesses.

This is when the dedicated math tutor will evaluate the student’s current thinking and reasoning skills.

Then, they Create Personalized Lessons.

When your child’s math tutor understands where your child needs help or could further their learning with more advanced concepts, they’ll create a personalized lesson plan designed to do just that.

These lessons establish a foundation and layer on new problems for the student to work through.

Think about this: If you’re learning a foreign language, the process is much easier if you can give the grammar and vocabulary some context. Then you can then apply those rules to other situations.

At Thinkster, our online tutoring does the same thing with math.

We create lifelong learners by anchoring problems to real-life situations that teach them contextual skills and critical thinking.

The deeper their understanding, the easier it will be to develop confidence and fluency.

Students Develop their Thinking Skills Using Our Library of Unlimited Worksheets built-in with Multiple Problem Strategies

According to the Foundation for Critical Thinking, developing this necessary skill usually occurs in six stages, defined as:

Stage One: The Unreflective Thinker

Stage Two: The Challenged Thinker

Stage Three: The Beginning Thinker

Stage Four: The Practicing Thinker

Stage Five: The Advanced Thinker

Stage Six: The Accomplished Thinker

Your child will use our unlimited mathematics worksheets to move from one stage of thinking to the next.

While they’ll start off totally unaware of how to “think outside the equation” as an Unreflective Thinker, they’ll begin to use feedback from the Thinkster math app and their math tutor to progress to a Challenged Thinker.

Eventually, we want each child to become an Accomplished Thinker!

To get to this level, students will learn to explain why a formula works, not just how to fill it in. They’ll also be able to explain the logic behind the steps they use to define concepts and solve for solutions. The Thinkster Math program also helps students become fluent in solving problems when they get exposed to multiple strategies that are provided in the attached video tutorials that come along with every worksheet. The multiple strategies also use the Singapore Math teaching methods to solve different math problems.

Students will learn to ask themselves questions to solve problems logically, such as:

  • What is the problem really asking?
  • What do I need to figure out?
  • What do I already know – what information have I been given?
  • What information am I missing in order to solve this problem?
  • What problems like this have I solved before?
  • Which types of solutions would work best in this specific situation?

Unlike math help websites that use a one-size-fits-all approach for math classes at set grade levels, Thinkster lesson plans and worksheets get harder as your student’s understanding and critical thinking develops.

Your Math Tutor Will Use Our Active Replay Technology (ART) To Visualize Student Thinking

Parents and math tutors at learning centers both have a big disadvantage when it comes to correcting homework.


Because, unless you’re sitting there watching them do it, you cannot really see how your child is working through problems and arriving at their answers.

A Thinkster experienced tutor has a distinct competitive advantage here.

Thanks to our proprietary ART technology, tutors are able to visualize student thinking so they can know precisely where errors or setbacks occurred.

The artificial intelligence and machine learning in our online math tutoring app will show your child’s tutor how long they spent thinking, which numbers they wrote down first, how fast they worked toward their answers, and much more.

The artificial intelligence and machine learning tools that come along with the Thinkster Math Tutoring program show our tutors the fragmentation patterns of how a student is thinking while he/she is solving a math problem. The ability to visualize a student’s thinking – how fast they worked, where did they pause, what did they do before they erased their work and re-did their math – all happening at the point of learning, is a significant advantage that Thinkster tutors have compared to all other programs.

Using these ART playback videos, your child’s math tutor not only understands what mistakes your child did but why they did it thus and provide the appropriate feedback to your child. This helps your child develop their reasoning skills and helps him or her understand where they went wrong, enabling them to get better.

Our Math Tutors Encourage Parents to Stay Involved

As your child develops their math and critical thinking skills, Thinkster provides real-time insights tailored to their individual strengths and weaknesses.

In fact, the Thinkster Parent Insight app allows you to monitor exactly how your child is progressing. You can view their worksheets, read the feedback provided by their math tutor and go over the data captured by the ART.

Ellen Galinsky, the author of Mind in the Making, includes critical thinking on her list of the seven essential life skills needed by every child. To further develop your child’s critical thinking skills beyond the math practice realm, she recommends:

  • Providing opportunities for play
  • Pausing before intervening when they struggle
  • Asking open-ended questions
  • Helping children develop hypotheses
  • Encouraging critical thinking in new and different ways

Ready to Let a Thinkster Math Tutor Help Your Child Master Critical Thinking?

Tutors often put pressure on students during math practice to solve for the right answer without necessarily providing the education to ensure they understand the foundational concepts and the underlying math theories.

Critical thinking helps students make smarter decisions because they actually understand difficult concepts better. It also makes them faster, more confident test-takers.

A Thinkster math tutor will not only help your child improve their math skills, but your child will also strengthen their overall academic performance, thanks to their budding critical thinking skills.

You could see results in as little as 12 weeks with our expert team of online math tutors and coaches. And that’s something tutoring centers and math help websites cannot boast about.

You can try Thinkster risk-free. Thinkster provides a full-fledged online tutoring platform (driven by AI, behavioral, and data science), as well as supplemental math worksheetsmath homework helptest prep, and more. Our Parent Insights App allows you to monitor your student‘s work and learning improvements at any time.

An elite, expert math tutor and online teaching system work together to help your student go beyond just learning math – we want them to master it.

Learn more about our curriculum and teaching style here.


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