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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 need the questions not the answers to math makes sense 6 page 76-77 show what you know # i-5 please help i need them now

Answers:What book?? Why not just type the questions out and ask for help??

Question:I'm trying to skip a grade in math from 9 to math 10 and not knowing some of the works I was wondering if I am doing this question right or wrong. The question goes along the lines of Water on the surface of a river moves quicker then water at the bottom, The formula to calculate the speed of water on the bottom of the river is The square root of B equals The square root of S minus 1.3 B symbolizes the bottom of the river's speed while the S symbolizes the surface's speed, both are In kilometers per hour. They give you the number 16 km/h as the surface speed then ask you to figure it out. Is this correct? The square root of 16 is 4. 4 minus 1.3 is 2.7. The square root of 2.7 is 1.6. Then you check in the back of the book and it says the answer is 7.3 km/h. Is my answer 2.7 km/h or their answer 7.3 km/h correct? Sorry for the extremely long question and thanks for you help.

Answers:book is correct sqrt(B) = 2.7 --->B = 2.7^2 = 7.3

Question:work as a fraction: 2 1/4 - x - 8 1/2 / 2^-2 = x - 9 1/2 (4) 9/4 - x - 17/2 / 2/1^-2 = x - 19/2 (4/1) 9/4 - x - 17/2 / 1/4 = x - 76/2 wat do i do next? i'm so confused cuz there are 2 unknowns! if u could will u plz do the rest 4 me? here's another (linear. plz do this one at least i suck at linears.) work as a decimal 4n - 9 + 2n - 6 -7n = 6n - 36 if u do these problems correctly with the correct answer i'll choose u as best answer and star 5 of ur questions! xoxo thanks omg Cristy ur bday is April 25 and ur Filipina 2! my bday is april 24 sorry ngb1311 i didn't mea n2 give u a thumbs down! whoops!

Answers:im not sure how to do the first one, but for the 2nd one you need to collect all of the like terms. 4n - 9 + 2n - 6 -7n = 6n - 36 -1n - 9 - 6 = 6n - 36 -1n - 15 = 6n - 36 add both sides by 1n -15 = 6n - 36 -15 = 7n - 36 add 36 to both sides 21 = 7n divide both sides by 7 3 = n

Question:work as a fraction: 2 1/4 - x - 8 1/2 / 2^-2 = x - 9 1/2 (4) 9/4 - x - 17/2 / 2/1^-2 = x - 19/2 (4/1) 9/4 - x - 17/2 / 1/4 = x - 76/2 wat do i do next? i'm so confused cuz there are 2 unknowns! if u could will u plz do the rest 4 me? if u answer correctly i will star 5 of ur questions!

Answers:9/4 - x - 17/2 / 1/4 = x - 76/2 Next, you want to get rid of that devision of fractions - division is the same as multiplying by the reciprocal, so we have: 9/4 - x - 17/2 * 4 = x - 76/2 Now simplify that: 9/4 - x - 34 = x - 76/2 Now we need to multiuply the 34 by 4/4 so you can do that subtraction: 9/4 - x - 136/4 = x - 76/2 -127/4 - x = x - 76/2 Now add (x + 76/2) to get the x's on one side and the contants on the other: -127/4 + 76/2 = x + x Make the fractions addable by finding LCD of 4: -127/4 + 152/4 = 2x 25/4 = 2x Now multiply everything by (1/2) x = (25/4)(1/2) x = 25/8 It's a pain the keep the fractions in tact - it's usually easier to multiply everything by the LCD first, then solve.

From Youtube

Math Finally Makes Sense - Watch to the End :From a strictly mathematical viewpoint: What Equals 100%? What does it mean to give MORE than 100%? Ever wonder about those people who say they are giving more than 100%? We have all been in situations where someone wants you to GIVE OVER 100%. How about ACHIEVING 101%? What equals 100% in life? Here's a little mathematical formula that might help answer these questions: If: ABCDEFGHIJKLMNOPQRSTU VWXYZ Is represented as: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26. If: HARDWO- R- K 8+1+18+4+23+ 15+18+11 = 98% And: KNOWLE- DGE 11+14+15+23+ 12+5+4+7+ 5 = 96% But: ATTITU- DE 1+20+20+9+20+ 21+4+5 = 100% THEN, look how far the love of God will take you: LOVEOF- GOD 12+15+22+5+15+ 6+7+15+4 = 101% Therefore, one can conclude with mathematical certainty that: While Hard Work and Knowledge will get you close, and Attitude will get you there, It's the Love of God that will put you over the top! It's up to you if you share this with your friends & loved ones. Have a nice day & God bless!!

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