What Math Did You Learn?

[liberalogic]

Just out of curiosity, how were taught math from elementary through high school? I was a part of the "new wave" of math techniques. I did Chicago Math throughout all of elementary and HS. The method deemphasized the basics and emphasized "everyday" application of mathematical concepts. I never really learned my multiplication tables, I never learned to do long division, I was taught to do multiple-digit multiplication through a method called Lattice (which required drawing a box to solve the problem) and I was given a calculator from fourth grade on. The curriculum was unstructured and jumped from topic to topic indiscriminately without providing any sort of foundation.

I began to work at a learning center a few years ago (no calculators allowed) and I was unable to help kids with long division because I had never done it. Since the kids at the learning center can't use calculators, they are more familiar with the ways numbers work (reducing fractions, finding shortcuts, etc.) than I am.

If anyone cares to share their math experience, I'm eager to hear. Also, the biggest question that I have is-- When did education shift from the basics and why did this happen? Who is behind the garbage that we are calling math?

 

[Kagom]

Don't know if it has a name, but for the first 7 years of my school years, I was NOT allowed to use a calculator. Then around High School and after I was encouraged to, but I didn't need to most of the time. I could do it in my head and a lot of people I was in class with couldn't. My boyfriend also can't do math to save his life because he has to have a calculator AND doesn't know his multiplication tables. :/

 

[Care4all]

Of course I am much older than you, but when I went to school we were not allowed to use a calculator grades 1-12. No Calculators allowed! (texas instrument was the only one that made calculators back then, if my memory serves me)

As far as a name given to how they taught math, none existed back then, but let's just say, everything was covered, done long form...division, multiplication etc.

in high school I took Algebra 1, algebra 2, Geometry and Calculous senior year.

 

[Truthmatters]

I was moved every year of my life during school very often in mid year.

I could not tell you what the hell methods were used.

I was all over southern California and cant even remember all the citys and counties.

I did pretty well at math and was put into algebra in my first year of High school, I was in full on rebelion mode and never opened the book.

I never took another math class until college.

I did fine in algebra 1 and 2 but never took anything higher.

 

[Bern80]

my earliest math memories are from 5th grade. We had a math masters program of independent study. Basically you progressed throught he basics and kept getting thrown harder and harder stuff. In 5th grade it topped out at long division with remainders instead of decimal places.

I know it's wrong to bring this up, but I think it's highly amusing this question was asked by someone named liberalogic.

I looked into it a little bit and found a link that may be of interest.

http://www.eklhad.net/chimath.html

also click the link on the that says something like peer reviews of chicago math.

out of curiosity what years are we talking for you in school when you learned this method?

 

[Annie]

my earliest math memories are from 5th grade. We had a math masters program of independent study. Basically you progressed throught he basics and kept getting thrown harder and harder stuff. In 5th grade it topped out at long division with remainders instead of decimal places.

I know it's wrong to bring this up, but I think it's highly amusing this question was asked by someone named liberalogic.

I looked into it a little bit and found a link that may be of interest.

http://www.eklhad.net/chimath.html

also click the link on the that says something like peer reviews of chicago math.

out of curiosity what years are we talking for you in school when you learned this method?

Funny you brought up the University of Chicago math program. When my now 20 year olds were in grammar school, our district bought into the program-for one year, it became obvious that the average students were not getting the 'processes'. It was a very expensive mistake for the district, but to their credit, they did chuck it quickly. Now the youngest was in it throughout, but that was in the 'gifted' math program, he's still excellent at math.

 

[liberalogic]

my earliest math memories are from 5th grade. We had a math masters program of independent study. Basically you progressed throught he basics and kept getting thrown harder and harder stuff. In 5th grade it topped out at long division with remainders instead of decimal places.

I know it's wrong to bring this up, but I think it's highly amusing this question was asked by someone named liberalogic.

I looked into it a little bit and found a link that may be of interest.

http://www.eklhad.net/chimath.html

also click the link on the that says something like peer reviews of chicago math.

out of curiosity what years are we talking for you in school when you learned this method?

