Conservatives Battle Liberals In The Classroom

[Dr.Traveler]

Ah, we hear from an NEA sponsor.

Trite response. Makes for a promising first line.

Have you ever taught a class of 22 first graders? (22 being the class size limit in Texas for elementary education the last time I checked) A third or more have an older sibling and enter knowing they can slack and the teacher cannot complain. Four or five have serious learning disabilities (generally at least 1 is a crack baby) and at least two (Perhaps from among the ones with Learning problems perhaps not) are chronic troublemakers. You are not allowed to fail more than two. You are not allowed to get rid of the troublemakers or send the truly brain damaged ones to special education.

So, your solution for this is....

The NCTM is trying to address the failings in the teaching of mathematics. If these are the problems teachers are facing, then the school systems and parents need to address them.

The point is, the bar has to be set high so the students rise to meet the challenge. Your paragraph above makes it sound like the appropriate response is to bring the bar lower and let the kids crawl under it.

Bottom line is this: Everyone knows there are problems in the classroom. The NCTM is trying to address the issues related to mathematics.

Now sure, if you start by selecting only the best candidates out of an entire county, then maybe you can begin working on something more than arithmetic at first grade.

So do so. Pull the ones that can handle the more advanced topics and teach them.

Maybe.
But if you have a set of typical students all the "extra" distractions will be just that - distractions from learning ANYTHING related to math.
Those students will never learn Algebra. They will never get beyond the ability to punch numbers in a calculator and hope for the right answer. They won't be able to manage a tight budget well, nor plan for their retirement properly. They will purchase the large economy size even when the price per unit is more than the smaller size because they can't do that much basic math.

More drivel along the lines of the first paragraph.

As for the Euclidean method - the teaching of Geometry in the classical era was mostly done for the already capable elite who had mastered the art of Arithmetic at an earlier age.

Those students that "mastered" Arithmetic probably learned from Nichomachus’ Introducto Arithmeticae, which like many textbooks of the day consisted of lists of problems with either no solution, or no indication of how the solution was derived.

Outside of Nichomachus' book or Diophantus book, it was only much later, basically the late 1400's or early 1500's, that mathematicians like Vieta really made Arithmetic a widespread study. Prior to that Arithmetic was done with geometric methods.

Children can learn to tell time because they have a concrete example how it works - the watch on their hand. It is a huge conceptual step from that to modular arithmetic as anyone who has worked with 6 year old children knows.

And with manipulatives you can teach children about symmetric groups or other modular math. The question is should we?

Cumulative tests? Of course tests are cumulative, this is math, where everything they learn build upon what they already know.

We say that in Mathematics, but if you've taught that you know it isn't 100% true once you're past the very basic concepts of Arithmetic. As I said before, when students reach me in Calculus they can't apply the power rule to a simple cube root.

I know for a FACT they were taught exponent rules. They've simply forgotten them as soon as it didn't show up on a test.

However, the students that inherently understood the logic behind how the exponent rules work recover faster than those that simply memorized to get through.

Subtraction (2nd grade) builds on addition. So does multiplication (3rd grade), as does Long Division (4th grade) - in fact starting in 4th grade everything is used for long division.
Trying for too much means the students have an excuse to fail, and justifying an approach because Enrico Fermi could do it that way is asinine.

So again, you're in favor of lowering the bar?

Yes, an advanced approach won't work for every student. Not every student can sum up the numbers from 1 to 100 in elementary school by developing the formula. However, it doesn't hurt to try, and if it sticks good.

Maybe the best way will turn out to be memorization and drilling instead of thinking and reasoning. I can guarantee you though, a student that gets by in life by simply memorizing algorithms will be dead in the water when faced with Integral Calculus, Differential Equations, Analysis, etc. If the goal is to produce more students that can succeed in advanced mathematics course, then more than memorization is required.

 

[Charles Stucker]

So again, you're in favor of lowering the bar?

It is clear they lowered the bar in your reading comprehension class.
The scattered approach which moronic liberals try to apply to teaching does not work
Then they "lower the bar" so everyone gets through.
Instead concentrate at the low levels on what they must have for upper levels.
Arithmetic.
Raise the bar so students have to be truly good at arithmetic to pass. None of the liberal gobbledygook "they learned the method and that's good enough" nonsense.
They learn to add or they repeat first grade. Period.
Repeat through the higher grades.

