| Box by my student Richard Bell as featured in Lee Valley Newsletter |
As I was on my evening walk last night, I thought about the odious word problems presented in math. There was one from the first SAT administered in 1926 in the margins of the Botstein's essay. It goes like this: "If a package containing twenty cigarettes costs fifteen cents, how many cigarettes can be bought for 90 cents?" It doesn't say how many multiple choices were offered or what they were, but the word problems offered in math are simply an attempt to show math used in contrived context in artificialized learning. The problem of word problems is obvious to anyone who has done math to solve real world problems as offered in wood shop.
Botstein asks that new tests be developed to replace the SAT. He says, "The truth is that the only legitimate test is one in which a question is put forward and an answer is required with no options or hints." I suggest that the only legitimate test is one in which the answer applies directly to real life, and its correctness is measured in the success of doing real things, not by the College Board. The questions to which there are right and wrong answers are the ones that are wrong to be asking kids if we are concerned about developing a lifelong love of learning.
Today I am signing a contract for another book, will travel to buy walnut for box making and will prepare for a weekend class. The tool box shown in the photo above was made by one of my students at Marc Adams School of Woodworking. I remember when he worked on it is class and I suggested he send it to the Lee Valley Newsletter. It was published in this week's edition.
Make, fix and create...
Sorry, I don't see why :
ReplyDelete"The problem of word problems is obvious to anyone who has done math to solve real world problems as offered in wood shop."
You can not learn Math without understanding the language, especially geometry theorems.
When you plan to build something in wood, you have to calculate how many boardfeet you will need; this is similar to the above problem.
Your woodworking classes are a way to connect reality with academic teaching. Why should it be forbidden to the math teacher? Math is useless (except if you like it for itself) if you can not put things yourself in equations. That is what is tested with word problems.
Sylvain
The problem with word problems is that they tend to be contrived and appear to the student as contrived, and of course there is no problem with a math teacher using language to build an understanding of math concepts. Figuring out how long it would take for car A to reach its destination relative to car B given car A left 1 hour before B but is traveling at a 10% higher speed, while the car B is going 45 mpg and reached its destination in one hour is the kind of thing I remember being asked to do in math classes or on SAT tests. That is all well and good, but you have to admit it is contrived and artificial, which was my point in this blog post.
ReplyDeleteMy point is not to forbid the math teacher from using word problems in an effort to make math appear useful, but that there are plenty of real things to do with math that would make it appear useful, relevant, and un-contrived.
Dear Doug,
ReplyDeleteIn Belgium in the years 1960, word problems were part of the curriculum for children between 10 and 12 years old. This part of the curriculum was not math in itself but was called ( if I remember well) "metric system". it was about length, area, volume/capacity in relation with simple géometric forms (square, rectangle, trapeze, circle, ..., sphere). School was mandatory up to the age of 14 (later extended to 16 and later to 18). I have vivid recollection of the teacher demonstrating liter and deciliter withe stndard measures and water, measuring the classroom with a tape rule etc. I think a child leaving the school at the minimum age should be able to calculate how many tiles he needs to pave its bathroom (a bit later obviously) or how many wall paper rolls he needs for a room etc. For this you must developp the ability to put real things in equation. That is why word problem solving is a usefull skill and not solely an artificial academic knowledge.
The same person must be able to sell what he makes or produces, so he must be able to price quantities. How can you be a full citizen if you can not compare, as a customer, prices and quantities?
Word problems with time and speed came later in secondary school in the physics curriculum.
Sylvain
Sylvain, My point is not that word problems are useless, but rather that they are most often presented to kids outside of context as isolated word problems. How much better it would be if word problems came up in the course of doing real things.
ReplyDelete