Teens criticize 'CHIMP' math (fuzzy math alert)

Times Herald-Record ^ | Dec. 3, 2002 | April Capochino

[mathluv]

I'm thinking that many people's perceptions of what constitutes word problems v. problem solving may be different than the perceptions of others.

I will try to give an example of each. to me, a word problem or a story problem can usually be worked out in a minute, two at most. In fact, some children will quit if they can not get an immediate answer.

Word Problem

Sound travels through air at a speed of 1,129 feet per second. At this rate, how far will sound travel in 1 minute?

Simple arithmetic can solve this problem. Not much thinking is required - just do more of what that lesson has been about.

Problem Solving/Critical Thinking

Create a multiplication problem where the product is 45.89 and one of the factors is a whole number.

This second problem has more than one answer. It can create some discussion in the class. Students must think! Their reasoning and explanations can let the teacher see the level of understanding reached, or where there may be additional teaching needed.

[meyer]

Word Problem

Sound travels through air at a speed of 1,129 feet per second. At this rate, how far will sound travel in 1 minute?

Simple arithmetic can solve this problem. Not much thinking is required - just do more of what that lesson has been about.

Well, that kind of question might be appropriate to one who is learning to apply multiplication. The basis could be made more difficult if the problem also asked what the distance was, in meters if they were learning metric/imperial measurement conversions at the time. Its a basic problem, but one that is part of the stepping stones to learning higher math.

Problem Solving/Critical Thinking

Create a multiplication problem where the product is 45.89 and one of the factors is a whole number.

This second problem has more than one answer. It can create some discussion in the class. Students must think! Their reasoning and explanations can let the teacher see the level of understanding reached, or where there may be additional teaching needed.

OK, this produces a new concept, and isn't a bad problem even if it doesn't show a practicality to calculating such a number. It teaches perhaps a different kind of thinking to a student that is learning long division, but I don't really see the significance of discussing it for more than about 2 minutes. I mean, what's to discuss? Johnny divided by 4 and Judy divided by 5. Why? Because Johnny likes the number 4 better? BTW, I'm hoping that the students given this question have already been taught the relationship between multiplication and division.

I prefer my math to be both exact and practical. In that respect, I don't think I see the real relavance of the latter method.

I don't see either question being offered at the high school level. At an elementary level, perhaps. But remember that elementary math is just a building block towards higher level math, algebra, and beyond. So, the types of problems that are given to a student as they progress through the different concepts must be prepared with the long-term goal in mind. Frankly, I think the former does a better job of that than the latter as it illlustrates usefulness. If math isn't found useful, why would anybody be expected to learn it?

[FreedomCalls]

The Evolution of Math Teaching

• 1960
  A logger sells a truckload of lumber for $100. His cost of production is 4/5 of this price. What is his profit?

• 1970 (New Math)
  A logger exchanges a set of L lumber for a set of M money. The cardinality of set M is $100, and each element is worth $100. Make 100 dots representing the elements of set M. The set of C of the costs of production contains 20 fewer points than set M.
  Represent the set C as a subset of M, and answer the following question: What is the cardinality of the set P of profits?

• 1980
  A logger sells a truckload of wood for $100. His cost of production is $80, and his profit is $20. Your assignment is to underline the number 20.

• 1990
  By cutting down beautiful forest trees, a logger makes $20. What do you think of this way of making a living?
  Topic for Class Participation: How do the forest birds and squirrels feel?

[A CA Guy]

Good God you were correct. All I can say is we need to disolve the F'ing Teachers Union and about 90% of the administrative jobs. The way they destroy kids just makes you want to fire these dolts instantly.

***********GROWL**************

[mathluv]

Both of these examples are 6th grade. By discussion, finding out how and what a child thinks can help get them going in the direction you want them to go, or get them turned around if they are headed the wrong way.

BTW, I'm hoping that the students given this question have already been taught the relationship between multiplication and division. In today's classrooms, with IMP or Saxon (opposite ends of the spectrum), don't count on it.

