A brief History of American k-12 Mathematics Education in the 20th Century



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The 1980s: Prelude to National Standards

In the early 1980s, there was widespread recognition that the quality of math and science education had been deteriorating. A 1980 report by a presidential commission pointed to low enrollments in advanced mathematics and science courses and the general lowering of school expectations and college entrance requirements.46 Among the various reports and commissions to investigate K-12 education in the early 1980s, two especially stand out: An Agenda for Action and A Nation at Risk. The different points of view and prescriptions for change expressed in these two reports characterize to some extent the opposing factions in the math wars of the 1990s.

The National Council of Teachers of Mathematics released An Agenda for Action in 1980. The report called for new directions in mathematics education which would later be codified in 1989 in the form of national standards. An Agenda for Action recommended that problem solving be the focus of school mathematics in the 1980s, along with new ways of teaching. The report asserted that "Requiring complete mastery of skills before allowing participation in challenging problem solving is counterproductive, " and "Difficulty with paper-and-pencil computation should not interfere with the learning of problem-solving strategies." Technology would make problem solving available to students without basic skills. According to the report, "All students should have access to calculators and increasingly to computers throughout their school mathematics program." This included calculators "for use in elementary and secondary school classrooms." The report also warned, "It is dangerous to assume that skills from one era will suffice for another," and called for "decreased emphasis on such activities as...performing paper and pencil calculations with numbers of more than two digits." This would be possible because "The use of calculators has radically reduced the demand for some paper-and-pencil techniques." The report also recommended that "Team efforts in problem solving should be common place in elementary school classrooms," and encouraged "the use of manipulatives, where suited, to illustrate or develop a concept or skill." An Agenda for Action also called for "a wider range of measures than conventional testing." All of these directions would later become issues of contention in the math wars of the 1990s.47

Perhaps the boldest and most far reaching recommendation of An Agenda for Action was its proposal for "Mathematics educators and college mathematicians" to "reevaluate the role of calculus in the differentiated mathematics programs." The report argued that "Emerging programs that prepare users of mathematics in nontraditional areas of application may no longer demand the centrality of calculus that has traditionally been demanded for all students." The de-emphasis of calculus, when carried out on a large enough scale, would support the move away from the systematic development of the prerequisites of calculus: algebra, geometry, and trigonometry. The so-called "integrated" high school math books of the 1990s contributed to this tendency. While those books contained parts of algebra, geometry, and trigonometry, the developments of these traditional subjects were not systematic, and often depended on student "discoveries" that were incidental to solving "real world problems."

In spite of the NCTM's enthusiasm for the objectives of An Agenda for Action, the report received little attention. It was largely eclipsed by the 1983 report, A Nation At Risk.48 This report was written by a commission appointed by Terrell Bell, the U.S. Secretary of Education, at that time. Unlike previous education reform efforts and reports by prestigious governmental bodies, this one captured the attention of the public. A Nation At Risk warned, "Our nation is at risk...the educational foundations of our society are presently being eroded by a rising tide of mediocrity that threatens our very future as a Nation and a people." Even sharper was the statement, "If an unfriendly foreign power had attempted to impose on America the mediocre educational performance that exits today, we might well have viewed it as an act of war."

A Nation at Risk addressed a wide variety of education issues, including specific shortcomings in mathematics education. Regarding remedial mathematics instruction, the report found that:
 

Between 1975 and 1980, remedial mathematics courses in public 4-year colleges increased by 72 percent and now [in 1983] constitute one-quarter of all mathematics courses taught in those institutions.

Business and military leaders complain that they are required to spend millions of dollars on costly remedial education and training programs in such basic skills as reading, writing, spelling, and computation.

Although the authors of A Nation at Risk did not attempt to analyze the causes of these deficiencies, the lack of attention to basic skills in elementary schools caught up in the Open Education Movement of the late 1960s and early 1970s surely contributed to the need for more remedial courses in the 1980s in high school and college.