To make classrooms more conducive to learning, remove the brain damaged crack babies and the chronic troublemakers.
Drill, Drill, Drill
On Arithmetic. Make lack of learning carry consequences, and poor behavior carry serious consequences.
Then, when the students reach higher grades, they can learn Algebra, Geometry, and other more advanced topics.
But without the foundation in Arithmetic, all the work in algebra will be gibberish to them. How can you convince a person that (7x+3y)+(9x+4y) actually equals 16x+7y if they are unable to add 9+7 or even 3+4?
The answer is you can't without taking the time to go back and cover basic arithmetic.
So get the basics first, then go to the advanced topics. If children have the right introduction to the basics, then most high school seniors can manage trig. All except the brain damaged ones can do Algebra and Geometry. About half can learn calculus.

But they don't and the reason is clear; the lamebrain scattergun approach so beloved of liberal idiots only works for the most gifted students. If you are comfortable teaching only one child in a thousand (or less) then that is your problem. I want to raise the bar and see half the students from every high school class able to use calculus to solve real world problems.

 

[rdean]

I see a lot of ignorance regarding the teaching of arithmetic.
6 year old children do not have the development to learn abstract algebra.
They can learn basic addition.
A good founding in arithmetic is essential to a better understanding of algebra in high school.
First grade math should drill the students daily in addition. Weekly tests measure their retention.
Second grade students drill daily in subtraction, with weekly tests.
Third grade Multiplication drills and tests
4th grade long division
5th grade fractions

Just like sports, the secret is drill, drill, drill.

It is not glamorous, it is not fun for the teacher, it is not a lot of things.
It is necessary to teach the children how to do basic arithmetic.
Calculators do not help, they hinder. They hinder because they become a crutch and excuse in one "I can use a calculator when I'm not in class."
Yes, but only if you can frame the right question. Which requires understanding the math, and that understanding begins with a facility at arithmetic which is sadly lacking in too many young people today.

You can catch up at a latter date, learning everything you need to know in college, but that tends to produce what I term neo-idiot savants; people who are highly trained in a very narrow field. Had they but received a better primary education they might be well rounded, but they are not, and the competitive nature of the workplace forces specialization which makes replacing those lost years all the harder.

Of course the math drill method is a very conservative teaching method, going back centuries, so it might not appeal to brain damaged liberals who want the "newest" trend.[/QUOTE]

And curiously, less than 6% of scientists identify themselves as "Republican".

For sure, memorization does take repetition. So, yes, for that reason, "drilling" does work. Of course, indoctrination is also memorization. But just remembering something cannot be equated with "learning".

If you expect to compete in the workforce, you can't just be a cog. There are machines that do that. You want to be one of those who design, operate, install or maintain one of those machines.

It's difficult getting into a debate with a conservative. Many will tell you the educated have no "common sense". Or that education is "just a piece of paper". It's no wonder. Coming from people who equate "memorization" with "learning".

Conservatives depend way more on those darn liberals. But it’s a trade off. Conservatives “breed” and liberals do everything else.

 

[PoliticalChic]

You seem to have experience in this area.

And it is interesting that none of our reliably doctrinaire liberal friends have found it beneficial to argue the points you made.

We use a curriculum pretty much as you outline it, and, of course, don't allow calculators.

I'm really very curious why you make a pointed attempt to disregard any view point in this thread that does not support yours. It seems you are not interested in intellectual debate, just more Con vs Lib bu11$h1t

Here's why"

1.. In 1989, the National Council of Teachers of Mathematics (NCTM), the chief professional organization for mathematics educators and education faculty, issued Curriculum and Evaluation Standards for School Mathematics. The document presented standards for grades K–12, including algebra. The underlying goals of the standards—never made clear to the general public—were social, not academic.

2. "...the employment of trendy, though empirically unsupported, pedagogical and organizational methods that essentially dumb down math content..."

3. "Some influential educators sought to dismiss the traditional curriculum altogether, viewing it as a white, Christian, heterosexual-male product ..."

4."According to cultural-historical activity theory, schooling as it exists today reinforces an illegitimate social order."

5. "...students construct their own understanding of mathematics and find their own math solutions."

6. "Teacher-directed learning goes out the window, despite its demonstrated benefits for students with learning problems..."

7."... they downplay basic arithmetic skills and practice, encouraging kids to use calculators from kindergarten on. The educators also neglect the teaching of standard algorithms (mathematical procedures commonly taught everywhere, with only minor variations, because of their general applicability)."

8. Pedagogy of the Oppressed, by the Brazilian educator Paulo Freire.This ed-school bestseller is, instead, a utopian political tract calling for the overthrow of capitalist hegemony and the creation of classless societies.

9. The pedagogical point of Freire’s thesis : its opposition to taxing students with any actual academic content, which Freire derides as “official knowledge” that serves to rationalize inequality within capitalist society.

10. From Annie's post: "The curriculum’s failure was undeniable: not one of my students knew his or her times tables, and few had mastered even the most basic operations; knowledge of multiplication and division was abysmal."



