Math has three important components with which any learner can have different levels of aptitude; computational fluency, number sense, and problem solving. On their own, each of these components have their rightful place in the learner’s toolbox. Combined, however, the three components unlock (or lock up) the comfort level of a user.
The first is computational fluency. This is simply a person’s ability to calculate the solution to a math problem incorporating two separate numbers and the basic mathematical operations of addition, subtraction, multiplication, and division. These are the basic facts and they are the foundation for ALL mathematical calculations that are done in the world. The most powerful supercomputers in the world are very fast at computing, but despite their great speed and efficiency, they are only calculating two numbers and one operation at a time. Calculators do the same thing…they calculate two numbers and one operation at a time. The human brain operates in this same way…dealing with two numbers and one operation at a time. I constantly encourage my own students to practice their basic math facts to increase their comfort, speed, and efficiency. I remind my own students that there are only four things that can be done in math: addition, subtraction, multiplication, and division. All other math skills are based on these key ideas. If you are trying to improve math performance, regardless of age, consider practicing your facts.
After fluency with basic facts has been established, learners can proceed to work on algorithms (processes) for working with numbers larger than single digit. This skill incorporates the second component, number sense. Number sense is identifying the relationships between numbers and how they work. This includes patterning, understanding place value, and using count-up and compensation strategies…just to name a few. Number sense is utilized when I ask students to estimate a solution to a problem prior to calculating an actual answer, or when I present a new skill by showing how the skill works on a simpler already mastered example. Number sense is employed when users explain their thinking of why they chose to solve a problem in a certain way (ex. Why do we “carry” numbers when we add multiple numbers or Why do we “borrow” or “trade” numbers when we subtract). Number sense will be a focus of many of my articles so that you can understand “why” numbers do what they do in our examples, thus improving your understanding.
The last component of one’s math toolbox is the problem solving aptitude. Many times, I see students who have excellent problem solving strategies (they can tell me how to get a solution), but they cannot compute the solution because of a lack of computational fluency or number sense. In other words, they can tell me that they know from the problem that they need to add some parts together to get a total, but they don’t know how to add the parts together (or they do so incorrectly). Problem solving can be very challenging for students on the other end of the spectrum, as well. Someone may be a computational expert, but have no idea what to do on a “story problem” or word problem. This real world application of math skills is what drives us all to either love or loathe math. I often tell my students that math problems don’t jump out from behind a bush and say, “I’m 2 plus 3…add me.” This makes my students chuckle, but it’s the truth. That math problem may present itself as this: I have 2 rubber ducks and I received 3 more as a reward, how many rubber ducks do I now have? This is the same problem that I illustrated before, except the math problem needs to be set up and solved by the student. This is where I incorporate the idea that math is its own language…I call it Mathanese. It’s a universal language spoken by anyone and everyone in the world who uses math. If someone is fluent in Mathanese, he/she can use problem solving skills to translate native language word clues/problems into mathematical expressions and sentences. Once translated into Mathanese, users can use their computational fluency and number sense to solve those problems for solutions. Those solutions can then be translated back into the native language and have labels applied so those solutions have real world meaning.
This is what I am here to help you with. I am here to help you learn Mathanese, because I speak Mathanese, and you will, too. The focus of my blog is to present you with strategies to practice computational facts, explanations of number sense reasoning to understand computational processes, and teach you the Mathanese terms you need to succeed as a mathematician. Choose a topic that is listed in the menu to learn more. If a topic you want to learn about isn’t available, send me an email and ask me to write something about it.
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Mr. H.