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##  Mathematics Standards for Pre-Kindergarten through Grade 2. ERIC                Digest.                                                                      

Concern about the mathematics achievement of America's youth has                reached a new level. It is clear in this increasingly technological             and global society that achievement in mathematics will have a major            impact on students' "career aspirations, their role in society, and             even their sense of personal fulfillment" (Malcom, 1999). This high             level of concern has resulted in a growing appreciation for the                 impact that early mathematics learning could have on the life course            of young children. Traditionally, mathematics has received little               attention in preschools and in many K-2 classrooms (Johnson, 1999).             This situation is changing as mathematics learning is recognized as             critical to school success. 
The National Council of Teachers of               Mathematics (NCTM, 2000) recently published Principles and Standards            for School Mathematics, building on its 1989 Curriculum and                     Evaluation Standards for School Mathematics. The current version                includes pre-kindergarten standards for the first time and outlines             the mathematics that children should learn as they progress through             school. While some observers question the appropriateness of any                standards for this age group, other critics argue that the current              standards may be less develop-mentally appropriate than the previous            standards, moving in the direction of content knowledge and product             orientation. This Digest discusses the latest mathematics standards             for young children and how teachers can use developmentally                     appropriate practices to help children meet these standards. WHAT             MATHEMATICS SHOULD PRE-K THROUGH GRADE 2

STUDENTS BE                         LEARNING?Many early childhood educators approach teaching                   mathematics with feelings of anxiety. However, the mathematics                  presented in Principles and Standards for School Mathematics                    provides a broad view of what mathematics is and can be for young               children--a view that early childhood educators implementing                    developmentally appropriate practices can use. Mathematics can                  provide children with ways to understand and appreciate the world               around them and enrich rather than narrow children's experiences.               Principles and Standards for School Mathematics identifies both                 content and process standards. 
Content Standards. The content                 standards are organized into several areas: (1) number and                      operations, (2) geometry, (3) measurement, (4) data analysis and                probability, and (5) algebra. Mathematics in the early years is not             just a simpler version of mathematics that children will learn                  later. Rather, teaching about mathematics in early childhood                    classrooms provides foundational concepts that are key to                       understanding more formal and abstract ideas. To be truly prepared              for later math, young children need to develop flexibility in                   thinking about numbers (NCTM, 2000). For example, they need to know             that 5 is 1 more than 4 and 2 less than 7. They need to know that 5             objects can be arranged in different ways: as 3 and 2 or 4 and 1,               and also as 2 and 2 and 1. They need to be able to solve problems by            using relationships such as 3 + 3 = 6, so 3 + 4 must be                         7 (Richardson, 1999a; Althouse, 1994). 
To understand measurement,             children first need to be aware of what can be measured. They need              to line things up, to cover spaces with blocks that fit together,               and to pour sand or water from one container to another. If children            are going to understand geometric principles, they first must put               together blocks to make new shapes and to recognize the difference              between a triangle and a rectangle. In short, children need to                  experience the applications of mathematics in their everyday                    lives. 
Process Standards. As stated in Principles and Standards               for School Mathematics, "Learning with understanding is essential to            enable students to solve the new kinds of problems they will                    inevitably face in the future" (NCTM, 2000, p. 21). 
The process               standards set out in Principles are congruent with developmentally              appropriate practice and include (1) problem solving, (2) reasoning             and proof, (3) communication, (4) connections, and (5)                          representation. The standards suggest that young children should be             encouraged to solve problems, investigate, and use mathematics to               find out things they don't already know. Children can be encouraged             to reason, to conjecture about the way things are, and to check                 those conjectures. The emphasis is on children thinking for                     themselves, rather than repeating what the teacher wants. Children              will want to communicate, listen, and clarify their own thinking in             the process of communicating with others. WHAT QUESTIONING                    TECHNIQUES CAN TEACHERS USE?Teachers' questioning                           techniques--including those intended to help children understand                concepts, hypothesize, and generate interesting questions--can help             children appreciate the mathematics that surrounds them. 