A Nation at Risk described high school course offerings as a "curricular smorgasbord" and reported, "We offer intermediate algebra, but only 31 percent of our recent high school graduates complete it; we offer French I, but only 13 percent complete it; and we offer geography, but only 16 percent complete it. Calculus is available in schools enrolling about 60 percent of all students, but only 6 percent of all students complete it."

The importance of student assessment was also addressed. The report envisioned a role for standardized tests that foreshadowed a movement toward accountability in the late 1990s49:


 

Standardized tests of achievement (not to be confused with aptitude tests) should be administered at major transition points from one level of schooling to another and particularly from high school to college or work. The purposes of these tests would be to: (a) certify the student's credentials; (b) identify the need for remedial intervention; and (c) identify the opportunity for advanced or accelerated work. The tests should be administered as part of a nationwide (but not Federal) system of State and local standardized tests. This system should include other diagnostic procedures that assist teachers and students to evaluate student progress.



A Nation at Risk called attention to the quality of teachers and complained, "Too many teachers are being drawn from the bottom quarter of graduating high school and college students." Teacher training programs were also criticized in the report:
 

The teacher preparation curriculum is weighted heavily with courses in "educational methods" at the expense of courses in subjects to be taught. A survey of 1,350 institutions training teachers indicated that 41 percent of the time of elementary school teacher candidates is spent in education courses, which reduces the amount of time available for subject matter courses.

The report also drew attention to teacher shortages, especially math and science teachers:
 

The shortage of teachers in mathematics and science is particularly severe. A 1981 survey of 45 States revealed shortages of mathematics teachers in 43 States, critical shortages of earth sciences teachers in 33 States, and of physics teachers everywhere.



A Nation at Risk also addressed the question of textbooks, proposing that they be upgraded to include more rigorous content. It called upon "university scientists, scholars, and members of professional societies, in collaboration with master teachers, to help in this task, as they did in the post-Sputnik era. They should assist willing publishers in developing the products or publish their own alternatives where there are persistent inadequacies." The report addressed the textbook adoption process as well, suggesting that:

In considering textbooks for adoption, States and school districts should: (a) evaluate texts and other materials on their ability to present rigorous and challenging material clearly; and (b) require publishers to furnish evaluation data on the material's effectiveness.

With widespread public concern about education, the release of A Nation at Risk resulted in newspaper headlines across the country. A number of states created task forces and commissions to measure their own state programs against the recommendations of A Nation at Risk.50 It is illuminating to compare these recommendations to the California mathematics education polices of the late 1990s. As described below, California's mathematics policies in 1998 became the leading obstacle to progressivist domination in mathematics education. Yvonne Larson, the vice-chair of the Commission that released A Nation at Riskin 1983, served as the president of the California State Board of Education 1997.  Whether by intent or coincidence, the California policies conformed rather well with a number of the recommendations of the 1983 report.

The 1989 NCTM Standards

With public opinion in support of a strong focus on basic skills and clear high standards, the NCTM took steps to recast its own agenda under the label of standards. In 1986 the NCTM established the Commission on Standards for School Mathematics. The Curriculum and Evaluation Standards for School Mathematics was developed during the summer of 1987 and revised in 1988 by four working groups whose members were appointed by John Dossey, the president of the NCTM at that time. During the 1987-88 school year, input was sought from classroom teachers across the country. The project was coordinated by Thomas A. Romberg. The final document was published in 1989, and during the following decade it was commonly referred to as the NCTM Standards, or as the Standards.51 Of the 24 working group members who had direct input into the writing of the Standards,none were mathematicians, and only two were concurrent K-12 teachers; the remainder were, for the most part, teacher education professors and instructors from universities. However, the NCTM successfully promoted the Standardsas if they were developed through a grass-roots, bottom-up process.52

The NCTM Standards were not standards in the usual sense of the word. Harold Stevenson, a psychologist at the University of Michigan, described them as follows:
 

In our view the NCTM standardspresent a vague, somewhat grandiose, readily misinterpreted view of what American children should learn in mathematics. Moreover, the view fails to meet what we would consider to be the meaning of "standards." Standards should involve a progression of accomplishments or competencies that are to be demonstrated at defined times in the child's schooling. The NCTM standards give no indication (beyond four-year intervals) of the sequence with which the content is to be presented and are not helpful to the classroom teacher in designing lessons that meet the standards.

