Modern School Mathematics
Ediger, Marlow, College Student Journal
There was much enthusiasm when the phrase "Modern School Mathematics" was coined shortly after the 1958 National Defense Education Act was passed. Many federally funded study groups such as the The Greater Cleveland Mathematics Project, The School Mathematics Study Group, as well as the The University of Illinois Arithmetic Project came into being. University mathematicians were employed to provide leadership and innovations into the mathematics curriculum. Mathematics textbooks were soon revised in terms of recommendations from the above named study groups. Schools ordered approved mathematics, science, and foreign language teaching materials. If approved by the state, the school district paid one half and the federal government paid the other one half. Many teachers received their master's degrees in mathematics or science through federally funded stipends. Teachers received university credit and stipends for attending approved classes, courses, and workshops in mathematics. This was the Golden Age of Education. It sounded as if this was the cure all for an improved mathematics curriculum.
Presently, criticisms in secondary teaching are just as great as it was in 1958. The criticisms are quite similar. The innovations recommended by federally funded study groups has had little impact in teaching mathematics in particular. The high school level of schooling receives rather continuous criticism, These criticisms are quite obvious when reading professional journal articles. Authors of these articles frequently are far apart on what is being recommended for secondary students. The elementary level of schooling does not receive nearly as much criticism as compared to the secondary level. This is surprising since the elementary level of schooling provides the foundation for later school years. An interesting and provocative comment for elementary teachers in the US was made by Xiaoxia Newton (2007), who received her formal years of schooling in Mainland China:
* The K-5 institutional design must free elementary teachers from being generalists. They need to become experts in specific subjects and will need opportunities to practicing teaching a single subject curriculum, to reflect, and to continue developing their content knowledge.
* The K-12 institutional design must free both elementary and secondary teachers from spending every second of their time in teaching. The system must build in time for other equally important activities, such as lesson planning, collaborating with colleagues, grading student work, and provide high quality feedback to students. The allocation of time to teaching and to other activities must reflect the complex demands of teaching.
Criticisms of the High School Curriculum
Innovations coming from the 1958 NDEA funded groups and soon appearing in mathematics textbooks were numerous. Rote learning and memorization of subject matter was heavily criticized, then as well as now. Why is it so difficult to make changes in the high school curriculum?
Much emphasis by the federally funded NDEA study groups focused on selected key ideas. First, the structure of knowledge was to be identified, generally by university mathematics professors, and these were to be made available to teachers to be used in teaching. Then too, structural ideas from the federally funded study groups were incorporated into mathematics textbooks. Presently, the term "structural ideas" is not used; however salient ideas are identified, perhaps, as mandated objectives of instruction. The writer believes "structural ideas" should again be studied, not only by university mathematicians, but also with the involvement of elementary as well as secondary public school math teachers. By involving all three of these categories, the structural ideas may become more developmentally appropriate for implementation in the public schools. Parents, too, need to be involved since they felt frustrated in helping their offspring with homework in the new "modern school mathematics." Much stress was placed upon providing for individual differences in any classroom. The following structural ideas, among others, were frequently written about in teacher education journals in what was then called "modern school mathematics;"
* the commutative property of addition and multiplication
* the associative property of addition and multiplication
* the distributive property of multiplication over addition
* the inverse property of subtraction and division
* the property of closure.
Set theory and venn diagrams received much emphasis, also, as did the concept of number systems as well as other bases than base ten. These are a few of the concepts stressed in modern school mathematics and are important presently also, except other bases. Separation of what is recommend today in the mathematics curriculum from what is actually practiced in the classroom makes for a wide divide.
Modern school mathematics stressed the importance of discovery learning. This tended to make mathematics exciting and emphasize thinking about number. Presently, there is much criticism of mathematics being boring with its emphasis being placed upon memorizing for annual mandated tests. The accountability movement has advocated pupils being tested in grades three through eight and an exit test on the high school level. Pupils need to pass the grade level tests to be promoted and the exit test to receive a high school diploma.
