Critical thinking and problem-solving skills have been dubbed the skills of the 21st century and can even be more desirable than a degree, according to some businesses. It is imperative that we help our children develop these sought-after abilities. Many publishers are trying to meet the demand, but how these skills are defined may depend on the curriculum. Some publishers claim that puzzles and analogies develop these skills; others claim that student research and projects do. Both may be right, and that is confusing. There is a more generally recognized list known as Bloom’s Taxonomy of Learning Objectives. According to Bloom, there are six skills: remembering, understanding, applying, analyzing, evaluating, and creating. The last three are known as higher order thinking skills and we should shoot for those as much as possible as we homeschool our kids.

Math is one subject where we tend to emphasize only the lower order thinking skills, though. We ask our children to memorize math facts. That is the most basic of thinking skills. When they round and make predictions or compare two amounts, then the next level of critical thinking—understanding—is used. Word problems force application—the third tier—and we often see holes in our children’s thinking at this point. Many kids struggle with word problems because they cannot envision the situation and do not truly understand what they are doing. If our children are only using worksheets to learn math, critical thinking often stops here if not earlier. Incorporating hands-on math and real-life situations can take their mathematical abilities to new heights.

Have you heard the quote, “I hear and I forget. I see and I remember. I do and I understand?” Math is an area where hands-on experiences are essential to true learning. Learning to add and subtract fractions on a worksheet often involves only remembering rules and applying them. What happens when you put that child in a kitchen to bake a cake and the ¼ measuring cup is missing? Will that child be able to evaluate the different options available and choose an alternate way to measure ingredients that is just as accurate? That is critical thinking at work. Let’s take a look at other specific ways that higher order critical thinking skills can be developed by hands-on math.


When we examine or investigate something methodically and thoroughly, we analyze. We ask questions and dig deeper. For example—is the circumference of a circle always pi times the diameter, no matter what size the circle? A child can investigate this by taking out a salad plate, a dinner plate, a round table, and a bicycle wheel. The act of actually measuring the diameter and circumference of each circle helps children prove for themselves that the formula is true. This guarantees that they truly understand and internalize the math. No need for drill. How about using paper folding to prove the formula for a triangle? By thoroughly investigating using objects, memorization is usually unnecessary. The experience lives with them instead.


Evaluating means that we form an idea of the value of something. We assess and judge. We weigh one idea against another and decide which one is best. When children are confronted with real-life problems, such as the baking dilemma described above, they must decide what is the best way to solve it. Another situation when children use evaluation is shopping. With their small allowance, they must make decisions about which toy to buy. That one is cheapest. But, wait. Another toy has a store rebate. That other one is 20% off. Children must do the math and compare. The more opportunities that they have to make decisions involving money, cooking, and building projects, the better they will be at evaluating.


Everyone knows what it means to create, imagine, or invent something. This is considered the pinnacle of critical thinking because it involves many of the other skills. Before someone can create or invent a new thing, they must master a body of knowledge, be able to understand and apply it, and decide the best course of action based on all that they know. Then, they set about creating. We want to encourage our children to create models and to imagine new ways of solving problems. Whenever possible, we need to allow them to make their own hands-on tools to help them learn math.

We don’t want our children to just be able to spit out a formula for a test or compute typical problems. Real understanding prepares them to use math in the demands of everyday life and work. After all, if they know how to do percentages on a worksheet but don’t know how to leave a fair tip at a restaurant, do they really know the math?

Copyright 2018, The Old Schoolhouse®. Used with permission. All rights reserved by the Author. Originally appeared in the Summer 2018 issue of The Old Schoolhouse® Magazine, the trade publication for homeschool moms.