The NCTM standards list goals with which no one would be likely to disagree. Of course we want children to value mathematics, to be mathematics problem solvers, to be confident of their ability, and to be able to reason and communicate mathematically. Certainly students must develop a number sense, have concepts of whole number operations, and the other kinds of skills and knowledge indicated under NCTM's curriculum standards. But the published standards do not integrate these two important components: the general attitudes and mathematical skills.53

The1989 NCTM Curriculum and Evaluation Standards for School Mathematics is comprised of sections devoted to general standards for the bands of grades: K-4, 5-8, and 9-12. Another section is devoted to "Evaluation Standards." In many respects, the 1989 NCTM standards promoted the views of An Agenda for Action, but with greater elaboration. The grade level bands included lists of topics that were to receive "increased attention" and lists of topics that should receive "decreased attention." For example, in the K-4 band, the Standards called for greater attention to "Meanings of operations," "Operation sense," "Mental computation," "Use of calculators for complex computation," "Collection and organization of data," "Pattern recognition and description," "Use of manipulative materials," and "Cooperative work."

Included on the list for decreased attention in the grades K-4 were "Complex paper-and-pencil computations," "Long division," "Paper and pencil fraction computation," "Use of rounding to estimate," "Rote practice," "Rote memorization of rules," and "Teaching by telling." For grades 5-8 the Standards were even more radical. The following were included on the list to be de-emphasized: "Relying on outside authority (teacher or an answer key)," Manipulating symbols," "Memorizing rules and algorithms," "Practicing tedious paper-and-pencil computations," "Finding exact forms of answers."

As in An Agenda for Action, the 1989 NCTM Standards put strong emphasis on the use of calculators throughout all grade levels. On page 8, the Standards proclaimed, "The new technology not only has made calculations and graphing easier, it has changed the very nature of mathematics..." The NCTM therefore recommended that, "appropriate calculators should be available to all students at all times." The Standards did concede that "the availability of calculators does not eliminate the need for students to learn algorithms," and it did acknowledge the need for "some proficiency with paper and pencil algorithms." However, these concessions were not supported in the classroom scenarios, or other parts of the document.

The NCTM Standards reinforced the general themes of progressive education, dating back to the 1920s, by advocating student centered, discovery learning. The utilitarian justification of mathematics was so strong that both basic skills and general mathematical principles were to be learned almost invariably through "real world" problems. Mathematics for its own sake was not encouraged. The variant of progressivism favored by the NCTM during this time was called "constructivism" and the NCTM Standards were promoted under this banner.54

The term "constructivism" was adapted from cognitive psychology by educators, and its meaning in educational contexts is different from its use in psychology. E.D. Hirsch Jr. provided a useful definition in his book, The Schools We Need: Why We Don't Have Them, which begins as follows:


 

"Constructivism" A psychological term used by educational specialists to sanction the practice of "self-paced learning" and "discovery learning." The term implies that only constructed knowledge--knowledge which one finds out for one's self--is truly integrated and understood. It is certainly true that such knowledge is very likely to be remembered and understood, but it is not the case, as constructivists imply, that only such self-discovered knowledge will be reliably understood and remembered. This incorrect claim plays on an ambiguity between the technical and nontechnical uses of the term "construct" in the psychological literature...