Modern school mathematics emphasized that learnings be meaningful. Pupils then are to understand what is taught. It is salient to make sense of mathematical content. With mandated test preparations, it appears that meaning theory is being neglected. Drill does not stress meaningful learnings. Much stress must be placed upon higher levels of thinking in the curriculum. Logic and critical thinking needs to be in evidence and should be at the heart of the curriculum. Creative thought too is needed in that new procedures of doing algorithms need to be found by pupils. There are generally several ways to perform an operation on numbers. Creative discovery of new procedures is important. Creativity in determining novel, unique ways of doing things is salient in the school curriculum as well as in society. Myers (2007) wrote:
We must de-emphasize answers and correctness as the only worthy goals in mathematics. Sure, "right answers" are an important part of mathematics, but they aren't always the bottom line. Instead of always asking, "What's the right answer?" we should also wonder, "What's the right question?" and "What's the most interesting way to find the answer?" Mathematics is about bold, adventuresome ideas and the history of the subject is therefore fraught with mistakes, confusion, and invalid convictions. Let's make the classroom a bit more like the discipline and allow our students to revere in the "wrong" while they pursue the "right."
New technologies help students understand concepts, methods of reasoning, and effective ways of presenting their ideas in mathematics. Wiske (2004) wrote the following pertaining to a Boston Academy teacher using a computer program called the Geometer's Sketchbook to stimulate high school students in inquiry approaches:
Her students constructed geometric figures and then analyzed such data as angles, side lengths, and ratios, among other different measures. They developed and tested their own conjectures for measuring, dragging, reshaping and comparing geometric shapes. The software, which records and displays the mathematical relationships allowed students to examine similar set of cases, observe patterns, and make generalizations. The accuracy and speed of the computer program freed students from the tedium of construction with traditional tools yet enabled them to experience the process of arranging and analyzing shapes.
Among other materials of instruction, technology might well assist students to attach meaning and understand in what is being experienced .Then too, varying activities can develop interest in learning.
Stimulating experiences may be a motivating factor in students achieving mathematical objectives of instruction.
Students should work individually as well as collectively in ongoing learning activities. A preferred learning style for some is to work by the self in assignments to complete, as well as doing voluntary work at an interest center. Others like to work collectively. In society, people work at things individually as well as within a group setting. Students should have opportunities to follow personal preferences in the preferred style of learning. Maximum learning from a student may accrue from the style of learning preferred (Ediger, 2006).
The mathematics supervisor or lead teacher can do much to assist teachers to improve instruction. The following means of inservice education might well be provided mathematics teachers to assist student achievement and progress:
1. talk to teachers about innovative ideas in teaching. The supervisor and teacher must learn from each other in improving the curriculum.
2. visit classrooms to guide in curriculum improvement.
3. read current literature on trends and developments in the curriculum.
4. attend state and national teacher education conventions.
5. meet with supervisors in the district.
6. conduct research to improve the curriculum for each student (Ediger, 2002).
Ediger, Marlow (2007), "Writing in the Mathematics Curriculum," Journal of Instructional Psychology. 33 (2),121.
Ediger, Marlow, (2002), "The Supervisor of the School," Education, 122 (3), 604.
Myers, Perla, "Why? Why? Why? Future Teachers Discover Mathematical Depth," Phi Delta Kappan, 88 (9),696.
Newton, Xiaoxia (2007), "Reflections on Math Reforms in the U.S.," Phi Delta Kappan, 88 (9), 685.
Wiske, S. (2004),"Using Technology to Dig for Meaning," Educational Leadership, 62 (1), 8.
DR. MARLOW EDIGER, PROFESSOR EMERITUS
Truman State University…
Questia, a part of Gale, Cengage Learning. www.questia.com
Publication information: Article title: Modern School Mathematics. Contributors: Ediger, Marlow - Author. Journal title: College Student Journal. Volume: 42. Issue: 4 Publication date: December 2008. Page number: 986+. © 2009 Project Innovation (Alabama). COPYRIGHT 2008 Gale Group.
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