There have always been certain areas of math that are well known to challenge teachers and students. Subtraction. Fractions. Division. All of this is very predictable. However, one area that goes less recognized is Fact Fluency with facts to 20. It’s not as obvious because students are not taking standardized tests to show mastery of these skills. It is also not something that you can assess from just looking at an answer!
See, the tricky part about facts to 20 is kids run out of fingers. And counting on or counting back is not an efficient strategy for these larger facts. In order to be fluent, we want kids to use their knowledge of composing and decomposing numbers, benchmarks of 5 and 10, and the relationship between addition and subtraction to be able to solve problems like 9+7 or 14-8 mentally.
So let’s take a problem like 12-8 and think about how children may solve this.
A learner might count back 12, 11, 10, 9, 8, 7, 6, 5, 4. This is inefficient but so many kids get stuck with this as their best strategy because they are lacking essential understandings.
A student who understands part/whole relationships might solve 12-8 by thinking of it as a missing addend addition problem. They may count on from 8 to 12. This shows that they understand the relationship between addition and subtraction. That’s good.
Another student may break up the 8 into 2+6 to subtract in chunks. They might go 12-2=10, and then 10-6=4. This shows understanding of place value and decomposing numbers. That’s good too.
Yet another learner may decompose the 12 instead. They might think of 12 as 10+2. They may take the 8 off of the ten, leaving them with 2. Then put the two left from the ten with the two ones from 12 to get 4. This also shows an understanding of place value and decomposing numbers.
Yet another student might push both numbers forward two to make an easier, equivalent problem. 12-8=14-10! This student understands that subtraction is not only take-away, but can also be thought of as the distance or difference between two numbers. That’s great!
There are even more ways that kids could think about this, and some of these strategies may sound confusing if you are unfamiliar with flexible, efficient strategies. Many of us were not taught math in ways that actually develop number sense. I know I did not think like this until I was an adult. Not because it’s hard for kids to learn to reason like this, but because for the most part, I was only taught one inefficient way to get an answer, and often lacked deeper conceptual understanding because of the way material was presented to me in school. Because of this, I struggled to apply any of the “fake math” I learned in school to problem solve. I thought math was misery. It really limited my choices for future careers, many of which I was interested in pursuing but felt were out of reach for me because I was petrified of math! In reality, I was never really doing math that entire time.
Each of these strategies can be modeled and practiced with hands on experiences. When students get the opportunity to use visuals, these are the types of things their brains naturally do. You may not understand these strategies yourself, YET…and HEY! No judgement! For real! You may wonder, who cares how they do it as long as they can get the answer? When I get that response, I usually ask-
Shouldn’t we ALL care about providing experiences that teach our kids how to think logically, build their reasoning and creativity, and develop complex problem solving skills? After all, they are going to be taking care of us when we are old yall.
It’s never too late to learn real math! And it’s never too late to learn to teach real math! If you are ready to drop your math anxiety and fall in love with mathematics…if you want your kids to cheer when it’s math time and beg for more math…call us! We can help YOU make this happen! YOU CAN DO IT!