I did Chicago Math in Elementary School from 1993 (first grade) to 2005 (my senior year in HS). The elementary program is called "Everyday Math" and is exactly as the lady from your link describes. The Junior HS/HS program begins with something called transition Math (7th grade), then Algebra I, Geometry, Algebra II, FST (Functions, Statistics, and Trig), and PDM (Precalc and Discrete Math). The JR HS and HS books focus on the reading of each section-- they give a few mathematical examples (which are the most important parts of the section), but these examples are surrounded by math history, complicated proofs (which we are not expected to know and are way above anything we can understand), and other unnecessary things. The problems at the end of each lesson focus on both the examples they show in the lesson and the reading (history, etc.). The questions should be focusing almost solely on those examples, but they don't. Instead, we have to waste time talking about Euler when we can't even figure out what the hell he did. Plus, calculators were permitted throughout all of JR and SR High School (in fact, most of the problems could not be solved without them).

 

[liberalogic]

Funny you brought up the University of Chicago math program. When my now 20 year olds were in grammar school, our district bought into the program-for one year, it became obvious that the average students were not getting the 'processes'. It was a very expensive mistake for the district, but to their credit, they did chuck it quickly. Now the youngest was in it throughout, but that was in the 'gifted' math program, he's still excellent at math.

Do you have any idea as to what spurred this reexamination of how we learn math?

 

[onedomino]

Do you have any idea as to what spurred this reexamination of how we learn math?

Very poor performance in standardized tests; especially tests designed to compare the results of math education by country. Such tests show that while US math test scores relative to other developed countries (usually about 30 countries are compared) are not too bad at the 4th grade level, by the time 12th graders are compared, the US is at or near the bottom of the heap. Math and science education in the US for the first 12 grades is weak compared to other countries. Tests have shown that in order to scrore moderately well in the tests that compare education results by country, US 12th graders need to be in advanced special calculus and physics classes. The typical math and science classes offered in US high schools are not competitive with what is offered in other developed countries.

http://www.csmonitor.com/2004/1207/p01s04-ussc.html
http://4brevard.com/choice/international-test-scores.htm
http://mwhodges.home.att.net/new_96_report.htm

 

[Annie]

Very poor performance in standardized tests; especially tests designed to compare the results of math education by country. Such tests show that while US math test scores relative to other developed countries (usually about 30 countries are compared) are not too bad at the 4th grade level, by the time 12th graders are compared, the US is at or near the bottom of the heap. Math and science education in the US for the first 12 grades is weak compared to other countries. Tests have shown that in order to scrore moderately well in the tests that compare education results by country, US 12th graders need to be in advanced special calculus and physics classes. The typical math and science classes offered in US high schools is not competitive with what is offered in other developed countries.

http://www.csmonitor.com/2004/1207/p01s04-ussc.html
http://4brevard.com/choice/international-test-scores.htm
http://mwhodges.home.att.net/new_96_report.htm

I agree the standardized tests scores would be the impetus, but the 'solution' is not the U of C program from what I understand. As I said, it's great for gifted kids or perhaps teachers that can 'leave the text', which is not most math teachers, at least until secondary school.

When looking at education results, i.e.; the US aggregate scores v. European or European modeled systems, which is most the world; one must keep in mind the basic differences in philosophy and objectives. In general the US public system believes every child should receive and education through the 12th grade, shoot for quite awhile, the US was saying that even those that are officially retarded should be able to meet the standards set by NCLB. They have I believe, added some exceptions, though few. Then there is the problem of ESL, again while the 'differences' are to be taken into account regarding teaching, NOT the outcome in test scores.

The European system rigidly sets markers, I believe in 3rd, 5th, and 8th grades, after each of which the students are streamed into ability groupings. THAT is not happening in the US, at least with the very small exception where available of good gifted programs and/or AP/Honors in secondary.

Arguments can be made for both approaches, my personal philosophy is much more 'American' than 'European', though when it comes to preparing for standardized tests, the European model will always win. Why? Because even if my 'class' was academically less gifted-I could emphasize basics, provide memorization of 'facts' for instance, something not usually necessary for more 'cognitively gifted' students, who need very little help in mapping out a complex structure using inferences and their abilities to evaluate and incorporate new information from that they already know.

When addressing a class of 18-30 students, where the abilities are perhaps skewed to one end, but with many falling or rising towards the other end, the teacher has to make some decisions of how long to remain in any one section. Some students may become totally bored, while others never catch up. Actually because of what I teach, social studies, it's pretty easy for me to provide assignments of varying complexity and emphasis on what my students need. I can have my higher ability kids working on more complex papers or readings, while my lower students are working on maps or helping design some sort of study guide or mini lesson for a lower grade class.