And so, my friend, I find little to recommend, for education, in the writings of those who agree with the clap-trap that sees 'social justice' as an aim, to any degree, in academic subjects.

My recommendation to teachers, to the school system, is simply "do your job."

Does that answer your question?

 

[Charles Stucker]

And curiously, less than 6% of scientists identify themselves as "Republican".

Conservatives depend way more on those darn liberals. But it’s a trade off. Conservatives “breed” and liberals do everything else.

Yet another ignoramus comments on education.
As an example of how the system fails, you are perfect.
Everything you said is more "blah blah blah" from someone who clearly has no idea concerning the topic at hand.
First grade students benefit far more from memorizing the addition tables than they do from "learning the abstract method" behind addition and then applying it to specific cases as needed. It's like putting the desert before the main course, you just ruin the meal. Children need to learn basic arithmetic before they attempt to go into algebra and higher topics.

The liberal method of teaching has failed for the last 30+ years. Go back to methods that worked.
Even if brain damaged liberals object to teaching something other than liberal indoctrination in schools.

In closing let me address your 6% of scientists claim.
"There are three types of lies: lies, damn lies, and statistics." Mark Twain

 

[PoliticalChic]

I see a lot of ignorance regarding the teaching of arithmetic.
6 year old children do not have the development to learn abstract algebra.
They can learn basic addition.
A good founding in arithmetic is essential to a better understanding of algebra in high school.
First grade math should drill the students daily in addition. Weekly tests measure their retention.
Second grade students drill daily in subtraction, with weekly tests.
Third grade Multiplication drills and tests
4th grade long division
5th grade fractions

Just like sports, the secret is drill, drill, drill.

It is not glamorous, it is not fun for the teacher, it is not a lot of things.
It is necessary to teach the children how to do basic arithmetic.
Calculators do not help, they hinder. They hinder because they become a crutch and excuse in one "I can use a calculator when I'm not in class."
Yes, but only if you can frame the right question. Which requires understanding the math, and that understanding begins with a facility at arithmetic which is sadly lacking in too many young people today.

You can catch up at a latter date, learning everything you need to know in college, but that tends to produce what I term neo-idiot savants; people who are highly trained in a very narrow field. Had they but received a better primary education they might be well rounded, but they are not, and the competitive nature of the workplace forces specialization which makes replacing those lost years all the harder.

Of course the math drill method is a very conservative teaching method, going back centuries, so it might not appeal to brain damaged liberals who want the "newest" trend.[/QUOTE]

And curiously, less than 6% of scientists identify themselves as "Republican".

For sure, memorization does take repetition. So, yes, for that reason, "drilling" does work. Of course, indoctrination is also memorization. But just remembering something cannot be equated with "learning".

If you expect to compete in the workforce, you can't just be a cog. There are machines that do that. You want to be one of those who design, operate, install or maintain one of those machines.

It's difficult getting into a debate with a conservative. Many will tell you the educated have no "common sense". Or that education is "just a piece of paper". It's no wonder. Coming from people who equate "memorization" with "learning".

Conservatives depend way more on those darn liberals. But it’s a trade off. Conservatives “breed” and liberals do everything else.

How about you start by 'memorizing' the methods for use of the quote feature on the board.

If that is too difficult, go back to your original method: cuneiform.

 

[Dr.Traveler]

The underlying goals of the standards—never made clear to the general public—were social, not academic.

I call bullshit. Publish these "secret goals" or retract.

 

[Dr.Traveler]

It is clear they lowered the bar in your reading comprehension class.

At this point, its clear you have little more than insults. Refrain from the insults if you want an honest debate. Using insults shows a mind of low class and lower skill.

I believe you probably have a valid viewpoint and are worthy of debate, but your conduct so far does not reveal that.

The scattered approach which moronic liberals try to apply to teaching does not work
Then they "lower the bar" so everyone gets through.
Instead concentrate at the low levels on what they must have for upper levels.
Arithmetic.

I've yet to see the NCTM advocate lowering the bar. I've yet to see them say to that arithmetic is not important. The point you're missing is that if you can get across the idea behind the method implied, it enhances reasoning skills and understanding.

A few years ago someone came stomping into my office to tell me about a "new method" on youtube to teach division and multiplication that was "new and wrong and stupid". I let them vent for a few minutes, and then asked them to play the video.

The new method for division that was so clearly "New and wrong and stupid": The Euclidean Algorithm.

The person was so tied to basic arithmetic they couldn't see that the method employed was logically equivalent to what they'd been taught. It was developed different, and as such was wrong.

