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From Wikipedia

Math wars

Math wars is the debate over modern mathematics education, textbooks and curricula in the United States that was triggered by the publication in 1989 of the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM) and subsequent development and widespread adoption of a new generation of mathematics curricula inspired by these standards.

While the discussion about math skills has persisted for many decades, the term "math wars" was coined by commentators such as John A. Van de Walle and David Klein. The debate is over traditional mathematics and reform mathematics philosophy and curricula, which differ significantly in approach and content.

Advocates of reform

The largest supporter of reform in the US has been the National Council of Teachers of Mathematics.

One aspect of the debate is over how explicitly children must be taught skills based on formulas or algorithms (fixed, step-by-step procedures for solving math problems) versus a more inquiry-based approach in which students are exposed to real-world problems that help them develop fluency in number sense, reasoning, and problem-solving skills. In this latter approach, conceptual understanding is a primary goal and algorithmic fluency is expected to follow secondarily.

A considerable body of research by mathematics educators has generally supported reform mathematics and has shown that children who focus on developing a deep conceptual understanding (rather than spending most of their time drilling algorithms) develop both fluency in calculations and conceptual understanding. Advocates explain failures not because the method is at fault, but because these educational methods require a great deal of expertise and have not always been implemented well in actual classrooms.

A backlash which advocates call "poorly understood reform efforts" and critics call "a complete abandonment of instruction in basic mathematics" resulted in "math wars" between reform and traditional methods of mathematics education.

Critics of reform

Those who disagree with the inquiry-based philosophy maintain that students must first develop computational skills before they can understand concepts of mathematics. These skills should be memorized and practiced, using time-tested traditional methods until they become automatic. Time is better spent practicing skills rather than in investigations inventing alternatives, or justifying more than one correct answer or method. In this view, estimating answers is insufficient and, in fact, is considered to be dependent on strong foundational skills. Learning abstract concepts of mathematics is perceived to depend on a solid base of knowledge of the tools of the subject.

Supporters of traditional mathematics teaching oppose excessive dependence on innovations such as calculators or new technology, such as the Logo language. Student innovation is acceptable, even welcome, as long as it is mathematically valid. Calculator use can be appropriate after number sense has developed and basic skills have been mastered. Constructivist methods which are unfamiliar to many adults, and books which lack explanations of methods or solved examples make it difficult to help with homework. Compared to worksheets which can be completed in minutes, constructivist activities can be more time consuming. (Reform educators respond that more time is lost in reteaching poorly understood algorithms.) Emphasis on reading and writing also increases the language load for immigrant students and parents who may be unfamiliar with English.

Critics of reform point out that traditional methods are still universally and exclusively used in industry and academia. Reform educators respond that such methods are still the ultimate goal of reform mathematics, and that students need to learn flexible thinking in order to face problems they may not know a method for. Critics maintain that it is unreasonable to expect students to "discover" the standard methods through investigation, and that flexible thinking can only be developed after mastering foundational skills.

Some curricula incorporate research by Constance Kamii and others that concluded that direct teaching of traditional algorithms is counterproductive to conceptual understanding of math. Critics have protested some of the consequences of this research. Traditional memorization methods are replaced with constructivist activities. Students who demonstrate proficiency in a standard method are asked to invent another method of arriving at the answer. Some teachers supplement such textbooks in order to teach standard methods more quickly. Some curricula do not teach long division. Critics believe the NCTM revised its standards to explicitly call for continuing instruction of standard methods, largely because of the negative response to some of these curricula (see below).

Reform curricula

Examples of reform curricula introduced in response to the 1989 NCTM standards and the reasons for initial criticism:

Critics of reform textbooks say that they present concepts in a haphazard way. Critics of the reform textbooks and curricula support traditional textbooks such as Singapore Math, which emphasizes direct instruction of basic mathematical concepts, and Saxon math, which emphasizes perpetual drill.

Reform educators have responded by pointing out that research tends to show that students achieve greater conceptual understanding from standards-based curricula than traditional curricula and that these gains do not come at the expense of basic skills. In fact students tend to achieve the same procedural skill level in both types of curricula as measured by traditional standardized tests. More research is needed, but the current state of research seems to show that reform textbooks work as well as or better than traditional textbooks in helping students achieve computational competence w


From Yahoo Answers

Question:I am having trouble with justifying each step, because I don't really have an idea of what she ( my teacher ) wants me to do, because honestly we never justified each step if I remember correctly, anyway the problem is: 13x-4+9x, simplify this expression, and then justify each step you make. T Thank you

Answers:Dunno what she means by justify either but just add the x's to get 22x-4 and common factor I guess if you want to go further to get 2(11x-2) solve for x maybe? 2(11x-2)=0 x=2/11

Question:1. Choose the property that justifies: 2(x-3)=2x-6 a. Distributive Property for Real Numbers b. Reflexive Property of Equality c. Substitution Property of Equality d. Symmetric Property of Equality 2. If the conditional and converse of a statement are true, the statement qualifies as a a. inverse b. counterexample c. converse d. definition 3. The phrase if and only if or iff is used in which of the following? a. biconditional b. counterexample c. converse d. definition 4. m
Answers:1) A 2) B 3) A 4) C 5) C 6) D

Question:What is the LAST step in this fraction problem ? 3/4 + 7/12 . a) Add. b) Find the LCD. c) Simplify d) Find the GCF. THANKS (:

Answers:b d a c

Question:

Answers:Expand: (x - 4)(x + 8) x + 8x - 4x -42 Simplify: x + 4x - 32 I think FOIL is a confusing way to remember it. Look at the following picture: http://i35.tinypic.com/a49yrb.png See the curved lines? To me, they look like a crab claw. That is how I remember how to expand: just draw a crab claw.

From Youtube

Writing and Solving Two Step Equations | Algebra 1 Math Help :This video Algebra 1 lesson focuses on solving two step equations. The contents of the video discuss how to write an equation and how solve the equation. Also discussed is how to write and algebraic proof, in other words how to justify the steps in solving a two-step equation. The final example models how to write an equation for a geometric situation.

Simplifying Rational Expressions - YourTeacher.com - Math Help :For a complete lesson on simplifying rational expressions, go to www.yourteacher.com - 1000+ online math lessons featuring a personal math teacher inside every lesson! In this lesson, students learn that when simplifying a rational expression, such as (m^2 + 7m - 30) - 3m), the first step is to factor both the numerator and denominator, to get [(m + 10)(m - 3)]/[m(m - 3)], and the next step is to cancel out the factors that match up, in this case, the (m - 3)'s, to get (m + 10)/m, which is the final answer.