Write a short essay (no more than two pages) taking either the "pro" or "con" position on the following proposition:
Proposition: Problem solving can not be a central part of the mathematics curriculum in the middle school because it takes too much time. There is too much other material in the curriculum that must be covered.
Note: Neither "pro" nor "con" is assumed to be "correct." I will "grade" this on the strength of the argument you make, which ever direction you take.
Problem solving can not be a central part of the mathematics curriculum in the middle school because it takes too much time.
The above statement cannot possibly be true. I have learned over the course of this class that Mathematics can be used as a instrumental tool to navigate oneself through life...all aspects of life. Now if we are discussing Mathematics in any middle school curriculum, problem solving can be integrated through all facets of the mathematical world. What I mean when I say this is that in all aspects of math, we can relate it to some real or even unreal world problem or situation. No, you may not be able to do this for every single unit or lesson, but you can incorporate it through the child's eyes in smallest of ways. Here are some suggested ways of doing so:
We can problem solve with fractions by using a candy bar (a real one which they can see some sort of outcome) and asking the class if they would like to eat (and stress eating) this candy bar today. The only stipulation you should say is that they must come up with a way of figuring out how each person in the class will get a fair and equal share...making sure not to leave anyone out. Everyone must get a piece of the candy bar. Now sit the candy bar in clear view of the class so they can visualize what their expectations are and so they will be "tempted by the lust of wanting the candy bar" to get the correct answer.
These tendencies definitely have to do with problem solving because kids need to be able to figure out what relationship one measure has to another measure, for example, how do the growth spurts of boys differ from the growth spurts of girls or the amount of money one company pays their employees versus another company. These ideas actually relate to kids and they will definitely want to know how much taller "Becky" will be in two to six months because if she gets taller than "Todd" she will not want to go out with him any more because he will be too short for her and so she will have to find a new boyfriend. As for the money situation...when the kids begin working at real jobs or even for family or friends in the neighborhood they will want to know who will pay them the most money.
Geometry can sometimes be a huge task for kids in the middle school arena. But one way to over come the fears and frustrations are by getting them more involved with the whats, the whys, and the hows. What does this stuff mean to me, they would ask...well show them...go out and look at the structures of buildings, the structures of ramps, etc., so they can see that without geometry, they will have a shabby home or a crappy skateboard ramp. The whys...why do I have to do this they will ask...well if you want your skateboard ramp to work and if you do not want that person who knows how to construct it to charge you an arm and a leg to build it, and you know that your career may not make you a multimillionaire, then...well...I am sure they will figure out the rest.
I tell you there are hundreds of situations where the child can be engaged in real world mathematics and real world problem solving if and when the child is ready and if and when you (the teacher) are ready. Ready means that you and the students will take a little extra time to talk about how this math affects their lives and how it affects their world around them...and then how it relates back to them.
There is too much other material in the curriculum that must be covered.
What happens to the child who is never exposed to problem solving? They will end up clueless about some realms of the world. Like me, I was never totally exposed to the world of problem solving or if I was, it was always such a painstaking task that I was forever turned off by the whole subject. I thought there could in fact be a world without problem solving and that Math just was not interesting if problem solving were involved. I have now learned after being in school for so long that I do not know how I even got by in this world thinking that way. I don't know how I even made A's in math in elementary, middle and high school...notice I did not include college in this...the reason is because this was my epiphany for the whys, the hows, and the whats of mathematics. The time in undergrad told me that I definitely was not the best in math (as I once thought...gee...not even close) and I needed to get some sort of groundwork started or finished or where ever I needed to be. Now that I am in grad school, I have realized that problem solving is the key to a healthy mathematical relationship with oneself and with life itself.
I now know that I still need to study math more...those things that I just memorized...those things that I just looked at but did not take a second look...those things that I made myself not learn or not understand because I simply said "I do not think this relates to me so why am I even trying to learn this?" I just heard someone say "if a kid does not get something how can he/she move on." If this is not true, I do not know what is. This statement is like a metamorphasis for life, for growth, and for knowledge. If the child does not know how to problem solve how will he/she ever become a productive citizen of this society? how will he/she ever become a functioning person for his/herself? how? how? how?
When anyone can find the answer to any of the above questions or find the answer to the question how can problem solving NOT be a central part (or just some part) of the middle school math curriculum, when it is such an integral part of our lives?