Mastering Mathematics

One of the questions that sometimes surfaces from prospective families at Paideia is: “Do you teach Common Core math?” This question usually bubbles up from either a visceral loathing of Common Core or a nervous fear that students who don’t do Common Core will somehow be “behind.”

Before answering that question, I like to ask some questions of my own. “What does Common Core math mean to you? What do you not like about it?” Or alternatively, “Why do you think it is important?”


Common Core math was created because educators noticed students having a lack in critical thinking skills in mathematics. Students appeared to just be memorizing ways to do problems in a “monkey see, monkey do” fashion, rather than understanding the why behind what they were doing. Common Core was an attempt to build number sense into mathematical learning, teaching students to recognize patterns and reason out steps on their own instead of simply memorizing processes.

But although creators of Common Core math correctly emphasized critical thinking skills, they incorrectly identified memorizing as a negative and as being at odds with comprehension. Over the last decade, addition, subtraction, multiplication, and division fact fluency has fallen by the wayside as the importance of memorizing basic arithmetic facts has been steadily deemphasized and denigrated. Students being able to reason out the process for the problem has become more important than students actually being able to complete the problem correctly. “Because…we all have calculators now, don’t you know?”


At Paideia, we believe that both number sense and fluency in arithmetic facts are important. In fact, the ability to do arithmetic fluently can actually lead to far greater number sense. The student who has no difficulty adding 5 and 16 in his head, will not have an extra barrier to contend with when understanding how to move numbers to opposite sides of the equation in Algebra. The student who is quick with her multiplication tables will be able to see at a glance how she can factor numbers out of the polynomial.

Memorizing math facts is important. Understanding place value, identifying patterns, decoding word problems, reasoning independently, and explaining your solutions are also important. As one of our favorite books, The Liberal Arts Tradition, puts it, imitation must be joined with reason before the art of arithmetic can be achieved. It is essential to realize that math fact fluency and critical thinking work together to build a strong math student.


The approach to math that we use at Paideia targets both of these skill sets. Our Math-U-See curriculum is consciously designed to foster number sense. Some of the ways of doing addition and multiplication in our Math-U-See curriculum can seem strange to parents at first. Students learn to estimate for approximate answers before solving for exact answers. Students expand the notation for their multiplication problems to understand what each number means according to its place value. “This isn’t how I learned to do math!,” some parents might think. “So how can I help my child?”

We are here to assist you. If you have questions about “the rule of four” or “the same-difference theorem” or any of the unfamiliar methods in our Math-U-See curriculum, don’t hesitate to ask. Most of our teachers would likely tell you that they understand how numbers work far better after learning the methods Math-U-See uses.


Along with inculcating number sense, we are always working to build arithmetic fluency. At the beginning of each elementary class, students do a timed math facts page, mental Calisthenics to “warm up” for the practice that lies ahead.

In 1st-6th grade you will also see math facts on the at-home work checklist. It can be tempting to skip over these instead of making a daily effort to master them. (I know from personal experience that students who struggle the most with math facts are the most prone to shirk practicing them…) However, skipping math facts practice because they are hard for your child is counter-productive and ensures that your child will struggle with math all the way up through algebra.

Lean into the hard. Use strategies like breaking addition facts into small chunks and doing them over and over. Practice skip counting 8s first, and then time how fast you can do the 8s multiplication facts. Try to better your time the next day.

Think of arithmetic as any other skill that needs to be learned. When your daughter learns basketball, you don’t just teach her “the process of a layup”, you make sure she has the muscle memory to put the ball in the basket over and over again. When your son gets a new Chopin prelude, you don’t let him settle for “understanding how the chords work”, you have him play it over and over again until his hands transition fluently through each cadence. Math, like sports and music, is a skill that requires drill.


Giving our children the gift of mathematical reasoning and fluency is more than an attempt to make them successful in college or a bid to get them a well-paying career as an engineer. In a very real sense, it is an attempt to open their eyes to the order, design, and beauty of the world in which they live.

One of Isaac Newton’s most famous quotes is that “God created everything by number, weight, and measure.” Numbers are built into the fabric of our world, and the more we learn about the numerical patterns, processes, precision, and predictability of Creation, the more we learn about the nature of the Creator.

Proverbs 25:2 says “It is the glory of God to conceal a matter, but the glory of kings is to search out a matter.” Let us teach our children the glory of the search.

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