That's what I've seen with most of these new methods: They are in fact very old methods or logically equivalent to earlier methods. However, because they're presented different, teachers without mathematical knowledge struggle to teach these methods and parents tied to understanding a problem in only one way don't get it.

We probably have some similar views on the problems facing Mathematics Education, but you're caught up in the Liberal vs. Conservative divide. Yes, there are problem teachers. Yes, there are problem students. Yes, social promotion needs to stop. Yes, something has to change. Yes, there are problems with the math literacy of the general populace.

I'm very interested in solutions because the students coming out of the high schools these days are not ready for Calculus in any shape or form. It isn't just a lack of Arithmetic, its a plan lack of reasoning skills and that needs to be addressed at some point in a child's education.

 

[Charles Stucker]

The underlying goals of the standards—never made clear to the general public—were social, not academic.

I call bullshit. Publish these "secret goals" or retract.

One apparent goal is to make students dependent on calculators

Even at this age, guided work with calculators can enable students to explore number and patterns, focus on problem-solving processes, and investigate realistic applications.

The whole mishmash of ideologue idiocy can be found at the NCTM page

 

[PoliticalChic]

The underlying goals of the standards—never made clear to the general public—were social, not academic.

I call bullshit. Publish these "secret goals" or retract.

Watch your language.

Here is the original quote to which you refer:
" The document presented standards for grades K–12, including algebra. The underlying goals of the standards—never made clear to the general public—were social, not academic."

The article is by Sandra Stotsky. Sandra Stotsky is a professor of education reform at the University of Arkansas and holds the 21st Century Chair in Teacher Quality. Would you like to compare your credentials to hers?

"Principles and Standards for School Mathematics has four major components. First, the Principles for school mathematics reflect basic perspectives on which educators should base decisions that affect school mathematics. These Principles establish a foundation for school mathematics programs by considering the broad issues of equity, curriculum, teaching, learning, assessment, and technology."
Overview: Introduction

It has been purposely made difficult to quote, as
" It would later be fiercely opposed by many parents and mathematics professionals, and rejected by many states and school districts who complained about replacing instruction in arithmetic with writing, coloring, counting, and inventing mathematics unrecognizable to any previous generation of mathematicians or educators. While the standards are available on the internet, full access by the public is only available by an expensive purchase or subscription."
Principles and Standards for School Mathematics | K12 Academics

Progressive education is an outgrowth of the Romantic Movement with roots going back to Jean Jacques Rousseau. John Dewey and William Heard Kilpatrick were instrumental in ensuring the dominance of progressive education theory in teachers colleges through most of the 20th century.[2] In the variant promoted by Kilpatrick, who was especially influential in mathematics education, subjects would be taught to students based on their direct practical value, or if students independently wanted to learn them.[3]
A quarter century of US 'math wars' and political partisanship

A broader understanding of the destruction of the American education system can be found in the following:

"University education departments began to tell future grammar school teachers that they should replace the traditional teacher-centered curriculum, aimed at producing educated citizens who embraced a common American ethic, with a new, child-centered approach that treats every pupil’s “personal development” as different and special. During the 1960s, when intellectuals and college students dismissed traditional American values as oppressive barriers to fulfillment, grammar schools generally jettisoned the traditional curriculum. “Education professors eagerly joined New Left professors to promote the idea that any top-down imposition of any curriculum would be a right-wing plot designed to perpetuate the dominant white, male, bourgeois power structure,” writes education reformer E. D. Hirsch, Jr., in his forthcoming The Making of Americans: Democracy and Our Schools.

When schools threw out the bourgeois values that had helped to sustain Weber’s “rational tempering” of the impulse to accumulate wealth, they removed the rationality in “rational self-interest,” or, as Tocqueville put it, “self-interest rightly understood.” The new “every child is special” curriculum prompted a sharp uptick in students’ self-absorption, according to psychologists Jean M. Twenge and W. Keith Campbell in The Narcissism Epidemic: Living in the Age of Entitlement. What resulted was a series of increasingly self-centered generations of young people displaying progressively more narcissistic personality traits, including a growing obsession with “material wealth and physical appearance,” the authors observe. Adam Smith’s The Theory of Moral Sentiments, traces the evolution of ethics from man’s nature as a social being who feels shame if he does something that he believes a neutral observer would consider improper. Modern experiments in neuroscience have tended to confirm Smith’s notion that our virtues derive from our empathy for others, therefore being self-centered is the antithesis of a sense of shame." [An extensive explanation of the Left’s control of education may be found in Pedagogy of the Oppressor, by Sol Stern at http://www.city-journal.org/2009/19_2_freirian-pedagogy.html]

Whatever Happened to the Work Ethic? by Steven Malanga, City Journal Summer 2009

The result is the dismal performance of American students based on comparison with other nations.

