| Traditional Mathematics |
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Traditional mathematics is the term used for the style of mathematics instruction used for a period in the 20th century before the appearance of reform mathematics based on NCTM Standards , so it is best defined by contrast with the alternatives. {Link without Title} A comparison of traditional and reform mathematics curricula in an eighth-grade classroom Education, Summer 2003 by Alsup, John K., Sprigler, Mark J. Several in times in history, traditional mathematics have been challenged by new methodology such as New Math , now largely abandoned and discredited. Standards-based mathematics is easily distinguished in curricula such as TERC in the deliberate omission of instruction of some or most traditional mathematics methods, and emphasis on goals outside the traditional field of mathematics such as equity for women minorities, preserving the environment, and promoting multiculturalism where most algorithms and methods had come from European cultures and men. This comes from the belief system that such instruction promotes failure, discourages minorities and women, and is harmful to basic mathematical understanding. The stated outcomes were to equip all students with mathematical power rather than tracking only a few students into advanced mathematics, and to make mathematics relevant to all groups, not only the successful. No such ambitious goals had ever been part of Traditional Mathematics programs which sought only to teach the same methods used by previous generations. Several such curricula were developed largely at federal expense. With the incentive of federal grants money, these were widely adopted by a Consensus process in the United States by the 2000s as an integral part of Standards-based Education Reform , another education initiative which had failed under its former name of Outcomes-based Education . It received bipartisan support by legislators and the public education bureaucracy, as well as business interests such as the Business Roundtable . Nevertheless, many adoptions of reform programs have been troublesome. Although many of these projects show research claiming they are effective, some of these students and parents would later complain that they entered college very poorly prepared for college mathematics. Reform math been the subject of harsh criticism from those knowledgeable about real life application of mathematics. Consequently, by the early 2000s, Standards-based Mathematics was also in a process of being abandoned and discredited as a massive failure in some school districts and states. Even the NCTM would abandon support of initiatives and texts which completely omitted traditional arithmetic, and texts such as TERC which had consistently omitted all traditional instruction {Link without Title} Quirk "TERC Omits All Standard Computational Methods" would restore some traditional methods and textbooks which parents could use to the curriculum. TRADITIONAL METHODS The topics and methods of traditional mathematics are well documented in books and open source articles of many nations and languages:
Most documents outside of Standards-based Mathematics texts only cover traditional methods. Most parents and those who work in professions that require mathematics such as accounting, science, or engineering were taught, and apply traditional mathematics. Most of mathematics notation and methods that are taught and used internationally in all languages have been standardized on traditional mathematics for thousands of years. Open source encyclopedias entries like those listed above contain very little information on reform mathematics computation methods such as circling, reasoning, Coloring In 100s Or 10,000s Charts , creating projects with Glue And Scissors, Singing, Working In Groups , creating a Fantasy Lunch , writing an essay about rain forests, or explaining how to two 1-digit numbers, or the lattice method of multiplication . The NCTM standards were proposed before curricula implementing the proposals had been created or tried, although they had been agreed upon by Consensus by many reputable math educators. Instead, curricula based on the standards were created after they were proposed. Use of the term "standards" is somewhat misleading, as "standards" based methods generally eschew any "standard method" of arithmetic or mathematics. Reform methods are generally not well known, or were developed with government grant money quite recently, being tested with actual students in pilot projects. Teachers trained in one method such as TERC will not be prepared for Everyday Mathematics because the methods taught are completely different. Neither teach methods familiar to teachers, parents, professional mathematicians or engineers. Elementary arithmetic generally covers content which was traditionally taught in elementary school, a level of education generally achieved even by immigrant populations with low rates of high school graduation. Most teachers and parents know enough math to be familiar with these concepts. Many reform text cover topics such as median, mode, bar-and-whisker charts, and concepts such similar and obtuse triangles as early as 4th grade which may not have been taught to parents who have completed a masters degree. Thus, reform programs generally require extensive teacher re-training. Letters to parents are sent explaining that "math is not what is used to be", as parents find it difficult to even comprehend the homework sent home which may require cutting, pasting, finding newspaper articles, or interviewing members of the family or playing card games, with very little classic arithmetic. POLITICAL MOTIVATION Supporting traditional or standards based mathematics has been called politically motivated. Yet traditional mathematics was largely concerned with arithmetic for its own sake. It was based on presenting content, practice, and testing for retention. Reform mathematics methods is motivated, as stated by the NCTM , to use mathematics to increase and create social equity between races, genders and classes, and promote awareness of issues such as the environment and multiculturalism. Many reform textbooks such as the Core-Plus Mathematics Project have a significant content of "context" such as rain forests, or diverse minority cultures, with "indexes of contexts", while traditional texts tend to be thinner, and are largely devoid of such content. Both the supporters and opponents of traditional math are often individuals driven by an Ideology who use specific instructional methodologies as wedges to introduce their political