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.[1]
- Reform mathematics emphasizes understanding of concepts and exploration. Traditional presents a concept, and then uses drill and practice.
- Reform uses extra materials which must be refreshed each year, some don't use traditional textbooks, or break them up into several booklets. Traditional mathematics use a single textbook for the entire year which can be used over several years. For example, here is the list of student materials included in the 2002 Grade 5 package for TERC Investigations: 4 rolls of adding machine tape; 36 blank 5/8" cubes; 1,000 stickers for blank cubes; 200 1-cm cubes; 16 transparent blank spinners; 4 450-piece sets of power polygons; 4 buckets of square color tiles (400 per bucket); 1,000 Snap(TM) cubes; 1 set of elementary bar mass set-Ohaus; 4 graduated measuring prisms (2-cm x 5-cm x 21-cm); 4-liter measuring pitcher (calibrated 100 ml - 1,000 ml); 4 spectrum school balance (includes 7-piece mass set); 4 sets standard measuring pitchers (3 pitchers: quart, pint, cup per set); 10 measuring tapes; 12 meter/yard sticks. The total package for Grade 5 is listed at $1,388.42, and within that total the cost of the just mentioned student materials, for a class of 32, is $817.00[2]
- Reform mathematics omits or de-emphasizes traditional concepts, terms or skills such as regrouping, long division, or average. Traditional mathematics uses concepts and terms which have changed little since their invention hundreds or thousands of years ago. For example, Core-Plus introduces a NOW NEXT notation unfamiliar to most mathematics professors, while TERC instructs teachers to not use the traditional add-the-sum and divide by the number of data points method to compute the average.
- Reform mathematics emphasizes multiculturalism. For example, TERC in one elementary unit asks the students to sing Happy Birthday, and as a variation sing it in one or more immigrant languages. Traditional textbooks such as Singapore Math reflect either no culture, or only one dominant culture.
- Reform mathematics emphasizes problem solving, while traditional has tended to teach basic skills. However, in a comparison of a traditional Houghton-Mifflin curriculum against the Cord Applied Math, there were no advantage SAT total scores and SAT problem-solving scores, but the students with the traditional text showed a significant improvement in SAT procedure scores, or basic skills.
- Reform mathematics is preferred by federal and state education agencies, as well as professional organizations such as the NCTM. Opposition to reform and preference for traditional mathematics has come from parents, college educators, and professionals in mathematics and science.
- Traditional mathematics separates students into pre-college and vocational tracks. Not all students are expected to take or master algebra, geometry, statistics, or calculus. Reform programs like Core-Plus teach the same advanced content, including matrix mathematics to all high school students for 3 years.
- Reform mathematics believes that mathematics classroom instruction must be changed to improve mathematics instruction and increase student achievement. Stronger connections must be made between mathematics and students' lives outside of the mathematics classroom. Traditional mathematics was abstract, and oriented towards college preparation. Traditional education expects different outcomes for different students rather than increasing achievement for all students every year.
- Reform mathematics is expensive to implement. Teachers must be trained and supplementary kits must be purchased. Traditional mathematics does not require teacher retraining, or extra consumable materials. The study of the Cord text concluded that that if a reform mathematics curriculum did not promote an increase in student achievement, such extra expense was not worthwhile.
- Reform mathematics is often funded by federal money from organizations such as the Department of Education and the National Science Foundation. School districts are not offered extra grant money to buy or promote traditional mathematics textbooks, which must be funded from local education dollars.
- Traditional math textbooks are more easily understood by parents and teaches the same methods parents learned, so they can help their children with homework. Some standards-based curricula do not have textbooks to bring home[3], 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 interpet 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.
- Traditional math text problems typically have only one correct answer. In a Core-Plus matrix problem, the student is asked to choose the best chart format for data, but multiple correct answers are possible.
[edit] External links
- Mathematically Correct, a website which supports traditional mathematics
- NYC HOLD, a New York-based organization of teachers, professional mathematicians, parents and others which has been extremely active in recent years in working for adoption of mastery-based, traditional math programs
- Illinois Loop - extensive web coverage of math issues and specific math programs
[edit] Notes
- ^ [1]A comparison of traditional and reform mathematics curricula in an eighth-grade classroom Education, Summer 2003 by Alsup, John K., Sprigler, Mark J.
- ^ [2] Reviews of TERC
- ^ [3] Back to basics on kids’ math 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."
