Can A Lack of Numerical Fluency Contribute to a Child Being Bored in Math?

Yes and here is how.

Students must know the basic facts of each operation (the times table, for instance, are “facts” for multiplication) before they can be successful with the more advanced computational algorithms (multi–column addition, subtraction, and multiplication, as well as long division). For far too many students, the beginning of the end of their mathematics education is their inability to handle single–digit addition fluently (easily, accurately, and articulately). 

In 1987, the Fourth Mathematics Assessment of Educational Progress reported: “Students may have trouble with two–step (word) problems for many reasons… many students have difficulty when they attend to two or more pieces of information…Many students do not know basic number facts.”

That mirrors our experience here at Mathnasium of Littleton. Many intermediate students and even middle students are still counting one-by-one to count the groups in multiplication facts or to add and subtract. This makes all of their more complex problems tedious, slow and ultimately, frustrating! These students lack the mental structures, the techniques for “figuring it out,” that are necessary for success with complex tasks. No wonder so many children hate long division! It requires fluency in all four areas!

The root of this problem lies in the way in which number facts are taught in the early grades. Great emphasis is put on memorizing addition, subtraction, multiplication, and division facts in kindergarten through fourth grade. Not only is this a painful process for everyone involved (kids, teachers, and parents), but in many cases it also does not result in the desired outcome.

Example 1: Take the example of a 4th grade classroom. The lesson of the day might be “Finding the Total Amount Spent.”

The teacher asks, “If you spend 70¢, 80¢, and 90¢, how much did you spend altogether?” The teacher wants to teach the “trick” of adding “7 + 8 + 9 = 24, and then putting a zero (0) at the end, to get $2.40.

Too many students are thinking, “7 + 8 = 7...8...9...10... 11...12...13...14...15,” then “15 + 9 = 15...16...17...18... 19...20...21...22...23...24...25 (oops).”

Sadly, “finger counters” (one–by–one counters) frequently get the wrong answer because they either count too many (as above) or too few, 23, because they start on 15 instead of 16 when adding on the 9.

Now, since the process of “getting it wrong” is so uninspiring and time–consuming, not surprisingly, many students report being “bored.” In addition, the process has taken so long that the student is no longer in the flow of the lesson, in this case, learning about how to “add a 0 at the end.” Another reason students get the wrong answer is their inability (usually through lack of training) to “retain numbers (subtotals) in their
heads.” Teacher and students are not having a good day.

Example 2: Here's another example. In a 3rd grade classroom, the lesson of the day could be “Making Change from a Dollar.” The teacher asks, “If you spend 83 cents, how much change will you get from
a dollar? Here is how we are going to figure that out. First, how far is it from 83 up to 90?”

If students have to count on their fingers to answer this, they will again be tied up in an inefficient task instead being in the flow of the lesson and they will likely miss the key to lesson or concept.

The solution to these problems is for students to have reliable, quick, knowable ways to handle single–digit addition, and ultimately, the basic facts for all four arithmetic operations. Instead of attempting to have students memorize the number facts, it is best for students to be taught to develop them. Real mathematical growth takes place when students are led through a process of building the concepts themselves, from the inside out. In addition to learning the number facts, in these cases, the students will also acquire the basic structures of multi–step problem solving.

The concepts and skills used in learning single–digit addition form the foundation of an organized approach for learning subtraction, multiplication, and division facts and are what make up Mathnasium's Numerical Fluency program. Although it may seem elementary, developing numerical fluency is one of the most important foundational programs we have - suitable and beneficial for all grades if the student was never exposed to or developed the techniques we teach. Call us to find out more! 303-979-9077.