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Colección: La Educación
Número: (119) III
Año: 1994


MAA’S A Call for Change

The Mathematical Association of America (MAA) is the largest professional organization devoted primarily to college-level mathematics. The MAA report, A Call For Change: Recommendations for the Mathematical Preparation of Teachers of Mathematics (Leitzel) describes the collegiate mathematical experiences necessary for teachers of school mathematics in order to meet the following vision of an “ideal” mathematics teacher for the 1990’s and beyond:
  • communicate mathematical ideas with ease and clarity;
  • organize and analyze information, solve problems readily, and construct logical arguments;
  • possess knowledge and an understanding of mathematics that is considerably deeper than that required for the school mathematics they will teach;
  • enjoy mathematics and appreciate its power and beauty;
  • understand how mathematics permeates our lives and how the various threads within mathematics are interwoven; and
  • naturally and routinely use technology in the learning, teaching, and doing of mathematics. (Leitzel xiii)
A Call for Change, written by the MAA Committee on the Mathematical Education of Teachers, acknowledges that mathematics is a dynamic field and that the teaching of mathematics can and should involve new mathematics, new technology, and new approaches for encouraging active learning and teaching. The document has four main sections: standards common to the preparation of teachers of mathematics at all levels, standards for teachers at the elementary level (K-4), middle grades level (5-8), and secondary level (9-12). A brief look at each of these sections shows a need for change in the college-level teaching of mathematics as well.

Common Standards for All Teachers of Mathematics

The first section, Standards Common to the Preparation of Mathematics Teachers at all Levels, addresses that preparation with the intent that teachers of mathematics:
  • view mathematics as a system of interrelated principles;
  • are able to communicate mathematics accurately, both orally and in writing;
  • understand the elements of mathematical modeling;
  • understand and use calculators and computers appropriately in the teaching and learning of mathematics;
  • appreciate the development of mathematics both historically and culturally. (Leitzel 1)
To accomplish this, collegiate mathematics courses must allow students to explore, conjecture, experiment, and prove their skills so that they become actively engaged in doing mathematics. The connections within different branches of mathematics as well as across different disciplines need to be explored through problem solving, problem posing, and classroom discourse. These explorations ought to include mathematical model building to develop multiple representations and multiple solutions to mathematical problems. College mathematics professors should incorporate symbolic/graphical/numerical manipulators as found in graphics calculator and computer technology in their teaching. These tools together with cooperative group work enhance students’ understanding of mathematics. All college mathematics courses should emphasize the human endeavor of mathematics, its culturally diverse origins, and the equally diverse needs of society today.

Standards for Grades K-4

The second section, Standards for the Elementary Grades (K-4), focuses on the concrete level of understanding of K-4 students and the related need for teachers of these students to understand the nature and use of number, geometry, measurement, pattern, and data at that level. A minimum of three years of high school college preparatory mathematics and 9 semester hours in content mathematics is recommended, but this content must be presented through a hands-on, exploratory manner. By working with appropriate manipulatives, prospective teachers can learn to use these tools as well as learn the content necessary to build a conceptual understanding. The philosophy that mathematics is dynamic is modeled in these courses by students exploring operations and properties of number, conjecturing and testing hypotheses with multibase blocks, fraction bars, geoboards, calculators, graphs, and the like. All these activities provide opportunities for preservice teachers to improve their reasoning and communication skills.

Standards for Grades 5-8

The third section, Standards for the Middle Grades (5-8), recognizes the importance of this level in students’ lives because of the changes associated with early adolescence, and as a result, the need for teachers to know not only what and how they are to teach, but also the relation between the middle grades and the elementary and secondary mathematics curriculum. At least 15 semester-hours of content mathematics are required, four years of high school college preparatory mathematics, and the experiences recommended in section two above for grades K-4. Most traditional college curricula are not suited to this level of teacher. Teachers need an intuitive understanding of limits, continuity, derivatives, and integrals, which traditionally do not occur in the first calculus course. Special courses to focus on place-value concepts, rational number arithmetic, functions, algebraic structures, probability and statistics, and intuitive geometry as well as calculus are needed. Middle-grade teachers need to learn through experimentation and exploration, by posing problems and testing problem-solving solutions, through a variety of hands-on activities and cooperative learning situations.

Standards for Grades 9-12

The fourth set of recommendations, Standards for the Secondary Level (9-12), include number concepts, geometry, functions, probability, statistics, data analysis, continuous change, discrete processes, and mathematical structures. Although students preparing to teach mathematics at this level will complete the equivalent of a major in mathematics, it is “one quite different from that currently in place at most institutions” (Leitzel 27). The emphasis once again is not so much on which topics to cover, but on how those topics are taught. Students will arrive in college classrooms having used graphics calculators and computers in high school. College-level mathematics curricula must reflect these changes. A year-long upper division sequence in some area of mathematics should be studied in depth with the purpose of having students (1) think deeply about mathematical ideas through exploration, conjectures, and justification of these hypotheses by way of discussion and proof, and (2) develop intellectual curiosity and self-directed learning. The 9-12 prospective teacher should explore other disciplines for applications of mathematics and an understanding of how other disciplines spawn new mathematics.

Summary

Teachers of mathematics need to know mathematics content, but they need to know it in ways different from the past. As we become more of an information society than an industrial society, the needs of society change. Citizens will need “emphasis on understanding the conceptual bases of mathematics, an ability to communicate mathematical ideas to others, the ability to reason mathematically, and familiarity with the use of various technological tools in learning and doing mathematics” (Leitzel 39). Students need opportunities to construct their own mathematical understanding; the process rather than the product becomes the priority.

In this section we have outlined the reforms for the preservice preparation of teachers of mathematics that are outlined in MAA’s A Call for Change. In sum, these recommendations call for an increase in the mathematics content studied by prospective teachers of mathematics at all levels, as well as for fundamental change in the nature of prospective teachers collegiate mathematics course experiences and the ways in which those courses are taught.