Nor will I have to retract anything.

The fault lies in your failure to see the bigger picture, in all of education, and the devolution of society.

 

[rdean]

And curiously, less than 6% of scientists identify themselves as "Republican".

Conservatives depend way more on those darn liberals. But it’s a trade off. Conservatives “breed” and liberals do everything else.

Yet another ignoramus comments on education.
As an example of how the system fails, you are perfect.
Everything you said is more "blah blah blah" from someone who clearly has no idea concerning the topic at hand.
First grade students benefit far more from memorizing the addition tables than they do from "learning the abstract method" behind addition and then applying it to specific cases as needed. It's like putting the desert before the main course, you just ruin the meal. Children need to learn basic arithmetic before they attempt to go into algebra and higher topics.

The liberal method of teaching has failed for the last 30+ years. Go back to methods that worked.
Even if brain damaged liberals object to teaching something other than liberal indoctrination in schools.

In closing let me address your 6% of scientists claim.
"There are three types of lies: lies, damn lies, and statistics." Mark Twain

I didn't say "drilling" was bad, but it can become bad very fast. By concentrating on "memorizing" you take away the "fun" in learning. Kids learn to hate math because they aren't taught the joy of problem solving.

It's conservatives who teach such nonsense like "magical creation" and "forced memorization". No wonder kids turn away from science when conservatives tell them that studying science can cause "mental illness".

We know that less than 6% of scientists admit to being Republican after about a dozen threads on this site put up links.

Many conservatives are the last people who should be teaching children. Because they aren't teaching. They are performing "indoctrination".

 

[Bfgrn]

The underlying goals of the standards—never made clear to the general public—were social, not academic.

I call bullshit. Publish these "secret goals" or retract.

To understand PC's agenda, you have to divest your own sense of decency and honesty...she has ONE agenda...bash liberals, blame liberals for all the wrongs in the world...and create FEAR of the liberal monster SHE creates for you...

To do this, first she has to build the monster...BUT, when you take time to look into the monster she creates, it always evaporates...


-----------------------------------------------------
Curriculum and Evaluation Standards for Mathematics Education. ERIC/SMEAC Mathematics Education Digest No. 1, 1990.

Dr Marilyn Suydam

Current OSU Appointment

Faculty Emeritus, School of Teaching & Learning

In 1989, the National Council of Teachers of Mathematics (NCTM) released a document of major importance for improving the quality of mathematics education in grades K-12. This document, "Curriculum and Evaluation Standards for School Mathematics," contains a set of standards for judging mathematics curricula and for evaluating the quality of the curriculum and student achievement. It represents the consensus of NCTM's members about the fundamental content that should be included in the school mathematics curriculum, establishing a framework to guide reform in school mathematics. Inherent in the STANDARDS is the belief that all students need to learn more, and often different, mathematics.

WHAT IS THE RATIONALE FOR THE STANDARDS?
Technology is changing the workplace, the home, and daily life. Moreover, the mathematics a person needs to know has shifted, and new mathematics is being created as technological applications emerge. Yet the teaching of mathematics has remained relatively unchanged. As it has for centuries, mathematics often relies on rote memorization.

The objectives of mathematics education must be transformed to meet the critical needs of our society: an informed electorate, mathematically literate workers, opportunity for all students, and problem-solving skills that serve lifelong learning. Both the content that is being taught and the way it is taught need to be reconsidered and, in many cases, transformed. To ensure quality, to indicate goals, and to promote change are the three reasons why NCTM issued the STANDARDS.

WHAT ARE THE UNDERLYING ASSUMPTIONS OF THE STANDARDS?
Several assumptions shape the vision of mathematics set forth in the STANDARDS: (1) Mathematical power can and must be at the command of all students in a technological society. (2) Mathematics is something one DOES--solve problems, communicate, reason; it is not a spectator sport. (3) The learning of mathematics is an active process, with students constructing knowledge derived from meaningful experiences and real problems. (4) A curriculum for all includes a broad range of content, a variety of contexts, and deliberate connections. (5) Evaluation is a means of improving instruction and the whole mathematics program.

WHAT GOALS ARE ESTABLISHED FOR STUDENTS?
All students should have opportunities to learn a broad spectrum of mathematics. Toward that end, the STANDARDS state five goals for students: to learn to value mathematics, to learn to reason mathematically, to learn to communicate mathematically, to become confident of their mathematical abilities, and to become mathematical problem solvers.

