Why are we still teaching algebra?

[John K Jordan]

...Formal operations (abstract thinking) starts about 10-12 years for most kids according to Piagetian theorists (a leading educational psychologist in the 50's-80's). But there have been cases of kids reaching that stage much, much earlier. ...

It would be a shame to start some types of education to fit the average and fail to identify and challenge those who might benefit earlier.

An example - a friend here started at the U of TN Animal Science when she was 13 and graduated number 1 in her class, in Vet school now. Fortunately, she had strong family support.

I've known some without such support and challenge - they seemed to always be bored and frustrated, some labeled trouble makers in public schools. Maybe there is better screening in public schools these days and special help for those on the far end of the spectrum.

[Charlie Velasquez]

It would be a shame to start some types of education to fit the average and fail to identify and challenge those who might benefit earlier.

An example - a friend here started at the U of TN Animal Science when she was 13 and graduated number 1 in her class, in Vet school now. Fortunately, she had strong family support.

I've known some without such support and challenge - they seemed to always be bored and frustrated, some labeled trouble makers in public schools. Maybe there is better screening in public schools these days and special help for those on the far end of the spectrum.

Actually, the last couple of decades I saw just the opposite.
With the advent of the No Child Left Behind legislation federal money was tied to student achievement. Achievement was measured in several ways including the number of students passing minimum grade level competency tests, the disparity between the scores of the whole group and various sub-groups of your student population, and having a minimum percentage of students taking the test so as to not inflate the scores by having low kids just not test. A district did not get points for how high students scored, only how many passed minimum competency (in Iowa that was at the 40th petcentile on the Iowa Test of Basiic Skills /Educational Development as measured on the 2001 tests).

Not only was federal money dependent on the scores, but state busing money and other ancillary expenses were affected. Newspapers published these scores and resultant labels (watch lists, schools or district in need of assistance). Realtors listed these when selling houses.

One can see immediately a school can improve their chances of staying off the bad lists by focusing their efforts on the students who were the bottom 40% or on the bottom of the at-risk populations (low social economic, English Limited Learners, special education). So that is what many districts did. District money and teacher inservices focused on these students. Schools' curriculum was modified to emphasize the types of problems the "bubble kids" were likely to have on the ITBS.

The first place money could be found to pay for this shift was from the budget of the talented and gifted as those students would hit the minimum level regardless. So, many did. In some districts there was immediate backlash. In Seattle parents of T&G students threatened to pull their kids from state tests if the T&G budget was not restored. This would reduce the number of kids passing, thereby increasing the percentage of kids not passing, and possibly reduce the participation number below the critical threshold.

Other districts handled it more discreetly; more stringent requirements to qualify for the T&G program or making the program a push-in rather than a pull-out (so the T&G teachers could also work with the other students in the class, freeing up the classroom teacher for a time to do remedial work with the lower 40%).

This new focus was successful. As a nation we did improve instruction for the lower 40%, and the spotlight on achievement gap of various sub-groups helped to identify where we were failing. But, there were casualties. Subjects not on the state assessments were left to hang in the wind. In our district penmanship, spelling, and social studies were de-emphasized. And, I suspect, the T&G and the near T&G kids got less indvidual attention.

[William Adams]

And that's it in a nutshell.

Education would be best if it enabled each student to reach their maximum potential and be the best possible citizen, and it's a disservice to society to fail to give any student the best education which they are suited for.

Getting back to the original topic, the game "Dragonbox" is essentially an Algebra tutorial --- highly recommended.

[Jim Koepke]

In Seattle parents of T&G students threatened to pull their kids from state tests if the T&G budget was not restored.

Even with my rusty algebra skills it wasn't difficult to solve for T&G.

Why are some students called Tongue & Groove?

Is this a special class in high schools now? Isn't it just part of wood shop?

jtk

[Dave Zellers]

Yes! Solve for T&G and show your work.

Now I understand why this thread became so long.

Both machine and hand tool answers will be accepted.

[Pat Barry]

Actually, the last couple of decades I saw just the opposite.
With the advent of the No Child Left Behind legislation federal money was tied to student achievement. Achievement was measured in several ways including the number of students passing minimum grade level competency tests, the disparity between the scores of the whole group and various sub-groups of your student population, and having a minimum percentage of students taking the test so as to not inflate the scores by having low kids just not test. A district did not get points for how high students scored, only how many passed minimum competency (in Iowa that was at the 40th petcentile on the Iowa Test of Basiic Skills /Educational Development as measured on the 2001 tests).

Not only was federal money dependent on the scores, but state busing money and other ancillary expenses were affected. Newspapers published these scores and resultant labels (watch lists, schools or district in need of assistance). Realtors listed these when selling houses.

One can see immediately a school can improve their chances of staying off the bad lists by focusing their efforts on the students who were the bottom 40% or on the bottom of the at-risk populations (low social economic, English Limited Learners, special education). So that is what many districts did. District money and teacher inservices focused on these students. Schools' curriculum was modified to emphasize the types of problems the "bubble kids" were likely to have on the ITBS.

The first place money could be found to pay for this shift was from the budget of the talented and gifted as those students would hit the minimum level regardless. So, many did. In some districts there was immediate backlash. In Seattle parents of T&G students threatened to pull their kids from state tests if the T&G budget was not restored. This would reduce the number of kids passing, thereby increasing the percentage of kids not passing, and possibly reduce the participation number below the critical threshold.

