Math is entirely abstract in nature despite its description of real world measures. Unfortunately, young children are only beginning to develop the cognitive abilities required to perceive abstract concepts and thinking when they start learning math. On the other hand, math helps develop these abilities as well. Because young students generally learn counting and basic math operations like addition, subtraction, division, and multiplication, improving their math skills revolves around making these concepts more concrete.
The first step in comprehending math involves understanding what numbers represent. The challenge is in teaching someone that numbers are sequential representations of a group of physical objects and ideas. Giving children the tools they need to grasp this concept comes in the form of any group of objects as well as a number line. Nothing is more sequential than a number line, so putting a simple ruler in front of children helps them recognize the meaning of each number as they count out their favorite toys or snack.
With a more concrete teaching aide in hand, the developing brain of a child does not have to stress over grasping every abstract element of the math. Teaching addition and subtraction are particularly easy when using something like a ruler. If the student needs to see addition, objects like toy cars can be added to a pile while a marker on the ruler is moved to the right. The inverse is true for subtraction. Meanwhile, jumping over a gap of numbers and starting out at known sums, i.e. the values we can readily add in our heads, helps students recognize the shortcuts they need to become more proficient in math.
As for multiplication and division, a number line is a bit cumbersome when it comes to showing values being multiplied. In fact, it may be useful to start off by teaching the concept of division. Because items like candy or toys can be divided quickly and easily, children may well grasp the division concept sooner than multiplication. Multiplication can then be shown as the reverse operation, thus the piles coming back together is an excellent start in teaching this very abstract concept. From there, more traditional methods like sorting columns can be used more effectively. In addition, students need to comprehend the relationships between math operations, so reversing what they already understand to teach something new is very helpful.
Moreover, improving math skills in young students is a tedious process. The reason is that these students are just learning the basic skills they need to build their theoretical understanding of the world. Math is entirely abstract and young students need to develop the proper cognitive abilities necessary to comprehend these abstract constructs and relationships. As such, improving a child’s math skills and cognitive abilities requires addressing their understanding of basic math operations. Where a connection cannot be immediately made, it is best to address math concepts that young children can understand far easier.