Number               and Operations: 
Rather than engaging in rote counting and numeral             recognition, children can be encouraged to ask: How many are there?             Can we find out without counting them all? How many do we need? Do              we have enough? Who has the most? Are there any extras? What happens            when we take numbers apart or put them                                          together? 
Geometry: 
Rather than simply learning the names of                basic shapes, children can discover: How are these shapes alike? How            are they different? Which ones fit together? Which ones leave                   spaces? What can we build with these? What other shapes can we make             using these shapes? 
Measurement: 
Rather than learning how to use            a ruler, children can determine: Which is bigger? More? Heavier?                Longer? Shorter? How can we find out? 
Data Collection: 
Children             can prepare to represent data in charts and graphs by sorting and               organizing objects into groups to find out which group has more or              less. "Do we have more red apples or more green                                 apples?" 
Algebra: 
Rather than using symbols to stand for various            amounts, children can work with ideas related to generalization and             predictability through the exploration of patterns. What comes next?            How do you know? 
Mathematics also helps children understand,                  organize, and analyze their science experiences. They can experience            the connections between math and music when exploring rhythm and                patterns, and between math and art when working with symmetry and               design. HOW CAN WE HELP ALL CHILDREN MEET THE                                 STANDARDS?Research suggests that children's math concepts are               often more sophisticated than traditionally assumed (Gelman, 1999).             However, in our eagerness to help children meet the standards, we               must take care not to use instructional methods that give the                   appearance of high math achievement but that, in fact, interfere                with real growth in understanding. Children are much more capable               and confident when they are allowed to make sense of things instead             of trying to follow someone else's thinking. Elkind (1999) reminds              us that, as we seek to determine what is possible for children, "the            only way to understand how children learn a concept is to observe               them in the process of acquiring it." 
Teachers, parents, and                  administrators will want to keep in mind that meeting the standards             is a long process. For example, one state lists in its Math                     Checklist for Kindergarten, "Identify, name and draw a circle,                  rectangle, triangle, hexagon, rhombus, trapezoid, and                           square" (Arkansas, 2000). Before children can meet this standard                with understanding, they must be able to recognize a variety of                 triangle shapes and distinguish these from a variety of hexagon                 shapes. They must be able to draw straight and diagonal lines of                similar lengths and connect them appropriately. In that same                    checklist is the standard "Counts and keeps track of up to 20                   objects." Even this seemingly straightforward skill is highly                   complex and understood in different ways as children develop                    competence over time (Richardson, 1997b, 1999a). Clearly, early                 childhood educators will need to continue to explore ways to                    individualize the mathematics curriculum for all                                children. CONCLUSIONThe most effective way to meet standards              is to work toward them by beginning wherever the child is. Any other            strategy simply wastes the child's time and prevents the development            of the essential foundational understandings and skills needed for              future success. It is important to be in tune with both the                     accomplishments and the still undeveloped ideas that are a part of              the child's growing understanding. It is exciting and even inspiring            to think that we can provide more mathematics for children than we              may have done in the past. We do not have to fear raised                        expectations as long as we look first to the child with respect for             wherever he or she is on the journey toward deeper understanding of             mathematics. FOR MORE INFORMATIONAlthouse, R. (1994).                     INVESTIGATING MATHEMATICS WITH YOUNG CHILDREN. New York: Teachers               College Press. 
American Association for the Advancement of                    Science. (1999). DIALOGUE ON EARLY CHILDHOOD SCIENCE, MATHEMATICS,              AND TECHNOLOGY EDUCATION. Washington, DC: Author. ED 427                        877. 
Arkansas Department of Education Web site. (2000). Available:            http://arkedu.state.ar.us/standard.htm. 
Bredekamp, S., & Copple,              C. (Eds.). (1997). DEVELOPMENTALLY APPROPRIATE PRACTICE IN EARLY                CHILDHOOD PROGRAMS(Rev. ed.). Washington, DC: NAEYC. ED 403                     023. 
