*By Kim Sukta and Caroline Hummel*

Lately, I have been saying—jokingly, but actually quite seriously—that I want a sign outside of my 4th grade math classroom that reads, “You must know your multiplication facts to ride this ride!”

Over the course of my teaching career, I have seen many students excel at math and I have seen others struggle at every turn. This disparity hinges on whether a student practices, understands, and utilizes math facts.

### The ABCs of Math

Math facts—basic addition, subtraction, and multiplication equations—are the ABCs of math. When we teach young students how to read, we teach them to decode new words by marking the vowels, diphthongs (vowel pairs), and digraphs (consonant pairs), and then to sound out each phonogram. Only after these decoding skills become second nature to students can we expect them to recode, and then to read, with fluency. After students learn these skills, they can sound out new words with what appears to outsiders to be intuition. In reality, they are simply applying previous knowledge.

Likewise, in math, we teach young students first to count objects and sing skip counting songs before progressing to mathematical fluency. Math facts are the underlying cornerstone of mathematical proficiency. They help establish number sense, which in turn prepares students for advanced problem-solving and critical thinking.

At Cedar Classical, we carve out time each day for math drills. Math drills include speed tests, mental math, and math games developed by Hillsdale College’s Barney Charter School Initiative. During math games, teachers will ask students questions like “Is 5 X 5 closer to 3 X 8 or 2 X 12?” or “How many ways can you make 15 using the numbers 2, 5, 5, and 10?” Students who can come up with quick and creative answers to these questions may seem like they are only exercising intuition, but they are likewise simply applying previous knowledge about operations, numbers, and relationships between numbers.

### Chunking Information

Cognitive scientists say that the reason why math fact fluency matters is that it frees up brain power or working memory to do more complex mathematical work. By breaking down, or “chunking,” large amounts of information into multiple sets of smaller data sets, the brain can streamline data and distill what information is yet to be solved. A good example of chunking information is the way that we memorize phone numbers. When you are trying to memorize the school’s phone number, you do not memorize each of the 10 numbers individually:

5 1 7 2 1 0 1 0 5 7

Instead, you likely group them into three or four groups of numbers:

517 210 10 57

Math facts allow a student’s brain to group mathematical concepts into smaller groups of numbers. If a student sets out to figure out how to structure a multi-step word problem, model a solution, or puzzle out systems of equations, but needs to calculate each basic step of the basic arithmetic, math will quickly become a source of frustration. But if a student is answering one of those math game questions (“Is 5 X 5 closer to 3 X 8 or 2 X 12?”) and knows by heart that 5 X 5 is 25 and 3 X 8 is 24, even if he needs to think for a moment to realize that 2 X 12 is 24, he will be able to answer that 3 X 8 is the same as 2 X 12 so 5 X 5 is only 1 away from both options.

### From Concrete to Pictorial to Abstract

The Concrete-Pictorial-Abstract (CPA) approach is what we implement in the Singapore Math curriculum that we use at Cedar. This approach uses hands-on learning, visual representations, and abstract reasoning. This thoughtful progression is instrumental in cultivating a profound understanding of number relationships. Through targeted drills and practice, students can gain fluency and confidence in their mathematical abilities over time.

The study of mathematics makes connections between the concrete and the abstract, between a group of five linking cubes and the abstract idea of *five*. For this reason, Greek philosophers like Plato and Pythagoras thought of mathematics as a precursor to philosophy.

As Christians who think of theology as the apex of education, we think even more strongly of mathematics as a precursor and buttress to theology. In an ever-changing world, we can rely on God’s steadfast order and design to help us have peace and security. Just as math facts never change, God’s love and character stay the same too. This fact should cause us to worship and enter into his presence in a fresh and new way.