Hirsch elaborated further on the psychological meaning of constructivism in his book. A more general and technical discussion was given in a paper by John R. Anderson, Lynne M. Reder, Herbert A. Simon entitled, Applications and Misapplications of Cognitive Psychology to Mathematics Education.55 Criticisms of educational constructivism, as in this article, were not well received by the education community. In an address before the California State Board of Education in April 1997, Hirsch described the treatment of this paper. "After a so-called peer review, Educational Researcher turned down the article, and agreed to print only a section of its critique of situated learning. This decision would have been unremarkable except that the three authors of the article happened to be among the most distinguished cognitive scientists in the world, John Anderson and two other colleagues at Carnegie Mellon, Lynn Reder, and Herb Simon. The latter happens also to be a Nobel prize winner."56

Mathematics education leaders drew support for educational constructivism from the writings of Jean Piaget and Lev Semenovich Vygotsky. Piaget's ideas about developmental stages of learning, and Vygotsky's concept, "Zone of Proximal Development," seemed to be consistent with the child-centered, cooperative learning approaches to education long favored by colleges of education.

In the fall of 1989, President George H. W. Bush, then in his first year of office, was invited by the nation's governors to an education summit in Charlottesville, Virginia. A bipartisan call went out for national standards. Participants at the 1989 Education Summit made a commitment to make U.S. students first in the world in mathematics and science by the year 2000.

Political leaders in the late 1980s were motivated by employers' complaints about the costs of teaching basic skills to entry level workers, and by the low standing of U.S. students in comparisons with foreign students in an era of economic competition.57 The timing for the NCTM Standards could not have been better. The nation was looking for benchmarks that could improve education. The NCTM Standards had just been published, and by default they became the national model for standards. The NCTM Standards were immediately and perfunctorily endorsed by a long list of prominent organizations such as the American Mathematical Society, the Mathematical Association of America, and the Council of Scientific Society Presidents.

Within a few years, the NCTM produced two additional documents as part of its standards. One published in 1991 was narrowly focused on pedagogy and the other, published in 1995, was focused on testing.58 By 1997 most state governments had adopted mathematics standards in close alignment with the NCTM standards.59

The National Science Foundation

The National Science Foundation (NSF) was the key to the implementation of the NCTM Standards across the nation. Without the massive support it received from the NSF, the sole effect of the NCTM Standards would have been to collect dust on bookshelves. Spurred by the 1989 Education Summit attended by President Bush and all of the nation's governors, the Education and Human Resources Division (EHR) of the NSF set about to make systemic changes in the way math and science were taught in U.S. schools. The blueprint for change in mathematics would be the NCTM Standards.

The NSF proceeded purposefully. The EHR developed a series of Systemic Initiative grants to promote fundamental changes in science and mathematics education in the nation's schools. The Statewide Systemic Initiatives were launched in 1991. These grants were designed in part to encourage state education agencies to align their state mathematics standards to the NCTM Standards. The result was a remarkable uniformity and adherence to the NCTM Standards at the state level.60

Recognizing that education is largely a matter of local control, the NSF also launched its Urban Systemic Initiative (USI) program in 1994. These USI grants were designed to implement the NCTM agenda at the school district level in large cities. The USI grants were followed by a program for Rural Systemic Initiatives. By 1999, the USI had evolved into the Urban Systemic Program. This program allowed renewals of awards made under the USI program.

At first, the Systemic Initiative grants were awarded to proposals generally aligned to the educational views of the NSF, but awardees were allowed substantial freedom to develop their own strategies for reform. As the program evolved, so did the guidelines. By 1996, the NSF clarified its assumptions about what constitutes effective, standards-based education and asserted that61:


    • All children can learn by using and manipulating scientific and mathematical ideas that are meaningful and relate to real-world situations and to real problems.

    • Mathematics and science are learned by doing rather than by passive methods of learning such as watching a teacher work at the chalkboard. Inquiry-based learning and hands-on learning more effectively engage students than lectures.

    • The use and manipulation of scientific and mathematical ideas benefits from a variety of contributing perspectives and is, therefore, enhanced by cooperative problem solving.