Bredekamp, S., & Rosegrant, T. (Eds.). (1995). REACHING                  POTENTIALS: TRANSFORMING EARLY CHILDHOOD CURRICULUM AND                         ASSESSMENT(Vol. 2). Washington, DC: National Association for the                Education of Young Children. ED 391 598. 
Burke, M. J., & Curcio,              F. R. (Eds.). (2000). LEARNING MATHEMATICS FOR A NEW CENTURY.                   Reston, VA: National Council of Teachers of Mathematics. 
Copley,              J. V. (Ed.). (1999). MATHEMATICS IN THE EARLY YEARS. Reston, VA:                National Council of Teachers of Mathematics. 
Elkind, D. (1999).               Educating young children in math, science, and technology. In                   American Association for the Advancement of Science, Dialogue on                early childhood science, mathematics, And technology education.                 Washington, DC: AAAS. ED 427 877. 
Gelman S. A. (1999). Concept                development in preschool children. In American Association for the              Advancement of Science, DIALOGUE ON EARLY CHILDHOOD SCIENCE,                    MATHEMATICS, AND TECHNOLOGY EDUCATION. Washington, DC: AAAS. ED 427             877. 
Johnson, J. R. (1999). The forum on early childhood science,             mathematics, and technology education. In American Association for              the Advancement of Science, Dialogue on early childhood Science,                mathematics, and technology education. Washington, DC: AAAS. ED 427             877. 
Malcom, S. (1999). Making sense of the world. In American                Association for the Advancement of Science, DIALOGUE ON EARLY                   CHILDHOOD SCIENCE, MATHEMATICS, AND TECHNOLOGY EDUCATION.                       Washington, DC: AAAS. ED 427 877. 
National Council of Teachers of             Mathematics. (2000). PRINCIPLES AND STANDARDS FOR SCHOOL                        MATHEMATICS. Reston, VA: Author. 
Richardson, K. (1997a). MATH                 TIME: THE LEARNING ENVIRONMENT. Norman, OK: Educational                         Enrichment. 
Richardson, K. (1997b). Too easy for kindergarten and             just right for first grade. TEACHING CHILDREN MATHEMATICS, 3(8),                432-437. EJ 543 623. 
Richardson, K. (1999a). DEVELOPING NUMBER                CONCEPTS. White Plains, NY: Dale Seymour. 
Richardson, K. (1999b).             UNDERSTANDING GEOMETRY. Bellingham, WA: Lummi Bay                               Publishing. 
Rowan, T., & Bourne, B. (1994). THINKING LIKE                     MATHEMATICIANS. Portsmouth, NH: Heinemann. ED 408 183. 
Wolf, D.               P., & Neugebauer, B. (Eds.). (1996). MORE THAN NUMBERS: MATHEMATICAL            THINKING IN THE EARLY YEARS. Redmond, WA: Child Care Information                Exchange. 
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ERIC/EECE Digests are short reports on topics            of current interest in education. Digests are targeted to teachers,             administrators, parents, policy makers, and other practitioners.                They are designed to provide an overview of information on a given              topic and references to items that provide more detailed                        information. Reviewed by subject experts who are content specialists            in the field, the digests are funded by the Office of Educational               Research and Improvement (OERI) of the U.S. Department of                       Education. 
All ERIC/EECE Digests are available free in original               printed form directly from the clearinghouse. For additional                    information on this topic, please contact ERIC/EECE directly at                 [email protected] or 1-800-583-4135.                                         **Title:** Mathematics Standards for Pre-Kindergarten through Grade 2. ERIC                Digest.                                                                      **Document Type:** Information Analyses---ERIC Information Analysis Products (IAPs) (071); Information Analyses---ERIC Digests (Selected) in Full Text (073); **Descriptors:**  Academic Standards, Developmentally Appropriate Practices, Early               Childhood Education, Learning Processes, Mathematical Concepts,                 Mathematics Activities,  Mathematics Education,  Young Children              **Identifiers:**  National Council of Teachers of Mathematics                                 
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