Keep in mind that I'm a secondary teacher of my subject, with multiple degrees in subject areas. A third or fourth grade teacher with an 'education degree' may not feel comfortable leaving the text so frequently or for extended periods of time. This I believe is multiplied in math, no pun intended.

Unfortunately most other textbook companies have basically followed the U of C program, due to their success in selling to districts, causing problems in math. For those to whom math is not 'logical' or easy, they need several examples and lots of practice, then perhaps more text on 'how the process works.' As liberalogic stated, these books give text, an example or two, 'practice' of a few, though confusingly often not the same as the examples. Then they through in some word problems, then onto the next 'process.'

 

[Psychoblues]

We should also keep in mind that you are also a whiner, a snitch, a pathological liar and an overall pitiful excuse for a human being. Lot's of posts available for verification of that observation.

 

[Annie]

Here's an AP article that examines the NCLB problem:

http://news.yahoo.com/s/ap/20070621/ap_on_re_us/failing_schools

2,300 schools face 'No Child' overhaul

By NANCY ZUCKERBROD, AP Education WriterWed Jun 20, 10:55 PM ET

The scarlet letter in education these days is an "R." It stands for restructuring — the purgatory that schools are pushed into if they fail to meet testing goals for six straight years under the No Child Left Behind law.

...

The pressure for principals is real, since principals often are replaced when schools don't make gains quickly enough. Nevertheless, Hallett has a calm, upbeat demeanor — though expressing a flash of anger when talking about the academic years that precede high school.

"You should know this: I have students who come into this building and they can't read," she said. "Schools have failed them. ... If I have a kid that can't read at grade level four, they're not going to pass a state examination."

...

The focus on tests worries some who say teachers are focusing too much on preparing kids for exams rather than spending time on important other instruction.

Long Branch, like Far Rockaway, has been organized into small academies where certain subjects are emphasized. The middle school, in a state-of-the-art building, also has moved to block scheduling, where core courses last roughly 90 minutes — twice as long as typical classes.

Louis DeAngelis, an eighth-grade English teacher, says that pushes him to be more thoughtful and creative about lesson planning. "You can't get up there and sing and dance. You should be able to go bell to bell," he said.

Whether it's the block scheduling or the other changes, student performance is moving in the right direction at Long Branch. Last year, only special education students missed annual No Child Left Behind benchmarks.

Test scores for students with disabilities, for immigrants, poor children and minorities must be separated out under the law. But if one group fails to hit testing benchmarks at a school — like last year at Long Branch — the whole school gets a failing grade.

Educators say that's too harsh, and lawmakers and the Bush administration seem open to an adjustment.

...

 

[liberalogic]

Very poor performance in standardized tests; especially tests designed to compare the results of math education by country. Such tests show that while US math test scores relative to other developed countries (usually about 30 countries are compared) are not too bad at the 4th grade level, by the time 12th graders are compared, the US is at or near the bottom of the heap. Math and science education in the US for the first 12 grades is weak compared to other countries. Tests have shown that in order to scrore moderately well in the tests that compare education results by country, US 12th graders need to be in advanced special calculus and physics classes. The typical math and science classes offered in US high schools are not competitive with what is offered in other developed countries.

http://www.csmonitor.com/2004/1207/p01s04-ussc.html
http://4brevard.com/choice/international-test-scores.htm
http://mwhodges.home.att.net/new_96_report.htm

Thanks for the links, but they really don't address the question at hand-- why do districts embrace this method of math? It seems to me that one of the graphs proves the failure of such methods: the SAT scores dropped dramatically since the 1960s. During the 1960s (when the scores were higher), math teachers generally embraced the basics. Why did we screw with a system that was working?

There's multiple reasons why we can't compete with other countries-- one of which is, of course, the quality of teachers and the despicable system of tenure. I have a friend who studied abroad in China during high school. She told me that being a teacher there is a revered position...like a doctor or a lawyer over here. The kids get up and erase the boards for the teachers out of respect. Here, for many, it's just another job.

