Person Making Small Talk: "How's work?"
Me: "Not much happening. I'm having some trouble filling a math position."
Person: "What's the problem no smart kids at the college?"
Me: "Plenty of smart people applying, but all of them would make terrible tutors."
Person: "What? If they know the material, why wouldn't you hire them?"
Person: "How have you been?"
Me: "Not bad. I'm struggling with this student grade school student I'm tutoring right now."
Person: "What? What are the learning?"
Me: "Fractions mostly."
Person: "Anybody could tutor that. Why would someone hire you?"
As a neophyte in the field, I asked these same questions myself. Indeed, I certainly understand the line of thinking which leads to them. However, they undeniably ignore the value and importance of an "educator." I know, I know, stop tooting your own horn. Seriously though, these people are important.
With that said, they tend to be overvalued by society given our current format of education. Teachers walk upon hallowed ground in our society when they should be universally lambasted. I think an unfortunate overemphasis on education theory over producing educated educators persists in our universities. I also think every educational paradigm erected by mainstream America leads to ignorance. However, a real need for true teachers does exist. I will not call myself one of these, but I will give a personal example of a distinction between an experienced educator and a lay person educator.
Let's take the second mock discussion produced above. Anyone with half a brain knows grade school addition of fractions. Anyone with half a brain can teach a normal, well adjusted, well behaved kid it then too right? Yes, but there's certain nuances which will tend to go unnoticed and analyzed.
The child I'm tutoring currently writes his addition problems in the following way.
Sorry for the formatting, but I want the process to be clear in its progression. Now, that's how this student writes his fractions. Good for him. It makes sense. He writes the problem down accurately. Now he goes to solve it.
Other kids (myself included), would instead write the problem like this.
I assume most people instantly notice the distinction between these two progression, and most people would recognize the difference while helping a child. I also assume most people would probably think little of the fact.
Anecdotal evidence means nothing in science. My personal experiences from an incredibly biased and small sample mean nothing in science. Education ain't exactly a science though. Nine times out of ten, the student who write his fraction in the former way has no idea what the hell he's doing. He can't add. He can't reduce fractions. He can't convert from mixed numbers to improper fractions. (Interestingly, he will be able to multiply easily and divide to some extent. However, it will come back to bite the kid when dealing with rational functions in algebra). Furthermore, you'll have twice as much trouble even teaching the kid who writes them in the former way.
In essence, this young man cannot understand the fraction as a concept. Many people, including adults, do not, but his muddled formulation expresses itself in an easily recognizable and pernicious way. His writing of the problem betrays this misunderstanding. He sees fractions as primarily an organizational construct between the horizontal lines on a ruled sheet of paper (I could write an entire post about my hatred of ruled paper. Seriously, requiring it is like teaching an art class using coloring books and a single crayon.). This leads to many common errors since with this conception he essentially sees two distinct problems of 1+2 and 2+3, merely linked together by this fraction bar which has little physical reality. Also, this presents special difficulties when attempting to reduce fractions. It becomes a chore to convince him that the same number must divide numerator and denominator to reduce. Luckily, I could recognize all of this within the first three seconds of working with the child. Yes, these difficulties make themselves known eventually. However, a distinct difference exist between a kid who just doesn't know the rules and a kid who has a flawed mental image of an object which will continually clash with the rules your try to teach him. People find fraction rules and procedures arbitrary, even after learning them, because of this collision between mental image and conceptual reality.
Another lay person mistake would occur after reading this post. I've shared this with one or two other people already. Unfortunately, despite being the field themselves, they remarked, "So why not just makes him write them the right way?" As I've said before, there's no right way. Further, you must be careful and have exceedingly good reasons to crush a child's style. Arbitrary rules and regulations and forced conformity turn children away from education. Most importantly though, this would not accomplish anything. Although his method of writing strongly suggests a lack of understanding, it does not cause it. Instead you must tasks yourself with building a correct concept in the child's head. He will then either change the way he writes his fractions from his own realization, or he won't. As long as he understands the concept though, it doesn't matter how he writes anything.
In other words, you still need to pay $50 / hour to tutor your kid in third grade level maths because I just told you so.
