A Brief History of Mathematics Education and the NCTM Standards (page 2)
One of the defining events in the history of mathematics education was the launching of Sputnik 1 by the Soviet Union in 1957. This marked the start of the space age and the space race between the United States and the Soviet Union. Concern that the United States was falling behind in the areas of math and science triggered major national reforms in these areas. These reforms brought about the “New Math” of the 1960s and 1970s. The emphasis of this New Math was on set language and properties, proof, and abstraction. However, the New Math curriculum failed to meet the challenge of increasing the nation’s mathematical prowess as a whole. Some would even say that the New Math created more math confusion than it eliminated, which brought about the trend of Back to Basics in the late 1970s and early 1980s. Back to Basics emphasized arithmetic computation and rote memorization of algorithms and basic arithmetic facts.
The 1989 NCTM Standards
In the later 1980s the focus shifted to critical thinking. In 1989 the National Council of Teachers of Mathematics (NCTM) released a groundbreaking document, Curriculum and Evaluation Standards for School Mathematics. This publication, sometimes referred to as the “NCTM Standards,” stresses problem solving, communication, connections, and reasoning. The key assumptions underlying the 1989 NCTM curriculum standards for Grades K–4, listed below, are addressed throughout this textbook.
The 1989 NCTM Standards include 13 curriculum standards addressing both content and emphasis. One theme common to the NCTM Standards and to the recent changes in mathematics education is that “the study of mathematics should emphasize reasoning so that students can believe that mathematics makes sense” (NCTM, 1989, p. 29). Although not discussed here, this document also includes similar sets of assumptions and standards for Grades 5 through 8 and for Grades 9 through 12.
The 1989 NCTM Standards list five goals for students. Although these are goals stated for elementary students, it is especially important that teachers of elementary students have attained them.
Professional and Assessment Standards for Teaching Mathematics
A second groundbreaking document released by the National Council of Teachers of Mathematics was Professional Standards for Teaching Mathematics. This set of standards “present[s] a vision of what teaching should entail to support the changes in curriculum set out in the Curriculum and Evaluation Standards. This document spells out what teachers need to know to teach toward new goals for mathematics education and how teaching should be evaluated for the purpose of improvement” (NCTM, 1991, p. vii). NCTM followed with the 1995 release of Assessment Standards for Teaching Mathematics. NCTM produced this important document because “new assessment strategies and practices need to be developed that will enable teachers and others to assess students’ performance in a manner that reflects the NCTM’s reform vision for school mathematics” (NCTM, 1995, p. 1).
In the 1990s the major focus of reform in mathematics education was directed toward teaching pedagogy. Numerous studies and articles promoted the use of manipulatives and technology in the classroom (Burns, 1996; Hatfield, 1994; National Association for the Education of Young Children [NAEYC], 1996; Roth, 1992). Key ideas of this era included the use of developmentally appropriate activities and the constructivist approach to teaching. The NCTM Standards continued to gain support and popularity among mathematics educators, and many states developed grade-level scope and sequences and competency-based model programs that reflected these standards. Proficiency testing became more widespread, with some states requiring a certain level of competency in subject areas such as mathematics for grade promotion.
Standards Update: The 2000 Principles and Standards for School Mathematics
In April 2000, the National Council of Teachers of Mathematics released its Principles and Standards for School Mathematics. This document updates the 1989 Curriculum and Evaluation Standards and includes some components of both Professional Standards for Teaching Mathematics and Assessment Standards for Teaching Mathematics as well.
With such far-reaching significant goals (see the standards box below), the 2000 Principals and Standards will certainly serve as a major influence in changes and trends in mathematics education and reform in the years to come. However, the focus of this document remains on curriculum, and so Professional Standards for Teaching Mathematics and Assessment Standards for Teaching Mathematics will both also continue to play major roles in math education and reform.
The 2000 Principles and Standards identifies six principles of high-quality mathematics education.
The 2000 Principles and Standards document describes in detail standards and expectations for grade levels Pre-K–2, 3–5, 6–8, and 9–12 for each of the five content strands:
- Number and Operations
- Data Analysis and Probability
Each of the content strands will be covered within the material of this textbook. Number and Operations is especially important in the early childhood curriculum. The Algebra strand includes patterns, relations, functions, and mathematical models. You may be surprised to see the various types of algebra that are included in today’s early childhood curriculum.
Process standards differ from content standards in that the process standards are not subject matter that can be learned but are the methods by which content knowledge can be acquired. The 2000 Principles and Standards document describes in detail the five process standards:
- Problem Solving
- Reasoning and Proof
Problem solving is the heart of any solid mathematics curriculum. Reasoning is also important. Students who are exposed to the logic behind mathematical procedures are more likely to be able to learn and correctly apply those procedures than students who attempt to apply rules without regard to their reasonableness (Carpenter, Franke, Jacobs, Fenemma, & Empson, 1998; Hiebert & Wearne, 1996; NCTM, 2003).
Communication is especially important for assessment. Students must learn to explain, write, draw, or otherwise show what they have learned. A variety of nonverbal forms of communication must be used in the early childhood classroom. Teachers must often devise alternate means of assessment and communication when dealing with students with disabilities or students who have limited-English abilities.
Connections refers to connections among mathematics topics as well as connections to other subject areas and to real-life situations. By stressing connections, one can show the relevance and importance of mathematics. Students must also be able to make connections among mathematical representations (Coxford, 1995).
There are often a variety of representations for a single mathematical concept. For example, to represent the amount twenty-five cents, one can use a word phrase such as “twenty-five cents” or “a quarter,” use actual coins (or representations of coins) to show the amount in a variety of ways (one quarter, two dimes and a nickel, etc.), draw a pictorial representation, or use a symbolic expression such as 25¢ or $0.25. By learning several representations for a single concept, teachers can adapt their teaching methods to the needs and abilities of their students. Students should learn a variety of representations to best express and use their mathematical knowledge.
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