Explaining Mathematics to Kids

Suppose you were to ask a student learning how to subtract two digit numbers the question "What is 25 minus 18?". Let us look at how the student learns mathematics. Students first learn how to count. Everything is reasoned with the real world. 1 apple, 2 apples and so on. Most students understand this and counting things will not be a problem. In fact counting in some form is built in for most creatures albeit limited for all except humans. This form of counting has been seen in the most basic of ancient humans where things were either existing as 1 unit, 2 units or many (more than 2). To see this, ask yourself what is 8 minus 5 and then what is 2 minus 1? Both are of the same level of difficulty but the problem 2 minus 1 is more hardwired deep in the brain where as 8 minus 5 is a learned function from school. It should be the case that 2 minus 1 is done quicker than 8 minus 5.
Making the connection with the real world to learn Mathematics is a well meaning intention of teachers but will hold the student back (sooner or later). Consider the student now learning how to subtract. The teacher showing the student 3 apples and saying "3 apples takeaway 1 apple is 2 apples" and removes one apple. This is how subtraction is learned worldwide. The student may repeat "1 apple takeaway 3 apples" and the teacher would stop them. "No, you can not takeaway 3 apples if you have 1" or something to the effect which would fuse into students that subtraction only works when the number being reduced is larger than the amount to reduce.



The end result is that when the student sees 25 minus 18 then sees the 5 and 8 and reasons that it must be 8 minus 5 as 5 minus 8 makes no sense! When students learn two digit subtraction the subtle ideas may be missed. The problem here was that mathematics is taught as if it is natural to the real world. Negative numbers have no meaning in the real world. We can not show the student a negative apple.
We need to teach students the rules of mathematics "as is" and should show connections to the real world secondly. Students can naturally learn rules, be it rules to a game or structuring a sentence. It just so happens that the students play games and structure sentences naturally and they can learn to naturally think about mathematics as well.