There is a myth. It is a myth that drives math instruction in the primary levels of public education. The myth is: Students who struggle to memorize their basic math facts will struggle to solve basic math problems. The myth is grounded in the idea that math facts are a requirement to solve basic math problems. The truth is, however, that we make it a requirement, not that it is one.
Basic math fact knowledge is an essential component of basic math competency. Research tells us that knowledge of basic addition, subtraction, multiplication, and division facts is an indicator of math success in grade school and beyond. According to Royer, Tronsky, Chan, Jackson, &Marchant(1999) math fact “retrieval” is a “strongpredictor of performance in standardized tests (Research Foundation &Evidence of Effectivenessfor FASTT Math, 2005).
What about the struggling student?
But, what about students who struggle to learn their math facts? Unfortunately, for this student, failure is almost an inevitable outcome. Research indicates that students who lack basic math fact knowledge are reluctant to participate in classroom math discussions and struggle with math problem solving. Despite this fact, there is great hope for these students. However, a different approach will be required to help them.
We teach math in what we believe to be a progressive order. At the kindergarten level, students are taught one-to-one number correspondence, and they are introduced to addition and subtraction using models and manipulatives. In first and second grade, teachers help students memorize all the addition and subtraction combinations involving two single-digits to 18. There are 155 combinations in all. Despite the fact that many of them are repeats due to the commutative property of addition, the traditional approach is to have students memorize them in order starting with 0 + 0 = and ending with 18 – 9 =. In second grade, students are also expected to master their 0, 1, 2, 5 and 10s multiplication facts. In third grade, the rest of the multiplication facts and all the division facts to 12 are taught. In total, by third grade, students are expected to memorize 467 facts; 100 addition facts, 55 subtraction facts, 156 multiplication facts, and 156 division facts respectively. Due to this overwhelming number of math facts that students use to perform basic math skills, many studentssimply have difficulty remembering them all.
There is a solution…Read on!
The solution lies in getting students to do math as opposed to memorizing math facts. Many students are able to memorize them. But many students are not. It is these students who are inhibited from doing basic math because of a deficiency in basic math fact knowledge.
For students who are not able or will not put the time into learning their basic math facts, the road to math success will only go as far as their math facts will take them. This should not be the case. The reality, however, is that most students can succeed in basic math at proficiency levels if they are taught how to solve math problems with basic counting skills involving one to one correspondence.
Basic Math Solutions is an approach which seeks to help students who struggle to learn their math facts find success at solving basic math problems. The approach simultaneously helps students learn their math facts as they apply simple and easy to remember strategies to solve basic addition, subtraction, multiplication, and division problems.
What students can do with Basic Math Solutions!!
Basic Math Solutions is based on the ability of students to count. Students who can count to 100 can easily add, subtract, multiply and divide multi-digit numbers to 10,000 and beyond. In addition, they can use their counting skills to add, subtract, multiply and divide fractions and easily simplify them to their lowest terms and determine equivalent fractions. Basic Math Solutions facilitates the learning of math facts while granting success in performing basic math skills.
Conceptual Understanding & Rational:
Adding, subtracting, multiplying, and dividing are, when reduced to their basic concepts, forms of counting. Understanding this opens up a whole new world of understanding for students, teachers, and parents and can make learning meaningful for all. More important, it makes the learning of these skills comprehendible and accessible for those students who have always struggled with the memorization of math facts and who have lagged behind peers who have not struggled to master them.
According to professor and researcher Arthur J. Baroody, quoted in an article entitled, “Number Sense Growth in Kindergarten: A Longitudinal Investigation of Children at Risk for Mathematics Difficulties,” “Counting puts abstractnumber and simple arithmetic within the reachof the child.” (1987). Counting is the basis of all basic math skills.
The approach taken here provides students with the opportunity to succeed where they have struggled or failed before. I believe it also provides teachers with the opportunity to accelerate learning by bringing students to the point of applying knowledge of basic math facts to solve single and multi-step word problems. Furthermore, it helps teachers apply the strategies found in Basic Math Solutions to help students solve more complex math problems.
Who can benefit?..Read on!
The skills explained in Basic Math Solutions can be easily taught at early elementary school levels, since counting one-to-one correspondence begins at the kindergarten level. The skills provided in this approach can be introduced and taught at early levels of education giving students a head start at achieving in math. The approach taken here will, in the process, help students who struggle with memorizing math facts to learn their math facts at a faster rate compared to more traditional approaches as they enter 1st, 2nd, and 3rd grade.
Understanding the approach…
As mentioned earlier, the approach taken here is grounded in the idea that adding, subtracting, multiplying and dividing are shortcuts to counting. Insisting that students memorize facts sets some students up for failure. Many students who lack the motivation or capability to memorize basic math facts begin to lag behind their peers, and then struggle to catch up. Many give up and some stay stranded for an unnecessary period of time while their peers advance. For many of these struggling students, they just need a different approach that teaches the conceptual understanding of mathematics while frontloading skills that can help students remember their math facts.
Upper grade elementary teachers who find themselves frustrated because students are not able to solve higher level math problems due to a deficiency in basic math facts, can use the approach found here to ease their frustration. I believe a deficiency in the conceptual understanding of mathematics is one of the reasons elementary students are unsuccessful in math.
The following is an explanation of how to navigate through simple and more complex math problems using an approach that is easy to use and understand. It will give students who struggle with achieving proficiency in memorizing addition, subtraction, multiplication and division facts a chance to be successful in math.