Thinking and reasoning are very important in learning math. Math is not always about practicality. If so, use a calculator. Funtionality is based on thinking and reasoning and applying what you have learned.

Math is changing - in some good ways and some not so good ways. My first year to teach was when "new math" started. The texts were new, and I had not had any of it in college - (like graphing inequalities on a number line). My ex tried to help our first grade son, and could not do the math - <, > were new in the texts. Now things are getting moved down further in the curriculum, and basics are getting less emphasis. Manipulatives were new 20 years ago in the US (40 in Europe), and are rarely used now. There are times when they are very beneficial, but teachers tend to teach how they were taught. Many consider them too time consuming.

Finding certified teachers is hard, whether math or otherwise. There are too many who are ill-prepared. I blame a lot of this on universities. The profs that can do research get more time and money. Those that can teach get run off. Teachers are not highly valued in our society. Discipline is becoming non-existant in our schools. All of this leads to kids learning less.

[maxwell]

Just get you some tungsten wire and hook it up to a voltage source and run some current through that sucker, dude... Well ya might wanna make sure about the resistance dependence on temperature...

[mlmr]

NO Saxon users I know of count on their fingers. Anyone who uses Saxon correctly has a child who is doing math.

[Billy_bob_bob]

"But Edison did invent the 20th Century."

I have to disagree. If any one person could be said to have "invented the 20th Century" that person would be Tesla, IMHO. Edison was great, no doubt about it. However, Tesla's inventions and contributions had even more impact and even further reach than Edison's. Again, IMHO.

[maxwell]

Create a multiplication problem where the product is 45.89 and one of the factors is a whole number. This second problem has more than one answer. It can create some discussion in the class. Students must think!

Actually it has an infinite number of answers, i.e. the set of integers. Real and imaginary both, I reckon... I don't think most kids would grasp that...

To get back to what you were saying about problem-solving, math, I see your point. I've been tutoring kiddies in algebra, etc. for a number of years, though, and one thing I see consistently is a lack of a basis by which to solve a problem at all... I think that is something that the Saxon curriculum addresses nicely...

[Doctor Stochastic]

I do that, and I'm only a customer.

[mathluv]

That may be true with kids being homeschooled, where parents are spending the time to teach math. I have seen kids counting on their fingers in the classroom. Teachers can not give the individual attention parents can.

[mathluv]

Actually, it is not the set of integers. It is the set of whole numbers. That excludes negatives.

[mathluv]

one thing I see consistently is a lack of a basis by which to solve a problem at all... I think that is something that the Saxon curriculum addresses nicely... I am guessing you mean real world application. I find very little of that in Saxon, compared to other books.

[maxwell]

Forgetting my math terminology here-- "whole numbers" = integers > 0?

[mathluv]

Whole Numbers = 0,1,2,3,...

[general_re]

Does anybody know about the mathematical/scientific background, or lack thereof, of "San Francisco State University professors Dan Fendel and Diane Resek"?

Dan Fendel
Diane Resek

[mathluv]

Both are listed as profs of math. His degrees say BS math Phd math. Hers don't. Her interest say a lot - women and math, etc.

California is known for its "new" ideas for education. IMP is a good example. (/sarcasm)

[maxwell]

I am guessing you mean real world application. I find very little of that in Saxon, compared to other books.

Well I suppose we will have to part ways on that one.

I still think that once a good solid basis is set, that any half-way bright kid will see his way to extrapolate, interpolate, or do whatever he has to. I may not've learned what a whole number is, haha, but I could solve the heck out of a high school physics problem...

[mathluv]

And Physics is not my favorite subject!

And as I said, in comparison to other books. Have you seen other texts besides Saxon?

[Spyder]

You left off the last one ;-)

Teaching Math in 2000: a logger sells a truckload of lumber for $100. His cost of production is $120. How does Arthur Andersen determine that his profit margin is $60?"