Question about elementary mathematics and teaching

[Alex Franke]

Who uses fractions of a foot other than surveyors? In practicality the questions would be "how many six inch pen blanks can I get from twenty one inches of zebrawood?" Which would be an easier 21/6 = 3 and a half.

It was just an example, but one in inches might have been better: Say I want to evenly space holes 1/2" apart across a 1 3/4" wide board for some fancy jig I'm making. How many holes would I end up with, and what's the remainder that I would split on either side of them? (Four holes, and 1/8" from each edge -- four holes because one is at "zero", and 1/8" because that's half of 1/4, which is the remainder, or 1/2 of 1/2" -- gosh, that hardly makes any sense at all when I try to write it out. :lol: But again, the specific example isn't really my point.)

My point is, really, that it seems easy to figure these out in context but it's not so easy out of context unless you remember the procedure. And, I think a part of the problem is that it's not so easy for us to come up with a "story" or context that matches the procedure. If the research is valid, then it seems like that link from procedure to story isn't being taught or learned -- for whatever reason.

Another thing to look at is errors in the study. The sample size was tiny, in fact statistically insignificant. The teachers tested may not teach these concepts and with math if you don't use it you lose it, especially with a elementary school teacher which is the "jack of all trades" when it comes to teaching.

I completely agree. It's clearly a small sample, and if the teachers don't teach it, then why would they be expected to know it?

But again, it seems like maybe it *should* be easier to create a conceptual story out of a problem like that, especially if the conceptual story is more intuitive or easier to solve.

[Alex Franke]

To put the example in question format would be redundant. "What is 1 3/4 divided by 1/2?" is already a word problem.

Yeah, it's two different ways of asking the same thing, but I think one method better illustrates the concept of dividing something by a fraction, while the other does not.

Mrs. Franke has baked two pies. She gives a quarter of a pie to Mr. Franke and has one and three quarters of a pie left. She will give a half a pie to each boy. How many half pie pieces does she have for the boys. Express your answer as whole numbers and fractions there of.

Pies cost a half dollar each. Alex has one and three quarters dollars. How much pie can Alex get. Express your answer as whole numbers and fractions there of.

Now I'm hungry.

[JR]

I have been reading a lot about elementary education over the last couple of weeks.

The LA Times has produced a very revealing, and controversial, series of articles on which teachers in LAUSD are more effective than others. "Effective" is defined as those whose 3rd-, 4th-, and 5th- grade students consistently do better on standard English and Math tests after having been in their class.

The data used for the analysis covers several consecutive years. Many surprises were in store. Teachers could be found in schools throughout the district, including those with high numbers of immigrants and economically disadvanaged, who always managed to get kids to perform better than they had previously. It was also found that some teachers, thought to be excellent, motived, involved educators, well respected by admistrators and peers, turned out to have mediocre results. Many schools thought to be "excellent" showed they were not better at improving test results than those thought to be poor performers.

There were two main controversies from the point of view of the teachers who wrote into the Times:

1. This form of analysis, which many found helpful, is clearly insufficient to form an entire picture of teacher capabilities. Even good teachers may be inhibited by admistrator deficiencies and other "bad school" problems. Also teachers with classes of expceptionally good students can hardly excell using this analysis method if the kids come into the class with perfect scores; the best they can do is stay level.

2. The data, including teacher names, was posted on latimes.com. This is going to cause all heck to break loose, as parents try to get their kids inot the "right" class, not to mention the advisability of posting a personnel matter for the public to see.

This data is not currently used in any way by the district. The Times obtained it using a freedom of information request. It is thought that by finding consistently effective teachers, they could be used as role models for other teachers who could learn their techniques. It is also thought that teachers who perform poorly could be more easily identified and helped to improve. To their credit, a few of the teachers writing to the Times were surprised by their low numbers and took it ias a challenge to improve.

FWIW - fifth graders must divide fractions on the math test.

JR

[LCHIEN]

one of the real challenges for math and science teachers must be to make the subject matter relevant. Another challenge is to make the math useful, i.e. being able to pose a question in english and then create the correct equation that will solve for the desired answer.
Finally problem solving needs to start with nothing but a question - and no statement of facts , e.g how many or how fast or whatever - in other words make the student determine what other numbers are required to get an answer.
Simply given: In what year will Bill be twice as old as Mary?
Student should ask: How old is Bill? How old is Mary? What year is the question being asked in?
One of the problems with the textbook approach to problems is that you always know that everything you need in the equation is there, AND almost certainly there's no information there that doesn't need to be used. In real life we're always posed questions with too little information, too much extraneous information and some that clearly isn't even trustworthy, but that's yet another matter (to determine a quality factor on the result).


English semantics are tough. There's a big difference between "divide by half" and "divide in half".

[Kristofor]

I knew the right answer but I think that says as much about my memory as my mathematics skills...

Rarely used skills/functions invite simple mistakes. Folks that can easily remember/calculate what 4^2 equals may have a brain fart if asked to calculate 4^(1/2), or 4^(-2).

Now, I could re-develop the answer if I happened to forget the rule (4/2 =2, 4/1 =4, 4 / 0.5 =8, etc.) and that's something I'd hope a teacher would be able to do when asked. But I can also understand folks making mistakes trying to answer off the top of their heads.

Additionally, as phrased, that question simply doesn't relate well to frequently made calculations. If you asked how many pints are there in 1.75 quarts it would be a much easier question (assuming they know their UOMs).

[gsmittle]

Mrs. Franke has baked two pies. She gives a quarter of a pie to Mr. Franke and has one and three quarters of a pie left. She will give a half a pie to each boy. How many half pie pieces does she have for the boys. Express your answer as whole numbers and fractions there of.

Pies cost a half dollar each. Alex has one and three quarters dollars. How much pie can Alex get. Express your answer as whole numbers and fractions there of.


Bill
blackberry pie

Mr. Franke distracts Mrs. Franke and runs off with both pies to his shop where he drips pie filling on his table saw. He eats both pies, then cleans off the saw. The boys go to DQ for an ice cream cake.

We don't need no stinkin' math!

g.

[vaking]

Many years ago my son brought home a problem from school:
3+2x2=?
We quickly went over the concept of order of operations and he proudly produced an answer 7. The next day I had an angry call from his teacher. She told me the school had better ways of teaching then parents and I should stop teaching my son any math. She gave my son a failing mark for this problem because in her opinion the correct answer was 10. When I mentioned order of operations she replied that elementary school students should not be learning that. After that incident I stopped wondering about what was wrong with his school. I made a point of monitoring what the school was teaching my son and how. And at first opportunity we moved to another town and different school. Fortunately in our family match/physics were the subjects we could teach our son ourselves regardless what the school was doing. My son ended up studying math as a major in college.

[MilDoc]

She told me the school had better ways of teaching then parents and I should stop teaching my son any math.... When I mentioned order of operations she replied that elementary school students should not be learning that.

Uh huh. Great teacher.

See my post #8.

That "teacher" is not unusual.

[twistsol]

[MilDoc]

I would say "ROFLMAO," but all too true.