Other districts handled it more discreetly; more stringent requirements to qualify for the T&G program or making the program a push-in rather than a pull-out (so the T&G teachers could also work with the other students in the class, freeing up the classroom teacher for a time to do remedial work with the lower 40%).

This new focus was successful. As a nation we did improve instruction for the lower 40%, and the spotlight on achievement gap of various sub-groups helped to identify where we were failing. But, there were casualties. Subjects not on the state assessments were left to hang in the wind. In our district penmanship, spelling, and social studies were de-emphasized. And, I suspect, the T&G and the near T&G kids got less indvidual attention.

T&G kids don't deserve more public funding than those with special needs or your typical, run if the mill, average students, do they? On the other hand, brining up the average by teaching the less than T&G makes the most sense. Not to say that the T&G should be neglected, but, lets face it, they are already ahead, so maybe they should be moved up a grade.

[Jim Becker]

Pat, the issue with "moving T&G students up a grade" is that it often puts them in with students that are at a different development level emotionally and socially and that can be a a real problem for many. By providing more challenging and stimulating material in their normal grade for age, they get what they need to develop intellectually without compromising them being normal, growing kids otherwise. The programs also benefit the more average students in that they (and their teachers) are not distracted by having time taken for more advanced studies in the mainstream classroom. The purpose of education is to help each and every student be the best they can be...poor funding aside.

[Pat Barry]

Pat, the issue with "moving T&G students up a grade" is that it often puts them in with students that are at a different development level emotionally and socially and that can be a a real problem for many. By providing more challenging and stimulating material in their normal grade for age, they get what they need to develop intellectually without compromising them being normal, growing kids otherwise. The programs also benefit the more average students in that they (and their teachers) are not distracted by having time taken for more advanced studies in the mainstream classroom. The purpose of education is to help each and every student be the best they can be...poor funding aside.

No good answer for sure, and I'm not convinced algebra can solve the problem. Probably involves calculus.

[Charlie Velasquez]

Pat, the issue with "moving T&G students up a grade" is that it often puts them in with students that are at a different development level emotionally and socially and that can be a a real problem for many. .....

This was the case for one of my students, similar to John's friend, a prodigy. Entered our school as a 5-year old kindergartener, a month later they put him in 1st grade with extra instruction. Skipped 2nd grade. Third grade with extra instruction. Fourth grade he came to my class for 5th grade math and science. Semester he was moved to my fifth grade class full time. We flip-flopped specials (art, music p.e.), he went with the other 5th grade section while my class had math. When my class had specials he stayed for one-on-one math.

His family moved to Moline, IL during the summer. I saw his dad the following October and asked how Chad liked middle school.
Dad replied, "He's not in middle school. We had him repeat fifth grade. As we got ready to register we told him of all the advanced things he would learn. He started crying. He told us all he wanted was to be able to play kickball with his classmates."

My class had always included him in recess games and things, but the kid was smart. He knew he was the worst kickball player, the slowest in races; he knew he was different. He had always had emotional support from our staff, his parents, and his classmates; but he still knew. Saw his mom many years later. Chad was married and was working for Qualcom (are they still around?). Said holding him back was the best decision they ever made.

[Jim Becker]

Your story about Chad doesn't surprise me...and it just reinforces my feeling that adapting the learning for more gifted students while letting them still have the opportunity to be kids with their age peers is a good thing. And thank you for being a teacher...the most important occupation in the world bar none.

[Jim Andrew]

I was that PITA kid who always could show the teacher a simpler way to solve a problem. In spite of my public school education, I found math skills very helpful in the construction business. Especially before I bought a calculator. I would have loved to be allowed to graduate a year or four early.

[Ole Anderson]

Algebra is basically the intro course to more complex math. How are you going to know math is your stuff if you don't try it out? My question is why Latin?

[William Adams]

Latin helps one to understand the well-springs of our language, and is an excellent foundation for the arts and sciences, all of which are helped by knowing it.

For the story about Chad --- that's why the school system which I attended for 3rd and 4th grade limited working ahead of one's grade level to academic courses only --- one still did recess and so forth with one's peers. It was a great system until the state Supreme Court ruled it illegal.

[Bob Glenn]

My school didn't offer Latin. I sure could have used it more than algebra. I agree, algebra is an intro to higher math, which most people don't use. A lot of the examples cited in the previous posts are simple arithmetic problems, nothing more. (is your six foot long board long enough if you need a 30 inch piece and an 18 inch piece? Really?) Please look to wikipedia for a description of algebra.

[Brett Luna]

A lot of the examples cited in the previous posts are simple arithmetic problems, nothing more. (is your six foot long board long enough if you need a 30 inch piece and an 18 inch piece? Really?) Please look to wikipedia for a description of algebra.

Wikipedia may not support your assertion as much as you think: "Whereas arithmetic deals with specified numbers,^[1] algebra introduces quantities without fixed values, known as variables.^[2]"

Yes, the problem as you presented it is arithmetic because it is the special case where the quantities are specified numbers...with the added wrinkle of asking if the stock board is long enough, yes or no. But another way of looking at it is: I have several boards on hand in various lengths. What's the shortest board I can use to cut a given number of shorter boards? In algebraic form you can express it as:

TL_min = L₁ + L₂ [... + L_n]

Where:

TL_min = total minimum length of stock board

L₁ = length of board 1

L₂ = length of board 2

L_n = lengths of additional boards

This is a generalized representation that can be applied to specific problems. It is both algebra and simple...so simple, most of us substitute for L₁ and L₂ then solve for TL_min on the fly, in our heads, without really giving it a second thought...or showing our work.