    • Technology can make learning easier, more comprehensive, and more lasting.

    • This view of learning is reflected in the professional standards of the National Council of Teachers of Mathematics, the American Association for the Advancement of Science, and the National Research Council of the National Academy of Sciences.

The NSF was clear in its support of the NCTM Standards and of progressive education. Children should learn through group-based discovery with the help of manipulatives and calculators. Earlier research funded by the NSF, such as "Project Follow Through," which reached very different conclusions about what works best in the classroom, would not be considered.62 Regardless of what cognitive psychology might say about teaching methodologies, only constructivist programs would be supported.

Along with the Systemic Initiative awards, the NSF supported the creation and development of commercial mathematics curricula aligned to the NCTM Standards. In the decade of the 1990s, the National Science Foundation sponsored the creation of the following mathematics programs for K-12:



elementary school

Everyday Mathematics (K-6)

TERC's Investigations in Number, Data, and Space (K-5)

Math Trailblazers (TIMS) (K-5)



middle school

Connected Mathematics (6-8)

Mathematics in Context (5-8)

MathScape: Seeing and Thinking Mathematically (6-8)

MATHThematics (STEM) (6-8)

Pathways to Algebra and Geometry (MMAP) (6-7, or 7-8)



high school

Contemporary Mathematics in Context (Core-Plus Mathematics Project) (9-12)

Interactive Mathematics Program (9-12)

MATH Connections: A Secondary Mathematics Core Curriculum (9-11)

Mathematics: Modeling Our World (ARISE) (9-12)

SIMMS Integrated Mathematics: A Modeling Approach Using Technology (9-12)

The development of NCTM aligned mathematics programs for K-12 was of obvious importance to the NSF (for a list of math programs explicitly endorsed by the NCTM, see the Appendix). How could the NCTM agenda be carried out without classroom materials that were specifically aligned to the NCTMStandards? An important component of the Systemic Initiatives was the aggressive distribution of NCTM aligned curricula for classroom use. The NCTM Standards were vague as to mathematical content, but specific in its support of constructivist pedagogy, the criterion that mattered most to the NSF. It should be noted that the Systemic Initiatives sometimes promoted curricula not on the list above, such as College Preparatory Mathematics, a high school program, and MathLand, a K-6 curriculum. MathLand was one of the most controversial of the widely used programs aligned to the NCTM Standards.63

In addition to aligning state math standards to the NCTM standards and creating and distributing math books and programs aligned to those standards, the NSF attempted with considerable success to push these approaches up to the university level. Most notable in this regard was the NSF's funding of a "reform calculus" book, often referred to as "Harvard Calculus," that relied heavily on calculators and discovery work by the students, and minimized the level of high school algebra required for the program.64

The NSF also funded distribution centers to promote the curricular programs it had helped to create. For example, an NSF sponsored organization created in 1997 called, "The K-12 Mathematics Curriculum Center," had a mission statement "to support school districts as they build an effective mathematics education program using curriculum materials developed in response to the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards for School Mathematics."

The Education and Human Resources Division of the NSF faced a serious hurdle in carrying out its Systemic Initiatives. U.S. K-12 education collectively was a multi-billion dollar operation and the huge budgets alone gave public education an inertia that would be hard to overcome. Even though the millions of dollars at its disposal made the EHR budget large in absolute terms, it was miniscule relative to the combined budgets of the school systems that the NSF sought to reform. It would not be easy to effect major changes in K-12 mathematics and science education without access to greater resources.