WHAT IS THE FRAMEWORK FOR SCHOOL MATHEMATICS?
The STANDARDS offer a framework for curriculum development--a logical network of relationships among identified topics of study. Although they specify the key elements of a high-quality school mathematics program, they neither list topics for particular grades nor show a "scope and sequence" chart. Instead, the 40 curriculum standards discuss the content at three grade-level groups: K-4, 5-8, and 9-12. The 14 evaluation standards provide strategies to assess the curriculum, instruction, and program.

The first three curriculum standards for each grade level and three of the evaluation standards deal with problem solving, communication, and reasoning. A fourth curriculum standard, Mathematical Connections, is predicated on the belief that mathematics must be approached as a unified whole. Consequently, curricula should deliberately include instructional activities to reveal the connections among ideas and procedures in mathematics and applications in other subject matter areas.

For each grade-level group, nine or ten content standards supplement the first four curriculum standards. While the titles are sometimes similar, the concepts and processes vary by level. In a lengthy presentation for each standard, the mathematical outcomes for students, the focus of the standard, discussion of what the standard means, and examples of how the content might be taught are provided.

WHAT STANDARDS ARE INCLUDED FOR EACH GRADE CLUSTER?
The 13 standards for K-4 are: Mathematics as Problem Solving, as Communication, and as Reasoning, and Mathematical Connections; Estimation; Number Sense and Numeration; Concepts of Whole Number Operations; Whole Number Computation; Geometry and Spatial Sense; Measurement; Statistics and Probability; Fractions and Decimals; and Patterns and Relationships.

There are 13 standards for grades 5-8: Mathematics as Problem Solving, as Communication, and as Reasoning, and Mathematical Connections; Number and Number Relationships; Number Systems and Number Theory; Computation and Estimation; Patterns and Functions; Algebra; Statistics; Probability; Geometry; and Measurement.

Fourteen standards pertain to grades 9-12: Mathematics as Problem Solving, as Communication, and as Reasoning, and Mathematical Connections; Algebra; Functions; Geometry from a Synthetic Perspective; Geometry from an Algebraic Perspective; Trigonometry; Statistics; Probability; Discrete Mathematics; Conceptual Underpinnings of Calculus; and Mathematical Structure.

WHAT STANDARDS ARE INCLUDED FOR EVALUATION?
Three standards pertain to general assessment: Alignment, Multiple Sources of Information, and Appropriate Assessment Methods and Uses. Seven standards concern student assessment: Mathematical Power, Problem Solving, Communication, Reasoning, Mathematical Concepts, Mathematical Procedures, and Mathematical Disposition. Finally, four standards are on program evaluation; Indicators for Program Evaluation, Curriculum and Instructional Resources, Instruction, and Evaluation Team.

WHAT ARE SOME SUGGESTED CHANGES THAT SHOULD BE INCLUDED IN MATHEMATICS INSTRUCTION?
Some aspects of doing mathematics have changed in the last decade, in large part because of technology. Changes in technology and the broadening of the areas in which mathematics is applied have resulted in growth and changes in mathematics itself. Technology makes it imperative that: (1) appropriate calculators should be available to all students at all times; (2) a computer should be available in every classroom for demonstration purposes; (3) every student should have access to a computer for individual and group work; and (4) all students should learn to use the computer as a tool for processing information and performing calculations to investigate and solve problems.

The availability of calculators does not eliminate the need for students to learn algorithms; some proficiency with paper-and-pencil computational algorithms is important. Contrary to the fears of many, there is no evidence to suggest that the availability of calculators makes students dependent on them for simple calculations. Students should be able to decide when they need to calculate and whether they require an exact or approximate answer. They should be able to select and use the most appropriate tool.

A constructive, active view of the learning process must be reflected in the way much of mathematics is taught. Thus, instruction should vary and include opportunities for: appropriate project work; both group and individual assignments; discussion between teacher and students and among students; practice on mathematical methods; and exposition by the teacher.

The STANDARDS were developed with consideration to the content appropriate for all students. This does not suggest that all students are alike; it does suggest that all students should have an opportunity to learn the important ideas of mathematics.

WHAT ARE SOME NEXT STEPS FOR TEACHERS AND ADMINISTRATORS?
The NCTM challenges all to work toward the goal of improving the school mathematics program as identified by the STANDARDS.

Teachers and administrators should obtain the materials listed in the reference section to learn more about the STANDARDS. The school staff should review the current program and instruction to identify changes that are desirable and begin to modify the experiences provided for pupils.

Several states and many school districts have started to modify programs. Materials describing these activities will be published in journals of the NCTM (The Arithmetic Teacher and The Mathematics Teacher) on a regular basis. Schools desiring more information or assistance should contact their state department of education mathematics education coordinator/ specialist, and periodically check Resources in Education and the Current Index to Journals in Education for information and materials.