agendas into educational activities. Research, such as that by Lightner, cited below has often shown little difference between the various approaches. RAISING EXPECTATIONS Rather than teaching to current expectations and ranking students against each other, Standards-based Education Reform is a movement in all areas of curriculum which builds up content-independent problem solving skills in place of learning specific facts and methods. It sets and demands higher standards for all students, and numerical goals and timetables with sanctions such as denying diplomas, based on the (some say unrealistic) belief that all students can perform at world class levels, regardless of native ability. Thus, even students in the top tenth percentile could be classified as failures if they failed to show improvement compared to last year's students. Yet many parents and professionals are less concerned about demanding skills for 20 or more years in the future than if their children or students were at least as capable as was expected 20 years ago. REPLACEMENT BY REFORM MATHEMATICS Since 1989, governments and education agencies have been in the process of replacing traditional mathematics with Standards-based Mathematics . However increasing numbers of schools districts are abandoning reform standards because of protests from parents, students, and mathematics experts and very low test scores, even from tests aligned with the new standards. CRITICISM Most standards-based mathematics methods are distinguished by either de-emphasizing, discouraging or completely omitting any instruction in traditional methods listed above. Many widely cited research papers such as The Harmful Effects Of Algorithms In Grades 1-4 take the position that instruction of such traditional methods is harmful to deep understanding of mathematics. Because of the popular movement against standards, traditional mathematics education has been called "Parrot Math" by critics. The direct instruction method (teaching that 2 + 2 = 4 as a fact rather than an exploration) has also been disparagingly called "drill and kill". The battle of philosophies has appeared so often on the front pages of national newspapers such as the Wall Street Journal and websites such as Mathematically Correct that the debate has been called the Math Wars . Traditional mathematics has been called a failure because only a few students achieve the highest levels of mathematics achievement such as calculus, and it is believed that not enough master even algebra, which is seen a gateway to high paying jobs such as computer programming. Because much of mathematics has roots in European culture, and developed by men, it is seen by some as not being appropriate for women, or people of color. STRATEGIES
Alarmed by low scores, Tacoma school officials OK added textbook DEBBY ABE; The News Tribune (Tacoma, WA) "parents need easier-to-understand math textbooks so they can help their children with homework." , or do not contain explanations of correct methods of solving problems directly. For example, a Core-Plus Mathematics Project unit introducing matrices asks to graph and interpret data on charts, but the text only provides information on Nike and Reebok sales. In another exercise, students are asked to draw a fantasy fractal picture, but are not given a definition of what a fractal picture is.
HOMESCHOOLING Home School students and parents often favor traditional texts. Since the parents are teachers, they are more familiar with standard methods that they were taught. Traditional texts also tend to be much simpler since they take generally only a few minutes to explain a skill, and a few more minutes to practice rather than long group-oriented projects that require mathematical communication, music or art projects, and nightly homework which requires a half to an hour of work on the part of the student and the parent, or the rest of the family in the case of interviews. They are generally based on inexpensive, thin books which contain only mathematical information rather than contexts on rain forests or running shoes or a tour of the United States, and do not require expensive manipulatives such as number cubes or blocks. Standards-based methods usually require a significant investment and specialized teacher training, often with federal grant money to be adopted by a large school district, and are not suitable for use in home school environment. TRADITIONAL MATHEMATICS TEXTS In general, any math textbook which contains instruction in standard arithmetic methods can be categorized as a traditional math textbook. Any math textbook which de-emphasizes or omits significant standard methods can be considered to be standards-based. The following current texts are often cited as good for those wishing for a traditional approach, often also favored by Homeschool ers. ORGANIZATIONS PROMOTING TRADITIONAL MATHEMATICS Most of these organizations are critical of Standards-based Mathematics and have given poor reviews to textbooks such as TERC , Mathland and Core-Plus Mathematics Project
WHICH TO CHOOSE Mathematics texts are generally chosen by local school districts, or promoted by state education agencies, often with the support of business organizations such as the Business Roundtable by a Consensus Process . A blue ribbon panel is created to determine that current math standards are inadequate and unacceptable, and draw up a plan to implement texts which are compliant with Standards-based Education Reform , of which mathematics is only one field of curricula. At no time is there a place for public debate of whether such new standards should be adopted. Instead, the public is invited to be informed of the new standards, and are invited to provide input, and break up into small groups on how they can help adopt and embrace the new standards. Similar standards-based curricula also exist for science, social studies, and language arts, also with their own controversies. Many districts apply for the federal grants which are generally given only to districts which adopt standards-based curricula. In general, only a small number of parents or mathematics experts are even aware of such an adoption process, and a few parents and citizens will be recruited to support such an adoption. Once adopted, citizens often find it difficult or impossible to persuade education officials to discard such curricula, despite a wide body of information about the ineffectiveness of such curricula, but citizens in some states and districts have succeeded in some cases such as California, and Tacoma, Washington. EXTERNAL LINKS
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