S2 E31: Developing Flexible Mathematicians

From Procedures to Problem Solvers: A New Era in Math Education

A Quick Look Back: Math in the “Industrial Age” Classroom

In the not-so-distant past, math was taught with an industrial mindset. Schools focused on producing reliable, efficient, and obedient workers. In math classes, that meant teaching fixed algorithms and routines. Students would practice a set procedure for addition, subtraction, multiplication, or division over and over until they could reproduce it without a mistake. But where was the spark? Where was the joy of learning? Education was treated as if it was about "filling a pail," to borrow from William Butler Yeats' famous quote, rather than "lighting a fire."

Today, however, the world has changed drastically. We’re no longer just preparing kids for factory jobs; we’re preparing them for a world that requires creativity, flexibility, and adaptability. Math education is now about empowering kids to think and solve problems in diverse ways, emphasizing deep understanding and mental flexibility over simple memorization.

Moving Beyond Memorization to Conceptual Understanding

One of the most significant shifts in modern math education is the focus on helping kids understand why a mathematical strategy works rather than just memorizing the how. For example, instead of teaching kids to stack the numbers vertically and then “carry” to regroup and solve 36 + 48, we might take 2 from the 36 and add it to the 48, making it an easy “benchmark” number or “friendly” 50, then adding the 34 we still have left. Or we might first explore what each number represents by breaking it down into tens and ones, adding 30 and 40, 6 and 8, and then adding 70 and 14 together to get the sum of 84. This approach helps kids understand what they’re actually doing with each number and why certain steps work, rather than just following a series of instructions.

Imagine the difference: a child who understands why will be better equipped to adapt their approach to different math problems and tackle challenges creatively. When kids build strong number sense, they see math as something they can interact with and understand on a deep level, rather than just a series of steps to memorize.

How to Encourage Flexible Math Thinking at Home

Here are some fun, easy ways to nurture this new way of thinking and support your child in becoming a flexible, confident mathematician.

1. Embrace Riddles and Puzzles

Riddles, logic games, and puzzles are excellent for building critical thinking skills. They encourage kids to experiment with various strategies and think outside the box. Even a simple question like, “If two cats caught three mice in two minutes, how many mice would six cats catch in six minutes?” can open up all kinds of reasoning without needing a single pencil or worksheet! Do a lot more talking about numbers than writing them down.

2. Make Math Relevant to Your Child’s World

Kids engage best when they can connect learning to their own interests. If your child loves dinosaurs, try creating math problems related to their sizes, species comparisons, or even dig into some of the data related to the species. You could go as far as making population graphs! If they’re into cooking, involve them in measuring ingredients to introduce concepts like fractions and volume. Half, double or triple a recipe to up the level of complexity. If your child is young, model this for them and share your thinking, what's happening in your own brain, aloud. You can even ask them to help make a grocery list or set a budget for an upcoming shopping trip. Not only does this make math feel useful, but it also shows them that it’s woven into everyday life.

3. Use Everyday Situations to Build Number Sense

Math is all around us, and number sense grows when kids feel comfortable playing with numbers. Try making a game out of counting steps to the car, estimating travel times, or setting the dinner table with the right amount of utensils. Ask them to find patterns or sums in addresses, license plates, or phone numbers. Let them see numbers and patterns all around them. These small moments make math a part of life instead of just a school subject.

4. Encourage Multiple Approaches to Solving Problems

Let your child know there’s often more than one way to solve a problem. For example, if they’re adding numbers, ask them, “Can you find another way to solve this?” Trying different methods helps build flexible thinking and teaches kids to appreciate that math isn’t about finding the “right” answer in only one way. This can also be an excellent opportunity to talk about mistakes as a natural part of learning and growth. On your own side, you may want to dig into the work of Carol Dweck.

5. Ask Open-Ended Questions

Instead of focusing only on right or wrong answers, ask open-ended questions that encourage discussion and exploration. For example, ask questions like, “What patterns do you see here?” or “What do you think would happen if…?” These questions invite children to think critically and develop their understanding in a deeper, more nuanced way.

Fostering a Future of Flexible, Confident Thinkers

It’s inspiring to see how far we’ve come from the days when math meant memorizing steps to get a “right” answer. Today’s math classrooms aim to create resilient, flexible problem-solvers who know that math is as much about thinking and exploring as it is about getting answers. Kids now get credit not only for finding the correct answer but for showing how they approached the problem, and this process-based focus is key to building lifelong learners, especially while they are early on in their learning journeys.

I hope today’s post has given you a peek into why these shifts in math education are happening and how you can support them at home. If you’re looking for more ideas on raising curious, flexible thinkers, feel free to join our free Raising Thinkers Community! And if you’d like more resources geared specifically toward math skills, check out my Raising Mathematicians subscription service.

Thank you for reading! Please share this post if you found it helpful, or share a comment on anything that has worked for you , or even questions you may have. Here’s to keeping that spark alive as we raise our future thinkers and problem-solvers!