SELECTED REFERENCES
"Curriculum and Evaluation Standards for School Mathematics." Reston, VA: National Council of Teachers of Mathematics, 1989. (Address: 1906 Association Drive, Reston, VA 20091; $25.00, with reduced prices for multiple copies).

Heid, M. Kathleen. "Uses of Technology in Prealgebra and Beginning Algebra." MATHEMATICS TEACHER 83: 194-198; March 1990.

Hirsch, Christian R. and Harold L. Schoen. "A Core Curriculum for Grades 9-12." MATHEMATICS TEACHER 83: 696-701; December 1989.

Mumme, Judith and Julian Weissglass. "The Role of the Teacher in Implementing the Standards." MATHEMATICS TEACHER 82: 522-526; October 1989.

Payne, Joseph N. and Ann E. Towsley. "Implications of NCTM's Standards for Teaching Fractions and Decimals." ARITHMETIC TEACHER 37: 23-26; April 1990.

"Reshaping School Mathematics: A Philosophy and Framework for Curriculum." MATHEMATICS SCIENCES EDUCATION BOARD, NATIONAL RESEARCH COUNCIL, National Academy Press, Washington, D.C., 1990. SE 051 291.

Rowan, Thomas E. "The Geometry Standards in K-8 Mathematics." ARITHMETIC TEACHER 37: 24-28; February 1990.

Schoen, Harold L. "Beginning to Implement the Standards in Grades 7-12." MATHEMATICS TEACHER 82: 427-430; September 1989.

Thompson, Alba G. and Diane J. Briars. "Assessing Students Learning to Inform Teaching: The Message in NCTM's Evaluation Standards." ARITHMETIC TEACHER 37: 22-26; December 1989.

Thompson, Charles S. "Number Sense and Numeration in Grades K-8." ARITHMETIC TEACHER 37: 22-24; September 1989.

 

[Charles Stucker]

I didn't say "drilling" was bad, but it can become bad very fast. By concentrating on "memorizing" you take away the "fun" in learning. Kids learn to hate math because they aren't taught the joy of problem solving.

Alas, you cannot reliably solve problems with a calculator unless you can solve them without a calculator. The calculator has become central to teaching math, to the point that children cannot perform any math without it and have no clue when they punch the wrong keys that they have the wrong answer.
Kids learn to hate math because too many elementary education teachers spout nonsense like "Don't worry if it confuses you, math is hard." and "I was never any good at math."

It's conservatives who teach such nonsense like "magical creation" and "forced memorization". No wonder kids turn away from science when conservatives tell them that studying science can cause "mental illness".

Where do you get this crap? From some liberal rag disguised as news? Talk about indoctrination.

We know that less than 6% of scientists admit to being Republican after about a dozen threads on this site put up links.

Sorry, wrong answer. How were those statistics compiled? How was the questionnaire worded? These are critical issues. Asking a scientist
Do you vote
a - Always Republican
b - Always Democrat
c - It depends on the candidate
could easily get a result of "c" from any reasonable person.
And then be used by a pollster to show only a small percent of the group polled were "Republicans"

Many conservatives are the last people who should be teaching children. Because they aren't teaching. They are performing "indoctrination".

Many liberals are the last people who should be teaching children. Because they aren't teaching. They are performing "indoctrination".

What you need are Teachers to do the teaching.

 

[chanel]

I'd say almost half of the teachers in my school vote Republican. And most of them send their kids to private school. What's that tell ya?

 

[Charles Stucker]

I'd say almost half of the teachers in my school vote Republican. And most of them send their kids to private school. What's that tell ya?

That they have more money than teachers in my area.
The part about private schools.
Half voting Republican probably means they are distributed about like society as a whole.

 

[PoliticalChic]

I didn't say "drilling" was bad, but it can become bad very fast. By concentrating on "memorizing" you take away the "fun" in learning. Kids learn to hate math because they aren't taught the joy of problem solving.

Alas, you cannot reliably solve problems with a calculator unless you can solve them without a calculator. The calculator has become central to teaching math, to the point that children cannot perform any math without it and have no clue when they punch the wrong keys that they have the wrong answer.
Kids learn to hate math because too many elementary education teachers spout nonsense like "Don't worry if it confuses you, math is hard." and "I was never any good at math."

It's conservatives who teach such nonsense like "magical creation" and "forced memorization". No wonder kids turn away from science when conservatives tell them that studying science can cause "mental illness".

Where do you get this crap? From some liberal rag disguised as news? Talk about indoctrination.

We know that less than 6% of scientists admit to being Republican after about a dozen threads on this site put up links.