To some extent private foundations contributed to the goal of implementing the NCTM Standards through teacher training programs for the curricula supported the by the NSF, and in other ways. The Noyce Foundation was especially active in promoting NCTM aligned math curricula in Massachusetts and parts of California. Others such as the W. M. Keck Foundation and Bank of America contributed as well. However, the NSF itself found ingenious ways to increase its influence. The strategy was to use small grants to leverage major changes in states and school districts. NSF Assistant Director Luther Williams, who was in charge of the Education and Human Resources Division, explained the strategy in a July 1998 Urban Systemic Initiative Summary Update:
 

The NSF investment that promotes systemic reform will never exceed a small percentage of a given site's overall budget. The "converged" resources are not merely fiscal, but also strategic, in that they help induce a unitaryÖ reform operation. The catalytic nature of the USI-led reform obligates systemwide policy and fiscal resources to embrace standards-based instruction and create conditions for helping assorted expenditures to become organized and used in a single-purpose direction.

NSF Assistant Director Williams gave successful examples of this strategy. "Cleveland devoted half of its available bond referendum funding" for USI-related instructional material. "Los Angeles is one of several cities in the USI portfolio that places all Title II funding resources under the control of the USI." "In the Fresno Unified School System, $31 million of Title 1 funds have been realigned in support of USI activities."65

The Systemic Initiatives were extraordinarily successful in promoting the NCTM Standards and implementing NCTM aligned curricula at the classroom level. Los Angeles Unified School District (LAUSD), the second largest school district in the nation, serves as an illustrative example.

LAUSD was awarded a five year Urban Systemic Initiative grant in 1995 for $15 million. The $3 million per year from the Los Angeles Systemic Initiative (LASI) amounted to only one-twentieth of one percent of LAUSD's annual budget of $5.8 billion, or about $3.79 per student per year in the district. Yet, the LASI project exerted almost complete control over mathematics and science education in the district. In addition to Title II funds, LASI gained control of the school district's television station and its ten science and technology centers. According to Luther Williams' July 1998 Summary update, "[LASI] accountability became the framework for a major policy initiative establishing benchmarks and standards in all subject areas for the entire school system." LASI developed the district standards not only for math and science, but also English and social studies. All four sets of standards were adopted by the school district in 1996.

The Los Angeles School district math standards were so weak and vague that they were a source of controversy. One typical standard, without any sort of elaboration, asked students to "make connections among related mathematical concepts and apply these concepts to other content areas and the world of work." The LASI/LAUSD standards stipulated the use of calculators and "other appropriate technology" before the end of third grade, thus raising the possibility that students would not be required to master arithmetic. The word "triangle" did not even appear in the standards at any grade level. By design, trigonometry and all Algebra II topics were completely missing.66 Like the NCTM Standards, the LAUSD/LASI standards were given only for bands of grades, rendering them at best useless, even if they had been otherwise competently written.

The 1996 LAUSD/LASI math standards paved the way for the dissemination of textbooks and curricula aligned to those standards, as well as staff development in their use. The LASI 1997 annual report explained:
 

LAUSDís urban systemic initiative is well under way with its efforts to renew and unify districtwide instruction using standards-based curricula. These curricula are characterized by hands-on, inquiry based, problem solving, integrated/coordinated, student-teacher interactive instruction in math, science, technology for grades K-12. These efforts are supported and strengthened by needs-based staff development, increased communication among teachers and staff, changes in administrative policies that are essential for student access to the systemic benefits, and checks on progress and process at preselected gates in the systemís superstructure.

LASI was successful in distributing "hands-on, inquiry based" curricula aligned to the NCTM Standards to LAUSD schools. LASI specifically recommended NCTM aligned curricula for all grades, including MathLand for K-5. By July 1998, more than half of all LAUSD schools were using math curricula aligned to the NCTM Standards, and LASI publicly announced its plan to require all LAUSD high schools to use one of four "integrated math" curricula within five years: Core-Plus, Interactive Mathematics Program, College Preparatory Mathematics, or McDougal Littell's "Integrated Math."67 Two of these were funded by the NSF. This plan was not carried out because of the adoption of a new set of mathematics standards by the state of California in December 1997. But long after these rigorous California State Mathematics Standards were adopted, LAUSD schools continued to use LASI endorsed material. At a meeting of the LAUSD school board on May 2, 2000, it was revealed that fewer than three percent of elementary schools in the district were using California state approved mathematics programs. MathLand was used by 45 percent of the 420 elementary schools in LAUSD, while Quest 2000, a similar NCTM aligned program, was used by another 24 percent of the district's elementary schools. Eventually, the 1997 California mathematics standards were accepted and implemented by LAUSD, but not before a generation of students was educationally disenfranchised by the NSF Systemic Initiative Program.