As I've worked for the past few years with kids from elementary to high school, I've seen education morph into a freer, more open, less-disciplined process. It's all about feelings and comfort. There's no aggression or intensity. The best teachers that I had were the ones who made me want to learn and were there to support me, but at the same time, they challenged me to think and work as hard as possible. There was no safety net-- you failed, you failed. But every time they knocked me down, they only made me want to get up that much more. To me, that's the sign of a great teacher.

That was a tangent, but I am still troubled and confused as to why this shift in education, specifically math, occurred and has remained when it has proven to be a failure.

 

[onedomino]

I agree the standardized tests scores would be the impetus, but the 'solution' is not the U of C program from what I understand. As I said, it's great for gifted kids or perhaps teachers that can 'leave the text', which is not most math teachers, at least until secondary school.

When looking at education results, i.e.; the US aggregate scores v. European or European modeled systems, which is most the world; one must keep in mind the basic differences in philosophy and objectives. In general the US public system believes every child should receive and education through the 12th grade, shoot for quite awhile, the US was saying that even those that are officially retarded should be able to meet the standards set by NCLB. They have I believe, added some exceptions, though few. Then there is the problem of ESL, again while the 'differences' are to be taken into account regarding teaching, NOT the outcome in test scores.

The European system rigidly sets markers, I believe in 3rd, 5th, and 8th grades, after each of which the students are streamed into ability groupings. THAT is not happening in the US, at least with the very small exception where available of good gifted programs and/or AP/Honors in secondary.

Arguments can be made for both approaches, my personal philosophy is much more 'American' than 'European', though when it comes to preparing for standardized tests, the European model will always win. Why? Because even if my 'class' was academically less gifted-I could emphasize basics, provide memorization of 'facts' for instance, something not usually necessary for more 'cognitively gifted' students, who need very little help in mapping out a complex structure using inferences and their abilities to evaluate and incorporate new information from that they already know.

When addressing a class of 18-30 students, where the abilities are perhaps skewed to one end, but with many falling or rising towards the other end, the teacher has to make some decisions of how long to remain in any one section. Some students may become totally bored, while others never catch up. Actually because of what I teach, social studies, it's pretty easy for me to provide assignments of varying complexity and emphasis on what my students need. I can have my higher ability kids working on more complex papers or readings, while my lower students are working on maps or helping design some sort of study guide or mini lesson for a lower grade class.

Keep in mind that I'm a secondary teacher of my subject, with multiple degrees in subject areas. A third or fourth grade teacher with an 'education degree' may not feel comfortable leaving the text so frequently or for extended periods of time. This I believe is multiplied in math, no pun intended.

Unfortunately most other textbook companies have basically followed the U of C program, due to their success in selling to districts, causing problems in math. For those to whom math is not 'logical' or easy, they need several examples and lots of practice, then perhaps more text on 'how the process works.' As liberalogic stated, these books give text, an example or two, 'practice' of a few, though confusingly often not the same as the examples. Then they through in some word problems, then onto the next 'process.'

Very thoughtful response. I think that math, perhaps more than any other subject, requires extensive homework and parent participation. No one "learns" analytic geometry in a few one hour classroom sessions. It requires more work than most are willing to provide, and more participation than many parents either are willing, or can, deliver. How many parents can help a 12th grader with a differiential equation? Very few. Yet such math is elemental for an appreciation of the physical sciences, much less the ability to solve problems. A far greater percentage of people are capable of excellent results in math than is often realized. But it takes hard work and long hours compared to many other subjects. Teachers need to do a better job of connecting the dots between excellence in math and potential professional and economic success in the future. But without parents focused on good math results for their children (including direct participation) US test scores will continue to suffer.

 

[Annie]

Very thoughtful response. I think that math, perhaps more than any other subject, requires extensive homework and parent participation. No one "learns" analytic geometry in a few one hour classroom sessions. It requires more work than most are willing to provide, and more participation than many parents either are willing, or can, deliver. How many parents can help a 12th grader with a differiential equation? Very few. Yet such math is elemental for an appreciation of the physical sciences, much less the ability to solve problems. A far greater percentage of people are capable of excellent results in math than is often realized. But it takes hard work and long hours compared to many other subjects. Teachers need to do a better job of connecting the dots between excellence in math and potential professional and economic success in the future. But without parents focused on good math results for their children (including direct participation) US test scores will continue to suffer.

