home visit early in the year. The home visit allowed the teacher to observe objects, colors, patterns, fabrics, and other materials that she could incorporate into her mathematics classroom. Early childhood teachers often wonder if they are doing

## Abstract

Catalyzing Change in Early Childhood and Elementary Mathematics: Initiating Critical Conversations recognizes that the strengths and needs of young children must be considered when addressing the continuity and alignment of mathematics education for this student group. It also identifies and addresses the critical conversations necessary to meet the following critical challenges:

- Broadening the purpose of school mathematics to prioritize development of deep conceptual understanding so that children experience joy and confidence in themselves as emerging mathematicians
- Dismantling structural obstacles that stand in the way of mathematics working for each and every student
- Implementing equitable instructional practices to cultivate students’ positive mathematical identities and a strong sense of agency
- Organizing mathematics along a common shared pathway grounded in the use of mathematical practices and processes to coherently develop a strong foundation of deep mathematical understanding for each and every child

### Susan Butterworth and Ana Maria Lo Cicero

As teachers of young children, we perceive a tension between the demands of parents and elementary schools—that young children be academically prepared to enter increasingly challenging kindergarten programs—and our philosophy of early childhood education—that fourand five-year-old children should experience creative nurturing in a setting that encourages free expression of childhood through spontaneous play. In the early childhood education community, we have embraced the Reggio Emilia approach, the idea that a successful curriculum grows from the children's own interests and that effective projects encompass multiple disciplines and may develop and change over an extended period.

## Early Childhood Corner: November 2001

### Early Number Instruction

### Arthur J. Baroody and Alexis Benson

Developing an understanding of number has historically been the focus of early childhood mathematics instruction and a foundation for subsequent instruction. When should mathematics “instruction” begin? On what topics should initial instruction efforts focus? How should such efforts be implemented? This article addresses these questions.

### Christine D. Oberdorf and Jennifer Taylor-Cox

Geometry is an essential component of mathematics instruction. “Geometry helps us represent and describe in an orderly manner the world in which we live” (NCTM 1989, 48). Research in the field of early childhood mathematics education (Fuys and Liebov 1993; Del Grande 1985; Fruedenthal 1973) confirms that children are naturally intrigued by, and motivated to learn more about, the geometry that defines their worlds. Although it is important to provide a rich geometry program in the primary grades, research reveals that the little attention given to geometry is typically for exposure purposes (Bruni and Seidenstein 1990; Porter 1989). Therefore, any classroom time devoted to geometry is precious.

## Early Childhood Corner: October 2001

### The Early Childhood Mathematics Collaborative: Communities of Discourse

### Juanita V. Copley

At 6:45 in the morning on the first day of the Early Childhood Mathematics Collaborative, I arrive at Jessup Elementary School and am greeted by several early kindergartners: “Hey, Mrs. Copley, is everyone coming?” “Where have you been? Hey, our class can get twelve people standing in the counting circle.” “I've lost a tooth since you were here!” A first-grade teacher walks in with me, explaining that she has wonderful work from her students: “Just wait till we meet and you see their word problems. The students' thinking and reasoning are so obvious!” As we begin to unload, two very nervous undergraduate students wander in and explain that they have arrived more than ninety minutes early “so we wouldn't be late!” They quickly explain that they have been up all night worrying about teaching mathematics to real children and that if possible, they would like to observe today and perhaps teach on another day. I smile and assure them that everything will be fine. Within two hours, more than 800 students, 40 preservice teachers, and 50 faculty members arrive. Another semester of the Early Childhood Mathematics Collaborative (ECMC) has begun.

Catalyzing Change in Early Childhood and Elementary Mathematics calls for a just, equitable, and inclusive mathematics education system for each and every child. To achieve this vision, all stakeholders must recognize that structures and practices

### Douglas H. Clements and Julie Sarama

In keeping with the early childhood chapter of *Principles and Standards for School Mathematics*, this department examines activities and children's thinking in geometry and, in the next issue, number. From prekindergarten to grade 12, the Geometry Standard addresses four main areas: properties of shapes, location and spatial relationships, transformations and symmetry, and visualization. For each area, we quote the goal of the Standard and the associated early-childhood expectations. We then present snippets of research and sample activities to develop ideas within each area with students.

### Nadine S. Bezuk

*Fractions*! This word evokes anxiety, discomfort, and even fear in many children (and even adults) and dismay in the teachers who have to teach them. However, experiences with fractions are part of children's everyday lives. Half a peanut butter sandwich, half an a pple, and a quarter of a dollar are fractions that children often encounter. The early childhood curriculum can capitalize on children's interest in their environment and their awareness of the existence of fractions in their world while laying the foundation for some important mathematics learning.

### Jennifer Taylor-Cox

Blocks are powerful mathematical tools when used to teach young children early concepts in measurement, number sense, computation, geometry, data analysis, and algebra. For nearly one hundred years, blocks have played a role in early childhood classrooms (Smith 2001). Yet not everyone understands the mathematics conceptbuilding power associated with blocks. From sorting to patterning, young children can build a strong mathematical foundation one block at a time. This article examines how blocks can be especially useful in engaging children in activities that address algebraic, geometric, and spatial thinking.