Should We Prioritize Math Facts?
Memorizing math facts and algorithms vs conceptual understanding of math is a huge debate. This debate is akin to sight words verses phonics. Which is better? The answer is BOTH.
The real pressure and anxiety of learning to read is also akin to the real pressure and anxiety of learning math; a Timeline. There is this invisible timeline that looms heavy over everyone these days.
It is the “Charlie, next door, has his math facts memorized and you are the same age.” The fact is memorizing math facts is one small, small, small facet to mathematics. It is a convenient tool but it isn’t what defines mathematical ability.
Math is the science of pattern finding. The ability to calculate quickly doesn’t make anyone good at pattern finding. It can certainly be a helpful tool though, but we must put math facts in its rightful place as a tool.
As a homeschooler, you have one advantage, you are free from this invisible timeline that plagues the world. So, take a deep breath and relax. You can have both conceptual math and math facts in time.
Children memorize the route to the local pool because of the joyful rides to the pool, the fun memories at the pool and the exhausted but happy ride back from the pool. This is what Gattegno calls efficient learning, true retention.
These interconnected happy stories hold a strong and firm memory of the route to the pool. I don’t have to tell my kids where we are going. They can figure it out as we pass by those familiar structures, and I never had to tell them to memorize the route either. It was a convenient result of the experience of going to and from the pool.
Memorizing math facts happens in the same fashion. When children immerse themselves in their own math stories, they begin to build those memories that make math facts a convenient by-product.
Noticing Structures First
My children didn’t learn the route to the pool in the first trip, but they probably did notice the general structure. It was a short ride or it was like the trip to the post office.
Noticing these structures will helped them to see the most efficient way to memorize the route. They build on previous experiences.
In the same way, children can learn math facts through interconnected experiences by first noticing structures. This is one of the benefits of teaching algebra before arithmetic. The student will notice structures first.
Algebra before arithmetic sounds scarier than it is. All we are doing is using the rods color names instead of assigning a number name to the rods. White verses one and red verses two. When we do this, students have more freedom to notice structures first.
I think there is a tendency by adults to think these math structures are apparent to the child. Often, they are not. And certainly, you can tell a child about the structure but you will have to keep telling them, over and over again until they memorize it. Without context and experience of seeing and noticing the structures for themselves, this "telling over and over" will prove to build a weak memory.
Mastering Math Facts through Complements
Math structures provide context and experience for students to master math facts in a way that makes retention easier. Let's examine an activity that develops a student's awareness of structures that improve math fact retention.
Building staircase complements is an exercise where students notice the structures of math facts. A complement is two rods that make the length of a particular rod. For example, the orange complements are any two rods that make the length of the orange rod, like white and blue or red and tan.
One structure students notice in this exercise is there are more compliments for longer rods than there are for shorter rods. Another structure children notice is the communicative property of addition. Red plus white is the same length as white plus red.
Using Stories to Increase Retention
But is building complements enough? It could be enough, but I am a strong believer in utilizing all tools necessary. Immersing children in stories and especially their own stories is a strong tool for memory building.
Scientifically, stories engage our senses in the same way real experiences do, and real experiences have stronger recall. Stories are also how we store and organize information. Most importantly, we love stories. We talk in stories, we think in stories and we yearn for stories. We are hardwired for stories.
I created the rescue the missing chick exercise to encourage children to practice complement building while engaging their need and love for stories. As students rescue each chick by finishing the ladder to the top, students are engaging their need for a story.
Using a picture book is another tool to fire up the child’s desire to be the hero of their own story. As my homestead experience has taught me, chicks are a handful, and “The Missing Chick” by Valeri Gorbachev compliments the Chick Rescue Mission play mats.
In Gorbachev’s picture book, Mama Hen searches everywhere getting the whole neighborhood involved from the firemen to the helicopters to all the neighbors. It is quite a fiasco for a chick who is found hiding in a laundry basket.
The Hero of Math Facts
One story element that resonates strongly with us all is the desire to be the hero of our own story. It is why we always imagine ourselves as the protagonist. These play mats are designed to engage that need while also providing them an opportunity to experience math.
You could certainly do this exercise without the play mats. You could have the children use their imagination and pretend about all the crazy places their chicks might end up. At the end of the day, I really want people to see the math opportunities that lie in their child’s own imagination.
Conceptual math doesn't come by memorizing math facts or algorithms. So if you are going to prioritize one over the other, hands down conceptual math should win. As your child immerses themselves daily into their math stories, they will build a strong conceptual understanding of math. Breath deep and know, Mama, that math facts will come in time and you have time.