I agree with what you are saying regarding parents and homework, especially in math. The texts though, have to be clear enough that a parent can 'refresh' what they knew and the 'proper way' that the teacher expects the work to be completed. If you pick up a math text today, my guess is you would be shocked by the lack of organization and topic cohesion within chapters.

I'm pretty sure your math abilities were at least as good as my youngest son's. Many of us do not 'naturally' come by math. It seems to me that it makes much more sense for a chapter to open with the reading discussing the whys and hows, then several models presenting increasing difficulty in problems and steps involved. Then practice, lots of it. Followed up by more detail and reinforced explanation of hows and whys.

 

[liberalogic]

I agree with what you are saying regarding parents and homework, especially in math. The texts though, have to be clear enough that a parent can 'refresh' what they knew and the 'proper way' that the teacher expects the work to be completed. If you pick up a math text today, my guess is you would be shocked by the lack of organization and topic cohesion within chapters.

I'm pretty sure your math abilities were at least as good as my youngest son's. Many of us do not 'naturally' come by math. It seems to me that it makes much more sense for a chapter to open with the reading discussing the whys and hows, then several models presenting increasing difficulty in problems and steps involved. Then practice, lots of it. Followed up by more detail and reinforced explanation of hows and whys.

Screw history. You should be writing the math textbooks.

 

[Annie]

Screw history. You should be writing the math textbooks.

Thank you. Honestly, I do NOT do math. Textbooks have seemed to taken up the concept that if material is presented in a confusing enough manner, they can't be taken to task. Most prevalent in math texts from what I've observed, but it's spreading to other subjects.

Regarding social studies, what jumps out organizationally is the every chapter whether warranted or not, has sections on 'Women's contributions' and 'minority contributions.' Somehow they find something, whether it's Ancient Greece, Mesopotamia, or 1970's America. While the last takes up a separate chapter, which can be warranted regarding important contributions on this topic, somehow the authors churn out over a page on the first two also. This is in a jr. high text, probably the best text on the market. If the teacher is not comfortable leaving the text, the less able students truly have a problem evaluating what's important and what isn't.

 

[Psychoblues]

As The World Turns, according to the pathological liar that calls herself kitty.

 

[onedomino]

Many of us do not 'naturally' come by math. It seems to me that it makes much more sense for a chapter to open with the reading discussing the whys and hows, then several models presenting increasing difficulty in problems and steps involved. Then practice, lots of it. Followed up by more detail and reinforced explanation of hows and whys.

I agree that much practice, with multiple problems, is necessary to embed math techniques. But math is far more than a collection of techniques for problem solving. There is a difference between the way math is taught and the way it exists in the real world. Beyond simple arithmetic, math should be taught as a history of human development. Many people learn algebra and geometry without ever realizing who invented it and why. Thus, it seems disconnected from the real world and enthusiasm for learning it is diminished. Why did Newton and Leibniz invent the calculus? What was the social pressure that drove them to do it, and what did it allow them to discover? Who were those guys, what were they looking for, and why? Math should be taught in combination with the cultural context of its development: it is a story of human achievement. The sense of wonder and discovery contained in that story is not often delivered by math teachers. Math is taught as a collection of techniques that are often difficult to learn. But real math is an exciting story and the language of discovery.

 

[Annie]

I agree that much practice, with multiple problems, is necessary to embed math techniques. But math is far more than a collection of techniques for problem solving. There is a difference between the way math is taught and the way it exists in the real world. Beyond simple arithmetic, math should be taught as a history of human development. Many people learn algebra and geometry without ever realizing who invented it and why. Thus, it seems disconnected from the real world and enthusiasm for learning it is diminished. Why did Newton and Leibniz invent the calculus? What was the social pressure that drove them to do it, and what did it allow them to discover? Who were those guys, what were they looking for, and why? Math should be taught in combination with the cultural context of its development: it is a story of human achievement. The sense of wonder and discovery contained in that story is not often delivered by math teachers. Math is taught as a collection of techniques that are often difficult to learn. But real math is an exciting story and the language of discovery.

Actually that is better addressed even within social studies then it was back when I was in school. Some of what you are speaking of though really does have to do with teachers particularly in the lower grades. They do not have the time or knowledge to present that kind of information. I also get the feeling that you see this 'topic' through your own eyes and abilities. 'Like, don't we all?' However, many students cannot make those connections until later in school, high school for quite a few.