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I just went back to read the article by A. Toom , in which he explains how he taught word problems to Algebra class students. He gives an example of the chart and stresses the importance of organized and clear writing.
When I was in school, I was taught to organize all problems in chemistry and physics in a chart. This skill is extremely useful when dealing with word problems.
Our teachers taught us to use the following chart (in math, physics, and chemistry alike):
Given:
Asked
Formula:
Solution:
Answer:
Consider the following problem: A block of unknown material weighs 100g and has the volume of 25 cm3. What is the density of the block?
Given:
m=100g
V=25cm3
Asked:
d=?
Formula:
d=m/V
Solution:
d=100g/25cm3=4g/cm3
Answer:
Density of a given block is 4g/cm3
So I used this type of chart routinely and could see clearly what is given in the text, what I have to find, what formula will suit my purpose, check if the units are correct, and a teacher could easily check my reasoning on each step.
When I went to a Community College in NY (confession - I didn't show my DVM diploma so I could be allowed to take undergraduate courses in English and get the financial aid in the beginning), I observed many students struggling with simplest chemistry problems because they could not organize them , and were lost in words. I tutored at least 20 Chemistry students during my years in college, and all troubles were gone as soon as they got the habit of using the chart.
When I started teaching physics to my 7th graders and, recalling my own physics classes in school, started giving them word problems, I faced the necessity of teaching them an organized manner of analysis. Yes, using the chart can be considered an analysis of a problem. It took me a month and 3 quizzes until they got it. I modeled the chart on the board for every problem we did (again, since American textbooks in physics do not have problems!, I had to make most of them myself or translate from the Russian text), I took points off for absence of the chart of absence of steps in solution, but we did it. By the end of physics part (oh, I hate general science! nothing is complete!), ALL 31 of them could solve word problems using the chart. Their math teacher told me that some of them were using the chart in math HW problems (obviously, she was giving some word problems, too)
I still didn't beat their sloppy handwriting, even though I had some students' works returned with F because I couldn't read it... It takes consistency and discipline. And math is the great helper in disciplining the mind.
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5 comments:
"It takes consistency and discipline. And math is the great helper in disciplining the mind."
Amen to this. I think the mental discipline acquired from math leads to success not just in the sciences, but also in professions such as accounting and law.
I think I may be reiterating what others have already said, but I get the feeling that a number of today's generation of teachers may not understand how important acquiring these traits are for success in many of the disciplines.
How can a child acquire discipline of the mind when there are those that work as hard as possible to create curricula that specifically avoid just this? Thinking is hard. Most people don't like doing it. It's easier to not require it.
If you require thinking some children will not do it and fail. We are assuming of course that the class has been taught properly, I don't mean this to be an excuse for the teacher to leave all the teaching up to the parent.
I will give you a foreign language example, in the immersion approach the students take many multiple choice tests which don't require them to know any grammar. A test item might look like this
What's the weather like today?
a) cloudy
b) pink
c) 14 years old
d) Nice to meet you.
That is very passive, perhaps good for the very first quiz in class but it requires no problem solving or decision making in the same way parsing and translating does. And the tests that come with the program are like this for two years, not just the first quiz. The questions are all concepts and no procedure. Of course it is not helpful either to have all procedure (writing out charts of verbs) but no concepts(communication).
I am sure there must be math ed equivalents.
THANK YOU!!!
Saxon teaches charts, Dolciani uses LOTS of charts, as does Brown in Basic Algebra...but somehow I got the idea that charts were "cheating."
I wasn't sure about using them to teach C. this summer.
Which article are you referring to?
How I Teach Word Problems. Primus,
v. VII, n. 3, September 1997, pp. 264-270.
That's the one.
And charts ARE NOT CHEATING - for sure!
It's just the way to organize information.
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