Sorry, wrong answer. How were those statistics compiled? How was the questionnaire worded? These are critical issues. Asking a scientist
Do you vote
a - Always Republican
b - Always Democrat
c - It depends on the candidate
could easily get a result of "c" from any reasonable person.
And then be used by a pollster to show only a small percent of the group polled were "Republicans"

Many conservatives are the last people who should be teaching children. Because they aren't teaching. They are performing "indoctrination".

Many liberals are the last people who should be teaching children. Because they aren't teaching. They are performing "indoctrination".

What you need are Teachers to do the teaching.

Hey, hey, hey-

Now you just leave Deanie-weenie alone!

Spanking him is my job, after all I selected him as the dumbest poster on USMB.

(And we try to encourage him, part of his therapy)

 

[PoliticalChic]

I'd say almost half of the teachers in my school vote Republican. And most of them send their kids to private school. What's that tell ya?

Public school teachers in urban areas are far more likely than city residents in general to send their children to private schools, according to a new analysis of 2000 Census data by researchers led by Denis P. Doyle, who previously analyzed 1980 and 1990 Census data.

While just 12.2 percent of U.S. families send their children to private schools, that figure rises to 17.5 percent among urban families in general and to 21.5 percent among urban public school teachers, almost twice the national average.
Where Do Public School Teachers Send Their Kids to School? - by Alan Bonsteel, M.D. - School Reform News

 

[Dr.Traveler]

Here is the original quote to which you refer:
" The document presented standards for grades K–12, including algebra. The underlying goals of the standards—never made clear to the general public—were social, not academic."

Never made clear to the general public is what I take issue with. That's always the start of a snow job.

The article is by Sandra Stotsky. Sandra Stotsky is a professor of education reform at the University of Arkansas and holds the 21st Century Chair in Teacher Quality. Would you like to compare your credentials to hers?

Don't know her. Do you usually make a practice of agreeing with folks with enough titles behind their name, or only when they seem to support your arguments?

"Principles and Standards for School Mathematics has four major components. First, the Principles for school mathematics reflect basic perspectives on which educators should base decisions that affect school mathematics. These Principles establish a foundation for school mathematics programs by considering the broad issues of equity, curriculum, teaching, learning, assessment, and technology."
Overview: Introduction

Nothing wrong with that.

It has been purposely made difficult to quote, as
" It would later be fiercely opposed by many parents and mathematics professionals, and rejected by many states and school districts who complained about replacing instruction in arithmetic with writing, coloring, counting, and inventing mathematics unrecognizable to any previous generation of mathematicians or educators. While the standards are available on the internet, full access by the public is only available by an expensive purchase or subscription."
Principles and Standards for School Mathematics | K12 Academics

Your quoted article owes it to the reader to actually list these questionable goals. The above section reads like the start of a conspiracy theory. The article in full is not much better.

"University education departments began to tell future grammar school teachers that they should replace the traditional teacher-centered curriculum, aimed at producing educated citizens who embraced a common American ethic, with a new, child-centered approach that treats every pupil’s “personal development” as different and special.

Nothing wrong here. Teachers have known for years that students learn, and respond, to different methods of teaching. That's why a really good teacher is willing to change up their methods from time to time to reach a particular class. I've had to do it even at the University level.

The fault lies in your failure to see the bigger picture, in all of education, and the devolution of society.

That quote tells me pretty much all I need to know about you.

 

[Dr.Traveler]

One apparent goal is to make students dependent on calculators

Even at this age, guided work with calculators can enable students to explore number and patterns, focus on problem-solving processes, and investigate realistic applications.

The whole mishmash of ideologue idiocy can be found at the NCTM page

Eh. You can hand a student a calculator and still not create "dependency". Teachers that tell students to "Just do it on the calculator" are being lazy and need to get slapped down. However, teachers that can use the calculator to enhance learning should be encourage. I'd bet that on that point you and I can agree.

I know that I "discovered" the factorial operation and e long before I was introduced to them in high school because I played around on a scientific calculator. I was too poor to afford a graphing calculator, but when they were available at school I probably learned more about curves by just playing around with equations on the calculator than I ever learned prior to Calculus.

I freely admit, I'm not the normal situation. Instead of teaching me football, basketball, or baseball my Dad taught me how to work Rubik's puzzles and math games. The result was that I was a big nerd, but when faced with the advanced Mathematics courses I always started ahead. For that, I'll always be grateful.

 

[Dr.Traveler]

Kids learn to hate math because too many elementary education teachers spout nonsense like "Don't worry if it confuses you, math is hard." and "I was never any good at math."

By the way, this is something I agree with. Enthusiasm makes a difference. As does a working knowledge of the topic. I think many innovations in mathematics instuction run into trouble due to a lack of familiarity with mathematics on the part of the teacher involved.