The NSF's Systemic Initiative programs in other parts of the country were similarly successful in promoting mathematics curricula funded by the NSF, or otherwise aligned to the NCTM Standards. El Paso, Texas serves as an example. The El Paso Urban Systemic Initiative grant was awarded in 1994 and administered under the direction of the El Paso Collaborative for Academic Excellence. This collaborative coordinated other NSF funded projects including the Partnership for Excellence in Teacher Education and Model Institutions for Excellence, as well as private foundation grants, including support from The Exxon Corporation, The Pew Charitable Trusts, and The Coca-Cola Foundation.

El Paso is geographically removed from other U.S. cities and is unusual in that it is a "closed system." The teachers trained at the University of Texas, El Paso (UTEP) teach almost exclusively in the El Paso school districts, and the teachers in the El Paso school districts almost exclusively undertook their university studies at UTEP. This made the effectiveness of the K-12 and university programs easier to assess. It also made the entire education system easier to control. During the 1990s, the K-16 education system in El Paso was highly coordinated and focused on implementing constructivist math and science education programs. For this reason, it became a model center for educators from other parts of the country to visit and study.68

The Collaborative in El Paso worked in close coordination with the Texas Statewide Systemic Initiative housed in the Charles A. Dana Center in Austin. The Texas SSI developed an Instructional Materials Analysis and SelectionScoring Grid for Texas school districts to use in selecting math textbooks. The recommended criteria for selecting K-8 mathematics curricula included:



  • Materials provide opportunities for teaching students to work in collaborative and cooperative groups

  • Materials provide opportunity for the appropriate use of technology

  • Students are engaged in the development of mathematical understanding through the use of manipulatives

  • Multiple forms of assessment activities, such as student demonstrations, rubrics, self-reflections, observations, and oral and written work are used throughout the instructional materials

  • Technology is built into the assessment tools

  • Assessment activities take into account the ways in which students' unique qualities influence how they learn and how they communicate their understanding

  • The instructional materials reflect cultural diversities and address historical perspectives

  • Problem solving permeates the entire instructional material through investigative situations

The curricula chosen for El Paso public schools by 1999 were all NSF sponsored: TERC's Investigations in Number, Data, and Space (K-5), Connected Mathematics (6-8), SIMMS Integrated Mathematics: A Modeling Approach Using Technology (9-12).

The El Paso Collaborative for Academic Excellence created a confidential student evaluation questionnaire to monitor teaching methods used in high school math classrooms in all of EL Paso's public high schools. The evaluation included the following questions to students:



  • How often do MOST STUDENTS talk with each other to describe or justify the strategy they used to solve a problem?

  • How often does THE CLASS go in depth on a few problems instead of covering a large number of problems in the class period?

  • How often does THE TEACHER TALK during most of the period?

  • How often do YOU show that you understand a solution to a problem by explaining it in writing?

  • How often do YOU use math in science and science in math?

  • How often does THE CLASS work in pairs or groups to explain solutions?

  • How often do YOU use hand calculators or computers to analyze data or solve problems?

The NSF awarded the Texas Statewide Systemic Initiative $2 million per year beginning in 1994. Yet, in spite of the low funding, the Texas SSI "provides leadership for a vast array of agency partnerships, and influences all aspects of education in Texas. Curricula, instructional practices, textbooks, assessment, professional development of teachers, teacher evaluation, teacher certification, and preservice teacher education all now fall under the purview of the Texas SSI."69
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