This post may end up being a big rant, but sometimes a good rant gets everyone thinking. I want people to think about the way some teachers are suggesting that math should be taught, because I think it's just not working. Allow me to explain...
At this conference were two very competent math teachers who had some very innovative ideas on how to teach math. Unfortunately, I really just didn't agree with them.
What I want to focus on here is the concept of giving problems to students without giving them the tools to solve them just to see if students can innovate ways to solve the problems. Here is an example that was given to us at the conference:
Mrs. Lin walks into the Sweets Emporium and buys 3 candies and 4 chocolates. It costs her 26 cents. You walk into the same store and buy 7 candies and 2 chocolates. It costs you 24 cents. What is the cost of the candy and the chocolates?
This problem is intended to be given to students who are not yet well versed in the method of using algebra to solve this type of problem. They are supposed to be given the candies and a bunch of pennies so they can figure out the answer visually. This is all well and good, but as far as I'm concerned it's a complete waste of time. Sure, we could give the students half an hour to mess around with the pennies until they come up with the correct answer. OR, we could give them a 10 minute lesson on algebra, give them the tools they need to solve the problem, and then let them have it at - they'd be done in half the time! The students who prefer algebra will solve it that way, and, to be honest, the students who aren't strong in algebra will solve it visually anyway.
They are giving students problems without first giving them the mathematical tools to solve them! This is completely backwards as far as I'm concerned.
It has been proposed to me that maybe I don't like this way of learning math because I wasn't taught that way, but I think that's just not true. I can easily think of two examples of how I was taught in high school that could have been improved.
1. In English we had to read Shakespeare. I wasn't a big fan of the old-style writing and so I found it difficult to follow along. Someone in one of my university classes the other day suggested an amazing method of using a diagram on the board to join different characters together visually with pictures and words to help people remember who's who. I think this would have helped me immensely and would have been a much better way than just having us read the book out loud.
2. In French classes in high school, we spent a huge amount of time on grammar and vocabulary, but very little time on conversation. This, I believe, was a mistake. We should have spent way more time on conversational French as this is what is needed to be able to speak the language well. I think 50/50 would have been a good proportion.
So, there you go. It's not just how you were taught that influences what you think works well and what doesn't when it comes to teaching.
The other big thing is, this way of teaching math is not how real life works. When you get hired for a job, they don't sit you down, give you a problem and tell you, "Now we're not going to give you the tools yet, we're going to see how well you do on your own," then come back a half-hour later to see how you're doing with your problem solving and then give you the tools. NO, they will give you the tools, equip you as best as they can, then let you do your job (time is money!).
Some may say that this method of having students problem solve without the tools may help in everyday life. But I beg to differ. If you have a loose doorknob, you're not going to MacGyver a solution. You're going to either Google it, or you're going to get yourself to Home Depot to ask an expert what to do. And what will they say? Not, "Why don't you go home and ponder it for a while.." No, they will lead you to the tools necessary to fix it!
Anyway, I'll end this rant now. To be honest, I know these teachers are very good at what they do, and they wouldn't be teaching us this method if it didn't work for their own students. However, for the reasons mentioned above, I must, respectfully, disagree.
BRAVO Rachel! I absolutely agree with you. Having taught math for 32 years, I have played with the delivery of curriculum in many ways and have come to the realisation that we are giving the students a toolbox to take out to solve problems with. I love you analogy of learning to being employed, you would never be asked to start a task without being trained. Why would we ever want our students to attempt a task without the proper tools. People argue that our teaching methods are out of date and not effective, but I beg to differ. These are the methods that have given us the progress of the last century! I am not saying that there is no value in investigative methods, but there is often better and far more efficient ways. Should we not rather focus on making sure those kids who are buying the candies can figure out what the cost should be, including tax, and know that they are not getting ripped off. How many students can know what the price of an item should be, particularly if there is a discount, without even trying to put tax on it. I am getting tired of correcting cashiers!! Is it reasonable to have a grade 11 University level student not be able to evaluate 1/3 -2???? Maybe he needs some pennies and candies???? You are right, a rant feels good!!!
ReplyDeleteThanks so much for your comment Roger! You are living proof that the "toolbox method" not only works well, but that students thrive on it (as evidenced by your many 5 star reviews on RateMyTeachers.com). I would also add that problem solving can be and is easily taught using the toolbox method. Once the students are equipped with the tools, you just give them progressively more intricate and complex problems that really make them think as to how the tools need to be used to solve them! That's how the problems in textbooks tend to work - from simple to complex - and I know that even now there are times when I take a look at one of those really complex textbook questions and I have to struggle to solve it; it really gives the brain a workout! Thanks for your support!
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